Embed Size (px)
Citation preview
þ°ÏÆÆ¬Æ Ø©
õ\¥U&¥Ônä?èO
Ø©ö ÞÆ Ò 0090349049 ©Ç; &Ò&E?nFFÏ 2 0 1 4c 11 24F
Submitted in total fulfilment of the requirements for the degree of Doctorin Signal Processing
Physical Layer Network Coding Designin Multiple Access Relay Channels
SHA WEI
Supervisor:
Prof. WEN CHEN
DEPART OFELECTRONICENGINEERING, SCHOOL OFELECTRONIC,
INFORMATION AND ELECTRONICENGINEERING
SHANGHAI JIAO TONG UNIVERSITY
SHANGHAI , P.R.CHINA
Nov. 24th, 2014
þ°ÏÆÆ Ø©M5(²<x(²µ¤¥Æ Ø©§´<3e§Õá?1ïÄó¤¤J"Ø©¥®²5²Ú^SN§Ø©Ø¹?ÛÙ¦<½8N®²uL½>L¬¤J"é©ïÄÑz<Ú8N§þ®3©¥±²(ªI²"<¿£(²Æ(Jd<«ú"Æ Ø©ö\¶µF ϵ c F
þ°ÏÆÆ Ø©¦^ÇÖÆ Ø©ö)Æk'3!¦^Æ Ø©5½§Ó¿Æ3¿I[k'ܽÅxØ©E<Ú>f§#NØ©Ú/"<Çþ°ÏƱòÆ Ø©Ü½Ü©SN?\k'êâ¥?1u¢§±æ^K<! <½×£EÃãÚ®?Æ Ø©" t§3 c)·^ÇÖ"Æ Ø©áu Øt"£3±þµS/K0¤Æ Ø©ö\¶µ \¶µF ϵ c F F ϵ c F
õõõ\\\¥¥¥UUU&&&¥¥¥ÔÔÔnnnäää???èèèOOOÁÁÁ X£ÄpéEâØäuÐÚ?Ú§±WIFI!·¶Ï&Ú7ßDZLÃÏ&E⮲¤DZ·F~)¹|¤Ü©"´§'ukä ó§ÃäN´É&Pá!´»Ñ!ÒKAÚ&mZ6ؽÏKDZ§¦&ÒDÑþü$§Ï UDZ^rJøékêâDÑÇ"Cc5§duMIMOXÚ!ÆÏ&Úä?è'Eâ2A^uÃÏ&ä§ÃÏ&XÚêâDÑÇÚªÌÇJp§l Ý/¢yä] Ün$^"©nÜÄÃÏ&3©8OÃ!5UÚ] ©¡I¦§3õ\¥U&¥O[Úêiü«a.ä?èÆÆ"©ÌM#ó8BXeµÄk§éDÚ[ä?è3¥U=uL§¥)D(A§&?Â(:målC¯K§©O¤éVÇ`2Â[ä?èÆƧ¡3[ä?èüA5§,¡qkJpXÚ5U"ÄuXÚ¤éVÇÚ&Â(ãþ(:îªålm'X§©JÑzîªål¥UCÝ5N¥UÂ&ÒuõÇÚ "? |^.KF¦)`CÝÚü& `uxõǧl ü$XÚ¤éVÇ"AO§CÝ´ü ݧ2Â[ä?èÒòzDZDÚ[ä?è"Ùg§éDÚêiä?è3uÿÚ¥UÈè*Ñü¯K§©JÑõÇg·Aêiä?èüѧ¦XÚQU÷©8§qU¼p?èOÃ"©ÏLò¥UõÇLÆDZõÇ ÏfÚõÇg·AÏf¦È§¡|^õÇ Ïf5³& -¥U&*ѧ,¡|^õÇg·AÏf5¢y& &Òéä?è&ÒN)ûuÿ¯K§¢yXÚ÷©8OÃ",§Äu¥UÚ&?Â(ãA:§©æ^/VÇO.ÚICªíXÚ— i —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOÎÒéÇ4ÜLª"ÄuÎÒéÇÚ(:îªålm'X§©`õÇg·AU?§l JpXÚ?èOÃ"§é¥UÈè*ѯK§DZJpÆó´|^ǧ©JѫŬä?èüÑ"¥U!:ÏL& -¥Uõ\&¥ä¯5û½Y=u&Òa.§)ä?è&Ò!E?èü& &Ò½öØÆ"©ÏL©Û?Ñ\eux&ÒÚÂ&Òmp&E§XÚ3Ŭä?èe¥äVÇ"ÏLïáØÓ¥U=u&ÒéAÂà(㧩?ÚÈèû«>.Lª§¿±dDZâéXÚ'AVÇ?1©Û"nþ¤ã§©l[ÚêiüÆݧéõ\¥U&¥D(!êiä?èuÿÚÈè*ѯK?1ïħJÑ2Â[ä?è!õÇg·Aä?èÚŬä?èn«ØÓÔnä?èüѧ©Ok/)ûDÚä?èØU÷©8Ú?èOÃ$õ¯K"nØ©ÛÚý¢(JL²§n«ä?èüÑѱ÷©8OÃ"Ï~5`§2Â[ä?èüѤé5U`uÙ¦üÑ" X¥Uål& 5§¥UÈèØVÇO\§æ^Óêiä?èÅŬä?èüÑ5UòÅì`uõÇg·Aä?èüÑ"'cµÆÏ& ä?è XÚVÇ `¥U¼ê
— ii —
Physical Layer Network Coding Design in Multiple Access
Relay Channels
ABSTRACT
In pace with the development and improvement of mobile networking techniques,
wireless communication technologies, such as WIFI, cellular communications and
bluetooth, have become essential parts of our daily life. However, compared to the
wireline networks, wireless networks are more vulnerable to the unreliable effects
caused by fading, pathloss, shadowing and co-channel interference, which greatly
degrade the quality of transmitted signals, thus can only provide very limited data
transmission rate. Recently, for the widely applications of key techniques in wire-
less communication networks, e.g., MIMO system, cooperative communication and
network coding, the data transmission rate and spectral efficiency of wireless system
have been highly boosted, which ultimately realize the efficiency of the network re-
sources. In the thesis, we comprehensively consider the requirement of diversity gain,
error performance and resource allocation in wireless communication, and design the
network coding protocols from the perspective of both analog and digital domains in
non-orthogonal multiple access relay channels. All the techniques and contributions
are summarized as follows:
Firstly, due to the amplification of the received noise of analog network coding
scheme at the relay node, the received constellation pointsat destination distribute too
close to each other. To address this problem, we design a pairwise error probability
optimal generalized analog network coding scheme, which keeps the simplicity of con-
ventional analog network coding and effectively improve the error performance of the
system. Based on the relationship between pairwise error probability and Euclidean
distances of neighboring points on destination received constellation, we propose a
relay function according to the maximizing the minimum Euclidean distance crite-
ria to adjust the transmission power and phase of the relay received signal. Then we
— iii —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOobtain the optimal solution of transformation matrix and sources transmission power
with Lagragian multiplier method, which decrease the system pairwise error probabil-
ity. Specially, when the transformation matrix is equivalent to a second-order identity
matrix, the generalized analog network coding is degraded to conventional analog net-
work coding.
Secondly, in the light of problems caused by detection ambiguity and error prop-
agation due to relay detection for conventional digital network coding, we propose
a power adaptive network coding scheme, which prompts the system to achieve full
diversity gain and obtain higher coding gain. Specifically,we express the relay trans-
mission power as the multiplication of a power scaling factor and a two-level power
adaptive factor, which mitigates the error propagation from sources-relay channels and
realizes the one-to-one mapping between sources signal pair and network coded signal
to solve the detection ambiguity problem, respectively. Thus, the system is proved to
achieve full diversity. Moreover, based on the characteristics of the received constel-
lations at both relay and destination nodes, we derive the closed-form expression of
symbol pair error rate with wedge probability model and coordinate transformation
method. According to the relationship between symbol errorrate and Euclidean dis-
tance between constellation points, we obtain the optimal power adaptation factors,
which improve the coding gain of the system.
Thirdly, aiming at the error propagation of the relay detection and improving the
efficiency of cooperative links, we propose an opportunistic network coding scheme.
The relay node determines the types of forwarded signal based on the outage events
of sources-to-relay multiple access channels, which including network coded signal,
repetition coded signal of individual source or not cooperate. Through the analysis of
mutual information between transmission signal and received signal with binary input,
we derive the outage probability of the opportunistic network coding scheme. Based
on the the received constellations at destination corresponding to different types of
forwarded signal from relay node, we determine the expression of decision regions of
detection and analyze the system bit error rate.
In summary, we investigate the noise amplification phenomenon, detection ambi-
guity and error propagation issues in a non-orthogonal multiple access channels from
— iv —
þ°ÏÆÆ¬Æ Ø© ABSTRACT
the point of views of both analog and digital network coding.We propose three dif-
ferent physical-layer network coding schemes, namely, generalized analog network
coding scheme, power adaptive network coding scheme and opportunistic network
coding scheme, which effectively solves the problems of notachieving full diversity
and low coding gain for conventional network coding strategies. Based on the theo-
retical analysis and simulation results, all the proposed network coding schemes can
achieve full diversity. Generally speaking, generalized analog coding outperforms the
alternative scheme in terms of pairwise error probability.As the distance between re-
lay and source nodes getting further, the detection error probability of relay increases,
and the opportunistic network coding scheme, which shares the same digital network
coding scheme as its counterpart, has better error performance than power adaptive
network coding scheme.
KEY WORDS: cooperative communication network coding system error prob-
ability optimal relay function
— v —
888 ¹¹¹ÁÁÁ i
ABSTRACT iii8¹ viiã¢Ú xivL¢Ú xiv ÑL xv1Ù XØ 1
1.1 ïĵįK . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 ÆÏ&ä?èïÄ¿Â . . . . . . . . . . . . . . 2
1.1.2 ä?èïÄįKÚEâJ: . . . . . . . . . . . . 6
1.2 ISïÄyGÚ'ó . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 [ä?è . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 êiä?è . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 SNSü9ÌM#: . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 ÌSN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.2 ÌM#: . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.3 |µe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Ù 2Â[ä?èO 19
2.1 Úó . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 'ïÄó . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
— vii —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO2.2.1 Eêä?è . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Ônä?è . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.3 [ä?è . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 XÚ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 CÝ`z . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.1 Ý`z . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.2 5UýÚ?Ø . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 CÝ`z¢y . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.1 &?`z . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5.2 ¥U?`z . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.6 ÄuCÝO& õÇ© . . . . . . . . . . . . . . . . . 39
2.7 5Uý©Û . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.8 ( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491nÙ õÇg·Aä?èO 51
3.1 Úó . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 XÚ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 õÇg·Aä?è . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 ¤éÎÒ5U©Û . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.1 /VÇO . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.2 Äu/VÇSPER5U©Û . . . . . . . . . . . . . . . 61
3.4.3 ÄuICSPERí . . . . . . . . . . . . . . . . . . 64
3.5 XÚ`z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5.1 ¥U?õÇ ÏfO . . . . . . . . . . . . . . . . . 72
3.5.2 õÇg·AÏfO . . . . . . . . . . . . . . . . . . . . 74
3.6 'uPANCÆÆ?Ú?Ø . . . . . . . . . . . . . . . . . . . . . 77
3.6.1 XÛÿÐ&?èXÚ . . . . . . . . . . . . . . . . . . 77
3.6.2 XÛÿÐpNXÚ . . . . . . . . . . . . . . . . 78
3.7 5Uý©Û . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.8 ( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
— viii —
þ°ÏÆÆ¬Æ Ø© 8 ¹1o٠Ŭä?èO 85
4.1 Úó . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2 XÚ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Ŭä?èüÑ . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3.1 ¥äVÇ'O . . . . . . . . . . . . . . . . . . . . . 87
4.3.2 Ŭä?èüÑ . . . . . . . . . . . . . . . . . . . . . . 89
4.4 Ŭä?è5U . . . . . . . . . . . . . . . . . . . . . . . 92
4.4.1 ¥U?5U . . . . . . . . . . . . . . . . . . . . . . 92
4.4.2 &?5U . . . . . . . . . . . . . . . . . . . . . . 93
4.5 5Uý©Û . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.6 ( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 991ÊÙ o(Ð" 101
5.1 n«Ônä?èüÑnÜ©Û . . . . . . . . . . . . . . . . 101
5.2 Ì(Ø . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3 ïÄÐ" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106N¹ A ½n2.1y² 109N¹ B ½n2.2y² 113N¹ C ½n3.1y² 117N¹ D ½n3.2y² 119ë©z 121 137 139ôÖÆ Ø©ÏmuLÆâØ©8¹ 143
— ix —
LLL¢¢¢ÚÚÚ1–1 ØÓä?èüÑé' . . . . . . . . . . . . . . . . . . . . . . . . 14
3–1 OVÇP (E|√ERxR = k1, T1)¤Iëê . . . . . . . . . . . . 64
3–2 OVÇP (E|√ERxR = k2, T2)¤Iëê . . . . . . . . . . . . 65
4–1 & ux&EØD(KDZÂ&Òm'X . . . . . . . 94
— xi —
ãã㢢¢ÚÚÚ1–1 æ^ä?èÆÏ&XÚe . . . . . . . . . . . . . . . . . 5
1–2 £Ä·¶Ï&XÚ¥þ1ó´«¿ã . . . . . . . . . . . . . . . 7
1–3 MARCXÚDÑNÝYnuÐã . . . . . . . . . . . . . . 8
1–4 õ\¥U&Ônä?èOEâ´ã . . . . . 10
1–5 ä?èüÑ©a . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1–6 ©Ù!e . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2–1 1ÙXÚµã . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2–2 Eêä?èüÑ . . . . . . . . . . . . . . . . . . . . . . . . . 21
2–3 o.¶/«~ . . . . . . . . . . . . . . . . . . . . . . . . . 25
2–4 õ\¥U&XÚ . . . . . . . . . . . . . . . . . . . . . 28
2–5 DÚ[ä?è²î¼ål . . . . . . . . . . . . . . . . . 37
2–6 2Â[ä?è²î¼ål . . . . . . . . . . . . . . . . . 38
2–7 4-QAMNe|µ5U . . . . . . . . . . . . . . . . . . . 42
2–8 16-QAMNe|µ5U . . . . . . . . . . . . . . . . . . 42
2–9 4-QAMNe|µ5U . . . . . . . . . . . . . . . . . . . 43
2–10 16-QAMNe|µ5U . . . . . . . . . . . . . . . . . . 43
2–11 4-QAMNe|µn5U . . . . . . . . . . . . . . . . . . 44
2–12 16-QAMNe|µn5U . . . . . . . . . . . . . . . . . . 44
2–13 4-QAMNe|µo5U . . . . . . . . . . . . . . . . . . 45
2–14 16-QAMNe|µo5U . . . . . . . . . . . . . . . . . . 46
2–15 4-QAMNe|µÊ5U . . . . . . . . . . . . . . . . . . 46
2–16 16-QAMNe|µÊ5U . . . . . . . . . . . . . . . . . . 47
3–1 1nÙXÚµã . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
— xiii —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO3–2 ]¥U(ã . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3–3 /VÇÄ.«¿ã . . . . . . . . . . . . . . . . . . . . . 59
3–4 ]&(ã . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3–5 IC¥UÂ(ã . . . . . . . . . . . . . . . . . . . . 68
3–6 IC&Â(ã . . . . . . . . . . . . . . . . . . . . 70
3–7 J[&. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3–8 r& -¥U&e5U . . . . . . . . . . . . . . . . . . . . 80
3–9 é¡&e5U . . . . . . . . . . . . . . . . . . . . . . . . 81
3–10r¥U-&&e5U . . . . . . . . . . . . . . . . . . . 81
4–1 1oÙXÚµã . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4–2 ü& õ\&ÇÚ¥ä« . . . . . . . . . . . . 88
4–3 ØÓ¹e&Â(ã . . . . . . . . . . . . . . . . . . . . 95
4–4 Ŭä?èÚÀJ-=uä?è¥äVÇ . . . . . . . . . . 97
4–5 Ŭä?èÚÀJ-=uä?è5U . . . . . . . . . . 98
5–1 |µ¥5U . . . . . . . . . . . . . . . . . . . . . . . . . 102
5–2 |µ¥5U . . . . . . . . . . . . . . . . . . . . . . . . . 103
5–3 |µn¥5U . . . . . . . . . . . . . . . . . . . . . . . . . 104
5–4 |µo¥5U . . . . . . . . . . . . . . . . . . . . . . . . . 105
— xiv —
ÑÑÑLLLANC Analog network coding
AWGN Additive white Gaussian noise
BER Bit error rate
CRC Cyclic redundancy check
CSI Channel state information
CXNC Conventional XOR-based network coding
DNC Digital network coding
DNF Denoise and forward
FFNC Finite-field network coding
GANC Generalized analog network coding
IDC Instantaneous destination constellation
IRC Instantaneous relay constellation
KKT Karush-Kuhn-Tucker
LAR Link adaptive ratio
LLR Log-likelihood ratio
MARC Multiple access relay channels
ML Maximum likelihood
MMSE Minimum mean square error
MMSED Maximizing the minimal squared Euclidean distance
MUI Multi-user interference
OFDM Orthogonal Frequency Division Multiplexing
PANC Power adaptive network coding
PEP Pairwise error probability
PLNC Physical-layer network coding
QCLP quadratically constrained linear programming
SNR Signal-to-noise ratio
SPER Symbol pair error rate
XOR Exclusive or
— xv —
þ°ÏÆÆ¬Æ Ø© 1Ù XØ111ÙÙÙ XXXØØØ
1.1 ïïïÄÄĵµµÄÄįKKKX£ÄpéEâØäuÐÚ?Ú§±WIFI!·¶Ï&Ú7ßDZLÃÏ&E⮲¤DZ<F~)¹|¤Ü©"´§'ukä ó§ÃäN´É&Pá!´»Ñ!ÒKAÚ&mZ6ؽÏKDZ§¦&ÒDÑþü$§Ï UDZ^rJøékêâDÑÇ"ÆÏ&£cooperative communication¤Eâ|^Ã>Å2ÂA5§ÏL©Ùª^rU§¤J[õÑ\õÑÑ£multiple input
multiple output, MIMO¤XÚ§JpÃÏ&XÚ&Nþ!ÃDÑþÚm©8OÃ", §Ã¥UÏ&EâÏDZÉ^rm&Z6Ú¥Uó´mKDZ§Ã?ÚJpõ^rÆXÚªÌÇ" ä?è£Network coding¤EâÏL¥U!:éõ& &E?1éÜ?è?n§JpªÌÇ!¢yäK1þï!OrÃä°5§Ý¢yä] Ün$^"Cc5§ÄuÔnä?èOÃÆÏ&XÚ§´UMIMOõUEâÃÏ&ä+Sqc÷ïÄK"&Pá´ÃÏ&¥ÌØ|Ï"uxà½öÂà±ÔNDÑ&ÒE¤õ»DÂAÒ)&Pá"ùõ»DÂ&ÒÂÅ&ÒÌmCz¥yÅÅÄ[1, 2]"&?uîPáG§Ãó´U¬äm§l ÂàÃÂ&E"©8Eâ±^5-|&PáéÃÏ&5Ø|KDZ"©8´ÏLÕá&EDÑÓ&ÒUå"ÏDZ3^Ï&ó´§ÂàÒ±ÈÑuxàu&Ò"ùDZÒü$¤k&Ñ?uîPá¹eÏ&¥äVÇ"lêÆþù§©8Oñ½ÂDZ[1, 2]
d = − limρ→∞
logPe
log ρ, (1–1)Ù¥§PeL«VǧρL«&D'£signal-to-noise ratio, SNR¤"l½Â¥±w§©8Oô^5ïþp&D'^eDÑVÇP~Ç
— 1 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOI"éuDÚ©8XÚ§VÇâ'~½Æ±L«DZPe = O(
1ρM
)§Ù¥f(x) = O(g(x))Léu~êaÚb÷v'Xªa ≤limx→∞
log f(x)g(x)
≤ b"©8OÃMÒuDÑ&ÒuxÂलÕá&ê"N5ù§3Xm©8!ªÇ©8Úm©8[1, 2]n«~©8a."m©8´3ØÓYpuxÓ&Ò)©8OÃ"DZy&Õá5§üDÑYmm7Lu&Zm"´§ù¦?nò§cÙ´3úPá&¥DZ²w"ªÇ©8´3v©lªãþuxÓ&Ò§l ÷v&Õá5)©8OÃ"´§XÚ3¼ªÇ©8Óã+°Ç§ÏdéuªÌ] D"Ãä ó§ªÇ©8Øäk2·^5"ém©8ڪǩ8":§<Åìæ^m©85é|&Pá"m©8±ÏL3uxàÚÂàÙõU¼§ÏdDZ¡DZU©8"zuUÚzÂUmÑU/¤Õá&"duõUEâØ=±Jøm©8§q±Jp°Ç§¤±CAcTEâ5õ'5§¿®A^u1o£ÄÏ&ä¥"3AÆm¥§z&ѱmè6 ج5&mZ6[3]"Ïd§uxà±ÀJuxõÕáè65Jp°|^ǧDZ±ÀJ^ØÓ&5õguxÓè65Jp&E5"ù«ÀJÒ´~^©8OÃÚE^OÃmò©[4]"ÃXÚ±ÏLæ^ØÓ?èüÑ5¼ØÓ§Ýò©J [5–7]"1.1.1 ÆÆÆÏÏÏ&&&äää???èèèïïïÄÄÄ¿¿¿ÂÂÂnØþù§XJ±3uxàÚÂàÙÃõU§Ò±¼Ãm©8OÃÚE^OÃ"´3¢SÏ&¥§du^rºÏ~§ÓüUmålvâUy&Õá5§Ïd3üÏ&þ~õU´Øy¢"ùMþÛ5ÃÏ&5Æ©8[8]ù#Vg"Æ©8Ø%g´æ^©ÙªU Ø´Ônþ uÓ/õU?1Ï&§l /¤«aqõUXÚJ[&§¦XÚ¼m©8OçJpDÑ5U"©ÙªU±´ÆÏuxà=u&Ò?¿Õá¥UþU"duz¥U&
— 2 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØѱJø^©8󴧤±3Pkþ¥UÃäpÒU¼wÍ©8OÃ"dum©8!ªÇ©8ÚU©8Éò´!°Úªà§ÏdUwÍJpm©8ÆÏ&É2'5"ÆEâ#N^rmp|^ÃXU!õÇÚ°] 5Jp©8OÃ"¦+'uÆÏ&'ïıJãþVÔc§´CùEââ¤DZïÄ+9:"â¥UöªØӧƥUÆƱN©DZüaµ[¥U=u[9–12]Úêi¥U=u[13–15]"3[¥U=u£q¡DZ-=u¤ÆÆ¥§z¥U!:´üéÂ&Ò3Eê¥?15ö§ò²L?n&Ò=uÂà"du\5D(ux&Ò·U3å§ùüÑÓÚ=u&ÒÚD("Ïd§[¥U=uÆÆ3$&D'e§?èOÃ$"ØÓ´§3êi¥U=u£q¡DZÈè-=u¤ÆÆ¥§z¥UIkÈÑuxà&E§,#?觿r?è&E=uÂà"Ïd§¦+ÈèÑkUE¤Ø&E=u§¥U!:é[¥U=uÆÆ5`§ux´Ø¹kD(X&Ò"l&EØÆÝ5ù§üêi¥UÆÆÃ÷Æ©8"´§XJ¥U±uÿÑÈèاkÀJux(&ÒÂà§Ò±#¼÷©8OÃ[13]"3¢SÏ&¥§XJõU§±Ó|^m©8ÚÆ©85`zXÚ5U"DZ?ÚJpXÚNþÚªÌǧ¥U±æ^ä?è[16–18]5Ü¿5gØÓ^r&E§2ò?néÜ&Ò Ø´õÕá&Ò=uÂà"2Âþ`§ä?è±´¥U!:??1?¿òÑ\NÑÑ?èö[19, 20]"DÚ:é:Ï&Úü?1;=u¥UÆÏ&'§ä?è3ØUCäÿÀ(ÚO\ó´Nþ¹e§¥U!:òõ& &E?1éÜ?è=u¤kÂà§ÃIÓ^õgªÌ] 5=u& &E§l UõªÌǧùéu°] FÃD"ÃÏ& ó´~`³"läN¢yÆÝ5`§¥U!:ÏLé& Ñ\&E?1?n§3nÜ&&EÚ丹e§éÑ\&E?1Ün?n2?èux&!:"§&!:nÜ|^ló´ÚÆó´Â& &EÚ¥U&E§)è¡E¤I& &E"ÏL— 3 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOéÜ&E?n§ä?è±ÏLO\kO§¦ä¥] \¿©|^§4XÚóéþ6-¤NNnØ.§~¥UÏDZõg=u5UÑm§¢yêâkØ §)ûDÚ|´dÚªEâÃ)û¯K"3¢¥§æ^ä?èÆÏ&XÚÃIéc3¦^¥UÚÄÕ?1MþNÚUħIé'^?1#Ú,?§4ùää?èÚ)èõU§¿3¢SÏ&L§¥±?1ü;=uªÚä?èª"ù§ä?èEâÒ±OrÚÖ¿ykÃÏ&Eâ"3ÃDÑ¥§ux&Ò¹´²LNÎÒ Ø´©&E'A"â·Ü& &EªØÓ§±òÃä?èüÑ©DZüa."31«a.üÑ¥§¥U±ÏLÈè¡EÑ5gØÓ& &E§,3kp#Ü¿ù'A6"ù«üÑ¡DZêiä?è£digital
network coding§DNC¤§DZ´3käpïÄÚuÐDÚä?è/ª",§DZz¥Uö§Ók|^ÃZ6ØÚõ^ruÿUå[21]§& &Ò±3Eê?1ÎÒmÜ¿"ù§ÈèL§Ò±Ñ§=ÃÏ&¥Ak[ä?èüÑ£analog network
coding§ANC¤"3¢SÏ&¥§DNCÚANC©O·Üêi¥U=uÚ[¥U=u"ã1–1Ñæ^ä?èÆÏ&XÚe"3ïÄ¥§kü«;.·Üæ^ä?è?1DÑXÚ.§=V¥U&£two-way relay channel§TWRC¤Úõ\¥U&£multiple access
relay channel§MARC¤"3TWRCä¥[22–26]§üªàÏL¥UÆ*d&E"duz& ÑU®gCux&E§¤±±éülÂä?è&Ò¥KgC&E§l ¡EÑé&Ò"âTWRCä.A:§Tao<[27]í«`ä?è¥U§[28]5z'AÇ",§3DÚI¡EÑü& &Ò2?1ä?èüÑÄ:þ§¥U±ÏLlZ6&Ò¥)ä?è&Ò[27, 29–31]5?ÚJpªÌǧ áÏ&m"ùä?èüÑDZ¡DZÔnä?è£physical-layer network coding§PLNC¤[29]"Wang<[32]òä?èí2õaTWRCä¥"|^ªÌÇÚ¥äVÇ`³§öy²`õa[ä?èÚõaO=uüÑÑ'Øæ^ä— 4 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØ
ã 1–1æ^ä?èÆÏ&XÚe§Ù¥¥U¬¥7Úµ|3êiä?襦^Fig 1–1 System architecture of cooperative communication with network coding, where the blue-
marked blocks are only included in digital network coding?èüÑäkÐäóéþ",¡§MARCXÚú@DZ´·¶Ï&ÚÃDaì䥫ÄÏ&."3MARCäÿÀ.¥§õ& ÏL¥UÆux&EÓ&";.A^|µ´3·¶XÚ¥§ü£Ä^r3¥UÆeÄÕÏ&§Xã1–2¤«"TWRCXÚØÓ´§MARCXÚ3&?kÏLó´¼Ø& &Ò&E"Ïd§MARCXÚ¥ä?èODZTWRCXÚئÓ"MARCXÚDÑNݲnãüC"31㧥Ué&ÒØ?Û?n§´ü;=u"ù«Ï&ªI²LoYâU¤DÑ"ùp±ü& S1ÚS2!¥URÚ&DMARCXÚDZ~§Xã1–3£a¤¤«"Äk§1Yp§& S12Â&E¥URÚ&D¶1Yp§¥U=u& S1&E&¶1nYp§& S22Â&E¥UÚ&¶1oYp§¥U=u& S2&E&"DÑ(å§&©OÈÑü& &E"31ã[33–39]§DZ;õ^rZ6§ü& 3cüY,— 5 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOæ©£time division¤/ªux&E¥UÚ&§Xã1–3£b¤¤«"ØÓ´§31nY§¥Uòü& &E?1ä?è2D&"ù«DÑ.DZ¡DZõ\¥Uä"±w§æ^ä?è1ã1ãÏ&ª!YDÑm§l JpªÌ|^Ç"31nã[40, 41]§ü^r31YÓDÑ&E¥UÚ&§¥U|^U,·Ü&E£ANC¤½öéÜÈèü^r&E2#?1ä?è£DNC¤§Xã1–3£c¤¤«"31Y§¥Uòä?è&E=u&"ù«DÑ.DZ¡DZõ\¥Uä"ÏL'nãDÑYüC±uy§3MARCXÚ¥Ú\ä?èüѧAO´|^ü& &ÒU,·UA5ä?èüѧ±wÍJpäóéþ"1.1.2 äää???èèèïïïÄÄÄÄÄįKKKÚÚÚEEEâââJJJ:::ÃØ´êiä?觴[ä?è§DÚä?èüÑA^uõ\¥U&¥§Ñ¬¡X¯KÚ]Ô"£1¤[ä?è¥D(¯K"[ä?èÏDZÙØ3*Ñ!ü´¢y!±÷©8OÃ`³3ÃÏ&¥2A^"Ó§3Ø?1D(³Úõ^ruÿ¹e§duõ^rZ6£multi-user
interference, MUI¤[42]Ú¥U?D(AKDZ§&!:?Â(ãþ(:¬'C§¦XÚl?èOÃÆÝ5ù§5U3$&D'eêiä?è"£2¤DÚêiä?è¥uÿ¯K"3DÚɽä?è£conventional XOR-based network coding, CXNC¤¥§5gü& &Ò¬âɽ5K§NDZä?è&Ò"´§3õ\¥U䥧XJæ^DÚɽä?è£conventional XOR-based network coding,
CXNC¤¬ÏDZõéN5uÿ£detection ambiguity¤¯K§l ¦XÚÃ÷©8[43, 44]"£3¤DÚêiä?è3Èè*ѯK"ÃØ´3ü ü´3õ ü¥UXÚ¥§¥UÈèØ´KDZêi¥UXÚ©8OÃÏ"´§DÚ¥UXÚ¥Èè³Å[45–49]éJA^3õ^r¥Uä?èXÚ¥" ÄuuÿÚÅ?èä— 6 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØ
ã 1–2£Ä·¶Ï&XÚ¥þ1ó´«¿ã§Ù¥ÚÚ7Úó´©OL1Ú1YÏ&&Fig 1–2 Diagram of uplink mobile cellular communication system, where the yellow-marked and
blue-marked links represent the communication channel in the first and second time slot, respec-
tively?èüÑ[37, 50–52]qÃA^uÃX$?nUå~kDaìäÃ&?èXÚ"yk?èXÚ¥é|*Ñ)ûY[53, 54]3ÂàO³üѧ¿¦kÛ&&E§l é§ÝþKDZ¢SÏ&¥¦^"DZü$Ø*Ñé&à5KDZ§ïÄö3ü ü¥UXÚ¥kJÑÀJ-=u£selective-and-forward¤[45, 46]!ó´g·A=u£link
adaptive¤[47]üÑ"3ÀJ-=uüÑ¥§¥U±â& -¥Uó´¥ä¹5û½1Y´Ä=u",§¥U±éÈè&Ò?— 7 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO1 2
1 2
1 2
ã 1–3 MARCXÚDÑNÝYnuÐãFig 1–3 Three evolution stages of transmission scheduling in a MARC system.1ÌPu£Cyclic Redundancy Check§CRC¤5ä´ÄkØ3[55, 56]"´ùüÑ3¿ïÈèØ&ÒÓDZ¿ïÜ©Èè(&Ò§Ïdü$XÚ?èOÃ",§æ^CRCEâ³üÑduO\XÚDgꧤ±ü$ªÌÇ" 3ó´g·A=u¥§öâ& -¥UÚ¥U-&ó´&OÃé5û½eDZux&ÒõÇ"äN5ù§XJ& -¥Uó´&OÃé¥U-&ó´&Oç@o¥UÒkéVǬÑyÈèØ"¤±31Y=u&Ò§¥UuxõÇc¡ÒI¦±u1ó´g·AÏf£link adaptive ratio§LAR¤5ü$Èè*ÑéÂà5K¡KDZ"XJ& -¥Uó´&OÃé¥U-&ó´&OÃ
— 8 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØ5ùЧ@o¥UÈèÑVÇéÒ¬"3ù«¹e§¥Uò31Y±÷õÇ=u&Ò&"nØíL²§DÚvk\\Ø*ѳÅÈè-=uüÑ´Ã÷©8§ ÀJ-=uÚó´g·A=uüÑÑy²3ü üXÚ¥±÷©8"Äuü ¥Uä¥'u*Ñïħõ\¥U&pêiä?èDZIOAØ*ѳÅ"nþ¤ã§?èOÃÚ©8OôÃÆÏ&¥~üXÚ5UI"3õ\¥U&¥§ÄuDÚ[ä?è3D(Aé?èOÃKDZ§±9DÚêiä?è3uÿÚ*ѯKé©8OÃKDZ§©l[Úêiü¡§JÑÄu¤éVÇ£Pairwise error probability§PEP¤`O2Â[ä?èüѧõÇg·Aêiä?èüÑÚŬä?èüѧ¦XÚØ=÷©8Oçp?èOÃ"©Eâ´Xã1–4¤«"1.2 IIISSSïïïÄÄÄyyyGGGÚÚÚ'''óóóe¡§©±¥U´ÄÈèDZ©aIO§l[ä?èÚêiä?èü¡§éykïĤJ?1o(8B§X㤫"1.2.1 [[[äää???èèè3Äu-=u[ä?èüÑ¥[21, 57, 58]§¥U!:ü/ÂU\&Ò§ Ø?1Èè§,=u&"«~;.Äu-=uä?èüÑ´©z[21]¥JÑ[ä?è£analog network
coding§ANC¤"3V¥U&¥§©z[21]JÑ«[ä?èüѧ٥§¥U=uÂZ6&Ò§ üªàÏLKgC&E5uÿéux&Ò"lþù§V¥Uä¥[ä?èüÑ´«/Ïk&E55ØgZ6"3©z[59]¥§ö3õ& -&éXÚ¥§íæ^[ä?èüÑe¥äVÇÚ©8-E^ò©",§3©z[60]¥§¥U!:æ^«ÆõÂ[ä?èÆƧùü&±|^Z6&Ò5¡EI&Ò"ö©ÛTüÑeǧ¿JÑ«lUÏ&¥¡EÑ&Ò"3©z[61]¥§ö3æ^©NVõ¥UXÚ¥JÑ«¥UÀJÚ— 9 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
ã 1–4õ\¥U&Ônä?èOEâ´ãFig 1–4 Technology route for physical layer network coding design in a non-orthogonal multiple
access relay channels[ä?èéÜ"3©z[62]¥§ö(Üý?èÚ[ä?èüѧü$D(AéV¥Uä5U5Ø|KDZ"Nõ©z[63–68]ïÄANCXڥǫÚþ1ó´?è£space-time code¤O"´§ù©ÙÑvkÄõ^rZ6éXÚ©8OÃ5KDZ"3[42]¥§öÄ¥U?3þz&G&EeÅå¤/O§¿|^Ï^©8Ýþ5ïÄõ^rZ6KDZ"— 10 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØAnalog Network Coding Digital Network Coding
Physical-layer
Network Coding
Denoise-and-Forward Compute-and-Forwardã 1–5ä?èüÑ©aFig 1–5 Classification of network coding strategies´§ù©ÙÄ]¥UõÇåeXÚ5U§ vkïÄÚO&G&Ee©8OÃ"Äuù*§ö[69]ïÄK^rþ1ó´3ANCÆÆe©8OÃ"â¥UõÇåØÓ§ö©ONïCþOÃ¥UÚ½OÃ¥UeXÚ5U"lí(J¥±*§3SNRØÿ§VÇLª¥¹éê§l 5©8OÃ"DÚANCÑ´ÄuÎÒ ö§=ÃPÁANC§Ãmÿ&?èSP&E5JpXÚ5U"Zhang<[70]JÑ«PÁANCüѧ٥¥U!:?æ^´^Ñ\^ÑÑÈèì§ùÒ±lU\&Ò¥)OþØ£minimum mean square error, MMSE¤"duæ^&?è§TÈèìÄêâSØÓÎÒm'X§l JpXÚþØ5U"´§ö¿vké[ä?èD(AÑA?n",§3pdõ¥U&¥§Yao<[71]ÏLr¥UÂ&ÒNCÄÚ^þ§¢yä?è3[þ5Ü¿"öÄuùN'X§íXÚÇ«ÚÇÚ"´§du¥Uux¢ê&Òäkõ«U5§ÏdO\&!:ÈèE,Ý",§övkÄPá&eTüÑ·^5Úè5"3ÃÔnS+§©z[72]íæ^[ä?è&SNþ3V¥Uf&¥L
— 11 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOª§¿ÄudOØÓÆÓZ6Y"1.2.2 êêêiiiäää???èèè3ÄuÈè-=uêiä?èüÑ¥§¥U!:ÈÑÂ'A6§¿^ɽ£exclusive or§XOR¤½öU\?èªÜ¿& &E§,2=u&"ÃÏ&kÏ&«OÒ´§2ÂA5"ù§!:ux&ÒÒ±õÙ¦!:§ !:DZ±ÓÂ5gØÓ!:&Ò"´§ù2ÂA5ÏDZÚ\Z6§´³ÃÏ&þÏ£'XIEEE802.11¤"1.2.2.1 ÔÔÔnnnäää???èèèÔnä?è[73, 74]ÏLrä?èVgA^Ôn§ò2ÂA5C¤Ãad hocä¥JpNþ`:"äN5ù§DÚä?èéÂêi'A6?1?è$ØÓ´§Ônä?è|^Ó>^ÅU,U\55?1?èö"ÏLnØíÚý¢§Zhang<[73, 74]y²Ônä?è'DÚä?èkÐNþ5U"§Zhang<?ÚïÄØÓÚ£=kÓÚؤéÔnä?èKDZ[75]"3BPSKNe§PLNC3kÓÚعe§,U'ä?èÐNþ5U"?Ú§Ônä?è*ÐõUV¥U&[76, 77]"d§¥UIÓJü!:·U&ÒÚ§¿r§Ñ=DZä?è/ª"üUeÔnä?è'§MIMOÔnä?èØé1Åî¦",§§E,Ýéu(ÚÓuxêâ6êþ´¥5'X"â?1Ônä?èö£½+!¤§Ônä?è±?Ú©DZkÔnä?èÚÃÔnä?è[78]"¦+Ônä?èkÃõ`:§´3Ù¢yL§¥DZ¡Ãõ]Ô[79]"'X§¥UI)ûVõ¥U&¥§5güªà&ÒÎÒÚ1Å ØÓÚ",§¥UI3Èèc?1&O"Lu<ÏL3ªÇ¢yä?è5)ûùX¯K[79]"3ªÇÔnä?襧ɽN´Äuz1Åþª©õ´E^Eâ£Orthogonal Frequency Division
Multiplexing§OFDM¤?1ö§ Ø´m"— 12 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØ1.2.2.2 DDD-===uuuüüüÑÑÑ,a3TWRCXÚ¥~êiä?èÆÆ´D-=uüÑ£Denoise-
and-Forward§DNF¤"Koike<âTWRC3õ\ãU\(A5§Ú\«(ÜNÚä?èOOK[30]"3QPSKNe§öy²XJ32ÂãUYæ^QPSKN§(Üä?èE,ÃéÐóéþ5U" 3Nõ&^e§Ø~5(ã%UÐóéþ"ö?Úæ^¥/æU£sphere packing¤5`z~5ä?èeN(",a¡DZDNFä?èüÑ[80]§Ó|^õ\ã&ÒU,U\A5§´¥U3=uU\&Ò&cKD(KDZ"3ÃD(&¥§DNFÚAF üÑÑDFüÑÐóéþ5U"Ù¥3$&D'e§DNFóéþ5U´n«üÑ¥Ð"Li<[81]?ÚrDNFÆÆí2pNªÚPá&¥§¿äké$OE,Ý" Zhao<[82]KrDNFÆÆòMIMOV¥U&¥"3kéªà!:|µ¥§öïÄÄuþØ£mean square error, MSE¤OKeÛ`ý?èO"3E,kõéªà!:|µ¥§ö|^&ÒO£signal alignment¤Eâ5é|ªàémZ6§l JpXÚ'AÇ"1.2.2.3 OOO-===uuuüüüÑÑÑ3õ\¥U&¥§ka;.Äupd&êiä?èÆÆO-=u£compute-and-forward¤üÑ[83, 84]"O-=uüÑ´Äuè£lattice point¤ê5|ÜE,´èù55Oä?èÆÆ"ÄuèùA5§¥UÁòÂ&ÒÈèDZuxèiê5U\"ùÚ\ààä?è&.§Ù¥DÑ&Ò±ÏL¦)|5§|5¡E"¹D(ä?èüÑ[85]Úþz-N-=uüÑ[86, 87]'§O-=uä?èüÑäkuxàÃI?Û&G&E`:[88]"Wei<[89] ÄuFincke-PohstÿÀ8|¢Úä?èXÚÝE§OO-=uä?èüÑ¥XÚëê§l `zõ^rõ¥UXÚ¥DÑÇ"O-=uä?èüѱÏLbuxà&G&E[90]§½öÚ\õU¥UÚ&[91, 92]5JpÙ5U",§©z[93–96] ¥0XÛ3O-=uüÑ¥E¢S
— 13 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOè"I5¿´§O-=uüÑ[88]Ä´vk& -&ó´õ\¥UXÚ§ù:©XÚ.kéO"1.2.2.4 ³³³äää???èèè¦+êiä?è[ä?è'§3¥U?QجD(DZج)P&E§´3¢SÏ&¥§Æ¥U!:¬)Èè"Ïd§êiä?èXÚÉ*ÑKDZ§ØU÷©8OÃ[13]"
Yune<[97]|^XÚ]'AVÇòõ\¥U&& -¥Uó´LÆDZd&OÃ"Äud& -¥U&§öJÑü«¥UÀJOK5³*Ñ:1«´d& -¥U&OÃÚ¥U-&&OÃ¥U¶1«´d& -¥U&OÃÚ¥U-&&OÃNÚ²þê¥U"cöÀJÑü^ó´¥´¶§ öéü^ó´?1²ï"ùüOK@dBletsas<[98]3ü õ¥UüXÚ¥JÑ"Nguyen<[99]3V¥U&¥|^éêq,'£log-likelihood ratio§LLR¤5³*Ñ"äN ó§¥U!:'Â&ÒéALLR½Km'X§ÀJ=u&Ýp'A §¿¿ï&Ý$'A "öÄü«Kª§«´Äuü'A§,«K´ÄuÜ¿'A "Pu<[100]3õ\¥U&¥JÑ«ÄuVÇɽä?èüѧ¿=u¢ê^&E&§ü$ÏDZMûØéXÚ5UKDZ"©z[100, 101]Ñrù«Äu^&EgA^&?èXÚ¥"L 1–1ØÓä?èüÑé'Table 1–1ä?趡 ux&Ò `: ":[ä?è[21, 61, 69] ¥U=u·U&Ò ü´¢y§Ø¬) U\D(Ônä?è[73, 74]
¥Uò·U&ÒNDZÄuɽä?è&Ò JpªÌÇ éÓÚ¦p§¥UKDZXÚ©8D-=uüÑ[30, 81, 82]
¥UKÂÅ?)D(§¿ò&ÒâØÓNªNä?è&Ò & &Òéä?èN ¥U?nE,ÝpO-=uüÑ[83, 86, 87]¥Uò·U&ÒNè¥ålC: ¥UÚ&à?nü èOE,Ýp
— 14 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØ1.3 SSSNNNSSSüüü999ÌÌÌMMM###:::1.3.1 ÌÌÌSSSNNN©ÌïÄõ\¥U&¥Ônä?èO¯K§Xã1–6¤«"ÌSNXeµ
ã 1–6©Ù!eFig 1–6 Chapter scheme of the thesis
• JÑ«2Â[ä?èüÑ[102]"éDÚä?è3¥U?D(A§©JÑ3¥U?|^CÝ5N¥U?Âü& ·U&ÒuõÇÚ §l 3[ä?èüA5§Ók/JpXÚ5U"ÄuXÚ¤éVÇÚ&?Â(ãþ(:mîªål;'X§©JÑ«zîªål`zOK§¿æ^.KF¦)`CÝ)Úü& `uxõǧJpXÚ?èOÃ"AO§CÝ´ü ݧ2Â[ä?èÒòzDZDÚ[ä?è"— 15 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO• JÑ«õÇg·Aêiä?èüÑ[43]"éDÚÄuɽä?èÃ3õ\¥Uä¥Ã÷©8¯K§©âÛ&&E§éDÚ¥U!:ä?èüÑ?1U?§g·AN¥U!:uxõÇþ?§l ;& &Òéä?èõéNE¤&uÿ§³¥UÈèØ*ÑéXÚ©85KDZ"?Ú§ÏLï¥UÚ&Â(㧩æ^/VÇO.XÚÎÒéÇ£symbol pair error rate, SPER¤4ÜLª"nØ©ÛÚ¢(JþL²§©JÑõÇg·Aä?èüÑ'uDÚä?è ó§Q±¦XÚ÷©8§q±¼p?èOÃ"• JѫŬä?èüÑ[103]"é¥UÈè*ѯK§DZJpÆó´|^ǧ©JѫŬä?èüÑ"¥U!:ÏL& -¥Uõ\&¥ä¯5û½Y=u&Òa.§)ä?è&Ò!E?èü& &Ò½öØÆ"©ÏL©Û?Ñ\eux&ÒÚÂ&Òmp&E§XÚ3¥U?1Ŭä?èe¥äVÇ"ÏLïáØÓ¥U=u&ÒéAÂà(㧩Èèû«>.Lª§¿±dDZâéXÚ'AVÇ?1©Û"
1.3.2 ÌÌÌMMM###:::©7ÃÏ&XÚÔn©8OÃÚ?èOÃ'¯K§3õ\¥U&¥JÑXä?èüÑÚõÇNÝY§ÌM#:Xeµ1. JѦ¤éVÇz[ä?èY§ü$D(Aé?èOÃ5KDZ"éDÚ[ä?è3¥U?D(A§©ÏL`¥U¼êz&Â(ãþ(:máî¼ål§l kUõ5U",§©ÏLÚ\¥mCþݧòz²îªål¯K=zDZà`z¯K§¿æ^.KF¦)`CÝ"3dÄ:þ§©éü& uxõÇ?1`z§?Úü$XÚ¤éVÇ"
— 16 —
þ°ÏÆÆ¬Æ Ø© 1Ù XØ2. JÑ«õÇg·Aêiä?èY§ü$uÿé©8OÃ5KDZ"3dY¥§õÇg·AÏfÏL(Üü²L`zU??ä?觢y& &Òé¥Uux&ÒN"ÄuþãO§JpXÚ©8OÃÚ?èOÃ"3dÄ:þ§©ÏL/VÇ.ÚIC§â¥UÚ&?(ã9ÙéAû«§íXÚÎÒéÇ4ÜLª"3. JÑÄuõÇ Ú¥ä¯ü«¥Uüѧ³¥UÈè*Ñé©8OÃ5KDZ"3g·Aä?èüÑ¥§JÑÏLä& -¥UÚ¥U-&&OÃé`5N¥UuxõÇõÇ Ïf§l å³*Ñ^"3Ŭä?襧©ÏL& -¥Uõ\&¥ä¯5û½¥U=u&Òa.§JpÃó´|^Ç"
1.3.3 |||µµµeee©Äk31Ù¥é[ä?è3=uL§¥éD(¯K§JÑ«2Â[ä?èüѧÏL*Âà(:mîªål5ü$D(éÈèKDZ"2Â[ä?èüÑ|^¤éVÇ`¥U¼êÚ`& DÑõÇJpXÚ5U"1nÙ¥§éDÚÄuɽêiä?è3uÿÚ¥UÈèØ*ѧXÚÃ÷©8OïK§©JÑ«õÇg·Aêiä?èüѧ¡ÏL¥U?õÇg·AÏfä?è(ܧ¢y& &Òéä?è&ÒN¶,¡ÏL3¥U?OõÇ Ïf5³ÈèØ*Ñ^§3÷©8OÃÓü$ØèÇ"3dÄ:þ§©ÏL/VÇ.ÚIC§íXÚÎÒéÇ4ÜLª"1oÙ¥§éÈèØ*ѯK§©JѫŬä?èüѧÏL& -¥Uõ\&¥ä¯5û½¥U=u&Òa."ÄuùO§©íAXÚ¥äVÇÚ5U"1ÊÙé©ó?1o(§¿é5ó?1Ð""— 17 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO111ÙÙÙ 222ÂÂÂ[[[äää???èèèOOO
2.1 ÚÚÚóóóÙ3õ\¥U&¥JÑ«ÄuPá&2Â[ä?è£generalized analog network coding, GANC¤üÑ[102]§^±¢y¤éVÇ£pairwise error probability, PEP¤z§XÚµãXã2–1¤«"äN5ù§ÙÌOz¤éVÇ`¥U¼ê"Äk§©JÑ«2Â¥U¼êLª"§±^5N¥U?Âü& ·U&ÒuõÇÚ "DZz`zÚ©ÛL§§ÂEê&ÒLÆDZdÙ¢êÚJêÜ©|¤&Òݧl ò¥U¼ê=DZCÝ/ª"ùCÝ´ü ݧ2Â[ä?èÒòzDZDÚ[ä?è"X§©ÄÏL`zCÝ5zXÚ¤éVÇ"ÏLòü& ux&Ò½ÂDZÎÒ駩Äu&?Â(ãѤéVÇÄLª"duXÚ¤éVÇ´d&?Â(ãþ(:îªålû½§©JÑ«z²îªålX=(x1, x2)
XR=RYRHR
Y2
H1
H2
YR
Y1
ã 2–11ÙXÚµãFig 2–1 System Diagram of Chapter 2
— 19 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO£maximizing the minimal squared Euclidean distance, MMSED¤`züÑ5JpXÚ¤éVÇ5U",§©y²JÑMMSED`z¯K±ÏLÚ\¥mCþݧl d=DZà`z¯K§Ïd±æ^.KFMMSED`CÝ)"äN5`§©ÏLe¡AÚ½òMMSED`z¯K=DZàg5`z¯Kµ£1¤^¼êOMMSED¯K¥8I¼ê§£2¤½Â^±`z¥mݧ§´¥U-&&ÝÚCݦÈ"ùÒ±^.KF¥?Ø.KFØÓ5¦)`)"e5§Äu`¥mÝÚ¥U-&&Ý_`CÝ"ÏL`Cݧ©?Ú`zü& uxõÇ5J,XÚ¤éVÇ"ý(JL²§2Â[ä?è'Ù¦êiÚ[?èüÑ5ù§ÃØ´æ^4-QAM´16-QAMN§Ñ±Ð¤éVÇ5U"2.2 '''ïïïÄÄÄóóó3ù!¥§©éõ\¥U&¥n«;.ä?èÆÆ?10Úo("2.2.1 EEEêêêäää???èèèõ^r¥UÆÏ&±¼m©8Oç*CX§¿q,ÈèÄõ^ruÿKDZ§±JpXÚNþ"ÄuùħWang< [44]JÑEêä?è"³Ûuä?èX^rêþO\ÃóéþE,½ØC'§Eêä?è±1
2ÎÒ/& /&£symbol per source per channel use§sym/S/CU¤óéþ"e¡§©V)o(Eêä?èXÚ.ÚÌ(Ø"Ädü& !&Ã¥Uä§Xã2–2¤«"z!:kU§ü^r£S1ÚS2¤¡ux&EÂàD§,¡ÏL¥UR=u&ÒD"31g&¦^£channel use§CU¤§¥UÓÂS1 ÚS2DÑ&Òθ1x1Úθ2x2§Ù¥ÏLÆÆθ1Úθ2gEêC"& êN = 2§kθi = ejπ(4n−1)(i−1)/2N"²L1g&¦^
— 20 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO1 1x
1 1x
2 2x
2 2x
1 21 2x x !
Time Slot 1
Time Slot 2ã 2–2Eêä?èüÑFig 2–2 Complex-field network coding§¥URÚ&D©OÂÎÒySR = hS1Rθ1x1 + hS2Rθ2x2 + nSR,
ySD = hS1Dθ1x1 + hS2Dθ2x2 + nSD,(2–1)Ù¥§hij ∼ CN (0, σ2
ij)LÑl"þ!DZσ2ijEpd©Ù&ëê§
nij ∼ CN (0, N0)L«Ñl"þ!DZN0Epd©Ù\5pdxD("]Ú²þSNR©Odγij = |hij |2γÚγij = σ2ijγL«§Ù¥γ = Px/N0§Px´gki18ÜAx& ÎÒx²þuxõÇ"3¥U??1q,È觱
(x1, x2)R = arg minx1,x2∈Ax
||ySR − hS1Rθ1x1 − hS2Rθ2x2||2. (2–2)3Eêä?襧ö3¥U?æ^ó´g·A2)£link-adaptive
regenerative, LAR¤Æüѧ=¥UuxõǬ?1 "duó´g·A2)üÑâ& -¥U-&ó´¹é¥UõÇ?1N§Ïd3©8OÃ!E,ÝÚõÇÇ¡Ñ'Ù¦ä?èüÑ[73]Ð"ù§31g&¦^§&Â&Ò±L«DZyRD = hRD
√α (θ1x1 + θ2x2) + nRD, (2–3)Ù¥§hRD ∼ CN (0, σ2
RD)§nRD ∼ CN (0, N0)§α´¥UuxõÇó´g— 21 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO·A Ïf§ÙDZα =
min γSR, γRDγRD
. (2–4)ùp§γSR = |hSR|2(dmin/2)2γ§|hSR| = dminSR /d
max, dminÚdmax©O´(θ1x1+θ2x2þÚî¼ål§ dmin
SR´(hS1Rθ1x1 + hS2Rθ2x2þî¼ål"ÏL¥U-&ó´&Ôö§±3&?hRD
√α"ù§Äuüg&¦^Â&Ò§&Dæ^q,Èèì¡EÑ& !:uxü&Ò§=
(x1, x2)D = arg minx1,x2∈Ax
||ySD − hS1Dθ1x1 − hS2Dθ2x2||2
+ ||yRD − hRD
√α (θ1x1 + θ2x2)||2.
(2–5)Eêä?è±1/2sym/S/CUóéþ"DÚüuxUÂUMISO£multiple input single output¤XÚ'§óéþþ´d¥UVóå5§=¥UØU3Ó&ÓUþÓuxÚÂ&Ò"ØJpóéþ±§Eêä?èJpXÚÎÒVÇ"öÄuùüѧJÑXeX(اé8ä?èOkééu¿Â"Eêä?èA:´&Òé(x1, x2)Ú¥U&Òu = (θ1x1 +
θ2x2)m÷vN'X§=ü& !¥UÚ&Ñ®θ1, θ2cJe§θ1x1 + θ2x2 6= θ1x2 + θ2x1=x1 6= x2, θ1 6= θ2¤á"ù==uÒUuÿÑx1Úx2"duÄuɽöä?è¿Ø÷vù5§=x1 ⊕ x2 = x2 ⊕ x1§Ïd³Ûuä?è)Ônä?è [73]ÑØUEêä?èóéþ"Ônä?èk3V¥Uä [29]¥âU1/2sym/S/CUóéþ" Eêä?è±Ó3V¥UäÚõ\¥U&¥1/2sym/S/CUóéþ"3³Ûuþ?1õ\¥U&ä?èO§DZI÷v& &Òé(x1, x2)Ú¥Uä&ÒN'X§âU¦XÚ÷©8OÃ"2.2.2 ÔÔÔnnnäää???èèè
Muralidharan<ÄuV¥U&¥Ônä?è [29]g´§3K^rõ\¥Uä¥JÑ«#.Ônä?èüÑ [104]"zg— 22 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOÏ&©DZüãµ£1¤31㧤k^ròg&EÓux¥UÚ&¶£2¤31㧤k^ræ^ØÓu1ãõÇux1ãÓ&E§Ó¥UDZòä?è&Ò=u&"31ã(姥Ué¤k^r&E?1È觿±.¶á£Latin
Hypercube¤DZOKòÈè&E±õé/ªNä?è&Òþ"DZ³¥U?Èè*Ñ&§ö3&?Ä¥U?دu)VÇ"Äu±þO§ù#.Ônä?è±3õ\¥Uä¥÷©8OÃ"´§du^r31Yux&Ò¬é¥UDÑä?è&ÒE¤Z6§ÏdO\&?ÈèìE,ݧÓü$?èOÃ"e¡§©V)o(Ônä?èXÚ.ÚÌ(Ø"31Ï&ã§K^r!:SiÓux²L &Òxi¥URÚ&D§=yR =
K∑
i=1
hSiR
√ESaixi + zR,
y1 =K∑
i=1
hSiD
√ESaixi + z1,
(2–6)Ù¥§~êai ∈ C, i ∈ 1, 2, · · · , KL^r?õÇ Ïf§zR , z1 ∈CN (0, 1)©ODZ¥UÚ&?Eê\5pdxD("©¥Ä´a|Pá§Ïd?¿ü!:jÚkm&ëê÷vhjk ∼ CN (0, σ2
jk), j ∈ Si, R, k ∈R,D, j 6= k"¥U!:RâÂ&ÒyR5O&Ò(x1, x2, · · · , xK)q,O(xR1 , xR2 , . . . xRK)§=
(xR1 , x
R2 , . . . x
RK
)= arg min
(x′1,x
′2,··· ,x′
K)∈SK
||yR −K∑
i=1
hSiR
√ESaix
′i||2 (2–7)31Ï&ã§^r!:Siux²LõÇ &Òxi§Ó¥URux&ÒxR = f(xR1 , x
R2 , · · · , xRK)&§Ù¥f : SK → S´õéN¼ê"ù§&!:31Ï&ã(åÂ&ÒDZ
y2 =K∑
i=1
hSiD
√ESbixi + hRD
√ESxR + z2, (2–8)Ù¥§~êai ∈ C, i ∈ 1, 2, · · · , KL^r?õÇ Ïf§z2 ∈ CN (0, 1)DZ&?Eê\5pdxD("DZ4^r!:?uxõÇuES§~êai
— 23 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOÚbiI÷v|ai|2 + |bi|2 = 1, ∀i ∈ 1, 2, · · · , K"K = 2§ai ÚbiDZa1 = 1, b1 = 0, a2 =1√2, b2 =
1√2"DZyXÚ±©8Oç¿ÑDÚq,ÈèìvkÄ¥UÈèØVÇ":§öJÑ«#Èèì(§=
(xD1 , x
D2 , . . . x
DK
)= arg min
(x1′ ,x2′ ,··· ,xK′ )∈SKm1 (x1′, x2′ , · · · , xK ′) ,
log (SNR) +m2 (x1′ , x2′, · · · , xK ′)(2–9)Ù¥
m1 (x1′ , x2′, . . . , xK ′) = ||y1 −K∑i=1
hSiD
√ESaixi′||2
+ ||y2 −K∑i=1
hSiD
√ESbixi′ − hRD
√ESf (x1′ , x2′, . . . , xK ′) ||2
m2 (x1′ , x2′, . . . , xK ′) = ||y1 −K∑i=1
hSiD
√ESaixi′||2
+ min
xR′ 6= f (x1′ , x2′, . . . , xK ′)
xR′ ∈ S
||y2 −
K∑i=1
hSiD
√ESbixi′ − hRD
√ESxR′ ||2
(2–10)¥Uux(ä?è&Ò§`q,Èèì¹m1 (x′1, x
′2, · · · , x′K)Ü©"¥UuxØä?è&Ò§=xR = f
(xR1 , x
R2 , · · · xRK
)6= f (x1, x2, · · · , xK)§`q,ÈèìDZm2 (x
′1, x
′2, · · · , x′K)"3pSNRe§¥UuxØä?èVÇ 1
SNR¤'§Ïd3m2c¡\\log(SNR)?1?"DZÑÔnä?è3õ\¥U&¥÷©8¿©^§©O½ÂÉèiÝÚüÉèiÝDZ
Cr (x1, x2, · · · , xK) =[a1x1 a2x2 · · · aKxK
b1x1 b2x2 · · · bKxK
]T
Cr (∆x1,∆x2, · · · ,∆xK) =[a1∆x1 a2∆x2 · · · aK∆xK
b1∆x1 b2∆x2 · · · bK∆xK
]T (2–11)
éuÔnä?è§DZ4(2–9)¥Èèì÷©8§¥U?ä?èN'XÚÉèiÝI÷v±e^— 24 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO• £1¤ä?èNI÷v
f (x1, x2, · · ·xi−1, xi, xi+1, · · · , xK) 6= f (x1, x2, · · ·xi−1, xi′, xi+1, · · · , xK)
for xi 6= xi′, ∀i ∈ 1, 2, · · · , K
(2–12)
• £2¤¤kÉèiÝCr (∆x1,∆x2, · · · ,∆xK)2 × 2fÝ7Lu2§∀∆x1,∆x2, · · · ,∆xK 6= 0"÷v1¿©^Nf¤êDZM!ÝDZK.¶á"3.¶ázÝþ§ÎÒ8ÜÑDZ0, 1, · · · ,M − 1zÎÒØÓ"3ã2–3¥§öÑ4.¶/"0
0 0
0
0
0
0
0 0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3 3
3
3
3
3
3 3
(a) Modulo-4 Latin Square (b) Bit-wise XOR Latin Squareã 2–3o.¶/«~Fig 2–3 Examples of Latin Square of order 4
2.2.3 [[[äää???èèè3©z [105]¥§öò[ä?èA^õ\¥U䥧¿:Äõ^rZ6éXÚ©85KDZ"3©Ù¥§ö©OÄ¥U3]õÇåeCþOÃÆüÑÚÏõÇåe½OÃÆüÑ"´3©Ù¥§övkéVÇé¥U¼ê?1`z§Ïdl?èOÃÆÝ5ù§5UÖu©JÑ2Â[ä?è"e¡§©V)o([ä?èXÚ.ÚÌ(Ø"©ÙÄdK^r§ü¥UÚü&|¤õ\¥U&"â¥UVóå§êâDÑ©DZüã¤"31㧤— 25 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOk^rÓ2Âgêâ"Ïd§¥UÚ&Â&Ò±©OL«DZysr =
√Pλsr
K∑
k=1
fksk + nsr,
ysd =√Pλsd
K∑
k=1
hksk + nsd,
(2–13)Ù¥§PL^ruxõǧλij , i ∈ s, r, j ∈ r, d, i 6= jDZ&Ñëê§fk, hk ∼ CN (0, 1)©OL«1k^r¥UÚ&&ëê§skDZ1k^rl8zUþ(Ω¥ÀÑux&Ò§=E|sk|2 = 1§nsdÚnsr DZEêpd\5xD("E(·)L«é)ÒSÅCþÏ""¥Uux&ÒDZxr = √
αPysr§Ù¥αDZ8z¥UuõÇÏf"3©Ù¥§öÄü«8z¥UuõÇ"éuCþOÃÆüѧ¥UõÇ3zDZÑI3P±S§=E(|xr|2∣∣f) = P, f = (f1, f2, · · · , fK)T"TüѦ¥U!:â¢&G5NÏf"αV GRLªDZ
αV GR =1
Pλsr∑K
k=1 |fk|2 + 1(2–14),§¥UDZ±æ^½ØCÏf"d§¥U²þuxõÇ3ãémp8zDZP§=E|xr|2 = P"½OÃÆüÑÏfαFGRLªDZ
αFGR =1
KPλsr + 1(2–15)²L·õÇ §¥U31ã¿=u&Ò&§=
yrd =√λrdgxr + nrd =
√αP 2λsrλrdg
K∑
k=1
fksk + nrd, (2–16)Ù¥§nrd =√αPλrdgnsr + nrd ∼ CN (0, αPλrd|g|2 + 1)DZd\5D("âÂ&ÒysrÚyrd§&æ^q,ÈèìéÜÈÑK^rÎÒ§=
sd = arg minsk∈Ω
|ysd −√Pλsd
K∑
k=1
hksk|2 +|yrd −
√αP 2λsrλrdg
K∑k=1
fksk|2
αPλrd|g|2 + 1(2–17)
— 26 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOP → ∞§½OÃÆüÑÚCþOÃÆüѤéVDZ©OL«DZPr (s→ s|FGR) P→∞≈ 16K
λrdλsd||∆s||4logPP 2 ≤ 16K
λrdλsdd4min
logPP 2
Pr (s→ s|V GR) P→∞≈ 16(K−1)λrdλsd||∆s||4
logPP 2 ≤ 16(K−1)
λrdλsdd4min
logPP 2
(2–18)Ù¥§dmin = mins,s∈Ω,s 6=s
|s− s|DZ8ÜΩ¥?¿üØÓ:máål"DZ£ã(2–18)¥éêé©8OÃKDZ§öò2©8OýÂDZ(d1,−d2)[42]§Ù¥§d1´£ã3~pSNReVÇCqLyÌ©8Oç d2û½3¥SNReXÚ§Ý"ÃØd2XÛ§d1 = 2§XÚK±÷©8"SNR~ÿ§¤éVDZCqL«DZO(
(log P )d2
P d1
)§=©8OÃDZd1 − d2log logPlogP
"¦+3~pSNRe§éêKDZ±ÑØO§= limP→∞
log logPlogP
= 0§´XÚ3¥SNRe¬²©8"'XP ≤ 30dB§ log logPlogP
≥ 0.28"½OÃÆüÑÚCþOÃÆüÑѱ÷©8OÃ(2,−1)§´kCþOÃÆüÑ3¥SNReجÉéê"lúª(2–16)¥±w§éuü^rCþOÃÆüѧÏf±L«DZαVGR =
(Pλsr|fk|2 + 1)−1 P→∞≈ 1
Pλsr|fk|2"ù§&Ò3pSNRe±heq,ksk§Ù¥&heq,k =√Pλrdge
jϕ(fk)E,Ñla|Pá§ϕ(fk)´&ëêfk " éuõ^rCþOÃÆüѧ&Ñfkg¥'"ÏDZfkgÑlVa|P᧤±Ò¬3¤éVÇLª¥Ú\éê"ÏL¤éVÇLª±w§X^rêKO\§©8OÃ5UجÉKDZ"´§ÏDZ¤éVÇK¥'§¤±X^rêO\?èOÃDZ5ü$",§duCþOÃÆüѱÏLzDZéuxõÇ?18z5~&PáKDZ§¤±CþOÃÆüѽOÃÆüÑ5UÐ"§öJѤéVÇλrd¥'¿Õáuλsr"ù§¥U-&ó´þû½XÚN5U"e¡§©[02Â[ä?è[SN"2.3 XXXÚÚÚ...Ädü& !ü¥U|¤õ\¥UXÚ"Ù¥§ü& S1ÚS2ÏLVó¥URƧòg&EDÑÓ&D§
— 27 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOFirst phase
Second phase
1Dh
2Dh
2Rh
1RhRDh
ã 2–4õ\¥U&XÚ§¹ü& !¥UÚ&Fig 2–4 The non-orthogonal MARC system with two sources, onerelay and one destination.Xã2–4¤«"zDѱϱ©DZüDÑã"31DÑãzÎÒYp§ü& ÓògÎÒx1Úx22Â&Ú¥U"31DÑãzÎÒYp§ü& ±·%§Ó¥U?nÂ&Ò¿=u²LÎÒxR&"üDÑã(å§&âÂ&ÒÈèü& &E"½Â& SauxM -QAMNÎÒDZxa§Ù¥a = 1, 2"zÎÒdÓxaIÚxaQ|¤§=xa = xaI+
√−1xaQ¿÷vUþåE(xax∗a) =
Ea"ùp§EaL& SauxõÇ"&Òxab´dxab = M(sab)§Ù¥b = I,Q§M(·)´√M -PAMNéA(N§sab ∈ 0, 1, · · · ,
√M − 1LxaVÇ©ÙÓÚ&E"ù§&Òxab±ÏLe¡úªO
xab =2sab − (
√M − 1)√
2(M − 1)/3. (2–19)3©¥§M -QAMN8ÜPΩ"b¤k&ÒÑ3ÓªãþDÑ"?¿ü!:vÚwm&^hvw 5L«§Ù¥§eIL«9ü!:§v ∈ 1, 2,R, w ∈ R,D¿v 6= w"b¤k&ëêhvwÑÑl"þ!DZγvwEpd©Ù"©ÄúPáXÚ§=3DѱÏS&ëê±ØC§¿3üDѱÏmÕáCz"
— 28 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOÄucXÚÚb§31DÑãzÎÒYS§¥UÚ&Â&Ò±©OL«DZyR =
√E1h1Rx1 +
√E2h2Rx2 + nR,
y1 =√E1h1Dx1 +
√E2h2Dx2 + n1,
(2–20)
Ù¥nRÚn1©OL¥UÚ&?"þ!zÝDZσ2/2Eê\5pdxD(£additive white Gaussian noise§AWGN¤"3Âü& pZ6&ÒyR§¥U!:ò¼êf(·)A^u&ÒyRþ"ù§¥U!:=òDÑ&Ò±LÆDZxR = f(yR), (2–21)Ù¥f(·)¼êäN½Âò3e©¥Ñ"b¥U!:?uõÇDZER§Ïd¥Uux&ÒI÷vE|xR|2 ≤ ERå"31DÑãzÎÒYp§&!:Â&Ò±L«DZ
y2 = hRDxR + n2, (2–22)Ù¥n2´"þ!zÝDZσ2/2Eê\5pdxD("úª(2–20)! (2–21)Ú(2–22)®²3Eêéõ\¥U&?1ï"DZBuY`zÚ©Û§ÏL·C/§±òEê&Ò?1¢êÝz#ï"äN5ù§úª(2–20)¥Â&ÒyRÚy1²L¢ÜÚJÜ— 29 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO ©§±LDZ[<yR=yR
]
︸ ︷︷ ︸yR
=
[1 0
0 1
]
︸ ︷︷ ︸I2
[<h1R <h2R=h1R =h2R
]
︸ ︷︷ ︸HR
[ √E1<x1√E2<x2
]
︸ ︷︷ ︸<x
+
[0 −1
1 0
]
︸ ︷︷ ︸I′2
[<h1R <h2R=h1R =h2R
]
︸ ︷︷ ︸HR
[ √E1=x1√E2=x2
]
︸ ︷︷ ︸=x
+
[<nR=nR
]
︸ ︷︷ ︸nR
,
[<y1=y1
]
︸ ︷︷ ︸y1
=
[1 0
0 1
]
︸ ︷︷ ︸I2
[<h1D <h2D=h1D =h2D
]
︸ ︷︷ ︸H1
[ √E1<x1√E2<x2
]
︸ ︷︷ ︸<x
+
[0 −1
1 0
]
︸ ︷︷ ︸I′2
[<h1D <h2D=h1D =h2D
]
︸ ︷︷ ︸H1
[ √E1=x1√E2=x2
]
︸ ︷︷ ︸=x
+
[<n1=n1
]
︸ ︷︷ ︸n1
,
(2–23)Ù¥x =[√E1x1,
√E2x2
]T"âúª(2–23)¥½Â§±yR = I2HR<x + I′2HR=x + nR,
y1 = I2H1<x + I′2H1=x+ n1.(2–24)A§Äu&ÒyR¥U¼êf(yR)±^ü¢êCÝRÚ¢êþyR¦ÈL«§=
xR = RyR, (2–25)Ù¥2× 1¢êþxR = [<xR,=xR]Td&ÒxR¢ÜÚJÜ|¤§CÝR½Â´R , βΘ, for β ∈ R
+,Θ ∈ R2×2,Tr(ΘTΘ) = 1, (2–26)¿÷v¥U?uxõÇå
β2 =ER
Tr yRyTR. (2–27)lúª(2–26)¥§±wÑCÝR¹üÜ©"ëêβ^aquDÚ[ä?è(2–14)¥õÇ8zÏfαVGR"ÝΘéÂ&ÒyRõ
— 30 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOÇÚ ?1N§¿±ÏLJp¤éVÇ5U?1`z"òÝR^ÙoL«DZR = [R11, R12;R21, R22]"ù§f(·)¼ê±DZf (yR) = (R11<yR +R12=yR) +
√−1 (R21<yR+ R22=yR) . (2–28)3¡Ù!p©¬?ØXÛ`zCÝR5z¤éVÇ"31DÑã§&!:?Â&Òy2±^¢êþ/ªL«DZ
y2 = H2xR + n2, (2–29)Ù¥y2 = [<y2,=y2]T§xR = [<xR,=xR]T§n2 = [<n2,=n2]T§¿kH2 =
[<hRD −=hRD=hRD <hRD
]. (2–30)DZz©Û§ùpØ5bD(σ2u"&ÄuÂ&Òy1Úy2§æ^q,Èè£Maximum likelihood, ML¤[105]5éÜÈÑü& ÎÒ§=
x = argminx∈Ω
∣∣∣∣∣∣y1 − I2H1<x − I′2H1=x
∣∣∣∣∣∣2
2+
∣∣∣∣∣∣y2 −H2R(I2HR<x − I′2HR=x)
∣∣∣∣∣∣2
2
Tr H2RRTHT2 /2 + 1
,
(2–31)Ù¥(·)LuÿÎÒ§ (·)Lb-uÿ¯K¥¢ÎÒ"duTr(RTR) =
β2§úª(2–31)Òmý1©1Ü©±,PDZTrH2RRTHT
2
= β2Tr
H2H
T2
. (2–32)éuBPSKN§q,Èè±zDZ
x = argminx∈Ω
(||y1 −H1x||22 +
||y2 −H2RHRx||22β2Tr H2H
T2 /2 + 1
). (2–33)du2Â[ä?èüÑ¥æ^q,Èèì(2–31)´ÄuÎÒ?1ö§ùzgÌÒ912M2ݦÚ7M2Ý\" éuANCüѧÏDZÙØIOH2R§¤±zgÌ911M2ݦÚ7M2Ý\"¦+©JÑ2Â[ä?è3OE,ÝþÑpuDÚANCüѧ´E,ÝOÌA3Xêþ êþ"lY5Uý¥±w§DZ,ã+OE,ݧ´2Â[ä?èüÑ?èOÃ`uANCüÑ"
— 31 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO2.4 CCCÝÝÝ`zzz!ò?ØXÛ`zCÝR5z¤éVÇ"Äk§©Ñ¤éVǽÂ"ÏDZXÚ¤éVÇ´d&àÂ(ãþ(:mî¼ålû½§Ïd©JÑzî¼ål£maximizing the minimal Euclidean distance§MMSED¤OK5Jp¤éVÇ5U"e5§©òà`zMMSED¯K=DZà`z¯K"¿3æ^.KF5¦)=à`z¯KÑCÝR4ÜLª"2.4.1 ÝÝÝ`zzzXÚ¤éVǽÂDZDÑÎÒéxØȤ,ÎÒéxVÇ"½ÂxiÚxj ´xüØÓ¢y"du3M -QAMN¥§þxiÚxjzÑkMU§Ïdki, j ∈ 1, 2, · · · ,M2, i 6= j"ùp§b½¤k&¢yþDZh = [h1R, h2R, h1D, h2D, hRD]"âúª(2–31)¥q,ÈèLª§ÎÒéxiȤxj¤éVÇLª±DZ
Pr (xi → xj |h) = Q
(√Dij
2
), (2–34)Ù¥Q(x)¼ê½ÂDZ[106]
Q(x) =1√2π
∫ ∞
x
exp(−z2/2)dz = 1
π
∫ π/2
0
exp
(− x2
2 sin2(θ)
)dθ, (2–35),§Dij´âúª(2–31)ÎÒéxixjmîªål"e¡§©òïĽ&¢yheo]&(ã£instantaneous
destination constellation§IDC¤"äN5ù§&(ãX¶´y1¢ê&ÒÜ©§=√E1<h1D<x1+
√E2<h2D<x2−
√E1=h1D=x1−
√E2=h2D=x2,
Y¶´y1Jê&ÒÜ©§=√E1<h1D=x1+
√E2=h2D<x2+
√E1<h1D=x1+
√E2<h2D=x2,
— 32 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOZ¶´y2¢ê&ÒÜ©§=
√ER(<hRD<xR − =hRD=xR),
T¶´y2Jê&ÒÜ©§=√ER(<hRD=xR + =hRD<xR).âïá]&(ã§&??¿ü(:m²îªål±
Dij =∣∣∣∣∣∣I2H1d
<ij + I′2H1d
=ij
∣∣∣∣∣∣2
2+
∣∣∣∣∣∣H2RI2HRd
<ij +H2RI′2HRd
=ij
∣∣∣∣∣∣2
2
β2Tr H2HT2 /2 + 1
, (2–36)Ù¥d<ij = <xi − xj§¿d=
ij = =xi − xj"AO§éuBPSKN ó§²îªål±ÑDZDij =
∣∣∣∣∣∣H1dij
∣∣∣∣∣∣2
2+
∣∣∣∣∣∣H2RHRdij
∣∣∣∣∣∣2
2
β2Tr H2HT2 /2 + 1
, (2–37)Ù¥dij = xi − xj"éuM -QAMN§ÏDZüØi = j ¹§¤±3M4 −M2²îªålDij"½ÂDminDZ²îªål§=Dmin = minD12, D13, · · · , Dij , · · · , DM2(M2−1).DZ`zÄuq,uÿ¤éVǧÒIz²îªålDmin"ÏDZùpÄ´úPá&§=&ëê3DѱÏS±ØC§¤±éuzDѱÏI`CÝR"âúª(2–36)¥Ñ²îªålLª§3¥UõÇå(2–27)eîªål`z¯K±ïDZ
R∗ = argmaxR
mind<
ij ,d=ij
Dij s.t. Tr(RRT ) = β2. (2–38)dumax−min`z¯KÏ~5ù´à§ÏdÄÚ\#CþDmin§Ó½Â¥mÝΨ , H2R",§½Âϕ , 1
β2TrH2HT2 /2+1
"— 33 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO²LüêÆ$§úª(2–38)¥ïáî¼ål`z¯K±#ïDZÄuDminÚΨz¯K§=max Dmin
s. t. Dij =∣∣∣∣∣∣I2H1d
<ij + I′2H1d
=ij
∣∣∣∣∣∣2
2+ ϕ
∣∣∣∣∣∣ΨI2HRd
<ij +ΨI′2HRd
=ij
∣∣∣∣∣∣2
2≥ Dmin,
Tr(ΨΨT ) =2(1− ϕ)
ϕ.
(2–39)duó´∣∣∣∣∣∣I2H1d<ij + I′2H1d
=ij
∣∣∣∣∣∣2
2´ÝΨpÕá"Ïd§DZzL㧽ÂDdirect
ij ,
∣∣∣∣∣∣I2H1d
<ij + I′2H1d
=ij
∣∣∣∣∣∣2
2",I5¿3úª(2–39)¤«1|å^¥3M4 −M2Uî¼ålDij"duz¯K(2–39)¥8I¼ê´¼ê§¿å^´CþΨg¼ê§¤±§ù´gå55y£quadratically
constrained linear programming§QCLP¤à`z¯K"ùÒ±æ^.KF¦f5`ΨÚDmin"äN5ù§.KF§±L (Ψ, Dmin, µij, λ) = Dmin +
M2∑
i=1
M2∑
j=1,j 6=i
µij
(Ddirect
ij + ϕ∣∣∣∣∣∣Ψuij
∣∣∣∣∣∣2
2−Dmin
)
− λ
(Tr(ΨΨT )− 2(1− ϕ)
ϕ
),
(2–40)Ù¥éu¤ki, j§µij ≥ 0DZ.KF¦f§,uij , I2HRd<ij + I′2HRd
=ij"duDmin, D
directij ÚϕéuΨ óÑ´~ꧤ±ùn~êéuΨ Ñu"",§âÝêÚ,'X§±'Xª∣∣∣∣∣∣Ψuij
∣∣∣∣∣∣2
2=
Tr(Ψuiju
TijΨ
T)"ÄuÝnاéu?¿üÝM1ÚM2kXe5K
∂Tr(M1M2MT1 )
∂M1
= M1MT2 +M1M2.ù§Karush-Kuhn-Tucker (KKT) ±de¡úªÑ
∂L∂Ψ
= ϕ
M2∑
i=1
M2∑
j=1,j 6=i
µijΨuijuTij − λΨ = 0,
∂L∂Dmin
= 1−M2∑
i=1
M2∑
j=1,j 6=i
µij = 0.
(2–41)
— 34 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOpÖtµ5^±µij
(Ddirect
ij + ϕ∣∣∣∣∣∣Ψuij
∣∣∣∣∣∣2
2−Dmin
)= 0,
λ
(Tr(ΨΨT )− 2(1− ϕ)
ϕ
)= 0.
(2–42)âúª(2–40)!(2–41)Ú(2–42)§±ÏL?Ø.KF¦f¦)`z¯K(2–39)"e¡½nÑ`ÝΨ∗Lª"½n 2.1. zDmin`ÝΨ∗±L«DZΨ∗ = argmax Dmin (Ψk,ij) , for i, j ∈ 1, 2, · · · ,M2, i 6= j, k = 1, 2, (2–43)Ù¥
Ψ1,ij =
[κij,1
uij,2
uij,1κij,1
κij,2uij,2
uij,1κij,2
], (2–44a)
Ψ2,ij =
[cos(π4
)− sin
(π4
)
sin(π4
)cos(π4
)]
∣∣∣(1−ϕ)
(uij12 +u
ij21 −2u
ij11 −2u
ij22
)+(Ddirect
vw −Ddirectij )
ϕ(uij12 +u
ij21
)∣∣∣ 0
0∣∣∣(1−ϕ)
(uij12 +u
ij21 +2u
ij11 +2u
ij22
)−(Ddirect
vw −Ddirectij )
ϕ(uij12 +u
ij21
)∣∣∣
12
(2–44b)ùp§κij,1Úκij,2´ütµCþ§§I÷vκij,1, κij,2 ∈ R+Úå^
κ2ij,1 + κ2ij,2 =2(1− ϕ)
ϕ(1 +
uij,2
uij,1
)2 . (2–45),§uij,1Úuij,2´þuij , I2HRd<ij+I′2HRd
=ijü; uij11 , u
ij12 , u
ij21 Úuij22 ´ÝUij , uiju
Tij − uvwu
Tvwo§Ù¥uvw , I2HRd
<vw + I′2HRd
=vw"y²: y²L§ëwN¹A. Äu`Ψ∗í(J§±tzDmin`CÝR§=
R∗ = (H2)−1Ψ∗. (2–46)
— 35 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO2.4.2 555UUUýýýÚÚÚ???ØØØã2–5Úã2–6©OЫDÚ[ä?è£ANC¤Ú2Â[ä?è²î¼ålã"3ù|ý¥§& DÑ´²L4-QAMNÎÒ¶)10000|&ëêh1R , h2R, h1D, h2DÚhRD¶XÚ&D'SNRDZ25dB"DZB*§X¶ÀDZlog(Dij)§¿þzDZ64§Y¶´log(Dij)VÇݼê"l㥱w§éDÚ[ä?è ó§2Â[ä?èüѲî¼ålþl11.53Jp20.33§åll[5.76, 17.31]*Ð[13.28, 27.39]"du`CÝLªE,§¤±éJlog(Dij)VÇݼê4ÜLª"ùp§±|^'~pd©Ù a1√
2πa3exp
(− (x−a2)2
2a3
)5[Ü2Â[ä?è²î¼ålVÇݼê§Xã2–6¥¢¤«"Ù¥§a1´ê'~ Ïf§a2Úa3©OL«log(Dij)Ï"Ú§,xlog(Dij)Ó"ý(JL²'DÚ[ä?è§2Â[ä?èé§ÝþO&Â(ãþ²î¼ål"ÄuN¹A¥'uCÝÚ²î¼ålDminm'X?ا±wÑDÚ[ä?èéACÝDZR = I2"Ïd§DÚ[ä?è´2Â[ä?èüÑ3det(Fij) = 0Úuij,1 = uij,1 = 2AϹ§Ù¥Fij½Â3úª(A–4)¥Ñ"3Ù¦¹e§ÏDZ2Â[ä?èüÑDminéDÚ[ä?èüÑ5ù§Ïd§¤é5UDZÒÐ"3ã2–5Úã2–6ý(J¥§ÏLDmin3üüÑeVÇݼêy²ù(Ø"duDÚ[ä?è±÷©8[105]§2Â[ä?èDZ±÷©8"ÏLúª(2–44a), (2–44b)Ú(2–46)Lª§·uy`CÝd&ëê¢y!& Ú¥UuõÇÚ& æ^NªÓû½"âN¹A¥?اk²î¼åléÙ¦²î¼ål§¥mCþÝΨdÆ&û½§=& -¥U&Ú¥U-&&"kü²î¼ål§¿éÙ¦²î¼ål ó§¥mCþÝΨdÛ&û½§=& -¥U&!¥U- &&Ú& -&&"ù´ÏDZúª(2–31)¥q,Èè´dó´ÚÆó´û½ü²î¼ålÚ"`zL§¥9²î¼ål§duó´éA²î¼ålØ´Ψ¼ê§Ψ(JÒdÆó´û½"`zL§
— 36 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO
4 6 8 10 12 14 16 180
0.01
0.02
0.03
0.04
0.05
0.06
log(Dij)
Pro
babi
lity
Den
sity
Fun
ctio
n
ã 2–5DÚ[ä?è²î¼ålFig 2–5 Squared Euclidean distance of the ANC scheme¥9ü²î¼ål§IÓÄó´ÚÆó´KDZ§l ²ïuÿ(J",§âØÓ¥mÝΨ∗§úª(2–46)¥`CÝR∗dÆó´½öÛó´û½"CÝdDZüü ÝDÚ[ä?èüѧ`CÝØ=¥UÂ&ÒDÑõǧ^=Â&Ò "ù§CÝOéÂ&Ò?1ØC§= Ú^=§l zXÚ¤éVÇ"32Â[ä?èüÑ¥§ÏDZ3.KF¦fpIÄ2(M4 −M2)²î¼ålDij§¤±XÚE,ÝdNêMû½"
2.5 CCCÝÝÝ`zzz¢¢¢yyyDZ`CÝR§6uØÓ§Ý"§`zL§Q±3&?DZ±3¥U?¢y"3ØÓ|µe§"E,ÝkéO"— 37 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
12 14 16 18 20 22 24 26 280
0.01
0.02
0.03
0.04
0.05
0.06
0.07
log(Dij)
Pro
babi
lity
Den
sity
Fun
ctio
n
ã 2–62Â[ä?è²î¼ålÙéApd[ÜFig 2–6 Squared Euclidean distance of the GANC scheme and itsscaled Gaussian fitting curve
2.5.1 &&&???`zzzlúª(2–44a)Ú(2–44b)Lª¥±wѧΨü)ѹü¢ê§=úª(2–44a)¥κ1Úκ2§Úúª(2–44b)¥1ÝpéÆþü"5¿DZÂ৥U±éN´¼& -¥U]&&E1§l ±Ouij,1 Úuij,2"DZÄu-=uÆÏ&XÚ~§&IXÚÛ&&E"3¦±H−12 ±§CÝRâΨ∗ØÓ§=úª(2–44a)½úª(2–44a)Ñ(J§dü½öo¢êû½"3¢SÏ&¥§`zL§3&?1§¥U!:ØI& -&Ú¥U-&&]&&E"ù´ÏDZ&±lOCÝR§,"2½ö4¢ê¥U"DZÎÜ¢SDѧ&±òÝR¥¢êþz¤k ê,u ¥U§ Ø´ux`R¥U"
1DZõ\& -¥Uó´]CSI§±3¥U?æ^©z[107, 108]¥0q,"— 38 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO2.5.2 ¥¥¥UUU???`zzz`zL§´3¥U!:?¢ÿ§"ØÓ§Ý]&G&E¬KDZ`CÝRO(5"Äk§Ä¥U®& -¥U&!& -&&Ú¥U-&&]&G&E|µ"3ù«¹e§&I"nEê½ö8¢ê¥U§=h1D , h2DÚhRD"¦+"dép§´±°(`CÝR"Ùg§Ä¥U®& -¥U&]&G&E§Ú& -&&Ú¥U-&&ÚO&G&E|µ"DZÂ!:§¥U±t¼& -¥U&]&G&E"Ïd§&ÃI"?Û]&G&E¥U!:"e5§©±BPSKNDZ~§)ºXÛÏLÚO& -&&&EÚ¥U-&&&E5¦CÝR"lúª(2–37)¥§±wÑó´'∣∣∣∣∣∣H1dij
∣∣∣∣∣∣2
2´&ÝH1¼ê"ÏLA^||AB||22 ≤ ||A||22||B||22ت§±
∣∣∣∣∣∣H1dij
∣∣∣∣∣∣2
2≤ ||H1||22
∣∣∣∣dij
∣∣∣∣22. (2–47)duk||H1||22ÚO&G&E§ùpÄ^E ||H1||225Oúª(2–47)¥||H1||22§Ù¥E·L«Ï"$"ª§ó´éA²îªål±CqODZ
Ddirectij = E
||H1||22
∣∣∣∣dij
∣∣∣∣22. (2–48),§±^ÚO&EE ||H2||225Oϕ¥TrH2H
T2
§=ϕ =
1
β2E ||H2||22 /2 + 1. (2–49)ÏLòúª(2–48)Ú(2–49)¥Ddirect
ij Úϕ©OODZDdirectij Úϕ§±úª(2–44a)Ú(2–44b)¥Ψ1,ijÚΨ2,ij"ùprÏLÚO&G&E`ÝΨ∗PΨ
∗"éuCÝR§±^EH−12 5Oúª(2–46)¥(H2)
−1§=R
∗= EH−1
2 Ψ∗. (2–50)
2.6 ÄÄÄuuuCCCÝÝÝOOO&&& õõõÇÇÇ©©©!òÄu1n!¥í`ÝΨ∗5`z& uxõÇEa§Ù¥a = 1, 2"DZL'§3ù!¥rΨ∗¤Ψ"DZBue5— 39 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO©Û§ùpòd<ij©)DZ& DÑõÇ'ÝÚux&Ò¢Ü'þ¦È§Ù¥i, j ∈ 1, 2, · · · ,M2, i 6= j§=d<ij , ESd
<ij =
[ √E1 0
0√E2
] [<x1i − x2i<x1j − x2j
], (2–51)Ù¥xaiÚxaj´æ^M -QAMN& a&Òxaü¢y"aq§±rålþd=
ij©)DZd=ij = ESd
=ij§Ù¥§d=
ij = [=x1i−x2i,=x1j−x2j]T"ù§É& uxoõÇåîªål`z¯K±ïDZÄuCþDminÚESz¯K§=maxDmin
s. t.∣∣∣∣∣∣H1ESd
<ij + I′2H1ESd
=ij
∣∣∣∣∣∣2
2+ ϕ
∣∣∣∣∣∣ΨHRESd
<ij +ΨI2′HRESd
=ij
∣∣∣∣∣∣2
2≥ Dmin,
||ES||22 = Etotal.(2–52)duúª(2–52)¥ùz¯K8I¼ê´¼ê§ å^´CþES g¼ê§Ïdù´gå5à`z¯K§ù±æ^.KF¦f5¦`& uxõÇ"äN5ù§.KFúª±DZ
L (Dmin,ES , µij, λ) = Dmin − λ(||ES ||22 − Etotal
)+
M2∑
i=1
M2∑
j=1,j 6=i
µij
(∣∣∣∣∣∣H1ESd
<ij + I′2H1ESd
=ij
∣∣∣∣∣∣2
2+ ϕ
∣∣∣∣∣∣ΨHRESd
<ij +ΨI′2HRESd
=ij
∣∣∣∣∣∣2
2−Dmin
).
(2–53)
Karush-Kuhn-Tucker DZ∂L
∂Dmin
= 1−M2∑
i=1
M2∑
j=1,j 6=i
µij = 0, (2–54a)
∂L∂ES
=M2∑
i=1
M2∑
j=1,j 6=i
µij
[(H1H
T1 + ϕ(ΨHR)(ΨHR)
T)ESd
<ij(d
<ij)
T
+((I′2H1)(I
′2H1)
T + ϕ(ΨI′2HR)(ΨI′2HR)T)ESd
=ij(d
=ij)
T
+2((I′2H1)
TH1 + ϕ(ΨI′2HR)TΨHR
)ESd
<ij(d
=ij)
T]
− λES = 02×2,
(2–54b)
— 40 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOpÖtµ5^±DZµij
(∣∣∣∣∣∣I2H1ESd
<ij + I′2H1ESd
=ij
∣∣∣∣∣∣2
2+ ϕ
∣∣∣∣∣∣ΨHRESd
<ij +ΨI′2HRESd
=ij
∣∣∣∣∣∣2
2−Dmin
)= 0,
(2–55a)
λ(||ES||22 − Etotal
)= 0. (2–55b)aqu1n!?ا©ÏL`zES5zDmin"eã½nÑ`& uxõÇLª"½n 2.2. ½& uxoõÇEtotal§zá²îªålDmin`& uxõÇÝES±L«DZ
E∗S = argmax
Dmin
(E
k,ijS
), for i, j ∈ 1, 2, · · · ,M2, i 6= j, k = 1, 2,
(2–56)Ù¥E
1,ijS =
√Etotal sin
(arctan
(−η4,ij
η3,ij
))0
0
√Etotal cos
(arctan
(−η4,ij
η3,ij
))
,
(2–57a)
E2,ijS =
√Etotal sin
(arctan
(−ϕ2,ij−ϕ2,vw
ϕ1,ij−ϕ1,vw
))0
0
√Etotal cos
(arctan
(−ϕ2,ij−ϕ2,vw
ϕ1,ij−ϕ1,vw
))
,
(2–57b)ùp§η3,ijÚη4,ij3úª(B–3)¥½Â§ϕ1,mtÚϕ2,mt3úª(B–9)¥½Â§mt ∈ij, vw"y²µy²L§ëwN¹B. 3¢SÏ&L§¥§&I2¢êü& §=η4,ij
η3,ijor
ϕ2,ij−ϕ2,vw
ϕ1,ij−ϕ1,vw§5¤õÇ©"l`z(J¥±wѧ`CÝÚ& uxõÇÑäk4Ü)"du©Ä´úPá&§z&Cz§XÚÑI#éCÝÚ& uxõÇ?1`z"Ù¥§CÝ'`zL§¹14(M4−M2)ݦÚ4(M4 −M2)Ý\" & uxõÇ'`zL§¹16(M4 −M2)ݦÚ5(M4 −M2)Ý\"¤k`
— 41 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
0 5 10 15 20 2510
−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PAã 2–7 4-QAMNe|µ5U
Fig 2–7 Error performance for Case 1 with 4-QAM modulation
0 5 10 15 20 2510
−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PA
4.5 5 5.5
10−0.3
10−0.2
ã 2–8 16-QAMNe|µ5UFig 2–8 Error performance for Case 1 with 16-QAM modulationzL§Ñ´3Ï&m©cl¤"Ïd§vv¹e§`zE,Ý´'$"DѪm©±§¥UIOg2 × 2CÝÚ2× 1&Òþm¦"
— 42 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO
0 5 10 15 20 2510
−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PAã 2–9 4-QAMNe|µ5U
Fig 2–9 Error performance for Case 2 with 4-QAM modulation
0 5 10 15 20 2510
−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PAã 2–10 16-QAMNe|µ5U
Fig 2–10 Error performance for Case 2 with 16-QAM modulation
— 43 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
0 5 10 15 20 2510
−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PAã 2–11 4-QAMNe|µn5U
Fig 2–11 Error performance for Case 3 with 4-QAM modulation
0 5 10 15 20 2510
−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PAã 2–12 16-QAMNe|µn5U
Fig 2–12 Error performance for Case 3 with 16-QAM modulation
— 44 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO2.7 555UUUýýý©©©ÛÛÛ!òÏLý¢5ïþJÑGANCüÑ5U"ùp§zvÝDZl = 10, 000"Ïd§zDѱÏÝÒDZ20, 000"duÄ´O·Pá&§Ïd&ëêh1R, h2R, h1D, h2DÚhRD 3zDѱÏSÑ´½ØC§ 3DѱÏmÕáCz"3ý¥§Ñæ^´»Ñ.γvw = d−2
vw§Ù¥γvwL&Oç v ∈ 1, 2,R, w ∈ R,D, v 6= w"bE1 + E2 = 2ER",§ý¥SNR½ÂDZρ = ER/σ2"
0 5 10 15 20 2510
−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PAã 2–13 4-QAMNe|µo5U
Fig 2–13 Error performance for Case 4 with 4-QAM modulationÄkÄé¡&|µ§dü& ¥UÚ&ål´"& Ú&mål8zDZ§=d1D = d2D = 1"¥U!: u& Ú&m"3ý¥§â¥U¤?nØÓ §Än«ØÓ¹§DZÒ´|µ§|µ§Ú|µn"äN ó§3|µ¥§Är& -¥Uó´|µ§Ù¥d1R = d2R = 0.3§¿dRD = 0.7"3|µ¥§KÄé¡|µ§Ù¥d1R = d2R = 0.5§¿dRD = 0.5"3|µn¥§Är¥U-&|µ§Ù¥d1R = d2R = 0.7§¿dRD = 0.3"3z|µ¥§©ýXeÔ«üѵ— 45 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
0 5 10 15 20 2510
−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PA
4.5 5 5.5
10−0.4
10−0.2
ã 2–14 16-QAMNe|µo5UFig 2–14 Error performance for Case 4 with 16-QAM modulation
0 5 10 15 20 2510
−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PAã 2–15 4-QAMNe|µÊ5U
Fig 2–15 Error performance for Case 5 with 4-QAM modulation
— 46 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èO
0 5 10 15 20 2510
−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
CXNCCFNCPNCANCGANC, STMGANC, ITMGANC, ITM+PA
4.5 5 5.5
10−0.5
10−0.3
ã 2–16 16-QAMNe|µÊ5UFig 2–16 Error performance for Case 5 with 16-QAM modulation
• £a¤DÚÄuɽä?è£conventional XOR-based network coding,
CXNC¤üÑ[29, 80]PEP5U"Ù¥§¥U!:31DÑãuxɽä?è&Ò&§PCXNC¶• £b¤Eêä?è£complex field network coding, CFNC¤üÑ [44]PEP5U"Ù¥§¥U!:31DÑãuxEêä?è&Ò&§PCFNC¶• £c¤Ônä?è [104]PEP5U"Ù¥§¥Uâ4.¶£Latin square¤(½ä?è&Ò§¿ü^rÚ¥U31YÑux&Ò§PPNC¶• £d¤[ä?èüÑ [21]PEP5U"Ù¥§¥U!:31DÑã&=uUþ8z&Ò§PANC¶• £e¤æ^`]CÝR£=`zL§3&??1¤Ú& uxõÇ£=E1 = E2 = ER¤GANC üÑPEP5U§PGANC,ITM¶
— 47 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO• £f¤æ^úª(2–50)ÑÚOCÝR£=`zL§3¥U??1¤Ú& uxõÇ£=E1 = E2 = ER¤GANCüÑPEP5U§PGANC,STM¶• £g¤æ^úª(2–46)¥Ñ`]CÝRÚ1o!`& õÇ©£power allocation, PA¤GANCüÑPEP5U§PGANC,
ITM+PA"lã2–7Úã2–8¥±wѧGANCüѧ=GANC,ITM+PA§GANC,ITMÚGANC,STMüѧ34-QAMÚ16-QAMNe§ÃØ´3ÃÏ&~^óSNR[5, 10]dB«m§´3?1©8OÃ*pSNR[20, 25]dB«m§ÑCXNC§CFNC§PNCÚANCüÑkÐPEP5U"GANCüÑPEP5U`uÙ¦üÑÏ´ÏDZGANC´¦PEPz`üѧ Ù¦üÑKØ,"du& -¥U&¥U-&&r§¤±dCFNCüÑPEP5U'ANCüÑÐ"äN5ù§éuCFNCüÑ ó§ä?èÎÒ5p§ùÒ¦Æ&&Ýp§l N5UDZÒÐ" éuANCüÑ ó§ÏDZ¥U!:D(A§¥U-&&îPáé5UkéKDZ"CXNCüÑ5U"31nÙ¥©òy²§duCXNCüÑ3¥U?vk¢yä?èÎÒÚ& &ÒéN§,DZvk'ü$ÈèØ*ÑŧÏdÃ÷©8"ã2–9§ã2–10§ã2–11Úã2–12©OЫ|µÚ|µn3æ^4-
QAMÚ16-QAMN^e5U"3ùü«¹e§GANCüÑѱ÷©8§¿ÃØ´34-QAM´16-QAMNe§Ñ'Ù¦üÑ5UÐ"X¥Uål&5C§ANCüÑ5UCFNCüÑ ó5Ð"CXNCüÑ5UE,´"lþã8ý(J¥±wXNêMO\§²þ¤éVÇ?èOÃ3eü"æ^`& õÇ©(JGANC,ITM+PAüÑ?èOÃæ^& uxõÇGANC,ITMüÑÐ"GANC,ITMüÑdu¼"5Ð?§¤±5UGANC,STMüÑÐ"GANCüÑÃØ´æ^]CÝ´ÚOCݧPEP5UÑ'Ù¦üÑÐ"du& -¥UaÈè*ÑÚõéä?èN5uÿ5 [43]§CXNCüÑU©8"& ?æ^ý?èO!¥U??1Eêä?èOCFNCüѱ÷©8"5¿´§DZ÷©8§
— 48 —
þ°ÏÆÆ¬Æ Ø© 1Ù 2Â[ä?èOCFNCüÑ3¥U!:?æ«ó´g·A'~£link-adaptive ratio§LAR
[44]§§¦&"¥U-&]&G&E¥U"3©z[105]¥§ANCüÑy²±÷©8"GANCüÑDZ±÷©8§ÏDZ§ÏLzîªål3zPEP"X¥U5C&§GANCüÑÙ¦ÄOüÑåÒ5"X3©z [105]¥öy²@§¥U-&&þÌ[ä?èN5U"Ïd§¥UC&§[ä?èüÑ5UÒЧ½," éuêiä?èüѧ=CXNCÚCFNCüѧ& -¥UaÈè*ÑéN5UKDZé"Ïd§¥UC& §êiä?è5UЧ½,",§©Äü& ´é¡|µ"äN ó§bd1R = 0.5d2R = 0.2dRD = 0.5d1D = 1§¿d2D = 0.7§P|µo¶d1R = 0.7, d2R = 0.2, dRD = 0.3, d1D = 1§¿d2D = 0.5§P|µÊ"ã2–13§ã2–14§ã2–15Úã2–16©OÑ|µoÚ|µÊæ^4-QAMÚ16-QAMNe5U"l㥱wѧGANCüÑPEP5UÙ¦üÑÐ"Ó§ý(JDZL²é¡|µeØÓüÑ'(Jé¡|µe´"2.8 (((Ù3é¡õ\¥U&¥JÑ«zXÚPEP2Âä?èüÑ"Äk§©©O3EêÚ¢êéDÑ&Ò.?1ï",§½ÂÄuq,uÿ²îªål§¿âPEPîªålm'X§JÑ«zîªål`zOK5JpPEP5U"ÏLò8I¼ê=DZ¼ê§¿Ú\¥mCþݧ©ò©max−min¯K=DZà`z¯K§¿æ^.KF?1¦)"ÏL?Ø.KF¦fØÓ§©`CÝ4ÜLª"X§Äu`CÝ©`z& DÑõÇ"ý(JL²GANCüÑÙ¦üÑ ó§ÃØ´é4-QAM´pQAMNÑkÐPEP5U"
— 49 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èO111nnnÙÙÙ õõõÇÇÇggg···AAAäää???èèèOOO
3.1 ÚÚÚóóóÙÄ3õ\¥UPá&¥O«#.êiä?èüÑ[43]§l ¦XÚU÷©8§¿¼p?èOçXÚµãXã3–1¤«"¦+ÏL3¥U?¿ïØ& -¥UÎÒ§kä?è£finite-field network coding, FFNC¤±Ó3Úõ\¥Uä¥÷©8[40]§´duk^&EDZ3ùL§¥¿ïK§Ïd3?èOÃþ¬k¤",§Ùòy²duõ^rZ6§DÚÄuɽä?è£conventional XOR-based network coding, CXNC¤3kÚvkØ*ѳŹeÑÃ3õ\ä¥÷©8"ùÜ©êiä?èOÄn¡SN"Äk§©ÄXÛ3õ\¥Uä¥÷©8OÃ"ÙJÑ«#.õÇg·Aä?èüÑ5÷©8Oç٥õÇþ?´õÇ ÏfÚküþ?õÇg·AÏf¦È"DÚÄuɽä?èØÓ´§õÇg·Aä?èüÑ¥ä?èÎÒ3)¤L§¥ÄÛ&&E§&=u´ü½Uþþ?¥Ù¥"äN5ù§3Âü& u(x1, x2)
SPER
h1R ,h2R
y2yR
y1|h1D|,|h2D|
|hRD|
1 2,
! "1 2,R RE x ! " "
, 1,2ii i ! " "
ã 3–11nÙXÚµãFig 3–1 System Diagram of Chapter 3
— 51 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOx&Ò±§d¥Uû½©=Uþþ?ä?èÎÒ"nØ©Ûy²3¥U?OõÇ ÏfUþg·Aä?èüѱ÷©8§=©8§ DÚÄuɽä?èU©8"Ùg§©ÄXÛïþXÚ5U"3Ù¥§ò5gü& üÎÒ½ÂDZÎÒé",§â¥UÚ&?]Â(㧩ïáÎÒéÇLª"duÂ(ãû«äk5KA5§æ^©z [109]¥JÑ/VÇO.5íÎÒéÇ"5¿Äu©(ã5í°(ÎÒéÇE,Ýép§©JÑ«IC5zíL§Ú(J"3IC¥§©ò©²1o>//G(ã=DZÝ/(㧿â#ïá(ãéAû«§íÎÒéÇCqLª"X§©ÄXÛp?èOÃ"3Ù¥§ÏL`züõÇg·AU?5zÎÒéÇ"äN5ù§©âÎÒéÇÂ(ãþ(:mî¼ålm'X§JÑ`zOK"ÏL¦)ùà`z¯K¼¥U?`õÇg·AU?"âþã?اÙk±eoÌM#:"(a)©JÑ«#.õÇg·Aä?èüÑ"§ÏL¥U?õÇg·AÏfO5÷©8"(b)â©(ãÚ§éAû«§©íXÚÎÒéÇ4ÜLª"(c)©JÑ«ICò©²1o>//G(ã=DZÝ/(ã§l zÎÒéÇí"(d)©`z¥U?õÇg·AU?5JpXÚ?èOÃ"ý(JL²:(a)ÄuICÎÒéÇéÐCq°(ÎÒÇí(J§¿E,Ý$§(b)æ^`õÇg·AÏfÚõÇ ÏfOõÇg·Aä?èüѱ÷©8§¿éÅÀõÇU?üÑ5ù§kÐ?èOÃ" (c)DÚÄuɽä?èüÑkÃæ^õÇ OÑÃ÷©8OÃ"3.2 XXXÚÚÚ...ÙE,Ä´dü& !¥UÚ&|¤õ\¥U.§Ù¥ü& S1S2ÏLVó¥UÆòg&EDÑÓ&"zDѱÏy©DZüã"31Ï&ã§ü& Ó
— 52 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOòg&Ex1 x22Â¥UÚ&"31Ï&ã§ü& ±·%"Ó§¥UÄk?ngCÂ&Ò§ò²Lä?è&ÒxRux&"üÏ&ãÑ(å§&ÏLéÜüãÂ&Ò§ÈÑ5gü& &E"b¤kDÑÎÒÑ´lBPSKN(ãþVÇÅÀJ§=x1, x2, xR ∈ ±1"Ó§b¤k&ÒÑ3ÓªãDÑ"©^hjk LÆ?¿ü!:jÚkm&§Ù¥j ∈ 1, 2,R, k ∈ R,D¿j 6= k",§b¤k&ëêhjkÑ´Ñl"þ!DZγjka|©ÙÅCþ"ùp§ÙÄ&ëê3DѱÏS´ð½úPáXÚ"DѱÏ(å§,DѱÏm©§&ëê¬u)ÕáCz"Äþ1ó´Úe1ó´é¡5§©¥ÏLe1ó´O&&Eéþ1ó´?11Å ÓÚ§l ¢y& -&Ú¥U-& þï [110, 111]"ù§¡±ü$ÄÕ?ÏDZþ1ó´ýþï5pE,ݧ,¡DZÃI3þ1OFDMv¥\ªÎÒ§l kü$XÚm"²Lþï?n§k& -&Ú¥U-&&Ò±wäk¢ê&ëêÚ¢êæD(¢ê&"3?1 ýþï§XÚ¤éÎÒVÇ£SPER¤Ú`¥UDÑõÇþ?κ1Úκ2±ÏL/ØVÇ©Û54ÜLª§l N´ZõÇDÑY"3DÑm©c§©Äé& &õ\&Ú¥U&&æ^ ýþïEâ"ù§k& -&&Ú¥U-&&Ò±wäk¢ê&ëêÚ¢êæD(¢ê&"3¢SÏ&¥±æ^©z [110]Ú [111]¥J'Eâ§|^þ1ó´Úe1ó´é¡5§ÏL3e1ó´®²&O&E5¢y1Å ÓÚ"ù§¡±ü$ÄÕ?ÏDZþ1ó´ýþï5pE,ݧ,¡DZÃI3þ1OFDMv¥\ªÎÒ"éu3½ æ8±¸§Ý!Ý&EÃDaìä ó§du&ëê3ØÓDZCzا'·Üæ^ ýþïEâ",§|^ ýþïEâ±BuXÚ/Ï/ØVÇ©Û5í¤éÎÒVÇ£SPER¤Ú`¥UDÑõÇþ?κ1Úκ24ÜLª"— 53 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOÄuþãXÚÚb§31DÑã(姥UÚ&Â&Ò±©OL«DZyR =
√E1h1Rx1 +
√E2h2Rx2 + nR,
y1 =√E1|h1D|x1 +
√E2|h2D|x2 + n1,
(3–1)Ù¥E1ÚE2©OL«& S1ÚS2DÑõǧnR´¥U?"þ!DZzÝσ2/2Eê\5pdxD(§n1K´&?"þ!DZσ2¢ê\5pdxD("du©3¥U?æ^õÇ Úg·AéÜOüѧ3zDѱϥ½&ëê¢ycJe§¥U?]uxõÇ`z5zÎÒéVǧÓ3&?÷©8OÃ"äN5ù§DZ¢yõÇ §©däN&^õÇ Ïfα (0 ≤ α ≤ 1)",§DZ¢yõÇg·Al å& &Òä?èN^§©ÄüõÇU?κ1Úκ2"§I÷võÇ^κ21 + κ22 ≤ 2EaveR ,Ù¥Eave
R LÆ´¥U²þDÑõÇ"'uëêα, κ1, κ2O©ò3YÙ!0"ù§31DÑã(å§&Â&Ò±y2 =
√ER|hRD|xR + n2, (3–2)Ù¥n2´&?"þ!DZσ2¢ê\5pdxD(§ER ∈ κ1, κ2L÷vκi = ακi§i ∈ 1, 2^¥UDÑõÇ"3Ù¥§'u]&G&E£channel state information§CSI¤®^kXeb"Äk§DZ¢y& ýþï§bü& ®h1D, h2DÚhRDùn]&G&E"Ùg§DZOõÇ Ïfα§b¥U®]&G&Eh1R, h2RÚhRD£½öÚO&G&EγRD¤",§DZDÑõÇ(κ1, κ2)¿3&?¢yéÜq,Èè§b&!:®h1D , h2D,
h1R, h2RÚhRDùo]&G&E"3.3 õõõÇÇÇggg···AAAäää???èèè3õ\¥UXÚ¥§DÚä?èæ^ɽ£XOR¤ª5Ü¿¥U?Èè& &E"3Ù! 3.5¥§©¬y²æ^DÚä?èõ\¥UXÚÃ÷©8"DZ¢y÷©8XÚO
— 54 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èO¦§©JÑ«õÇg·Aä?è£power adaptive network coding§PANC¤ÆÆ"3ùÆÆ¥§¥UâÂ&Ò§DÑä?èÎÒÚýk`zõÇU?¦È&"Äk§¥U!:æ^q,ÈèlÂ&ÒyR¥ü& &EÎÒé(x1, x2)§=
(x1, x2) = argminx1,x2∈±1
∣∣∣∣yR −√E1Rh1Rx1 −
√E2Rh2Rx2
∣∣∣∣2
, (3–3)Ù¥(·)L«uÿÎÒ§(·)L«b-uÿ¯K¥ÁÎÒ"X§¥UéüuÿÑ&Ò?1ä?èö"3PANCÆÆ¥§©^ÎÒ5L«ä?èö§±«DÚä?è¥É½ö«O1"ùp§¥Uux&ÒxRLªDZxR = x1 x2 = sign(|h1R|x1 + |h2R|x2)”1Ú§¥UâÈèÑÎÒÀJõÇU?ER"XJ(x1 =
1, x2 = 1)½ö(x1 = −1, x2 = −1)§¥U©õÇU?κ1éAä?èÎÒ"XJ(x1 = 1, x2 = −1)½ö(x1 = −1, x2 = 1)§¥UK©õÇU?κ2éAä?èÎÒ"©¤±æ^#ä?èöÚõÇU?©´DZ3&?²1o>//GÂ(ã"Ù¥§(x1 = 1, x2 = 1)éA(:(x1 = −1, x2 = −1)éA(:3^éÆþ" éuæ^ɽöä?è§ÃØXÛ?1õÇU?©§&?Â(ãÑ´Ø5Ko>/"¥U!:uxõÇU?κ1Úκ2dõÇ ÏfαÚõÇg·AÏfκ1κ2Óû½"¥Uâ& -¥U&OÃÚ¥U-&&OÃé5û½õÇ Ïf",§&â®]&&E5z]ÎÒéÇ£symbol pair error rate§SPER¤5`õÇg·AÏfκ1κ2§¿3DѪm©c§ò§"¥U"¥U^õÇ ÏfÚõÇg·AÏf¦ÈÓû½`õÇU?5uxä?èÎÒxR"5¿´§õÇg·AÏfκ1κ23zDѱÏS´±ØC"1¦+©JÑPANCÆÆæ^4-PAMNÈè=uüÑkq?§§kXþO"ÏDZ©æ^õÇU?κ1Úκ2¿Ø4-PAMN@´½ØC"ùüU?´&â]&&E`z§"¥U&E"æ^ùü`zU?§±¼ÐXÚ5U"
— 55 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO¥U?PANCÆƱd]¥U(ã£instantaneous relay
constellation§IRC¤5ã" IRC¡Ù!0SPERík'"äN5ù§yR&ÒÜ©§=√E1h1Rx1 +
√E2h2Rx2§±w´±Ù¢êÜ©DZX¶§JêÜ©DZY¶IRCþ(:"½ÂVi , i ∈ 1, · · · , 4DZIRCþ(:§^5L«oU±√
E1h1R ± √E2h2R",§½Â& ÎÒéDZTi , (x1, x2)§=T1 , (1, 1), T2 , (−1, 1), T3 , (1,−1)ÚT4 ,
(−1,−1)"ã 3–2ЫdVi|¤²1o>//GIRC"Ø© [112]¥Voronoiãaq§û«d²1o>/z^>R²©y©m5"Ù¥§l12,l13, l24Úl34 ©O´>V1V2, V1V3, V2V4ÚV3V4R²©"M1´l12l13:§M2´l24 l34:"Mij´>ViVj¥:"(:V1éAû«dΩV1L«§Xã 3–2¥/«l12 −M1 − l13§§½ÂªDZ
ΩV1 ,
<h2R=h2R
<yR + =yR − =h1R −√E1<h1R<h2R
=h2R< 0 and
<h1R=h1R
<yR + =yR − =h2R −√E2<h1R<h2R
=h1R≥ 0
.
(3–4)aq§±LÆÑ(:V2, V3ÚV4éAû«ΩV2, ΩV3ÚΩV4"âùoû«§©½Â(:Úä?èõÇU?mN'XDZ√ERxR =
κ1 if (<yR,=yR) ∈ ΩV1 ,
κ2 if (<yR,=yR) ∈ ΩV2 ,
−κ2 if (<yR,=yR) ∈ ΩV3 ,
−κ1 if (<yR,=yR) ∈ ΩV4 ,
(3–5)
ù§ÄuÂ&Òy1Úy2§&±|^îªålÈèì5éÜÈèü& &E§=(x1, x2) = argmin
x1,x2∈±1
(∣∣∣∣y1 −2∑
j=1
|hjD|xj∣∣∣∣2
+
∣∣∣∣y2 − |hRD|√ER (x1 x2)
∣∣∣∣2),
(3–6)Ù¥ER ∈ κ1, κ2dx1Úx2û½"— 56 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èO
−1.5 −1 −0.5 0 0.5 1 1.5−1.5
−1
−0.5
0
0.5
1
1.5
ℜ YR
ℑY
R
l24
ΩV
4
ΩV
1
ΩV
2
l34
V4
M13
M34
l12
V2
M12
M2
M1
M24
l13
ΩV
3 V3
V1
ã 3–2]¥U(ã,Ù¥JL«û«.Fig 3–2 Instantaneous relay constellation, where dashed lines represent boundaries of decision
regions.
3.4 ¤¤¤éééÎÎÎÒÒÒ555UUU©©©ÛÛÛ3ù!¥§©ïĽ&&Eþh = [h1R, h2R, h1D, h2D, hRD]ePANCÆÆ]SPER5U[113]"b& &ÒuxVÇþ§ù§PANCÆÆeXÚSPER±L«DZ
Pe,inst =4∑
i=1
P (E|Ti, h)P (Ti) =1
4
4∑
i=1
P (E|Ti, h), (3–7)Ù¥Ti´!3.3¥½Â¤éuxÎÒ§EL«&?òý¢ux&ÒÈèDZØ&ÒÎÒد"ùp§ÃØ´x1½öx2kÈèا½ö´x1Úx2ÑÈèا©ÑòÙ½ÂDZد"P (E|Ti, h)L½ux&ÒTiÚ&&Eh^SPER"P (Ti) = 14L«ü& ux&ÒéTiVÇ"duV1ÚV4éAû«´é¡§V2ÚV3éAû«DZ´é¡§±P (E|T1) = P (E|T4)ÚP (E|T2) = P (E|T3)"Ïd§ú
— 57 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOª(3–7)±,DZPe,inst =
1
2(P (E|T1, h) + P (E|T2, h))
=1
2
2∑
i=1
∑
k∈±κ1,±κ2P (E|k, Ti, h1D, h2D, hRD)P (
√ERxR = k|Ti, h1R, h2R)
,
(3–8)Ù¥P (√ERxR = k|Ti, h1R, h2R)´½¥U&ÒxR©õÇU?|k|^VǧP (E|k, Ti, h1D, h2D, hRD)´½& ux&ÒéTi§&ûØ^VÇ"DZL«'§¡òÑ&&EÜ©§rü^VÇPDZP (√ERxR = k|Ti)ÚP (E|k, Ti)"3YÜ©§©ò^ü«5íPe,inst"1«´Äu/VÇ [109, 114]5OXÚ]SPER"´§ù«du9ØÓ«a/VÇO§ CéE,DZéÑ"Ïd§©?Ú|^IC5zíL§"Ùd´3$&D'§½O(5"3.4.1 ///VVVÇÇÇOOO/VÇO [109, 114, 115]±^5OØ5Kû«¥SPER"e¡§©Ñã 3–3¥¤«Ê«Ä/VÇO"Äk£©z[114]¥Jü«/O(J"½ÂViDZ(:§^Mk5L«/º:"b_ÆÝDZ§^ÆÝDZK"(:Vi u/Üÿ§3Xü«a./VÇ"Ù¥§φ1φ2 ≥ 0§Xã 3–3£1¤¤«§kXe/ØVÇ [114]
Pw1(dik, φ1, φ2) =1
2
Q2
(√2dik sinφ2;
tan2 φ2 − 1
tan2 φ2 + 1
)
−Q2
(√2dik sinφ1;
tan2 φ1 − 1
tan2 φ1 + 1
),
(3–9)Ù¥§Q¼êLªDZ[106]
Q2 (x, y; ρ) =1
2π√1− ρ2
∫ ∞
x
∫ ∞
y
exp
[−u
2 + v2 − 2ρuv
2 (1− ρ2)
]dvdu (3–10)
— 58 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOl1
l2 l3
(4)
(1) (2) (3)
11
1
1
2 2
2
2
3
4
1
2 1 2 !
(5)
1 2 3
1 2
4
ikD
ikD
ikDikD
ijD
iV
iV
iV
iV
iV
ijD
kM kM
kMkM jM
jM
kMikD
ã 3–3/VÇÄ.«¿ã"Ù¥§dik (½dij)L«(:Ú/º:Mk (½Mj)m8zål"£1¤Ú£2¤¥¤«/®3©z[114]¥Ñ'0¶£3¤L«/l1 − Mk − l2Úl1 − Mj − l3m«§ùp^l2 − Mk − Mj − l3L«"ùpl1Úl2´/l1 −Mk − l2ü^>§l3´/l1 −Mj − l3^>"φii ∈ 1, · · · , 4´ãViMk(½ViMj)/>lmm ∈ 1, 2, 3mYƶ3£4¤¥§φii ∈ 1, 2DZãViMkÚ/ü^>YƧ§÷vφi + φi = π¶3£5¤¥§φii ∈ 1, 2´ãViMkÚ/ü^>YƧ§DZ÷vφi + φi = π§φ3 = ∠ViMjMk§φ4 = ∠MjViMk
Fig 3–3 Demonstrations for the basic patterns of wedge probabilities. dik (or dij) is the normalized
distance between CPVi and wedge vertexMk (orMj). In particular, both (1) and (2) are introduced
in [114]; (3) is the wedge difference between wedgel1 − Mk − l2 andl1 − Mj − l3, denoted as
l2 − Mk − Mj − l3, in which bothl1 andl2 are sides of wedgel1 − Mk − l2, andl3 is the side
of wedgel1 − Mj − l3, respectively. Andφi with i ∈ 1, · · · , 4 are included angles between
line ViMk (or ViMj) and wedge sidelm for m ∈ 1, 2, 3. In (4),φi with i ∈ 1, 2 are included
angle between lineViMk and wedge sides; andφi + φi = π. And in (5), φi with i ∈ 1, 2are included angle between lineViMk and wedge sides; andφi + φi = π; φ3 = ∠ViMjMk and
φ4 = ∠MjViMk, respectively.x = y§Q2(x, x; ρ)±DZQ2 (x; ρ) =
1
π
∫ arctan(√
1+ρ
1−ρ
)
0
exp
[− x2
2sin2φ
]dφ (3–11)©ò:ViÚ:Mkm8zålPdik§=dik = |Vi−Mk|2
σ2 "— 59 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOaq§φ1φ2 < 0§Xã 3–3£2¤¤«§/ØVDZL«DZPw2(dik, φ1, φ2) =
1
2
Q2
(√2dik sinφ1;
tan2 φ1 − 1
tan2 φ2 + 1
)
+Q2
(√2dik sin(−φ2);
tan2 φ2 − 1
tan2 φ1 + 1
).
(3–12)duû«U´ü/m§DZL«B§½Âü/«mVÇOª§Xã 3–3£3¤¤«"âφ1φ2ØÓÚü/m§kXe/ØVÇOªPw3(dij , dik, φ1, φ2, φ3, φ4,m, n) = Pwm
(dij, φ1, φ2)− Pwn(dik, φ3, φ4), (3–13)Ù¥§m,n ∈ 1, 2§YÆφ1Úφ2´éº:Mj ó§YÆφ3Úφ4´éº:Mk ó"e¡§©Äk?ØÈè(VÇO§=Â&Ò?u(:Vi¤éA/û«SÜ"âû«/GØÓ§ã3–3£4¤Ú£5¤^ü«ØÓ5L(VÇO"äN5ù§Â&Ò?u±MkDZº:/«SÜVǧXã3–3£4¤¤«§±L«DZ
Pw4(dik, φ1, φ2)
=1
2π
2∑
n=1
(1−
∫ φn
0
exp
(− dik sin
2 φn
sin2(φn + φ)
)dφ
)+φ1 + φ2
2π
=1
2π
2∑
n=1
(Q2
(√2dik sinφn;
tan2 φn − 1
tan2 φn + 1
)− πQ1
(√2dik sinφn
))+φ1 + φ2 + 2
2π.
(3–14),§(:Vi¤éAû«´d^ãMjMkÚ,ü^å©:©ODZMjÚMk|¤AÛã/§Xã3–3£5¤¤«§Â&Ò?uù|Ü/û«SÜVDZL«DZPw5(dik, dij , φ1, φ2, φ3, φ4)
=1
2π
3∑
n=1
Q2
(√2dij sinφn;
tan2 φn − 1
tan2 φn + 1
)−
2∑
n=1
πQ1
(√2dij sinφn
)
−Q2
(√2dik sin(φ3 + φ4);
tan2(φ3 + φ4)− 1
tan2(φ3 + φ4) + 1
)+ φ1 + φ2 + φ4 + 3
.
(3–15)
— 60 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èO3.4.2 ÄÄÄuuu///VVVÇÇÇSPER555UUU©©©ÛÛÛdu&&EÅ5§&ÒéTi3¥U!:Ú&!:û«Ñ´5K//G"ã 3–2Ы¥U?«UÂ(ãÚ§éAû«"Ïd§3ù!¥§©|^/VÇO.5ïÄPANCÆÆ¥SPER5U"Äkí¥U?VÇP (√ERxR = k|Ti)§k ∈ ±κ1,±κ2"â!3.3¥ïáIRC§©âúª (3–14)Ú(3–15)¥½Â/VÇPw4ÚPw55©OO¥UÈè¤õVÇP (√ERxR = κ1|T1)ÚP (√ERxR = κ2|T2)",§©òâúª(3–9)! (3–12)Ú(3–13)5©OO¥UÈèVÇP (√ERxR ∈ ±κ2,−κ1|T1)ÚP (√ERxR ∈ ±κ1,−κ2|T2)"âIRC¤/¤²1o>/>²1o>/éݧ²1o>/YƧ±9R²©YƧ©ò]¤õVÇÚØVÇO©DZ±e8«¹
V1V4 > V2V3
M1,M2 /∈ PV1V2 > V1V3,¹V1V2 ≤ V1V3,¹
M1,M2 ∈ P , ¹nV1V4 ≤ V2V3
M1,M2 /∈ PV1V2 > V1V3,¹oV1V2 ≤ V1V3,¹Ê
M1,M2 ∈ P , ¹8 (3–16)
e¡§©±¹nDZ~§ÑVÇP (√ERxR = k|Ti)¢SO(J"3¹n¥§V1V4 > V2V3§¿M1,M2 ∈ P§Ù¥P½ÂDZ²1o>/SÜ«"P (
√ERxR = κ1|T1) = Pw4
(d11, arcsin
(V1M13
V1M1
), arcsin
(V1M12
V1M1
)),
P (√ERxR = κ2|T1) = Pw3(d12, d11,∠V1M2M24, π − ∠V1M2M1,
∠V1M1M12,∠V1M1M2, 1, 1),
P (√ERxR = −κ2|T1) = Pw3(d11, d12, π − ∠V1M1M2, π − ∠V1M1M13,
∠V1M2M1,∠V1M2M34, 1, 1),
P (√ERxR = κ2|T2) = Pw5
(d21, d22, π − arcsin
(V2M12
V2M1
), arcsin
(V2M24
V2M2
),
∠M1V2M2,∠V2M1M2) ,
P (√ERxR = κ1|T2) = Pw2(d21,∠V2M1M12, π − ∠V2M1M13),
P (√ERxR = −κ1|T2) = Pw2(d21,∠V2M1M34, π − ∠V2M1M13).
(3–17)
— 61 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
y1
y 2
M13D
V8D
V2D
l24D
M24D
V4D
V9D
M2D
V10D M
34D
M1D
M12D
l12D
V5D
l13D
V6D
V7D
V3D
V1D
ΩV
1
DΩV
2
D
ΩV
4
D ΩV
3
Dl34D
ã 3–4]&(ã§Ù¥JL«û«.Fig 3–4 One possible instantaneous relay constellation, where dashed lines represent boundaries
of decision regions.âVÇOK§±P (√ERxR = −κ1|T1) = 1−
∑
k∈κ1,±κ2P (√ERxR = k|T1),
P (√ERxR = −κ1|T2) = 1−
∑
k∈κ1,±κ2P (√ERxR = k|T2).
(3–18)aq§±|^/VÇúªO,Ê«¹eVÇ"X§©Ä&?^ØVÇP (E|k, Ti)"âîªålÈ觱y1&ÒÜ©DZX¶§Ó±y2&ÒÜ©DZY ¶ïá]&(ã£instantaneous destination constellation§IDC¤§Xã 3–4¤«"¥UÈè(§±Xeo(:V D1 = (
√E1|h1D|+
√E2|h2D|, κ1|hRD|), V D
2 = (−√E1|h1D|+
√E2|h2D|, κ2|hRD|),
V D3 = (
√E1|h1D| −
√E2|h2D|,−κ2|hRD|), V D
4 = (−√E1|h1D| −
√E2|h2D|,−κ1|hRD|).
(3–19)IRCaq§âVoronoi5Æ[112]§IDCû«DZ±d²1o>/z^>R²©y©"Ù¥§lD12§lD13§lD24ÚlD34©O´>V D1 V
D2 §
— 62 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOV D1 V
D3 §V D
2 VD4 ÚV D
3 VD4 R²©"MD
1 ´lD12lD13:§MD2 ´lD24ÚlD34:"ãMD
1 MD2 ´éÆV D
2 VD3 R²©"ù§&?(:V D
1 éAû«Ò±L«DZΩV D
1,
2√E1|h1D|
(κ1 − κ2)|hRD|y1 + y2 +MD
1 > 0 and2√E2|h2D|
(κ1 + κ2)|hRD|y1 + y2 +MD
2 > 0
,
(3–20)Ù¥MD1 = −1
2(κ1+κ2)|hRD|−2
√E1E2|h1D||h2D|(κ1−κ2)|hRD|§MD
2 = −12(κ1−
κ2)|hRD| − 2√E1E2|h1D||h2D|(κ1 + κ2)|hRD|"aq§±,nû«ΩV D
i§i = 2, 3, 4"& ux&ÒT1ÚT2§¥Uux(ÎÒ^e&ØVDZ©OL«DZP (E|√ERxR = κ1, T1
)ÚP (E|√ERxR = κ2, T2)"©^dDikL«ã 3–4¥(:V D
i ¥:MDk m8zål§=dDik =
|V Di −MD
k|2
σ2 "VÇP (E|√ERxR = κ1, T1)í(JDZ
P(E|√ERxR = κ1, T1
)= 1− Pw4
(dD11, φ1, φ2
). (3–21)½ÂPDDZIDC¥²1o>/SÜ«"úª(3–21)¥ÆÝφ1, φ2Oke¡¹"V D
1 VD2 < V D
1 VD3 ¿MD
1 ,MD2 ∈ PD§kφ1 =
π − arcsin(
V D1 MD
13
V D1 MD
1
)§φ2 = arcsin(
V D1 MD
12
V D1 MD
1
)¶V D1 V
D2 ≥ V D
1 VD3 ¿MD
1 ,MD2 6∈
PD§kφ1 = arcsin(
V D1 MD
13
V D1 MD
1
)§φ2 = π−arcsin(
V D1 MD
12
V D1 MD
1
)¶V D1 V
D2 ≥ V D
1 VD3 ¿MD
1 ,MD2 ∈ PD§kφ1 = arcsin
(V D1 MD
13
V D1 MD
1
)§φ2 = arcsin(
V D1 MD
12
V D1 MD
1
)"VÇP (E|√ERxR = κ2, T2)O(JDZ
P(E|√ERxR = κ2, T2
)= 1− Pw3
(dD21, d
D22, φ1, φ2, φ3, φ4
), (3–22)Ù¥φ3 = ∠MD
1 VD2 M
D2 §¿φ4 = ∠V D
2 MD1 M
D2",§úª(3–22)¥ÆÝφ1, φ2©DZ±eA«¹"V D
1 VD2 < V D
1 VD3 ¿MD
1 ,MD2 ∈ PDÿ§kφ1 = arcsin
(V D2 MD
12
V D2 MD
1
)Úφ2 = π − arcsin(
V D2 MD
24
V D2 MD
2
)"Ù¦^e§kφ1 =
arcsin(
V D2 MD
12
V D2 MD
1
)Úφ2 = arcsin(
V D2 MD
24
V D2 MD
2
)"¥UÈèÑÿ§úª(3–19)¥ë(:¬â¥UØû(JUC"äN5ù§ü^rux&ÒéT1¿¥U=uØ&Òκ2,−κ2, κ1§ã 3–4¥ë(:V D1 ¬©OCDZV D
5 §V D6 ÚV D
7 "ü— 63 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO^rux&ÒéT2¿¥U=uØ&Òκ1,−κ2,−κ1§ã 3–4¥ë(:V D2 ¬©OCDZV D
8 §V D9 ÚV D
10"ü^rux&ÒéT1¿¥U=uØ&Òκ2 ,−κ2, κ1§&ÈèØVDZL«DZP(E|√ERxR = k1, T1
)=
1− Pw4(d
Dj1, φ1, φ2), whenV D
j ∈ ΩV D1,
1− Pw1(dDj1, φ1, φ2), whenV D
j 6∈ ΩV D1,
(3–23)Ù¥k1 = κ2,−κ2, κ1§©Okj = 5, 6, 7"'ÆÝφ1, φ2, φ3Úφ4OdL3–1Ñ"ü^rux&ÒéT2¿¥U=uØ&Òκ1,−κ2,−κ1§&ÈèØVDZL«DZP(E|√ERxR = k2, T2
)=
1− Pw3(d
Dl1, d
Dl2, φ1, φ2, φ3, φ4, 1, 1), whenV D
l ∈ ΩV D2,
1− Pw3(dDl2, d
Dl1, φ1, φ2, φ3, φ4, 1, 1), whenV D
l 6∈ ΩV D2,
(3–24)Ù¥k1 = κ1,−κ2,−κ1§©Okl = 8, 9, 10"'ÆÝφ1, φ2, φ3Úφ4OdL3–2Ñ" L 3–1OVÇP(E|√ERxR = k1, T1
)¤IëêTable 3–1 Correspondence Parameters ofP
(E|√ERxR = k1, T1
)
V Dj ∈ ΩV D
1
M1,M2 6∈ PD M1,M2 ∈ PD
V D1 V D
2 < V D1 V D
3 V D1 V D
2 ≥ V D1 V D
3 -
φ1 = ∠V Dj MD
1 MD12
φ2 = π − ∠V Dj MD
1 MD13
φ1 = π − ∠V Dj MD
1 MD12
φ2 = ∠V Dj MD
1 MD13
φ1 = ∠V Dj MD
1 MD12
φ2 = ∠V Dj MD
1 MD13
V Dj 6∈ ΩV D
1
M1,M2 6∈ PD M1,M2 ∈ PD
V D1 V D
2 < V D1 V D
3 V D1 V D
2 ≥ V D1 V D
3 -
φ1 = π − ∠V Dj MD
1 MD12
φ2 = ∠V Dj MD
1 MD13
φ1 = ∠V Dj MD
1 MD13
φ2 = π − ∠V Dj MD
1 MD12
φ1 = ∠V Dj MD
1 MD12
φ2 = π − ∠V Dj MD
1 MD13
3.4.3 ÄÄÄuuuIIICCCSPERíííduÅ&ëêõ5§Äu/VÇSPERy©DZõ«¹"¦+Äu/VÇO.í~°(§SPERíL§%~E,"— 64 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOL 3–2OVÇP(E|√ERxR = k2, T2
)¤IëêTable 3–2 Correspondence Parameters ofP
(E|√ERxR = k2, T2
)
V D
l∈ Ω
V D2
V D
l6∈ Ω
V D2
- V D
lis above lineMD
1MD
2V D
lis below lineMD
1MD
2
- MD
1,MD
26∈ PD MD
1,MD
2∈ PD MD
1,MD
26∈ PD MD
1,MD
2∈ PD
φ1 = ∠V D
lMD
1MD
12
φ2 = ∠V D
lMD
2MD
24
φ3 = ∠V D
lMD
1MD
2
φ4 = ∠MD
lV D
1MD
2
φ1 = ∠V D
lMD
1MD
2
φ2 = π − ∠V D
lMD
1MD
12
φ3 = π − ∠V D
lMD
2MD
1
φ4 = π − ∠V D
lMD
2MD
24
φ1 = π − ∠V D
lMD
2MD
1
φ2 = π − ∠V D
lMD
2MD
24
φ3 = ∠V D
lMD
1MD
2
φ4 = π − ∠V D
lMD
1MD
12
φ1 = π − ∠V D
lMD
2MD
24
φ2 = ∠V D
lMD
2MD
1
φ3 = π − ∠V D
lMD
1MD
12
φ4 = π − ∠V D
lMD
1MD
2
φ1 = π − ∠V D
lMD
1MD
12
φ2 = π − ∠V D
lMD
1MD
2
φ3 = ∠V D
lMD
2MD
24
φ4 = ∠V D
lMD
2MD
1Ïd§©JÑ«ÄuICSPERí"ù«±3ÌÝã+$SNRe°(5¹eÌÝü$OE,Ý"äN5ù§IC±ò©²1o>//GÂ(ã=DZÝ//G(ã"Äu#(㧩¦ÑéAû«"e¡ÚnÑ¥U?ICÝ"Lemma 1.ò²1o>/>/GÂ(ãIRC=DZ±:DZ¥%Ý/(㧿±(ã>>ØCCÝCDZ
C = QA−1, (3–25)Ù¥ÝQ´úª(3–31)¥ÝB = ATΣ−1AAÆþéAݧ±Q =
B(1,2)
(λ1−λ2)
√B(1,1)−λ1
λ2−λ1
√B(1,1)−λ1
λ2−λ1
√B(1,1)−λ1
λ2−λ1− B(1,2)
(λ1−λ2)
√B(1,1)−λ1
λ2−λ1
, and A−1 =
[ <h1R2|h1R|
<h2R2|h2R|
=h1R2|h1R|
=h2R2|h2R|
].
(3–26)Ù¥AÆλ1Úλ2dúª (3–32)Ñ"y²µÄk½ÂZ = [<yR,=yR]TDZ©(ãþ:§Ù¥(·)TL«Ý½öþ=",§½Â2 × 1þZ′DZIC¥mCþ§ADZIC¥mL§¥Ý":ZÚþZ′'X±L«DZZ = AZ′§Ù¥A´2× 2ݧ¿÷vdet(A) 6= 0"ù§CþZ— 65 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOVÇݼê±^Z′L«DZfZ(z) =
1
2π|Σ|1/2 exp(−1
2(z−Vi)
TΣ−1(z−Vi)
)
=1
2π|Σ|1/2 exp(−1
2(z′ −A−1Vi)
TATΣ−1A(z′ −A−1Vi)
),
(3–27)Ù¥§Σ = [σ2/2, 0; 0, σ2/2]§|Σ|DZÝΣ1ª§i ∈ 1, · · · , 4"5¿ÆÝB , ATΣ−1AØ´éÆÝ"Ïd§ÏLéÝB?1AÆ©)§±fZ(z) =
1
2π|Σ|1/2 exp(−1
2(z′ −A−1VT
i )T [ψ1, ψ2]
T
[λ1 0
0 λ2
][ψ1, ψ2](z
′ −A−1VTi )
),
(3–28)Ù¥§ψi, i = 1, 2Úλi©ODZÝBAÆþÚAÆ"ù§,½ÂþDZVi = [ψ1, ψ2]A−1VT
i §ÆDZ[λ1, 0; 0, λ2]EpdÅCþZ =
[ψ1, ψ2](z′ − A−1VT
i )§§´C(ãþ:"½ÂAÆþéAÝQ = [ψ1, ψ2]§ù3²LICÚ'±§©Â&ÒZÚICÂ&ÒZm§±9©(:ViÚIC(:Vim'XÒ±©OL«DZZ = QA−1Z and Vi = QA−1VT
i , (3–29)DZò©²1o>//G(ã=DZ±:DZ¥%Ý/§¿±AÛã/>ØC§=−−−→V iV j =
−−→ViVj§CÝA7LDZ
A =
[ −−→V1V2 −−−→
V1V2−−→V1V3
−−→V1V3
][V1(1) V2(1)
V1(2) V2(2)
]−1
=2
β
[|h1R|=h2R −|h1R|<h2R−|h2R|=h1R |h2R|<h1R
],
(3–30)Ù¥§β = <h1R=h2R − <h2R=h1R§ÝBDZB = 4
βσ2
[B (1, 1) B (1, 2)
B (2, 1) B (2, 2)
].
B (1, 1) = |h1R|2=2h2R+ |h2R|2=2h1R,B (1, 2) = B (2, 1) = −|h1R|2<h2R=h2R − |h2R|2<h1R=h1R,B (2, 2) = |h1R|2<2h2R+ |h2R|2<2h1R
(3–31)
— 66 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èO ÝBAƱL«DZλi =
B(1, 1) +B(2, 2)±√B(1, 1)2 +B(2, 2)2 + 4B(1, 2)2 − 2B(1, 1)B(2, 2)
2.
(3–32)Ù¥i = 1, 2"ÝBÚ§AÆLªL²ÝB´¢é¡Ý"Ïd§AÆþéAÝQKDZ^=Ý"ù§²LÝAC(ã´Ý/§¿§ü^>ÚI¶²1"²LAÆ©)§#(ãE,´Ý/§´_^=ÆÝθ§Ù¥Q = [cos(θ), sin(θ);− sin(θ), cos(θ)]T"úª(3–39)ÑAÆþÝQLª"§NICÝC±DZC = QA−1, (3–33)Ù¥§A−13úª (3–39)¥Ñ" e5§©Ñ#(ãéAû«"ùp^Vi5LÆ(:¶^Z5L«Â&Ò:(<yR,=yR)²LICéA&Ò¶^ΩVi
5L«(:ViéAû«"âVoronoi5K§±û«LªDZΩV1
:<Z − =Z > 0
and
<Z+ =Z ≤ 0
,
ΩV2:<Z − =Z > 0
and
<Z+ =Z > 0
,
ΩV3:<Z − =Z ≤ 0
and
<Z+ =Z > 0
,
ΩV4:<Z − =Z ≤ 0
and
<Z+ =Z ≤ 0
.
(3–34)úª (3–34)L²#û«´mÝ/§¿û>.DZü2"ã 3–5ÑIC¥U(ãÚÙéAû«"ÄuïáICIRCÚÙéAû«§©^/VÇO.5íúª(3–8)¥SPER"Äk§O¥U?VÇP (√ERxR =
k|Ti), k ∈ ±κ1,±κ2"|^úª(3–14)¥½ÂPw35O¥UÈè(VÇP (√ERxR = κ1|T1)ÚP (√ERxR = κ2|T2)",§±|^úª(3–9)¥½ÂPw15O¥UÈèØVÇP (√ERxR ∈ ±κ2,−κ1|T1)ÚP (√ERxR ∈±κ1,−κ2|T2)"
2I5¿´§¢Sû>.VoronoiOKéAR²©k[ØÓ"ùDZÒ´DZoICSPER(J3$SNRe°(SPER(Jk[O"XSNRO§¢S>.ûCR²©Ü— 67 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
!Re Z
!
ImZ
1V
2V
3V
4V
O
1V"
2V"3V"
4V"
ã 3–5IC¥UÂ(ãFig 3–5 Received constellation at relay after coordinate transformation.äN5ù§½& ux&ÒéT1§¥UÈè(VÇDZ
P (√ERxR = κ1|T1)
=
∫ ∞
0
d(=Z)∫ =Z
−=ZfZ(Z;<
V1
,=V1
)d(<Z)
= Pw3
(||V1||/σ2, | arg(V1)− θ|, |π
2− arg(V1) + θ|
),
(3–35)
Ù¥fZ(·)´úª(3–28)¥ÑÅCþZVÇݼê§Vi(1)ÚVi(2)©O´ViY²IÚRI§||Vi||Úarg(Vi)L«±ODZ:þOViÌÝÚ̧,θ = arcsin
(√B(1,1)−λ1
λ2−λ1
)DZ^=ÆÝ"úª(3–35)aq±VÇP (√ERxR = k|T1)§k ∈ ±κ2,−κ1§±9½& uxT2§¥UÈèÂ&ÒyR¤õÚVǧ(Jdú— 68 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOª(3–36)Ñ"P (√ERxR = κ2|T1) = Pw1
(||V1||/σ2, |π
2− arg(V1) + θ|, |π − arg(V1) + θ|
),
P (√ERxR = −κ2|T1) = Pw1
(||V1||/σ2, | arg(V1)− θ|, | arg(V1)− θ|+ π
2
),
P (√ERxR = κ2|T2) = Pw3
(||V2||/σ2, |θ − arg(V2)|,
π
2− |θ − arg(V2)|
),
P (√ERxR = κ1|T2) = Pw1
(||V2||/σ2,
π
2− |θ − arg(V2)|, π − |θ − arg(V2)|
),
P (√ERxR = −κ1|T2) = Pw1
(||V2||/σ2, |θ − arg(V2)|, |θ − arg(V2)|+
π
2
).
(3–36)âVÇúª§±P (√ERxR = −κ1|T1) = 1 − ∑k∈κ1,±κ2
P (√ERxR =
k|T1)ÚP (√ERxR = −κ1|T2) = 1− ∑k∈κ1,±κ2
P (√ERxR = k|T2)"e¡ÄIC§XÛO&?^ØVÇP (E|k, Ti)"3eãÚn¥§©Ñ&?ICÝCD"
Lemma 2.3&?§ò©²1o>//GÂ(ãIDC=DZ±:DZ¥%Ý//G(㧿±(ã>ÝØCICÝCDDZCD = QDA
−1D , (3–37)Ù¥ÝQDDZúª(3–38)¥ÝBDAÆþÝ
BD =2
β2Dσ
2
[d21(κ1 + κ2)
2|hRD|2 + 4d21|h2D|2 d1d2(κ22 − κ2
1)|hRD |2 − 4d1d2|h1D||h2D |d1d2(κ
22 − κ2
1)|hRD|2 − 4d1d2|h1D||h2D | d22(κ2 − κ1)2|hRD |2 + 4d22|h2D|2
],
(3–38)Ù¥βD = |hRD| (|h1D|(κ1 + κ2) + |h2D|(κ2 − κ1))§d1 =√4|h1D|2 + (κ1 − κ2)2|hRD|2§d2 =
√4|h2D|2 + (κ1 + κ2)2|hRD|2"Ïd
QD =
BD(1,2)
(λD1 −λD
2 )
√BD(1,1)−λD
1λD2 −λD1
√BD(1,1)−λD
1
λD2 −λD
1
√BD(1,1)−λD
1
λD2 −λD
1− BD(1,2)
(λD1 −λD
2 )
√BD(1,1)−λD1
λD2 −λD1
(3–39)Ù¥λD1ÚλD2´ÝBDAÆ"¿§A−1D LªDZ
A−1D =
1
βD
[(κ2 − κ1)d2|hRD| 2d2|h1D|(κ1 + κ2)d1|hRD| −2d1|h2D|
](3–40)
— 69 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
1
D
V
2
D
V3
D
V
4
D
V
1D
D
V
2D
D
V
3D
D
V
4D
D
V
(1)DZ
(2)
DZ
5*D
V
6*D
V
7*D
V
8*D
V
9*D
V
10*D
V
ã 3–6IC&Â(ãFig 3–6 Received constellation at destination after coordinate transformation.y²µÏL¥U?CÝqíL§±&?CÝCD"y²." e¡§©ÑICIDCéAû«"ùp§V
Di L«IC(:§Â&Ò²LICÝCD&ÒDZZD§ΩD
VDi
L«(:VDi éAû«"âVoronoiOK§û>.±L«DZ
ΩDV
D1
:ZD(1)− ZD(2) > 0
⋂ZD(1) + ZD(2) ≤ 0
,
ΩDV
D2
:ZD(1)− ZD(2) > 0
⋂ZD(1) + ZD(2) > 0
,
ΩDV
D3
:ZD(1)− ZD(2) ≤ 0
⋂ZD(1) + ZD(2) > 0
,
ΩDV
D4
:ZD(1)− ZD(2) ≤ 0
⋂ZD(1) + ZD(2) ≤ 0
,
(3–41)
Ù¥ZD(1)ÚZD(2)©OL«&ÒZDY²IÚRI"ã 3–6ѲLIC&?(ãÚÙéAû«"& DÑ&ÒéT1ÚT2§¥Uux(&Ò§&àØVDZ©OL«DZP (E|√ERxR = κ1, T1)ÚP (E|√ERxR = κ2, T2
)"ÄuIC— 70 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOIDCû«§VÇP (E|√ERxR = κ1, T1)LªDZ
P(E|√ERxR = κ1, T1
)
=
∫ ∞
0
d(ZD(2))
∫ ZD(2)
−ZD(2)
fZD
(ZD;V
Di (1),V
Di (2)
)d(ZD(1)),
= Pw3
(||V D
1 ||/σ2, | arg(V D1 )− θD|, |
π
2− arg(V D
1 ) + θD|)”
(3–42)Ù¥§fZD(·)´ÅCþZDVÇݼê§V
Di (1)ÚV
Di (2)©OL(:V
Di Y²IRI§θD = arcsin
(√BD(1,1)−λD
1
λD2 −λD
1
)´^=ÝQDéA^=ÆÝ"Ó§VÇP (E|√ERxR = κ2, T2)O(JDZ
P(E|√ERxR = κ2, T2
)= Pw3
(||V D
2 ||/σ2,1
2|θD − arg(V D
2 )|, π2− |θD − arg(V D
2 )|).
(3–43)ùp§^V Di §i ∈ 5, · · · , 105L«²LICë:"& ux&ÒéT1§¿¥U=uØ&Òκ2,−κ2,−κ1 §&ÈèØVDZL«DZ
P(E|√ERxR = k1, T1
)
=
1− Pw3
(||V D
j ||/σ2, | arg(V Dj )− θD|, |π2 − arg(V D
j ) + θD|), whenV D
j ∈ ΩV D1,
1− Pw1
(||V D
j ||/σ2, |π2− θD + arg(V D
j )|, |π − θD + arg(V Dj )|), whenV D
j 6∈ ΩV D1,
(3–44)Ù¥k1 = κ2,−κ2,−κ1§éAkj = 5, 6, 7"& DÑ&ÒéT2§¥U=uØ&Òκ1,−κ2,−κ1§&ûØVÇDZP(E|√ERxR = k2, T2
)
=
1− Pw3
(||V D
l ||/σ2, | arg(V Dl ) + θD|, |π2 − arg(V D
l )− θD|), whenV D
l ∈ ΩV D2,
1− Pw1
(||V D
l ||/σ2, |π − arg(V Dl )− θD|, |3π2 − arg(V D
l )− θD|), whenV D
l 6∈ ΩV D2,
(3–45)Ù¥k1 = κ1,−κ2,−κ1§éAkl = 8, 9, 10"3.5 XXXÚÚÚ`zzz!ÏL©OíõÇ ÏfÚõÇg·AÏf5¦`uxõÇU?"Äk§©òE,MARCXÚòzDZJ[ü !ü¥U!ü&
— 71 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èODÚnÆ¥U."du¥UuõÇI²ï& -¥U&OÃÚ¥U-&&OçÄuùg´ÑõÇ ÏfLª"ù§¥UÈ賧PANCÆÆy²±4XÚ÷©8OÃ",§©òõÇg·AÏf`z¯KïDZg`îªål`z¯K§l |zXÚSPERõÇg·AÏfκ1Úκ2"3.5.1 ¥¥¥UUU???õõõÇÇÇ ÏÏÏfffOOO30XÛO¥U?õÇ Ïfc§Äk3½n 3.1¥ÑDÚä?èüÑ£CXNC¤ÚPANCüÑ©85U"3CXNCüÑ¥§¥UØæ^?Û?nª5£O½öíØÈèØ&E§5³Øl& -¥U&DÂ&8"ù?nª)µ¥ä¯£O§ÌPè£CRC¤§±9Ù¦U?nÃã"DZïþPANCÚCXNCüÑ3pSNRG¹e5U§½Â©8êD [4, 116–121]DZ
D = − limρ→∞
logP ((x1, x2) 6= (x1, x2))
log ρ, (3–46)Ù¥§ρL«uxSNR§(x1, x2)DZ^r&Òé§(x1, x2)DZ&àÈè&Òé§P ((x1, x2) 6= (x1, x2))DZSPER"½n 3.1. 3¥UvkõÇ Ïf¹e§MARCXÚePANCüÑÚCXNCüѧduØDÂϧÑU©8"y²µy²L§ëwN¹C. l½n3.1¥§±w& -¥UaØ*Ѭü$XÚ5U"Ïd§©OõÇ Ïf§ÏLN¥UuõÇ5·A&^§l ~Ø*ÑéXÚ5KDZ"aq&g·A2)üÑ£LAR¤
[47]3ü Èè=uXÚ¥ÄgJÑ"´§LARüÑØUÿÐõ^rPANCXÚ¥"DZòLARVg*Ðõ ¥U&¥§ÄkïáJ[& -¥U-&&§Xã3–7¤«"31Ï&ã§ü& Óò&Eux¥UÚ&"éuùõ\&§SPERéܱDZPMAC ≤ P upper
MAC = Q1
(√2E1|h1R|2/σ2
)+Q1
(√2E2|h2R|2/σ2
)
+Q1
(√2|√E1h1R +
√E2h2R|2/σ2
),
(3–47)
— 72 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOVirtual Source
Relay: Destination
SR RD
Sx Dx
SD
1 2( , )R RE x ! " "
Power Levels: !1 2,
!Power Adaptation Factors
Power Scaling Factor
1 2( , )
ã 3–7J[&.. Ù¥§J[&éA&OÃγSRÚγSDò¬3Yãáp0"ÏLxS = x1 x2$§æ^xSL«J[& &E"xR´ý¢¥Uux&E"&&ExDDZux1 x2"Fig 3–7 Virtual channel model. In particular, the channel gainsγSR andγSD with respect to virtual
channels will be introduced in detail in the following paragraph.xS is the virtual source message,
which is generated from the original transmitted signal asxS = x1x2. xR is the real transmitted
signal from the relay to destination. AndxD is also equal tox1 x2.Ù¥§ªmý1L«¥Uvk¤õÈÑ&Òx1´¤õÈÑ&Òx2VÇ"aq§1L«¥Uvk¤õÈÑ&Òx2´¤õÈÑ&Òx1VÇ"1nL«¥UQvk¤õÈÑ&Òx1qvk¤õÈÑ&Òx2VÇ"ùéÜP upperMAC±?ÚCqDZ
P upperMAC ≈ Q1
(√2min
[E1|h1R|2/σ2, E2|h2R|2/σ2, |
√E1h1R +
√E2h2R|2/σ2
])
(3–48)duQ¼êQ1(x)XxOP~鯧ÏdùCq(J3E1|h1R|2/σ2§E2|h2R|2/σ2§|
√E1h1R +
√E2h2R|2/σ2±9§v´~;"ùCq(J`:´±^üÑ\üÑÑJ[&5LÆõ\& -¥U&§Ù¥J[&Ñ\DZxS = x1 x2§]ÂSNRDZγSR , min(E1|h1R|2/σ2, E2|h2R|2/σ2, |
√E1h1R +
√E2h2R|2)/σ2"ùp]ÂSNRL& -¥U&SNR3"ÏDZ3¥U?æ^ä?觤±©ÄòJ[&& &EDZw´ä?è(J"ù§l& &J[DÑ&EÒÚ¥UÆux&E±§=xS = xR"æ^í&OÃγSRÓ§
35¿´§ùpéõ\&CqØ©[122]Ú[123]¥Jd&ØÓ"ÏDZ3ùü©Ù¥§öÄÑ´õ\¥U&— 73 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO±òõ\& -&&Cqw&OÃDZγSD:é:&"ùp§&OÃγSD½ÂDZγSD , min
(E1|h1D|2
σ2,E2|h2D|2
σ2,|√E1|h1D|+
√E2|h2D||2
σ2
). (3–49)8cDZ§E,MARCXÚ®²¤õòzDZDÚnÆ."â©z [47]¥(ا½]&OÃγSR andγRDeõÇ Ïfα±L«DZ
α = min
(γSRγRD
, 1
). (3–50)5¿´§]&OÃγRD±ODZÚO&OÃ&EγRD§ù:ò3½n 3.2y²¥Ñ[`²"æ^ÚO&OÃ&EγRD õÇ Ïfα`:´¥UÃI&"¥U-&&&E§l ü$XÚE,Ý"e¡½n`²|^]½öÚO¥U-&&OÃ&Eѱ4PANCüÑ3MARCXÚ¥÷©8"½n 3.2. ®]& -¥U&Oç]£½öÚO¤¥U-&&Oç²LõÇ PANCÆƱ3ü& MARCXÚ¥©8§=÷©8"´²LõÇ DÚä?èU©8"y²µy²L§ëwN¹D.
3.5.2 õõõÇÇÇggg···AAAÏÏÏfffOOOlXÚ]SPRí(J¥uy§SPERLªd¥UõÇg·AÏfκ1Úκ2û½"Ïd§DZzSPER§©I`zκ1Úκ2"´§duSPER 'uκ1Úκ2E,¼ê§ÏdzSPERéJκ1Úκ24ÜLª"ùp§©JÑ«g`OK5z]SPER"3ùOKp§©ÏLz&?(ãáî¼ål5¢yzSPER8"duÄ´úPáXÚ§=&ëê3DѱÏS´ð½§¤±õÇg·AÏfκ1Úκ2`z(J3zDѱÏS´ØC"äN5`§3¥UõÇ^e§záî¼ål`z¯K櫓e/ª(κ∗1, κ
∗2) = argmax
κ1,κ2
mink,j=1,2,3,4;k 6=j
||V D
k − V Dj ||2
s. t. κ21 + κ22 ≤ 2EaveR , κ1, κ2 ∈ R,
(3–51)
— 74 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOÙ¥IDCü^>Ý©ODZV D1 V
D2 = ||V D
1 −V D2 ||2 = 4E1|h1D|2+|hRD|2(κ1−
κ2)2ÚV D
1 VD3 = 4E2|h2D|2 + |hRD|2(κ1 + κ2)
2§,kIDCéÆÝ©ODZV D2 V
D3 =
(−2√E1|h1D|+ 2
√E2|h2D|
)2+ 4|hRD|2κ22Ú
V D1 V
D4 =
(2√E1|h1D|+ 2
√E2|h2D|
)2+ 4|hRD|2κ21.½Â8ÜV§§¹IDCü^>ÝÚü^éÆݧ=
V ,
V D1 V
D2 , V
D1 V
D3 , V
D2 V
D3 , V
D1 V
D4
. (3–52)Ó§Ú\#Cþu , minV"²L$§zîªål`z¯K±?ÚLãDZz¯K§=
maxu
s. t. 4E1|h1D|2 + |hRD|2(κ1 − κ2)2 ≥ u,
4E2|h2D|2 + |hRD|2(κ1 + κ2)2 ≥ u,
c1 + 4|hRD|2κ22 ≥ u,
c2 + 4|hRD|2κ21 ≥ u,−(κ21 + κ22) ≥ −2EaveR ,
(3–53)
Ù¥§c1 = (−2√E1|h1D|+ 2
√E2|h2D|
)2§c2 = (2√E1|h1D|+ 2√E2|h2D|
)2"ÏDZ#`z¯K(3–53)¥8I¼ê´¼ê§¤kå^Ñ´Cþκ1Úκ2g¼ê§¤±§´à`z¯K"ùp§©æ^à`z¯K¥²;.KF¦f5)Aà`z¯K"äN5ù§.KFúª±DZL(κ1, κ2, u, µ1, µ2, µ3, µ4, µ5) = u+ µ1(−u+ 4E1|h1D|2 + |hRD|2(κ1 − κ2)
2)
+ µ2(−u+ 4E2|h2D|2 + |hRD|2(κ1 + κ2)2) + µ3(−u+ c1 + 4|hRD|2κ22)
+ µ4(−u+ c2 + 4|hRD|2κ21) + µ5(−κ21 − κ22 + 2EaveR ).
(3–54)ÏL?Ø.KF¦f±íÑ`z¯K)"µi = 0§§L«1iå^Ø´;"d§±ÑK1iå^§ÏLéܦ).KF§ÚÙ¦KKT5¦)Cþκ1Úκ2"µi 6= 0§§L«1i— 75 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOå^´;"Ïd±ÏL1iå^§'uCþκ1Úκ2ª"Þ~5`§µ1 6= 0§k'Xªu− 4E1|h1D|2 − |hRD|2(κ1 − κ2)
2 = 0. (3–55)ù§ÏL?Ø.KF¦fµi§±32|)"Ù¥é¦u¢ê)DZ(κ∗1, κ
∗2) =
(√Eave
R +c1 − c28|hRD|2
,
√Eave
R +c2 − c18|hRD|2
). (3–56)éuICIDC§3í`κ1Úκ2IÄÝ/ü^>"ÏDZ3Ý/¥§ü^>Ýo´uéÆÝ"Ïd§÷v¥UuõÇåîªål`z¯K±ïDZ
(κ∗1, κ∗2) = argmax
κ1,κ2
minj=2,3
||V D
1 − V Dj ||2
s. t. κ21 + κ22 ≤ 2EaveR , κ1, κ2 ∈ R,
(3–57)duéIDCIC´ïá3±²1o>/>ØCÄ:þ§¤±Ý/ü^>>,uV D1 V
D2 = V D
1 VD2 = ||V D
1 − V D2 ||2 = 4E1|h1D|2 +
α|hRD|2(κ1 − κ2)2ÚV D
1 VD3 = V D
1 VD3 = 4E2|h2D|2 + α|hRD|2(κ1 + κ2)
2"aq§½Â8ÜVDZV ,
V D1 V
D2 , V
D1 V
D3
(3–58)Ó§Ú\#Cþu , minV"²L$§îªål`z¯K±?ÚLãDZz¯K§=
max u
s. t. − (4E1|h1D|2 + α|hRD|2(κ1 − κ2)2) ≤ −u,
− (4E2|h2D|2 + α|hRD|2(κ1 + κ2)2) ≤ −u,
κ21 + κ22 ≤ 2EaveR .
(3–59)ùà`z¯K.KF§±DZL(κ1, κ2, u, µ1, µ2, µ3) = u+ µ1(u− 4E1|h1D|2 − α|hRD|2(κ1 − κ2)
2)
+ µ2(u− 4E2|h2D|2 − α|hRD|2(κ1 + κ2)2) + µ3(κ
21 + κ22 − Eave
R ).(3–60)
— 76 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOù§ÏL?Ø.KF¦fµi§±8|)"Ù¥¦u¢ê)DZκ∗1 =
1
2
(√2 (αEave
R |hRD|2 + E2|h2D|2 − E1|h1D|2)α|hRD|2
+
√2 (αEave
R |hRD|2 + E1|h1D|2 − E2|h2D|2)α|hRD|2
),
κ∗2 =1
2
(√2 (αEave
R |hRD|2 + E1|h1D|2 − E2|h2D|2)α|hRD|2
−√
2 (αEaveR |hRD|2 + E2|h2D|2 − E1|h1D|2)
α|hRD|2
).
(3–61)
§òõÇ Ïf(J(3–50)Ú©IDCéAõÇg·AÏf(J(3–56)£½öICIDCéAõÇg·AÏf(J(3–61)¤éÜå5§Ò±¥U?`uõÇLªDZκi = ακ∗i§i = 1, 2"3.6 '''uuuPANCÆÆÆÆÆÆ???ÚÚÚ???ØØØ3.6.1 XXXÛÛÛÿÿÿÐÐÐ&&&???èèèXXXÚÚÚéuæ^&?èXÚ§bü& S1ÚS2Ñæ^&?è§'XLDPC?è§5©Ouxèix1Úx2"3¥U!:?§æ^õ^rSÈèì£ë©z[124]¥õ^rSÂà(O¤5SuÿÚÈèü^r&E"3ÈèÑ&Òxi§¥U!:æ^LDPCè5?è&ESi§l èixRi"bèixR1ÚxR2ݧ¥U!:âúª(3–5)¥ªéèixR1ÚxR2æ^ÅÎÒNö§l Nä?èþxR"äN5ù§éuxRi¥1kÎÒ§=xRi,k§â1n!1ã¥J5KòÎÒé(xR1,k, xR2,k)N(κ1, κ2,−κ2,−κ1)§Ù¥κ1 = ακ1§κ2 = ακ2"3&à§ÂìÄk?n¥U!:DÑ&Òy2"Âìly21k&Ò¥¼VÇݼêp (y2,k|xR,k = κ)§=
p (y2,k|xR,k = κ) =1√2πσ2
exp
−(y2,k − hRDκ)
2
2σ2
. (3–62)
— 77 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOâp (y2,k|xR,k = κ)§±xR1,kéêq,'(log-likelihood ratio, LLR)§=lxR1,k
= logp(y2,k|xR,k = κ1)P (xR,k = κ1) + p(y2,k|xR,k = κ2)P (xR,k = κ2)
p(y2,k|xR,k = −κ2)P (xR,k = −κ2) + p(y2,k|xR,k = −κ1)P (xR,k = −κ1),
(3–63)Ù¥§kVÇP (xR,k = κ1)§P (xR,k = κ2)§P (xR,k = −κ1)ÚP (xR,k = −κ2)Ñu14"aq§±OLLRlxR2,k
"ù§¥U!:±òLLRlxR1,k
ÚlxR2,kDZLDPCèÑ\§l z& &EÎÒLLR"l(R)
xi,kL«â¥U&ÒÎÒxi,kLLR"X§éu& -&ó´&Òy1§&!:æ^õ^rSÈèì5SuÿÚÈèÑü& &E"â©z [124]¥§&?uÿìly11k&Ò¥ÎÒxi,kLLRlxi,k§i ∈ 1, 2"§uÿìòüLLR&El(R)
xi,kÚlxi,kÜ¿å5§¿ò§ÚxÈèì§l #xi,kLLR"3uÿìÚÈèì²LkgêS§&âxi,kLLRÑMû"l©8OÃÆÝ5w§ÏDZPANCÆÆ3vk&?èXÚp®²±÷©8§¤±±éN´y²3k&?èXÚp§PANCÆÆE,±÷©8"
3.6.2 XXXÛÛÛÿÿÿÐÐÐpppNNNXXXÚÚÚ¦+8cDZ©Ì?Ø´BPSKN&Ò§´ùÜ©ó±*ÐpNXÚ¥"äN5ù§3¥U!:?PANCüÑ¥§^ëêκ1Úκ2©OL«pÚ$õÇ?"¥Uux&Ò±L«DZxR =
x1 x2 = sign(|h1R|<x1+ |h2R|<x2) + isign(|h1R|=x1+ |h2R|=x2)§Ù¥iL«ü Jê"éuXÚ©Û§½ÂTi = (m1 + in1,m2 + in2)§m1,m2, n1, n2 ∈±κ1,±κ2§^SPERéÜ.5ïþJÑPANCüÑ5U§=SPER ≤
∑
i,j∈1,··· ,4,i 6=j
∑m,n∈±κ1,±κ2
P(Tj∣∣√ERxR = m+ in, Ti, h1D, h2D, hRD
)
P(√
ERxR = m+ in |Ti, h1R, h2R).
(3–64)
— 78 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOéuõÇ Ïf§ÏDZXÚëêαäNNª´Ã'§¤±§²Lüê$±éN´y²J[&.éupNE,·^§=& -¥U&Ú& -&&OÃþdÙ¥&OÃû½"DZÒ´`§3pNXÚ¥^ÓõÇ ÏfE,±÷©8"éuõÇg·AÏf`z§±ÏL¦)eã`z¯K5`ëêκ1Úκ2min
∑i,j∈[1,16],i 6=j
P(Ti→Tj) (κ1, κ2)
s.t. κ21 + κ22 ≤ 2EaveR ; κ1, κ2 ≥ 0; κ1 ≥ κ2.
(3–65),«ÀJ´§±^îªål`z5`ëêκ1Úκ2§=max u
s.t. − ViVj ≤ −u;κ21 + κ22 ≤ 2Eave
R ; κ1, κ2 ≥ 0;κ1 ≥ κ2,
(3–66)Ù¥Vi = (√E1|h1D|x1 +√E2|h2D|x2, |hRD|xR
)§xRL«¥U?& &E(x1, x2)éA(ä?è&Ò"3.7 555UUUýýý©©©ÛÛÛ3ù!¥§©ÏLý¢5ïþPANCÆÆ5U"Äü(kIXÚ§Ù¥ü& S1§S2Ú&DI©ODZ(0,
√33)§(0,−
√33)Ú(1, 0)" ¥U!:3:(0, 0)ÚX¶þ:(1, 0)m$Ä"3ý¥§´»Ñ.DZγij = d−3
ij §Ù¥γijL«&Oçdij§i ∈ S1,S2,R, j ∈ R,DL?¿üÏ&!:mål"bDÑõÇ÷vE1 = E2 = Eave
R = 1§¿ý¥SNR½ÂDZρ = E1/σ2"²þSNRDZ[0, 30] dB"DZzýã¥ã~§©^-sim.L«Akâý(J§-thy.L«nØí(J"DZ\ïÄPANCÆÆXÚ5U§©Ä¥U?uØÓ §ùÒ±ØÓ&|µ"Äk§Ä¥U u:(0, 0)?"ù¥Uål& C§l /¤kr& -¥U&é¡ä§ý(JXã 3–8¤«"X§Ä¥U u:(1
3, 0)?§ù§¥U& Ú&ål§l /¤é¡ä§ý(JXã 3–9¤«"§Ä
— 79 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
0 5 10 15 20 25 3010
−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
The
Ave
rage
SP
ER
CXNCCXNC
α
GenieRandomFixedOrigin−simOrigin−thyCT−simCT−thyã 3–8r& -¥U&e5U"
Fig 3–8 Error performance with strong source-relay channel.¥U u:(0.8, 0)?§ù& -¥Uålu¥U-&ål§l /¤kr¥U-&&é¡ä§ý(JXã 3–10¤«"éuz«¥U!: §©ýXe¹¥PANCüѵ(a)©Â(ãeSPER5U§Ù¥õÇg·AÏfκ1Úκ2dúª(3–56)û½§AkâýÚnØí(Jý©O^Origin-simÚOrigin-
thyL«" (b)²LICÂ(ãeSPER5U§Ù¥õÇg·AÏfκ1Úκ2dúª (3–61)û½§AkâýÚnØí(Jý©O^CT-simÚCT-thyL«"DZ맩ýXeüѵ£a¤©z [29, 80]¥JÑCXNCÆÆSPER5U§Ù¥¥U!:31Ï&ãuxɽ$ä?è&Ò&§P CXNC¶£b¤3¥U?\\õÇ ÏfCXNCÆƧ٥¥U!:31Ï&ãux²LõÇ ä?è&Ò&§P CXNCᶣc¤©z [40]¥JÑÀJ-=u£Selective-and-
Forward¤ä?èüÑSPER5U§P Selective-and-Forward¶£d¤°(Ï£genie-aided¤ePANCÆÆSPER5U§=b¥U±ÈÑ— 80 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èO
0 5 10 15 20 25 3010
−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
The
Ave
rage
SP
ER
CXNCCXNC
α
GenieRandomFixedOrigin−simOrigin−thyCT−simCT−thyã 3–9é¡&e5U"
Fig 3–9 Error performance in a symmetric network.
0 5 10 15 20 25 3010
−7
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
The
Ave
rage
SP
ER
CXNCCXNC
α
GenieRandomFixedOrigin−simOrigin−thyCT−simCT−thyã 3–10r¥U-&&e5U"
Fig 3–10 Error performance with strong relay-destination channel.
— 81 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOü& &E§¿õÇg·AÏfκ1Úκ2 æ^úª (3–56)¥(J§P Genie¶£e¤æ^Å)¤õÇg·AÏfκ1Úκ2PANCüÑSPER5U§Ù¥ÅCþκ1Ñl[1,√2]mþ!©Ù§κ2 =
√2Eave
R − κ21"zDѱÏ#)|#õÇg·AÏf§P Random¶£f¤æ^½õÇg·AÏfκ1Úκ2 PANCüÑSPER5U§Ù¥3zDѱϥÑkκ1 = 3κ2 = 3/√5§P Fixed"Äk§ÏLý(J±w§du½n 3.1¥Jl& -¥Ua)Ø*ѯK§vkæ^õÇ CXNCüÑU©8"ÏDZMARCXÚõ^rZ6¯K5ä?èÚ& &EâyN¯K§¤±æ^õÇ CXNCüÑ,Ã÷©8"æ^õÇ PANCüÑÃØæ^oõÇg·AÏfÑU÷©8§ùÒÏLý¢y½n 3.2¥(Ø",§ÃØ´3ÃÏ&~^óSNR[5, 10]dB«m§´3?1©8OÃ*pSNR[20, 25]dB«m§
PANCüÑ5UÑÙ¦êiä?èüÑÐ"du3GenieüÑ¥b¥U©ªux(&E&§¤±ùüÑ´XÚ5UÄO"Ùg§3$SNR«£l0dB5dB¤§ÄuIC(ãSPERÄu(ãSPER ó§´310dB±§öSPER5UÒªu"ù´ÏDZÄuIC(ãuÿìé`MLuÿì ó´g`"Ïd§ÄuIC(ã5U3$SNR«'Äu(ã5U"XSNRO§ICc(ãþ(:máî¼ålDZO"ù§5UÒªu"5¿ICcnØí(JÚAkâý(JÜ"ùÒL²SPER4ÜLª´O(",§3¥U?©ØÓõÇ?¬¦XÚLyÑØÓ?èOÃ"äN5ù§æ^î¼ål`zõÇg·AÏfκ1Úκ2PANCüÑ3ICc§SPER5UÑ´Ð"duvkUg·A]&G&E§æ^Žö½õÇg·AÏfPANCüÑSPER5U¬k$?èOÃ"¦+æ^ÀJ-=uä?èüѱ÷©8§´§?èOÃéPANCüÑ5`"ù´ÏDZÀJ-=uüÑØ=¿ïÈèØ&ÒÓDZ¿ïÜ©Èè(&Ò§l ü$XÚ?èOÃ"— 82 —
þ°ÏÆÆ¬Æ Ø© 1nÙ õÇg·Aä?èOdu3l& -¥Ua&*ѧ¥U?uØÓ þ§æ^`õÇg·AÏfPANCüÑ°(ÏPANCüÑmmY´ØÓ"äN5ù§& -¥U&r§ùmYé"X¥U5C&§ùmYDZC5"ù´ÏDZ§& -¥U&Ч¥U¬)&El ü$*ÑéXÚSPER5KDZ"3.8 (((ÙÄkJÑ«õÇg·Aä?èüÑ5¦XÚ÷©8"Ù¥§¥U!:uxõÇ©DZüU?§§Ñ´õÇ ÏfÚõÇg·AÏf¦È"DÚÄuɽä?èØÓ´§PANCüÑ¥¥U!:3)¤ä?è&ÒÄÛ&G&E§¿¢yä?èÎÒ& ux&ÒmN"ÏL½n3.1Ú3.2§©y²PANCüѱ3MARCXÚ¥©8§ CXNCüÑU©8"Ùg§©ÑÎÒéÇLª§¿3¥UÚ&!:?ïáÂ(ã"duÂ(ãéAû«´5K§©Äkké©Â(ãæ^/ÝOí°(SPER"du&ëêÅ5§ùíL§~E,"Ïd§©?ÚJÑ«IC5z'uSPERí"ICò©²1o>//G(ãCDZÝ/(ã§l ¦ÑCqSPERLª"§©ÏLzXÚSPER5¦`üõÇg·Aþ?"âSPERîªålm'X§©JÑzîªålIO§¿|^.KF¥U?`õÇg·Aþ?"ý(JL²µ£a¤ICcSPERnØ(JAkâý´Ü¶£b¤ICSPERíICc(JCq§¿ü$E,ݶ£c¤æ^õÇ ÏfÚõÇg·AÏfPANCüѱ÷©8§¿éæ^Å¥UuõÇüÑ5ù§Pkp?èOö£d¤DÚÄuɽä?èüÑÃØæ^õÇ ÏfÄÑÃ÷©8"
— 83 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èO111oooÙÙÙ ÅÅŬ¬¬äää???èèèOOO
4.1 ÚÚÚóóóDÚä?è´ïá3& -¥Uó´Ø¥ä§½ö¥UU¤õÈÑ& ux&EùbÄ:þ"´3¢SÏ&L§¥§& -¥Uó´kU²îPáE¤&¥ä"d§XJæ^Èè=u§¥U¬)pÈèVÇ"3õ^r¥U䥧XJk&Ò3¥U?ȧ@oä?è&EÒÃÏ&!:¡E& &E"ÏdIOÜnÅ5³¥U*ÑéXÚ5U5KDZ"¦+3©z[125–127]¥§ö3ü ¥Uä¥JÑÀJÈè-=uüѧ´vk'Ø©éõ\&JÑÄu¥ä¯ÀJ-=uÆÆ"ÙJѫŬä?èüÑ[103]§k¤k& -¥U&ÑØu)¥ä§¥Uâ=uä?è&Ò&!:"ÄK§¥U½½=uØ¥äó´éA&Ò&§½öÀJ·%"©íXÚ¥äVÇ"du31Ï&ã§ü& !:Óux&Ò¥UÚ&§ÏdÂà´pZ6&E"l §¥ä¯©ÛJÝõ\¥U& [128]¥p",§©ÏLïáØÓ¹e]&(ã§íŬä?è'AVÇ"©JÑŬä?èüÑÚü ü¥U&¥ÀJ-=uüÑ[45, 46]Ñ´Äu& -¥Uó´¥ä¹5û½1Y=uG§XÚµãXã4–1¤«"´ÀJ-=uüÑØÓ´§©JÑŬä?è´âõ\&¥ä¹5O¥Uüѧ:é:&E,",§Å¬ä?è¦U=uk&E&"k^& -¥Uó´¥ä§Å¬ä?è,¬æ^E?èª=uü& &Ò&§ Ø´¿ïùÜ©&Ò"kü^& -¥Uó´Ñ¥ä§â¬ÀJØÆ"4.2 XXXÚÚÚ...ùpE,Ädü& !ü¥U!ü&|¤õ\¥UX
— 85 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO(x1, x2) h1R ,h2R
y2yR
y1
|h1D|,|h2D|
|hRD|
R2 1x
R1
2x
1 2x x ã 4–11oÙXÚµãFig 4–1 System Diagram of Chapter 4Ú"Ù¥§ü& S1ÚS2ÏLVó¥URƧòg&EDÑÓ&D"b?¿ü!:jÚkm&^hjk 5L«§Ù¥§eIL«9ü!:§j ∈ 1, 2,R, k ∈ R,D¿j 6= k"b¤k&ëêhjkÑÑl"þ!DZ1/λjkEpd©Ù"ëêλjk d&Ñ.û½§¿ü!:mål¥'§=λjk ∝ (djk)
γ§Ù¥§djkL'!:mål§γDZP~ê"©ÄúPáXÚ§=3DѱÏS&ëê±ØC§¿3üDѱÏmÕáCz"zDѱϱ©DZüã"31ã§ü& Óògèix1Úx22Â&Ú¥U"31ã§ü& ±·%§¥UéÂ&Ò?1?n§¿=u2)èixR&!:"DѱÏ(å§&éÜüãÂ&Ò§Èè& &E"b¤kux&Òxi, i = 1, 2ÚxRÑæ^BPSKN"3DÑm©c§é& &õ\&Ú¥U&&æ^ ýþïEâ"ù§k& -&&Ú¥U-&&Ò±wäk¢ê&ëêÚ¢êæD(¢ê&"Äu±þXÚ§¥UÚ&31ãÂ&Ò±©OPyR =
√E1h1Rx1 +
√E2h2Rx2 + nR,
y1 =√E1|h1D|x1 +
√E1|h2D|x2 + n1.
(4–1)Ù¥§E1ÚE2©OL«& S1ÚS2DÑõǧnR´¥U?"þ!DZzÝσ2/2Eê\5pdxD(§n1 K´&?"þ!— 86 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èODZσ2¢ê\5pdxD("²LÈèÚ#?觥U=u&ÒxR&§=y2 =
√ER|hRD|xR + n2 (4–2)Ù¥§ERL«¥Uuxõǧn2´&?"þ!DZσ2¢ê\5pdxD("
4.3 ÅÅŬ¬¬äää???èèèüüüÑÑÑ!òÄu& -¥U&n«Øӥ䯧JÑŬ.ä?èüÑ"TüÑÏLux(Èè)ä?è&Ò½ü& &Ò§k³¥U?Èè*ÑéXÚØVÇKDZ"4.3.1 ¥¥¥äääVVVÇÇÇ'''OOODZBuYÜ©'u¥äVÇL«§Äkí& S1½S2¥Uó´N¥äVǧÚü& ¥Uó´Ñ¥äVÇ"ùpÑ3?Ñ\¹ep&EO"31Y§& -¥U&/¤ü^rõ\XÚ"&h1RÚh2RþDÑÇ©OPR1 ÚR2"ù§(R1, R2)²¡©DZo«[129]§Xã4–2¤«"3«1p§lS1ux&Ò3¥U?ȧ S2ux&Ò¤õÈÑ"Ïd§rx1wpdD(§R2uǧ=R2 ≤ I(x2;YR|h1R, h2R)"3¡0¥§DZLãB§òÑK^VÇp&G&Eh1RÚh2R"aq§3«2¥§&Ex2ȧ &Ex1¤õÈÑ",§«3LÆ&Ex1Úx2ÑÈèØ«"«4´ü^rõ\&Ç«"3ÃÏ&¥§ØVDZ§¥äVÇ´,«ïþXÚ3Pá&þ5ULy~^OK"?¿ü!:m¥äVÇPo½ÂDZp&EIuXÚ½ªÌ|^ÇRVǧ=Po = Pr(I < R)"ùp^Po,i5L«z«¥äVǧ٥i = 1, 2, 3"bR1 = R2 = R§±'Xª
Po,1 = Pr [I(x1; yR|x2) < R, I(x2; yR) ≥ R] ,
Po,2 = Pr [I(x1; yR) ≥ R, I(x2; yR|x1) < R] ,
Po,3 = Pr [I(x2; yR|x1) < R, I(x1; yR|x2) < R, I(x1, x2; yR) < 2R] ,
(4–3)
— 87 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOR2
R1
I(X1;Ym|X2)I(X1;Ym)
I(X2;Ym|X1)
I(X2;Ym)
1
2
3
4
ã 4–2ü& õ\&ÇÚ¥ä«Fig 4–2 Achievable rate region and outage region of two-usermultiple access channelsÄuþã©Û§S1½öS2¤ux&EN¥äVǧ±9S1ÚS2ux&EÓ¥äVDZ©Ode¡úªÑ
Po,S1 = Po,1 + Po,3, (4–4)
Po,S2 = Po,2 + Po,3, (4–5)
Po,S1,S2 = Po,1 + Po,2 + Po,3. (4–6)e5§©òÑ3?Ñ\^e§O¥äVÇ'p&E"^p&EI(x1; yR|x2)§I(x2; yR|x1)Ú::p&EI(xR; y2)±d©z[130]¥0:é:ó´Pá&p&EO"±¥UÚ&!:mp&EDZ~§I(xR; y2)LªDZI(xR; y2) =
1
2
∑
x∈±1
∫ ∞
−∞Pr (y2|xR = x) log
2 Pr (y2|xR = x)
Pr (y2|xR = −1) + Pr (y2|xR = +1)dy2,
(4–7)3¢Sö¥§Pr (y2|xR = x)±ÏLAkâý"— 88 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èO,§ép&EI(x1, x2; yR)ÚI(xi; yR)§±æ^eã?1í"½ÂCN (µ, σ2)´þDZµ!DZσ2 Epd©Ù"Ïd§yR'^VÇݼê±DZp(yR|x1, x2) = CN (h1Rx1 + h2Rx2, σ2)"ÏDZ¤kuxÎÒÑ´ÕáÓ©Ù§¤±kVÇP (x1 = u, x2 = v) = P (x1 =
u)P (x2 = v) = 14"ù§p&EI(x1, x2; yR)LªDZ
I(x1, x2; yR) =1
4
∑
u=±1
∑
v=±1
∫ ∞
−∞p(yR|x1 = u, x2 = v) log
4p(yR|x1 = u, x2 = v)∑w,z∈±1
p(yR|x1 = w, x2 = z)
dyR.
(4–8)e5§Op&EI(x1; yR)§Ù¥'^VÇݼêDZp(yR|x1) =
∑
u=+1,−1
p(yR|x1, x2 = u)P (x2 = u)
=1√2πσ2
(exp
−(yR −
√E1h1Rx1 −
√E2h2R)
2
2σ2
+exp
−(yR −√
E1h1Rx1 +√E2h2R)
2
2σ2
).
(4–9)
@o§I(x1; yR)OLªDZI(x1; yR) =
1
2
∑
u=−1,1
∫ ∞
−∞p(yR|x1 = u) log
(2p(yR|x1 = u)
p(yR|x1 = 1) + p(yR|x1 = −1)
)dyR.
(4–10)
4.3.2 ÅÅŬ¬¬äää???èèèüüüÑÑÑ3Ŭ.ä?èüÑ¥§¥U!:â& -¥Uó´¥ä¯§ÀJuxä?è&E§½öuxüÈè¤õ^r&E½ö31Y±·%"&!:âÂ&ÒØÓa.§æ^q,ÈèìéüDÑã&Ò?1éÜÈè"31DÑã§^rS1ÚS2Ó2Â&Òx1Úx2¥UÚ&"bX3¥UR?§±en^Ó÷vI(x1; yR|x2) > R, (4–11)
I(x2; yR|x1) > R, (4–12)
I(x1, x2; yR) > 2R, (4–13)
— 89 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO@o¥U!:Ò±|^q,Èèì¤õÈÑü^r&Ò§=(x1, x2) = argmin
x1,x2∈±1|yR −
√E1h1Rx1 −
√E2h2Rx2|2, (4–14),31㧥UR=u&ÒxR = x1 ⊕ x2&D"´§S1R&h1R²Pá§ÓS2R &þЧ^(4–11)Ã÷v§¿I(x2; yR) > R¤á"d§¥U!:±ÏLòS1ux&Òx1D(§Èèx2§=
x2 = arg maxx2∈±1
exp
(−(yR−
√E1h1R−
√E2h2Rx2)
2
2πσ2
)
+ exp
(−(yR+
√E1h1R−
√E2h2Rx2)
2
2πσ2
) (4–15)aq§^(4–11)Ã÷v§¿I(x1; yR) > R¤á§R±ÏLòS2ux&Òx2ÀD(§Èèx1§=x1 = arg max
x1∈±1
exp
(−(yR−
√E1h1Rx1−
√E2h2R)
2
2πσ2
)
+ exp
(−(yR−
√E1h1Rx1+
√E2h2R)
2
2πσ2
) (4–16)¥UU¤õÈÑx1½öx2§Ræ^E?誧31ãuxxR = x1 or xR = x2D"§S1ÚS2R&ѲîP᧥UQäõÈèx1§DZäõÈèx2"ù§¥U31ãÒØux?Û&Ò§=ÀJØÆ& ?1=u"â& -¥U&þØÓ§±ò¥äÚØ¥äO©DZo«ØÓ¹"DZBuL㧽Â&El!:jk¤õDѯDZE(j,k)§¥ä¯PE(j,k)
4.3.2.1 111«««¹¹¹¥UU¤õÈÑü& &E§R31ã=u√ERxRD"ùpr&!:Ü¿l& -¥Uó´Ú& -¥U-&Æó´)¥ä¯PED"ÏdXÚ¥äVDZDZ
P 1o = Pr
(E(S1,R)
⋂E(S2,R), ED
), (4–17)
— 90 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èOÙ¥§þI1£)YÑy2!3Ú4¤L¹IÒ§Pr(E(S1,R)
⋂ E(S2,R)
)=
Po,S1,S2 L«¥U±¤õÈèS1ÚS2&EVÇ",§VÇPr(ED)OúªDZ
Pr(ED)= Pr
(log2
(det
(I(2) +
H1H†1
Σ
))< 2R
), (4–18)Ù¥§H1 =
[ √E1h1D
√E2h2D 0
0 0√ERhRD
]"4.3.2.2 111«««¹¹¹¥U¤õÈÑ&Òx1§´U¤õÈÑ&Òx2§R31ã=ux1D"dXÚ¥äVDZ
P 2o = Pr
(E(S1,R)
⋂E(S2,R), ED
), (4–19)Ù¥§Pr
(E(S1,R)
⋂ E(S2,R)
)= Po,1L«¥UUÈÑx1´ØUÈÑx2VÇ" 1«¹eVÇPr(ED)OúªDZ
Pr(ED)= Pr
(log2
(det
(I(2) +
H2H†2
Σ
))< R
), (4–20)Ù¥§H2 =
[ √E1h1D
√E2h2D√
ERhRD 0
]"4.3.2.3 111nnn«««¹¹¹¥U¤õÈÑ&Òx2§´U¤õÈÑ&Òx1§R31ã=ux2D"dXÚ¥äVDZ
P 3o = Pr
(E(S1,R)
⋂E(S2,R), ED
), (4–21)Ù¥§Pr
(E(S1,R)
⋂ E(S2,R)
)= Po,2§,§Pr
(ED)±ÏL1«¹eÝH2¥H2(2, 1)ÚH2(2, 2)¼"
— 91 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO4.3.2.4 111ooo«««¹¹¹§Ä¥UQÃÈÑx1DZÃÈÑx2¹"ù§¥U31ãÒØ=u?Û&E"XÚ¥äVÇÒûu& -&ó´§=
P 4o = Pr
(E(S1,R)
⋂E(S2,R), ED
), (4–22)Ù¥§Pr
(E(S1,R)
⋂ E(S2,R)
)= Po,3"Pr
(ED)±æ^¥U?aqõ\&e¥äVǦ"éÜ(4–17)! (4–19)! (4–21)Ú(4–22)±XÚN¥äVÇLª
Po,sys =4∑
i=1
P io. (4–23)
4.4 ÅÅŬ¬¬äää???èèè555UUU!ò©ÛŬä?è3õ\&¥'AÇ£bit error
rate, BER¤"3¢SÏ&¥§=¦&Øu)¥ä§XÚE,3ØèVÇ"âÆÏ&½Â§& -¥Uó´&OÃo´ru& -&ó´&OÃ"Ïd§bXJ¥U?u)Èèا@o&?DZ½¬)ÈèØ"ù§XÚBER±DZPe,sys =
4∑
i=1
PRei
+(1− PR
ei
)PDei
, (4–24)Ù¥§PR
eiÚPD
ei©OL«31i«¹e¥UÚ&!:u)ÈèØVǧ
i = 1, 2, 3, 4"4.4.1 ¥¥¥UUU???555UUUe¡§ÄkOo«ØÓ¥ä¯e§¥U!:?BER5U"
• 1«¹: ¥UU¤õÈÑü& &E§R31ã=u√ERxRD"d§¥U!:?BER±DZ
PRe1
=
Q(
|h2R|σ
)+ 1
2
[Q(
2|h1R|−|h2R|σ
)+Q
(2|h1R|+|h2R|
σ
)]|h1R| > |h2R|
Q(
|h1R|σ
)+ 1
2
[Q(
2|h2R|−|h1R|σ
)+Q
(2|h2R|+|h1R|
σ
)]|h1R| ≤ |h2R|
;
(4–25)
— 92 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èO• 1«¹: ¥U¤õÈÑ&Òx1§´U¤õÈÑ&Òx2§R31ã=ux1D"d§¥U!:?BER±DZPRe2
=
12
[Q(
|h1R|+|h2R|σ
)+Q
(|h1R|−|h2R|
σ
)], |h1R| > |h2R|
Q(
|h1R|σ
)+ 1
2
Q
(2|h2R|+|h1R|
σ
)+Q
(|h2R|−|h1R|
σ
)
−Q(
|h1R|+|h2R|σ
)−Q
(2|h2R|−|h1R|
σ
) , |h1R| ≤ |h2R|
;
(4–26)
• 1n«¹: ¥U¤õÈÑ&Òx2§´U¤õÈÑ&Òx1§R31ã=ux2D"d§¥U!:?BER±DZPRe3 =
Q(
|h2R|σ
)+ 1
2
Q
(2|hR|+|h2R|
σ
)+Q
(|h1R|−|h2R|
σ
)
−Q(
|h2R|+|h1R|σ
)−Q
(2|h1R|−|h2R|
σ
) , |h1R| ≤ |h2R|
12
[Q(
|h1R|+|h2R|σ
)+Q
(|h2R|−|h1R|
σ
)], |h1R| > |h2R|
;
(4–27)
• 1o«¹: ¥UQÃÈÑx1DZÃÈÑx2§R31ãÒØ=u?Û&E"ÏdPRe4 = 0"
4.4.2 &&&???555UUUe¡§©ò©ÛŬä?è3&?BER5U"éÜló´Â&Òy1ÚlÆó´Â&Òy2§&æ^º,Èèì¡EÑü& &E§=(x1, x2) = arg min
x1,x2,xR∈±1|y1−
√E1|h1D|x1−
√E2|h2D|x2|2+|y2−
√ER|hRD|xR|2.
(4–28)DZíBER5U§ùpr& 3ó´þuxü&Ew&Òéxs , (x1, x2)"éuæ^Zuÿ¥UÚ&!: ó§±& ux&Ò§±9¥UÚ&?KD(KDZÂ&Ò3ØÓ¥ä¯e'X§XL4.4.2¤«§Ù¥y1 ,√E1|h1D|x1 +
√E2|h2D|x2, y2 ,
√ER|hRD|xR"Äu±þ'X§±y1DZX¶§y2 DZY ¶ïá&?Â(ã"â|h1D|Ú|h2D|é§√
ER|hRD|§±9x1 Úx2ÎÒ§(:Mi 38«ØÓ "Ø5§bó´S1-D&OÃ'ó´S2-D &OÃ"l §(: êü$DZ4"ùp§— 93 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOx1 x2 y1
y2
Case One Case Two Case Three
+1 +1√E1|h1D|+
√E2|h2D| |hRD|κ1 |hRD| |hRD|
+1 -1√E1|h1D| −
√E2|h2D| |hRD|κ2 |hRD| −|hRD|
-1 +1 −√E1|h1D +
√E2|h2D| −|hRD|κ2 −|hRD| |hRD|
-1 -1 −√E1|h1D| −
√E2|h2D| −|√ER|κ1 −|hRD| −|hRD|L 4–1& ux&EØD(KDZÂ&Òm'X©ÑØÓ¹eÂ(ã!û«§±9BEROLª§Xã4–3¤«"
4.4.2.1 111«««¹¹¹¥UU¤õÈÑü& &E§R31ã=u√ERxRD"d§Â(ãdã4–3(a)Ñ"Ù¥§ãl1Úl2d(:Mi|¤Ý/ü^R²©§û«^ÎÒΩiL«§i = 1, 2, 3, 4"äN ó§û«ΩiÊ^©.lk§DZ
l1 : y2 = − 2√E1|h1D|
|hRD|(κ1+κ2)y1 +
4√E1E2|h1D||h2D|+|hRD|2(κ2
1−κ22)
2|hRD |(κ1+κ2)
l2 : y2 =2√E2|h2D|
|hRD|(κ2−κ1)y1 +
|hRD|2(κ22−κ2
1)−4√E1E2|h1D||h2D|
2|hRD|(κ2−κ1)
l3 : y2 = − 2√E1|h1D|
|hRD|(κ1+κ2)y1 +
4√E1E2|h1D||h2D|+|hRD|2(κ2
2−κ21)
|hRD|(κ1+κ2)
l4 : y2 =2√E2|h2D|
|hRD|(κ2−κ1)y1 +
|hRD|2(κ21−κ2
2)−4√E1E2|h1D||h2D|
2|hRD|(κ2−κ1)
l5 : y2 =|hRD|√
E1|h1D|+√E2|h2D| y1+
|hRD|2(κ21−κ2
2)−4√E1E2|h1D||h2D|
2|hRD|(κ2−κ1)
(4–29)
,§/û«Ωi§DZΩ1 = l1 > 0 ∪ l2 ≤ 0; Ω2 = l2 > 0 ∪ l3 ≤ 0 ∪ l5 > 0;Ω3 = l3 > 0 ∪ l4 > 0; Ω4 = l1 ≤ 0 ∪ l4 ≤ 0 ∪ l5 ≤ 0.
(4–30)ÏDZ§n1Ún2´ÕáÓ©Ù¢êpdD(§¤±1«¹eVDZÏL±eúª¦PDe1
=4∑
i=1
1−
∫∫
Ωi
N (y1, y2;xi,yi, σ2/2)dΩi
, (4–31)Ù¥xiÚyi©OL(:MiîIÚpI"
— 94 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èO
M1=(|h1D|+|h2D|,|hRD|)M2=(-|h1D|+|h2D|,|hRD|)
M3=(|h1D|-|h2D|,-|hRD|)M4=(-|h1D|-|h2D|,-|hRD|)
12
34
l1
l2
l3
l4
l5
(a) Constellation of Case One
(c) Constellation of Case Three
M1=(|h1D+|h2D|,|hRD| 1)
M2=(-|h1D|+|h2D|,-|hRD| 2)
M3=(|h1D|-|h2D|,|hRD| 2)
M4=(-|h1D|-|h2D|,-|hRD| 1)
1
2
3
4
l1
l2
(b) Constellation of Case Two
M1=(|h1D|+|h2D|,|hRD|)
M2=(-|h1D|+|h2D|,-|hRD|)
M3=(|h1D|-|h2D|,|hRD|)
M4=(-|h1D|-|h2D|,-|hRD|)
1
2
3
4
l1
l2
l4
l3
l3
1y
2y
1y
1y
2y
2y
l5
l5
ã 4–3ØÓ¹e&Â(ãFig 4–3 Destination received constellation for different cases
— 95 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO4.4.2.2 111«««¹¹¹¥U¤õÈÑ&Òx1§´U¤õÈÑ&Òx2§R31ã=ux1D"d§Â(ãdã4–3(b)ѧ٥§ãlk´d(:Mi|¤²1o>/o^>R²©§l5´²1o>/éÆ"äN ó§û«ΩiÊ^©.lk §DZ
l1 : y1 =√E1|h1D|;
l2 : y2 = −√E1|h1D ||hRD| y1 −
√E1E2|h1D||h2D|
|hRD| ;
l3 : y1 = −√E1|h1D|;
l4 : y2 = −√E1|h1D ||hRD| y1 +
√E1E2|h1D||h2D|
|hRD| ;
l5 : y2 =|hRD|√
E1|h1D |+√E2|h2D |y1
(4–32)
,§/û«Ωi§DZΩ1 = l1 > 0 ∪ l4 > 0; Ω2 = l3 > 0 ∪ l4 ≤ 0 ∪ l5 ≤ 0;Ω3 = l2 ≤ 0 ∪ l3 ≤ 0; Ω4 = l1 ≤ 0 ∪ l2 > 0 ∪ l5 > 0.
(4–33)ù§1«¹VÇÒ±ÏLòþãû«\úª(4–31)¥"4.4.2.3 111nnn«««¹¹¹¥U¤õÈÑ&Òx2§´U¤õÈÑ&Òx1§R31ã=ux2D"d§Â(ãdã4–3(c)ѧ٥§ãlk´d(:Mi|¤²1o>/o^>R²©§l5´²1o>/éÆ"äN ó§û«ΩiÊ^©.lk §DZ
l1 : y1 =√E2|h2D|;
l2 : y2 = −√E2|h2D||hRD| y1 −
√E1E2|h1D||h2D|
|hRD| ;
l3 : y1 = −√E2|h1D|;
l4 : y2 = −√E2|h2D||hRD| y1 +
√E1E2|h1D||h2D|
|hRD| ;
l5 : y2 =|hRD|√
E1|h1D|+√E2|h2D| y1.
(4–34)
,§/û«Ωi§DZΩ1 = l1 > 0 ∪ l4 > 0 ∪ l5 ≤ 0; Ω2 = l1 ≤ 0 ∪ l2 > 0 ∪ l5 > 0;Ω3 = l3 > 0 ∪ l4 ≤ 0 ∪ l5 ≤ 0; Ω4 = l2 ≤ 0 ∪ l3 ≤ 0 ∪ l5 > 0.
(4–35)
— 96 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èOù§1n«¹VÇÒ±ÏLòþãû«\úª(4–31)¥"4.4.2.4 111ooo«««¹¹¹¥UQÃÈÑx1DZÃÈÑx2§R31ãÒØ=u?Û&E"Ïd§±ë4-PAMN&ÒVÇ5í[131]§=
PDe4
=2(M − 1)
M·Q(√
6 log2Mρ
M2 − 1
), (4–36)Ù¥§M = 4§]SNRρ = EE1|h1D|2 + E2|h2D|2/σ2.
0 5 10 15 2010
−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Out
age
Pro
babi
lity
Selective−and−ForwardONC−simONC−thyã 4–4Ŭä?èÚÀJ-=uä?è¥äVÇ
Fig 4–4 Outage probability of opportunistic network codingand selective-and-forward based net-
work coding
4.5 555UUUýýý©©©ÛÛÛÙÏLý¢5ïþŬä?èÆÆ5U"zvÝDZl = 10, 000"Ïd§zDѱÏÝÒDZ20, 000"duXÚ.¥Ä— 97 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO´O·Pá&§Ïd&ëêh1R, h2R, h1D, h2DÚhRD 3zDѱÏSÑ´½ØC§ 3DѱÏmÕáCz"3ý¥§´»Ñ.DZλjk = d−2vw§Ù¥γvw L&Oç v ∈ 1, 2,R, w ∈ R,D, v 6=
w"b& Ú¥UuxõÇ÷v^E1 +E2 = 2ER",§ý¥SNR½ÂDZρ = ER/σ2"
0 2 4 6 8 1010
−4
10−3
10−2
10−1
100
SNR
BE
R
ONC−simSelective−and−ForwardONC−thy
ã 4–5Ŭä?èÚÀJ-=uä?è5UFig 4–5 Error performance of opportunistic network coding and selective-and-forward based net-
work codingbü& uxõÇ!DÑǧ±9¥UÚ&!:ålÑ"& ¥UålDZdR = 0.5§¥U&ålDZdRD = 0.5§& &ålDZdD = 1"&P~êDZγ = 2"ã 4–4ЫSNRl0dB20dBeÄuɽŬä?è¥äVÇnØ©Û(JÚAkâý§©O^ONC-thyÚONC-simL«§±9æ^ÀJ-=uüÑDÚä?è¥äVÇ[40]§dSelective-and-ForwardL«"lý(J¥±w§nØíŬä?è¥äVÇAkâý(J´Ü",§Å¬ä?èduÏL¥ä¯û§³¥UÈè*ѧÓ3ü^& -¥UØ¥ä¹e§=uA& — 98 —
þ°ÏÆÆ¬Æ Ø© 1o٠Ŭä?èO&E§l (¦U¿ï(&E"¤±ÄuÀJ-=uüÑDÚä?èüÑ¥äVÇ5UÐ",§ÃØ´3ÃÏ&~^óSNR[5, 10]dB«m§´3?1©8OÃ*pSNR20dB§ONCüÑ5UÑSelective-and-ForwardüÑÐ",§ã 4–5ЫSNRl0dB10dBeÄuɽŬä?è5UnØ©Û(JÚAkâý§±9DÚä?è5U"lý(J¥±w§nØíŬä?è5UAkâý(JDZ´Ü",§Å¬ä?èduÏL¥ä¯û§3³¥UÈè*ÑÓ¦U¿ï(&E§¤±ÄuÀJ-=uüÑDÚä?èüÑ5UÐ"d§©ò31ÊÙ¥§é1Ù2Â[ä?è!1nÙõÇg·Aä?èÚÙŬä?è3ØÓÔn|µ¥?1î'"4.6 (((Ù3õ\¥U&¥JѫŬä?èüÑ"â& -¥U&Øӥ䯧¥U!:û½31Y=uä?觽öü& &E§½öØ?1Æ"ÄuùO§ÙíŬä?èüÑ¥äVÇ",§â&!:?n«ØÓ¹eÂ(ã§ÙíXÚBER"ý(JL²§Å¬ä?è¥äVÇÚ5UnØ©ÛÚAkÛýÑ´Ü"ÏDZ3*ѳL§¥§Å¬ä?è¦U/¿ï(&E§¤±Å¬ä?èDÚä?è?èOÃp"
— 99 —
þ°ÏÆÆ¬Æ Ø© 1ÊÙ o(Ð"111ÊÊÊÙÙÙ ooo(((ÐÐÐ"""8c§X£ÄpéEâØäuÐÚ?Ú§ÃEâÚ®²¤DZ·F~)¹¥Ø½"Ü©"´duÃ&^U,ؽ5§ÃäUDZ^rJø~kêâDÑÇ"3¢SÏ&L§¥§Ã&ÉPá!´»Ñ!ÒKAÚ&mZ6ÃõÏKDZ§DÑ&Òþü$"DZÃÏ&¥«;.äÿÀ(§õ\¥U&®²¤DZc£ÄÏ&XÚ¥ïÄ."ÏLÜnä?èO§õ\¥U&U÷©8OçJpXÚVÇÚªÌÇ"
5.1 nnn«««ÔÔÔnnnäää???èèèüüüÑÑÑnnnÜÜÜ©©©ÛÛÛe¡§©éJÑn«ØÓä?èüѧ=2Â[ä?èüÑ!õÇg·Aä?èüÑÚŬä?èüѧ?1nÜ'"DZ'ú²§b& Ñæ^BPSKN§¿& -&&Ú¥U-&&?11Å ýþï?n",§¥Uæ^Ŭä?èüÑ¿uxä?è&ҧĥU¢ÄuõÇg·AŬä?è§=xR = x1 ⊕ x2, ER ∈ κ1, κ2"ù§Å¬ä?èÚõÇg·Aä?è'§ØÓ/´cöÏL¥U?é¥ä¯ä5?1*ѳ§ ö´ÏLõÇ Ïf5?1*ѳ"Äk§ÙÄü& ¥UÚ&ål´¹en&|µ"& Ú&mål8zDZ§=d1D = d2D = 1"¥U!: u& Ú&m"3ý¥§â¥U¤?nØÓ §Än«ØÓ¹"äN ó§¹Ä´r& -¥Uó´|µ§Ù¥d1R = d2R = 0.3§¿dRD = 0.7"¹Äé¡|µ§Ù¥d1R = d2R = 0.5§¿dRD = 0.5" ¹nÄ´r¥U-&|µ§Ù¥d1R = d2R = 0.7§¿dRD = 0.3",§ùÜ©ýÄ& ´é¡|µ"äN ó§bd1R = 0.5d2R = 0.2dRD = 0.5d1D = 1§¿d2D = 0.7§ù& P|µo"— 101 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
0 5 10 15 20 2510
−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
PANCGANC, ITM+PAONC
ã 5–1|µ¥5UFig 5–1 Error performance of Case 1z«!: ¢y©OýXen«üѵ
• £a¤GANCüÑ£1Ù¤§Ù¥Ræ^úª(2–46)¥Ñ`]CÝÚ`& õÇ©£power allocation, PA¤§PGANC;
• £b¤PANCüÑ£1nÙ¤§Ù¥õÇg·AÏfκ1Úκ2dúª(3–56)û½§PPANC¶
• £c¤Å¬ä?èüÑ£1oÙ¤§Ù¥¥Uuxä?è&Òkκ1 = 3κ2 = 3/√5§PONC.ã5–1§ã5–2§ã5–3Úã5–4©OÑGANC!PANCÚONCüÑ3oØÓ|µe5U'"ÏLý(J±w§1Ù¥JÑGANCüÑ!1nÙJÑPANCüѱ9ÙJÑÄuõÇg·AŬä?èüÑѱ÷©8OÃ"3¤k|µ¥§GANCüÑPEP5U`uÙ¦üÑÏ´ÏDZGANC´¦PEPz`üѧ
— 102 —
þ°ÏÆÆ¬Æ Ø© 1ÊÙ o(Ð"
0 5 10 15 20 2510
−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
PANCGANC, ITM+PAONC
ã 5–2|µ¥5UFig 5–2 Error performance of Case 2Ù¦üÑKØ,"3|µe§ÏDZ& ål¥Uål¥U-&ó´C§¤±¥UÑVÇDZ'$"d§æ^ONCüѬ¿ïKk^&E§Ïdæ^õÇ ÏfPANCüÑONCüÑ?èOÃp"X¥Uål& 5§¥UÑVÇO\§ONCüÑ5UÅìLPANCüÑ"Ó§ý(JDZL²é¡|µeØÓüÑ'(Jé¡|µe´"3©1ÙÚ1nÙ¥æ^ØÓõÇY"Ù¥§31Ù¥§©éü& uxõÇ?1`z§¿3¥U??1õÇ8z?n"ùp§& ?uxõÇ`z´DZ?ÚJpXÚ5U§ ¥U?õÇ8z´DÚ[ä?èö",§©ÏLN¥U?Â&ÒÆÝ¢y&?Â(ãþî¼ålz§l `zXÚ¤éVÇ"31nÙ¥§©é¥UuxõÇ?1`z§l ¡¦XÚU÷©8Oç,¡UÐ?èOÃ"ùp§©vké& uxõÇ?1`z§3Yó¥§ö
— 103 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO
0 5 10 15 20 2510
−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
PANCGANC, ITM+PAONC
ã 5–3|µn¥5UFig 5–3 Error performance of Case 3òéÜ& Ú¥UõÇ?1éÜ`z§éTÜ©SN?1?ÚÖ¿ÚÿÐ"8§©òé1oÙŬä?èÜ©?1õÇ`z¡òÚÿÐ"
5.2 ÌÌÌ(((ØØØäN5ù§©Ì¤JLãXeµ1. JѦ¤éVÇz[ä?èY"|^.KF¦)`¥U¼ê§N¥UÂ&ÒõÇÚ §¦&Â(ãþ(:î¼ålO§ü$XÚ¤éVÇ"ý(JL²§©JÑÃØ3M -QAMNXÚ¥'Ù¦DÚä?èüѧÑäkФéVÇ5U"2. JÑõÇg·Aêiä?èY§¦XÚ÷©8OÃ"©ÄkÏLä& -¥UÚ¥U-&&OÃé5N¥U?u
— 104 —
þ°ÏÆÆ¬Æ Ø© 1ÊÙ o(Ð"
0 5 10 15 20 2510
−6
10−5
10−4
10−3
10−2
10−1
100
SNR(dB)
Pai
rwis
e E
rror
Pro
babi
lity
PANCGANC, ITM+PAONC
ã 5–4|µo¥5UFig 5–4 Error performance of Case 4xõǧõÇ ÏfLª§³*Ñ"?Ú§©ÏL(Ü`zõÇU??ä?è§õÇg·AÏf§¢y& &Òé¥Uux&ÒN§)ûuÿ¯K"ù§¥U`õÇU?Ò±©)DZõÇ ÏfÚõÇg·AÏf¦È"Äu±þO§©ÏL/VÇ.ÚIC§â¥UÚ&?(ã9ÙéAû«§íXÚÎÒéÇ4ÜLª§éÐ/êÜAkâý(Ø"ý(JL²©JÑõÇg·Aä?èüÑØ=÷©8§Jp?èOÃ"
3. JѫŬä?èüѧ³Èè*Ñ"©3¥U!:?§ÏL& -¥Uõ\&¥ä¯5û½Y=u&Òa.§)ä?è&Ò!E?èü& &Ò½öØÆ"Äu±þO§©ÏL©Û?Ñ\eux&ÒÚÂ&Òmp&E§XÚ¥äVÇ"ÏLïáØÓ¥U=u&ÒéAÂà(㧗 105 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO©Èèû«>.Lª§¿±dDZâéXÚ'AVÇ?1©Û"5.3 ïïïÄÄÄÐÐÐ"""nþ§ä?èEâäÌÝJpÆÏ&XÚóéþ!J,XÚªÌÇ!¢yêâØ Úü$ªàUÑ`³"´IÑ´§ä?èEâA^L§¥Iıe¢S¯Kµ£1¤DZ¢yä?觥U!:?OUåIOr±·Ak«E,$"k û½ä?è'E,Ý"Ïd3Oä?èÆÆÿ§I3äóéþÚ$E,Ým?1ò©Ä§¡yÂàÈè¤õVǧ,¡DZ±OE,Ý3½S"£2¤3êiä?襧éÂ&Ò)èÚ#?èѬ5XÚò¯K"duêiä?覥Uà?1)èÚ?è§ÏdXv!NêÚ& êëêO\§?!)èmDZ¬A/O"AO´éuÑÏ!6xNDÑ¢5¦pÖ5ù§ÒI?Ú(ÜÙ¦'ÃÏ&Eâ§ü$XÚò"£3¤DZ·AÔnä?èEâ§Iéþ´d!DÑÆÆÚNÝÅ?1#O"DZ)û±þ¯K§±ÏLª`zªõÄuÃä?èXÚ¥] ©§¦ä?èØÉägÚ§§Ý¢yykäEâÚ(Ö¿ÚKÜ"ù§X'uä?èÆïÄØä,\§ïÄöI¡Ää?è3¢SA^L§¥k|ÚØ|ϧØä÷ä?è¢^|µ§3uä?èyk`³Ó§(ÜcÃDÑEâÑE,Ý¡Øv§l ?ÚJpÃÏ&k5Ú°5"¦+'uõ\¥U&¥ä?èïÄ®²kéõïĤJç´æ^Uþæ8.[132]õ^r¥U&¥5U©Û!ä?èO!¥U&Ò?n¡E?uïÄx"Uþæ8´l±¸[133–136]½öÙ¦Uþ5 £X<N9U!vÜÀÂU¤[137, 137–139]æ8Uþ§¿òÙ=DZ>UEâ"XJæ8Uþ v¿¥y±Ï5½ö±Y5£'XU§ºU¤§@oÃDaì!:Òò[Èø
— 106 —
þ°ÏÆÆ¬Æ Ø© 1ÊÙ o(Ð">"(Ü<ïÄ%§e¡JÑ(ÜUþæ8EâÚõ^r¥UXÚïÄ"1. 3V¥U&¥§üªàÚ¥U!:ѱÏLU½öÃ>ÅU?1ø>"XÛ3TUþæ8.e?1ä?èüÑO§¿?1'õÇNݱ¢yDÑÇÚ5U`zE,´m¯K"XJXÚæ^Ã>ÅUDZUþæ8 §Uþæ8mÚÏ&m©'~DZ¬éDÑ5UE¤KDZ"Ïd§XÛ¢yõÇNÝÚm©'~éÜ`z§DZ´Æ)û¯K",§lnØ©ÛÆÝþù§I'53Uþæ8.e§æ^DÚêiÚ[ä?èV¥U&´ÄE,U÷©8OÃ"2. 3÷¶ä¥§½õ\¥U&Âà´«ÄÕ"Ïd§ÄÕ±3Ï&m©c±Ã>ÅUªé^rÚ¥U?1¿>"3ù#.Uþæ8XÚ¥§XÛ?1êiÚ[ä?èÆÆO§¿(ÜõÇNݱ¢yéÜÇ`zE,´m¯K"aq§±ïÄÄÕ¿>mÚ^r3þ1ó´Ï&m©'~éXÚ5UE¤KDZ"XÛ¢yõÇNÝÚm©'~éÜ`z§DZ´Æ)û¯K"3. 3æ^Ã>ÅU?1¿>½õ\¥U&¥§XÛOÜnä?èY±¢y5U`zDZ´m¯K"?Ú§±ïÄ3ùXÚ¥KDZ©8OÃÏ"Äuêiä?èüÑõ\¥U&§©ÌÄ3¥U?OÜnõÇNÝY5÷©8§=¢yä?è&ÒÚ^ré&ÒNõÇg·AÏfÚ¢y³õÇ Ïf"3æ^Uþæ8Eâ§I?ÚïÄÙ¦KDZ©8Où§XUþæ8mÚÏ&m©'~"Äu[ä?èüÑõ\¥U&§©ÌO`z¤éVÇ`¥U¼ê"3æ^Uþæ8Eâ§I(Ü#Uþå§#í#¥U¼ê"
— 107 —
þ°ÏÆÆ¬Æ Ø© N¹ A ½n2.1y²NNN¹¹¹ A ½½½nnn2.1yyy²²²e¡§·ÏL?ØDminU5í`ÝΨ"éuM -
QAMN§DminÏ~3Xü«¹µ£1¤k=k²îªål'Ù¦ål§=Dmin = Dij¶Ú£2¤kü²îªålÑueÙ¦ål§=Dmin = Dij = Dvw§Ù¥i, j, v, w ∈1, 2, · · · ,M2, i 6= j, v 6= w"b3Xuü²îªål*d'eÙ¦ålѧ@ozéålѱÝΨ"XJùíÑÝΨ´Ó§@o·IÙ¥?¿éålÒv`ÝΨ∗"ÄK§ÒØ3ùÝΨ÷vkü±þ²îªålù^"Þ~f5`§·b3náål§=Dmin = Dij = Dvw = Dlz§Ù¥i, j, v, w, l, z ∈ 1, 2, · · · ,M2, i 6= j, v 6= w, l 6= z"·?ÚbΨ1ÚΨ2©O´§Dij = DvwÚDij = Dlz)"XJΨ1 = Ψ2§@o·±ÏL¦)§Dij = Dvw½Dij = DlzDij = Dvw = Dlz)"XJΨ1 6= Ψ2§@o§|Dmin = Dij = Dvw = DlzÒvk)"lù~f¥§·±w?ØüüålÒv±nåláÝΨ)"ù(رéN´í2Lnålá¹"Ïd§·Òvk7?ØkLü²îªål¹"ù§úª(3–53)¥©`z¯K±©)DZ2(M4 −M2)f¯K"¦)zf¯K§·Ñ¬ÝΨk,ijÚ§éAá²îªålDk,ij
min §Ù¥1þIk = 1, 2L«´1A¹§ 1éþIijéA9îªålDij"l §`ÝΨ∗Ò´éAXålDk,ijmin
@"31«¹e§k=k²îªåluDmin§=µij > 0, µvw =
0, λ 6= 0§Ù¥i, j, v, w ∈ 1, 2, · · · ,M2, i 6= j, v 6= w"lúª(2–42)¥pÖtµ^·§d=3.KF¦fµij > 0§=Dmin = Dij = Ddirect
ij + ϕ∣∣∣∣∣∣Ψ1,ijuij
∣∣∣∣∣∣2
2, (A–1)Ù¥§Dij´éAµij²îªål" eÙ¦.KF¦fÑu0§
— 109 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO=µvw = 0"Ïd§lúª(2–41)¥1KKT^§·kµij = 1"ù§ÝΨ1,ij±ÏL¦)eã§|
ϕΨ1,ijuijuTij − λΨ1,ij = 0,
Tr(Ψ1,ij(Ψ1,ij)T )− 2(1−ϕ)ϕ
= 0.(A–2)PþuijÚÝΨ1,ij©ODZ
uij = [uij,1, uij,2]T and Ψ1,ij =
[ψ
1,ij1 ,ψ
1,ij2
], (A–3)Ù¥§2 × 1þψ1,ij
a ´ÝΨ1,ij1a§a = 1, 2"²LXO§Ψ1,ij±L«DZ[ϕ(uij,1)
2 − λ ϕuij,1uij,2
ϕuij,1u1,ij2 ϕ(uij,2)
2 − λ
]
︸ ︷︷ ︸Fm
[ψ
1,ij1
ψ1,ij2
]T= 02×1” (A–4)XJdet(Fij) = 0§=λ = ϕ((uij,1)
2 + (uij,2)2)§uij,1, uij,2 6= 0§·kψ1,ij
2 =uij,2
uij,1ψ
1,ij1 "Ú\ütµCþκij,1Úκij,2§Ù¥κij,1, κij,2 ∈ R
+§@oÝΨ1,ijLªdúª(2–44a)Ñ"duTr(Ψ1,ij(Ψ1,ij)T
)= 2(1−ϕ)
ϕ§¤±tµCþκij,1Úκij,2I÷vúª(2–45)¥Ñå^"AO§det(Fij) = 0, uij,1 = uij,2 = 0ÿ§Ψ1,ij±DZ÷v¥UuõÇå?¿Ý"Ïd§Ψ1,ijDZH2I2DÚ[ä?è±´zîªål`z¯K)"ÄK§XJdet(Fij) 6= 0§úª(A–4)¥§ÒÃéψ1,ij
1 ,ψ1,ij2 )"31«¹¥§3ü²îªåluDmin§=µij > 0, µvw >
0, µlz = 0, λ 6= 0§Ù¥i, j, v, w, l, z ∈ 1, 2, · · · ,M2, i 6= j, v 6= w, l 6= z"lúª(2–42)¥pÖtµ^§·kD2,ijmin = Dij = Dvw§=
Ddirectij + ϕ
∣∣∣∣∣∣Ψ2,ijuij
∣∣∣∣∣∣2
2= Ddirect
vw + ϕ∣∣∣∣∣∣Ψ2,vwuvw
∣∣∣∣∣∣2
2. (A–5)3A^5K∣∣∣∣∣∣Au
∣∣∣∣∣∣2
2= Tr
(ATAuuT
)ÚTr(A) + Tr(B) = Tr(A + B)§úª(A–5)±?ÚTr((Ψ2,ij)TΨ2,ij (uiju
Tij − uiju
Tvw
))=Ddirect
vw −Ddirectij
ϕ. (A–6)
— 110 —
þ°ÏÆÆ¬Æ Ø© N¹ A ½n2.1y²Ú\¥mCþBij§=Bij = [bij11 , b
ij12 ; b
ij21 , b
ij22 ] = (Ψ2,ij)TΨ2,ij§,
Uij = [uij11 , u
ij12 ; u
ij21 , u
ij22 ] = uiju
Tij − uvwu
Tvw” (A–7)@o§3éÜÄ1pÖtµ^§·±ÏL)eã§5¥mCþBij)DZ
Tr(BijUij) = u
ij11 b
ij11 + u
ij21 b
ij12 + u
ij12 b
ij21 + u
ij22 b
ij22 =
Ddirectvw −Ddirect
ij
ϕ,
Tr(Bij) = bij11 + b
ij22 =
2(1− ϕ)
ϕ.
(A–8),§·bÝBij´¢é¡Ý§¿éÆþ§=bij11 = bij22 Úbij12 = b
ij21 "Äuùb§¡§·±3ØÚ\tµCþcJeBij(½)",¡§ÏLAÆ©)§ÝΨ2,ij±dÝBijAÆÚAÆþL«Ñ5"äN ó§·ÄkÏLúª(A–8)Ú¢é¡b5íÝBij§·k
Bij =
1−ϕϕ
(Ddirectvw −Ddirect
ij )−2(1−ϕ)(uij11 +u
ij22
)
ϕ(uij12 +u
ij21
)
(Ddirectvw −Ddirect
ij )−2(1−ϕ)(uij11 +u
ij22
)
ϕ(uij12 +u
ij21
) 1−ϕϕ
.
(A–9)éu¢é¡ÝBij§§AÆþ±ÀJDZ¢!*dDZ§=Bij = QijΛij(Qij)T , (A–10)Ù¥§Qij´Ý§Λij´éƧ§éÆþDZÝBijAÆ"duBij = (Ψ2,ij)TΨ2,ij§Bij´AÆDZê½Ý"XJúª(A–9))BijØDZ꧷ÒÃéΨ2,ij)"ÄK§·kΨ2,ij = Qij|Λij| 12§äN)dúª(2–44b)Ñ1"
1ùp§·¤±éÝΛijý駴ÏDZ·o±4B
ijAÆDZmaxbij11 , b
ij12 − minb
ij11 , b
ij12 Úmaxb
ij11 , b
ij12 + minb
ij11 , b
ij12 "ùÒyΨ
2,ij´¢Ý"— 111 —
þ°ÏÆÆ¬Æ Ø© N¹ B ½n2.2y²NNN¹¹¹ B ½½½nnn2.2yyy²²²aq½n2.1¥?ا31«¹e§k=k²îªåluDmin§=µij = 1, µvw = 0§Ù¥i, j, v, w ∈ 1, 2, · · · ,M2, i 6= j, v 6= w§
λ 6= 0"lKKT^(2–54b)¥§·kC1ESd
<ij(d
<ij)
T +C2ESd=ij(d
=ij)
T +C3ESd<ij(d
=ij)
T − λES = 02×2, (B–1)Ù¥C1 = H1HT1+ϕ(ΨHR)(ΨHR)
T§C2 = (I2′H1)(I2′H1)T+ϕ(ΨI2′HR)(ΨI2′HR)
T§¿C3 = 2((I2′H1)
TH1 + ϕ(ΨI2′HR)
TΨHR
)"·PES = Diag
(√Etotal cos(ϑij)
√Etotal sin(ϑij)
)§Ù¥ϑij ∈ (0, π/2)"òÝCq^§L«DZ[c11q , c12q ; c21q , c22q
]§q = 1, 2, 3"½Âd<ij(p)DZþd<ij(p)1p§p = 1, 2"ӽªDZ±A^ud=ij"ù§úª(B–1)Òý±#[
(η1,ij − λ)√Etotal sin(ϑ) + η2,ij
√Etotal cos(ϑ) η3,ij
√Etotal sin(ϑ) + η4,ij
√Etotalcos(ϑ)
η5,ij√Etotal sin(ϑ) + η6,ij
√Etotal cos(ϑ) η7,ij
√Etotal sin(ϑ) + (η8,ij − λ)
√Etotal cos(ϑ)
]
(B–2)Ù¥η1,ij =
(d<ij(1)
)2c111 +
(d=ij(1)
)2c112 + d<ij(1)d
=ij(1)c
113 ,
η2,ij = d<ij(1)d<ij(2)c
121 + d=ij(1)d
=ij(2)c
122 + d=ij(1)d
<ij(2)c
123 ,
η3,ij = d<ij(1)d<ij(2)c
111 + d=ij(1)d
=ij(2)c
112 + d=ij(2)d
<ij(1)c
113 ,
η4,ij =(d<ij(2)
)2c121 +
(d=ij(2)
)2c122 + d=ij(2)d
<ij(2)c
123 ,
η5,ij =(d<ij(1)
)2c211 +
(d=ij(1)
)2c212 + d=ij(1)d
<ij(1)c
213 ,
η6,ij = d<ij(1)d<ij(2)c
221 + d=ij(1)d
=ij(2)c
222 + d=ij(1)d
<ij(2)c
223 ,
η7,ij = d<ij(1)d<ij(2)c
211 + d=ij(1)d
=ij(2)c
212 + d=ij(2)d
<ij(1)c
213 ,
η8,ij =(d<ij(2)
)2c221 +
(d=ij(2)
)2c222 + d=ij(2)d
<ij(2)c
223 ,
(B–3)
— 113 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO¿§§du
(η1,ij − λ) η2,ij
η3,ij η4,ij
η5,ij η6,ij
η7,ij (η8,ij − λ)
︸ ︷︷ ︸Gij
[ √Etotal sin(ϑ)√Etotal cos(ϑ)
]= 04×1. (B–4)
XJrank(Gij) = 2§@oES = 02×2"ÄK§XJrank(Gij) = 1§=Gijþ´5'§·±òϑL«DZϑ = arctan(−η4,ij
η3,ij
)"Ïd§`& õÇ©ÝdESúª(2–57a)Ñ"31«¹e§kü²îªåluDmin§=µij >
0, µvw > 0, µlz = 0, λ 6= 0"lúª(2–55a)tµ^¥§·k||H1ESd
<ij + I2′H1ESd
=ij||22 + ϕ||ΨHRESd
<ij +ΨI2′HRESd
=ij||22
= ||H1ESd<vw + I2′H1ESd
=vw||22 + ϕ||ΨHRESd
<vw +ΨI2′HRESd
=vw||22
(B–5)§du(d<ij
)TET
SL1ESd<ij +
(d=ij
)TET
SL2ESd=ij + 2
(d=ij
)TET
SL3ESd<ij
=(d<vw
)TET
SL1ESd<vw +
(d=vw
)TET
SL2ESd=vw + 2
(d=vw
)TET
SL3ESd<vw,
(B–6)Ù¥L1 = HT1H1+ϕH
TRΨ
TΨHR§L2 = HT1 (I′2)
TI′2H1+ϕH
TR (I′2)
TΨTΨI′2HR§¿L3 = HT
1 (I′2)TH1+ϕH
TR (I′2)
TΨTΨHR"òÝLq^§L«DZ[l11q , l12q ; l21q , l
22q
]§q = 1, 2, 3"Ïd§úª(B–6)±?Ú[
(ϕ1,ij − ϕ1,vw)E21 + (ϕ2,ij − ϕ2p)E1E2 (ϕ3,ij − ϕ3,vw)E1E2 + (ϕ4,ij − ϕ4,vw)E
22
(ϕ5,ij − ϕ5,vw)E21 + (ϕ6,ij − ϕ6,vw)E1E2 (ϕ7,ij − ϕ7,vw)E1E2 + (ϕ8,ij − ϕ8,vw)E
22
]= 02×2,
(B–7)§du
(ϕ1,ij − ϕ1,vw) (ϕ2,ij − ϕ2,vw)
(ϕ3,ij − ϕ3,vw) (ϕ4,ij − ϕ4,vw)
(ϕ5,ij − ϕ5,vw) (ϕ6,ij − ϕ6,vw)
(ϕ7,ij − ϕ7,vw) (ϕ8,ij − ϕ8,vw)
︸ ︷︷ ︸Zij
[Etotal
√sin (ϑ)
Etotal
√cos (ϑ)
]= 0 (B–8)
— 114 —
þ°ÏÆÆ¬Æ Ø© N¹ B ½n2.2y²Ù¥ϕ1,mt = l111
(d<mt(1)
)2+ l112
(d=mt(1)
)2+ 2l113 d
<mt(1)d
=mt(1),
ϕ2,mt = l211 d<mt(1)d
<mt(2) + l212 d
=mt(1)d
=mt(2) + 2l213 d
<mt(1)d
=mt(2),
ϕ3,mt = l121
(d<mt(1)
)2+ l122
(d=mt(1)
)2+ 2l123 d
<mt(1)d
=mt(1),
ϕ4,mt = l221 d<mt(1)d
<mt(2) + l222 d
=mt(1)d
=mt(2) + 2l223 d
<mt(1)d
=mt(2),
ϕ5,mt = l111 d<mt(1)d
<mt(2) + l112 d
=mt(1)d
=mt(2) + 2l113 d
<mt(2)d
=mt(1),
ϕ6,mt = l211
(d<mt(2)
)2+ l212
(d=mt(2)
)2+ 2l213 d
<mt(2)d
=mt(2),
ϕ7,mt = l121 d<mt(1)d
<mt(2) + l122 d
=mt(1)d
=mt(2) + 2l123 d
<mt(2)d
=mt(1),
ϕ8,mt = l221
(d<mt(2)
)2+ l222
(d=mt(2)
)2+ 2l223 d
<mt(2)d
=mt(2),
mt ∈ ij, vw
(B–9)
XJrank(Zij) = 2§@oES = 02×2"ÄK§XJrank(Zij) = 1§=ÝZijþ5'§@o·kϑ = arctan(−ϕ2,ij−ϕ2,vw
ϕ1,ij−ϕ1,vw
)"`& uxõÇÝES±dúª(2–57b)L«"5¿§duúª(B–4)¥éÝES^kéî"Ïd§·b 1φ≤ tan(ϑ) ≤ φ for φ > 1"vk)÷vKKT^§·^ÝES¥ϑ>.^5O§¦Dmin@>.^Ò3DZ/`0)"
— 115 —
þ°ÏÆÆ¬Æ Ø© N¹ C ½n3.1y²NNN¹¹¹ C ½½½nnn3.1yyy²²²Äk§·Ä& ux&ÒT1ÈèØ"3&!:?§&ÒT1ØȤT4²þVÇDZ
P (T1 → T4) = EP (T1 → T4|h)
= E
∑
k∈±κ1,±κ2P (T1 → T4|
√ERxR = k, T1, h1D, h2D, hRD)P (
√ERxR = k|T1, h1R, h2R)
= E
Q1
√2((∑2
i=1
√Ei|hiD|
)2+ |hRD|2a2
)
√(E1|h1D|2 + E2|h2D|2 + |hRD|2a2)σ2
[1−
2∑
i=1
Q1
(√2 (Ei|hiR|2/σ2)
)
−Q1
√√√√2
(2∑
i=1
√EihiR
)2
/σ2
+Q1
√2((∑2
i=1
√Ei|hiD|
)2+ |hRD|2ab
)
√(E1|h1D|2 + E2|h2D|2 + |hRD|2a2) σ2
Q1
(√2 (E1|h1R|2/σ2)
)
+Q1
√2((∑2
i=1
√Ei|hiD|
)2 − |hRD|2ab)
√(E1|h1D|2 + E2|h2D|2 + |hRD|2a2) σ2
Q1
(√2 (E2|h2R|2/σ2)
)
+Q1
√2((∑2
i=1
√Ei|hiD|
)2 − |hRD|2a2)
√(E1|h1D|2 + E2|h2D|2 + |hRD|2a2) σ2
Q1
√√√√2
(2∑
i=1
√EihiR
)2
/σ2
.
(C–1)Ø5§·3Yy²¥bE1 = E2 = ER = E"·½Âρ = E/σ2DZXÚSNR"oN5ù§éuQ¼ê¦²þ§·kE
Q1
(√2ρ|hij|2
)=
1
π
∫ π/2
0
(1 +
ργijsin2 θ
)−1
dθρ→∞≈ 1
4γijρ−1. (C–2)aq§·kE
Q1
(√2ρ∑
t∈ij,mn |ht|2)
ρ→∞≈ 316γijγmn
ρ−2§EQ1(
√2ρ∑
t∈ij,mn,pq |ht|2)§ρ→∞≈ 532γijγmnγpq
ρ−3"â©z¥(ا3pSNRe§— 117 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èO·kXeCq(JE
Q1
√2((∑2
i=1
√Ei|hiD|
)2 − |hRD|2ab)
√(E1|h1D|2 + E2|h2D|2 + |hRD|2a2) σ2
≈ γRD
γ1D + γ2D + γRD. (C–3)âúª(C–2)Ú(C–3)¥Cq(J§úª(C–1)¥VÇP (T1 → T4|h)é&©Ù¦²þ§·±?Ú
P (T1 → T4) ≈5
32γ1Dγ2DγRDρ−3 +
5
128γ1Dγ2DγRDγ1Rρ−4
+γRD
4γ2R(γ1D + γ2D + γRD)ρ−1 +
γRD4γSR(γ1D + γ2D + γRD)
ρ−1,
(C–4)Ù¥γSR = γ1R + γ2R"aq§·±íVÇP (T2 → T3)"k& &Òȧ·±P (T1 → T2) ≈
316γ1DγRD
ρ−2 + 14γ1R
ρ−1 + 14γ2R
ρ−1 + 14γSR
ρ−1, when κ1 > κ2,3
16γ1DγRDρ−2 + 1
4γ1Rρ−1 + 3
64γ1DγRDγ2Rρ−3 + 3
64γ1DγRDγSRρ−3, when κ1 < κ2,
316γ1DγRD
ρ−2 + 14γ1R
ρ−1 + 116γ1Dγ2R
ρ−2 + 116γ1DγSR
ρ−2, when κ1 = κ2.
(C–5)Ón§·±íVÇP (T1 → T3)ÚP (T2 → T4)"lúª(C–4)Ú(C–5)¥§·±Ñù(ا=vkæ^õÇ PANCüÑ3MARCXÚ¥U©8"éuæ^DÚä?èMARCXÚ§ØVÇé&ëꦲþ§·±P (T1 → T4) ≈
5
32γSDγRDγ1Rρ−3 +
5
32γSDγRDγ2Rρ−3 +
1
4γSDρ−1,
P (T1 → T2) ≈3
16γ1Dγ1Rρ−2 +
3
16γ1Dγ2Rρ−2 +
3
16γ1DγRDρ−2.
(C–6)Ón§·±íVÇP (T1 → T3)§P (T2 → T3)ÚP (T2 → T4)"ù§·Ò±(ا=æ^DÚä?èMARCXÚØU÷©8"— 118 —
þ°ÏÆÆ¬Æ Ø© N¹ D ½n3.2y²NNN¹¹¹ D ½½½nnn3.2yyy²²²·|^J[&.5y²½n3.2¥(Ø"¥U!:æ^õÇ Ïfα§·±CqSPERe.DZ
Pv , P ((x1, x2, xR) → (x1, x2, xR))
=E
[Q
((√E1|h1D| (x1 − x1) +
√E2|h2D | (x2 − x2)
)2+ α|hRD |2(xR − xR)
2
√E1|h1D |2(x1 − x1)2 + E2|h2D|2(x2 − x2)2 + α|hRD |2(xR − xR)2
)]
(x+y)2≤2(x2+y2)≤ E
Q
(√
E1|h1D | (x1 − x1) +√E2|h2D| (x2 − x2)
)2+ α|hRD |2(xR − xR)2
2
√(√E1|h1D |(x1 − x1) +
√E2|h2D |(x2 − x2)
)2+ α|hRD |2(xR − xR)2
.
(D–1)òêìÅåQ1(x) ≤ 12exp
(−x2
2
)\þª§·±?ÚPv ≤ E
[1
2exp
(−(√
E1|h1D|(x1 − x1) +√E2|h2D|(x2 − x2)
)2+ γSRD|xR − xR|2
4
)]
ρ→∞≈ 1
2
(r∏
k=1
Λi
)−1
ρ−r
(D–2)Ù¥ΛiÚr©O´Ý[ (√E1|h1D|(x1−x1)+
√E2|h2D|(x2−x2))2
4, 0; 0, γSRD(xR−xR)2
4]"AÆÚ"γSRD = minγSR, γRD´þDZ γ1Rγ2RγRD
γ1Rγ2R+γ1RγRD+γ2RγRD§Ñlê©ÙÅCþ"·±|^Xeí5ù(Ø"·½ÂT = min(E1|h1R|2, E2|h2R|2)"ÏDZγSRD = minE1|h1R|2, E2|h2R|2, (
√E1|h1R|+√
E2|h2R|)2, γRD§d§·k2γSRD ≥ min2E1|h1R|2, 2E2|h2R|2,
2∑
i=1
Ei|hiR|2, 2γRD
≥ 2minT, γRD.(D–3)ÏDZXJXÚY´üþ©ODZvxÚvy§¿ÕáÓê©ÙÅCþ§@ominX, Y DZþuvx + vy§ÓÑlê©ÙÅCþ"Ïd§·±y²γSRD´Ñlê©ÙÅCþ"د½öüدÓu)§üéÆþÑ´"§·
— 119 —
þ°ÏÆÆ¬Æ Ø© õ\¥U&¥Ônä?èOkmaxx 6=x
Pr (x→ x) = O (ρ−2)"5¿§XJ·òúª(D–2)¥]&OÃγRDODZ²þ&OÃγRD§¿Ø¬UC©8ê"dd§·±`æ^õÇ PANCüÑ3MARCXÚ¥±÷©8"XJ·éDÚCXNCüÑDZæ^õÇ §kØu)§=xi = −xi, i ∈ 1, 2§·kP ((x1, x2, xR) → (−x1, x2, xR))
≈ E
[Q
(2E1|h1D|2√
E1|h1D|2(x1 − x1)2 + E2|h2D|2(x2 − x2)2 + α|hRD|2(xR − xR)2
)].
(D–4)éúª(D–4)¥VÇé&¦²þ§·±?ÚP ((x1, x2, xR) → (−x1, x2, xR)) ≈
1
4γ1Dρ−1. (D–5)Ïd§·±(ا=æ^õÇ CXNCüÑE,Ã÷©8"
— 120 —
[1] PROAKIS J. Digital Communications, 4th ed.[M]. New York: McGraw-Hill,
2001.
[2] TSE D, VISWANATH P. Fundamentals of wireless communication[M]. New
York: Cambridge University Press, 2005.
[3] TELATAR E. Capacity of multi-antenna Gaussian channels[J]. Europ. Trans.
Telecomm., 1999, 10:585–595.
[4] ZHENG L, TSE D N C. Diversity and multiplexing: a fundamental tradeoff in
multiple-antenna channels[J]. IEEE Transaction on Information Theory, 2003,
49(5):1073–1096.
[5] TAROKH V, SESHADRI N, CALDERBANK A R. Space-time codes for high data
rate wireless communication: performance criterion and code construction[J].
IEEE Transaction on Information Theory, 1998, 44(2):744–765.
[6] ALAMOUTI S M. A simple transmit diversity technique for wireless com-
munications[J]. IEEE Journal of Selected Areas in Communications, 1998,
16(8):1451–1458.
[7] FOSCHINI G J, GANS M. On the limits of wireless communication in a fading
environment when using multiple antennas[J]. Wireless Personal Communica-
tions, 1998, 6:311–335.
[8] NOSRATINIA A, HUNTER T E, HEDAYAT A. Cooperative communication in
wireless networks[J]. IEEE Communications Magazine, 2004, 42(10):74–80.
[9] LI J, CHEN W, NOSRATINIA A, et al. On The Throughput-Reliability Trade-
off for Amplify-and-Forward Cooperative Systems[J]. IEEE Transactions on
Communications, 2013, 61(4):1290–1303.
— 121 —
[10] WEN C K, WONG K K, NG C T K. On the Asymptotic Properties of Amplify-
and-Forward MIMO Relay Channels[J]. IEEE Transactions on Communica-
tions, 2011, 59(2):590–602.
[11] ISSARIYAKUL T, KRISHNAMURTHY V. Amplify-and-Forward Cooperative
Diversity Wireless Networks: Model, Analysis, and Monotonicity Proper-
ties[J]. IEEE/ACM Transactions on Networking, 2009, 17(1):225–238.
[12] KRIKIDIS I, THOMPSON J, MCLAUGHLIN S, et al. Optimization Issues for
Cooperative Amplify-and-Forward Systems Over Block-Fading Channels[J].
IEEE Transactions on Vehicular Techonology, 2008, 57(5):2868–2884.
[13] LANEMAN J N, TSE D N C, WORNELL G W. Cooperative diversity in wireless
networks: Efficient protocols and outage behavior[J]. IEEE Transactions on
Information Theory, 2004, 50(12):3062–3080.
[14] TORBATIAN M, DAMEN M O. Diversity Multiplexing Tradeoff of Asyn-
chronous Decode-and-Forward Cooperative Networks[J]. IEEE Transactions
on Communications, 2014, 62(7):2340–2352.
[15] . [D].[S.l.]:
, 2009.
[16] A. C P, Y. W, K. J. Practical network coding[C]//Proc. of Allerton Conference
on Communication Control and Computing. .[S.l.]: [s.n.] , 2003:40–49.
[17] HO T, MEDARD M, SHI J. On randomized network coding[C]//Proc. of Aller-
ton Conference on Communication Control and Computing. .[S.l.]: [s.n.] ,
2003:11–20.
[18] , . [J]. ,
2009:17–25.
[19] AHLSWEDE R, CAI N, LI S Y R, et al. Network information flow[J]. IEEE
Transaction on Information Theory, 2000, 46(4):1204–1216.
— 122 —
[20] HO T, LUN D S. Network coding: An introduction[M].[S.l.]: Cambridge
University Press, 2008.
[21] KATTI S, GOLLAKOTA S, KATABI D. Embracing wireless interference: anal-
ogy network coding[R].[S.l.]: Computer Science and Artificial Intelligence
Laboratory, MA, 2007.
[22] WANG C L, CHO T N, YANG K J. On Power Allocation and Relay Selection
for a Two-Way Amplify-and-Forward Relaying System[J]. IEEE Transactions
on Communications, 2013, 61(8):3146–3155.
[23] VAZE R, HEATH R W. On the Capacity and Diversity-Multiplexing Tradeoff
of the Two-Way Relay Channel[J]. IEEE Transactions on Information Theory,
2011, 57(7):4219–4234.
[24] AMARASURIYA G, TELLAMBURA C, ARDAKANI M. Two-Way Amplify-and-
Forward Multiple-Input Multiple-Output Relay Networks with Antenna Selec-
tion[J]. IEEE Journal of Selected Areas in Communications, 2012, 30(8):1513–
1529.
[25] HAVARY-NASSAB S, V.AND SHAHBAZPANAHI, GRAMI A. Optimal Dis-
tributed Beamforming for Two-Way Relay Networks[J]. IEEE Transactions
on Signal Processing, 2010, 58(3):1238–1250.
[26] . [D].[S.l.]: ,
2012.
[27] CUI T, HO T, KLIEWER J. Memoryless relay strategies for two-way re-
lay channels[J]. IEEE TRANSACTION ON COMMUNICATIONS, 2009,
57(10):3132–3143.
[28] GOMADAM K S, JAFAR S A. Optimal relay functionality for SNR maximiza-
tion in memoryless relay networks[J]. IEEE Journal of Selected Areas in Com-
munications, 2007, 25(2):390–401.
— 123 —
[29] ZHANG S, LIEW S C. Channel coding and decoding in a relay system oper-
ated with physical-layer network coding[J]. IEEE Journal of Selected Areas in
Communications, 2009, 27(5):788–796.
[30] KOIKE-AKINO T, POPOVSKI P, TAROKH V. Optimized constellations for
two-way wireless relaying with physical network coding[J]. IEEE Journal of
Selected Areas in Communications, 2009, 27(5):773–787.
[31] WEI L, CHEN W. Efficient Compute-and-Forward Network Codes Search for
Two-Way Relay Channels[J]. IEEE Commun. Lett., 2012, 16(8):1204–1207.
[32] WANG G, XIANG W, YUAN J. Generalized wireless network coding schemes
for multihop two-way relay channels[J]. IEEE Transactions on Wireless Com-
munications, 2014, 13(9):5132–5147.
[33] ZEITLER G W J, G.AND BAUCH. Quantize-and-Forward Schemes for the Or-
thogonal Multiple-Access Relay Channel[J]. IEEE Transactions on Communi-
cations, 2012, 60(4):1148–1158.
[34] KRAMER G, GASTPAR M, GUPTA P. Cooperative strategies and capacity theo-
rems for relay networks[J]. IEEE TRANSACTION ON INFORMATION THE-
ORY, 2005, 51(9):3037–3063.
[35] BAO X, LI J. Adaptive network coded cooperation (ANCC) for wireless relay
networks: matching code-on-graph with network-on-graph[J]. IEEE Transac-
tions on Wireless Communication, 2008, 7(2):574–583.
[36] DU J, XIAO M, SKOGLUND M. Cooperative network coding strategies for
wireless relay networks with backhaul[J]. IEEE Transactions on Communica-
tions, 2011, 59(9):2502–2514.
[37] XIAO M, SKOGLUND M. Multiple-User Cooperative Communications Based
on Linear Network Coding[J]. IEEE Transactions on Communications, 2010,
58(12):3345–3351.
— 124 —
[38] LI J, YUAN J, MALANCY R, et al. Full-Diversity Binary Frame-Wise Net-
work Coding for Multiple-Source Multiple-Relay Networks Over Slow-Fading
Channels[J]. IEEE Transactions on Vehicular Technology, 2012, 61(3):1346–
1360.
[39] LI J, YUAN J, MALANEY R, et al. Network Coded LDPC Code Design for a
Multi-Source Relaying System[J]. IEEE Transactions on Wireless Communi-
cation, 2011, 10(5):1538–1551.
[40] XIAO M, KLIEWER J, SKOGLUND M. Design of Network Codes for Multiple-
User Multiple-Relay Wireless Networks[J]. IEEE TRANSACTION ON COM-
MUNICATIONS, 2012, 60(12):3755–3766.
[41] GONG C, YUE G, WANG X. Analysis and optimization of a rateless coded
joint relay system[J]. IEEE Transactions on Wireless Communications, 2010,
9(3):1175–1185.
[42] KOYUNCU E, JAFARKHANI H. Distributed beamforming in wireless multiuser
relay-interference networks with quantized feedback[J]. IEEE Transactions on
Information Theory, 2012, 58(7):4538–4576.
[43] WEI S, LI J, CHEN W, et al. Power Adaptive Network Coding for a Non-
orthogonal Multiple-Access Relay Channel[J]. IEEE Transactions on Commu-
nications, 2014, 62(3):872–887.
[44] WANG T, GIANNAKIS G B. Complex Field Network Coding for Multiuser
Cooperative Communications[J]. IEEE Journal of Selected Areas in Commu-
nications, 2008, 26(3):561–571.
[45] ONAT F A, ADINOYI A, FAN Y, et al. Threshold selection for SNR-based se-
lective digital relaying in cooperative wireless networks[J]. IEEE Transactions
on Wireless Communication, 2008, 7(11):4226–4237.
[46] ONAT F A, FAN Y, YANIKOMEROGLU H, et al. Asymptotic BER analysis of
threshold digital relaying schemes in cooperative wireless systems[J]. IEEE
Transactions on Wireless Communication, 2008, 7(12):4938–4947.
— 125 —
[47] WANG T, GIANNAKIS G, WANG R. Smart regenerative relays for link-adaptive
cooperative communications[J]. IEEE Transactions on Communications, 2008,
56(11):1950–1960.
[48] WANG T, CANO A, GIANNAKIS G B, et al. High-performance cooperative
demodulation with decode-and-forward relays[J]. IEEE Transactions on Com-
munications, 2007, 55(7):1427–1438.
[49] SELVARAJ M D, MALLIK R K, GOEL R. Optimum receiver performance with
binary phase-shift keying for decode-and-forward relaying[J]. IEEE Transac-
tions on Vehicular Technology, 2011, 60(4):1948–1953.
[50] CHEN Y, KISHORE S, LI J. Wireless diversity through network cod-
ing[C]//Proc. IEEE Wireless Communications and Networking Conference.
.[S.l.]: [s.n.] , 2006:1681–1686.
[51] HAN Z, ZHANG X, POOR H V. Cooperative transmission protocols with
high spectral efficiency and high diversity order using multiuser detection and
network coding[J]. IEEE Transactions on Wireless Communication, 2009,
8(5):2352–2361.
[52] AL-HABIAN G, GHRAYEB A, HASNA M, et al. Threshold-based relaying in
coded cooperative networks[J]. IEEE Transactions on Vehicular Technology,
2011, 60(1):123–135.
[53] NASRI A, SCHOBER R, UYSAL M. Error rate performance of network-coded
cooperative diversity systems[C]//Proc. IEEE Global Telecommunications Con-
ference. .[S.l.]: [s.n.] , 2010:1–6.
[54] IEZZI M, RENZO M D, GRAZIOSI F. Closed-form error probability
of network-coded cooperative wireless networks with channel-aware detec-
tors[C]//Proc. IEEE Global Telecommunications Conference. .[S.l.]: [s.n.] ,
2011:1–6.
— 126 —
[55] ZHU K, BURR A G. Two-way non-coherent Physical-Layer Network Coded
differential distributed space-time block coding[C]//Proc. of IEEE Wireless
Communications and Networking Conference. .[S.l.]: [s.n.] , 2013:2416–2421.
[56] SUGIURA S, CHEN S, HAAS H, et al. Coherent Versus Non-Coherent Decode-
and-Forward Relaying Aided Cooperative Space-Time Shift Keying[J]. IEEE
Transactions on Communications, 2011, 59(6):1707–1719.
[57] POPOVSKI P, YOMO H. Wireless network coding by amplify-and-forward for
bi-directional traffic flows[J]. IEEE Communications Letters, 2007, 11(1):16–
18.
[58] ZHANG S, LIEW S C, LAM P P. Hot topic: physical-layer network cod-
ing[C]//Proc. ACM MobiCom. .[S.l.]: [s.n.] , 2006:358–365.
[59] ZHAO A, HE C, JIANG L G. Outage behavior in wireless networks with ana-
log network coding[J]. IEEE Transactions on Vehicular Technology, 2012,
61(7):3352–3360.
[60] ARGYRIOU A, PANDHARIPANDE A. Cooperative protocol for analog network
coding in distributed wireless networks[J]. IEEE Transaction on Wireless Com-
munications, 2010, 9(10):3112–3119.
[61] SONG L, HONG G, JIAO B, et al. Joint relay selection and analog network cod-
ing using differential modulation in two-way relay channels[J]. IEEE Transac-
tions on Vehicular Technology, 2010, 59(6):2932–2939.
[62] . [D].[S.l.]: ,
2011.
[63] CHEN D Q, AZARIAN K, LANEMAN J N. A case for amplify-forward re-
laying in the block-fading multiple-access channel[J]. IEEE Transactions on
Information Theory, 2008, 54(8):3728–3733.
[64] BADR M, BELFIORE J C. Distributed space time codes for the amplify-
andforward multiple-access relay channel[C]//Proc. IEEE International Sym-
posium on Information Theory. .[S.l.]: [s.n.] , 2008.
— 127 —
[65] JAFAR S A, GOMADAM K S, HUANG C C. Duality and rate optimization
for multiple access and broadcast channels with amplify-and-forward relays[J].
IEEE Transactions on Information Theory, 2007, 53(10):3350–3370.
[66] DING Z G, RATNARAJAH T, LEUNG K K. On the study of network coded AF
transmission protocol for wireless multiple access channels[J]. IEEE Transac-
tions on Wireless Communications, 2009, 8(1):118–123.
[67] JAFAR S A, GOMADAM K S. The effect of noise correlation in amplify-
andforward relay networks[J]. IEEE Transactions on Information Theory, 2009,
55(2):731–745.
[68] BERGER S, WITTNEBEN A. Cooperative distributed multiuser MMSE re-
laying in wireless ad-hoc networks[C]//Proc. Asilomar Conference on Signals,
Systems and Computers. .[S.l.]: [s.n.] , 2005.
[69] GUAN W, LIU K J R. Diversity analysis of analog network coding with multi-
user interferences[J]. IEEE Transactions on Wireless Communications, 2013,
12(2):668–679.
[70] ZHANG S, LIEW S C, ZHOU Q, et al. Non-memoryless analog network cod-
ing in two-way relay channel[C]//Proc. of IEEE International Conference on
Communications. .[S.l.]: [s.n.] , 2011:1–6.
[71] YAO S, SKOGLUND M. Analog network coding mappings in Gaussian
multiple-access relay channels[J]. IEEE Transactions on Communications,
2010, 58(7):1973–1983.
[72] . [D].[S.l.]: ,
2012.
[73] ZHANG S, LIEW S C, LAM P P. Hot topic: Physical layer network cod-
ing[C]//Proc. of the 12th Annual International Conference on Mobile Comput-
ing and Networking. .[S.l.]: [s.n.] , 2006:358–365.
[74] ZHANG S, ZHU Y, LIEW S C. Soft network coding in wireless two-way relay
channels[J]. Journal of Communications and Networks, 2008, 10(4):371–383.
— 128 —
[75] ZHANG S, LIEW S C, LAM P P. On the synchronization of physical layer
network coding[C]//Proc. of Information Theory Workshop. .[S.l.]: [s.n.] ,
2006:404–408.
[76] ZHANG S, LIEW S C. Physical layer network coding with multiple anten-
nas[C]//Proc. of IEEE Wireless Communication and Networking Conference.
.[S.l.]: [s.n.] , 2010:1–6.
[77] .
[D].[S.l.]: , 2012.
[78] ZHANG S, LIEW S C, LU L. Physical layer network coding schemes over finite
and infinite fields[C]//Proc. of IEEE Global Telecommunications Conference.
.[S.l.]: [s.n.] , 2008:1–6.
[79] LU L, WANG T, LIEW S C, et al. Implementation of physical layer network
coding[C]//Proc. of IEEE International Conference on Communications. .[S.l.]:
[s.n.] , 2012:4734–4740.
[80] POPOVSKI P, YOMO H. The Anti-Packets Can Increase the Achievable
Throughput of a Wireless Multi-Hop Network[C]//Proc. IEEE International
Conference on Communication (ICC 2006). .[S.l.]: [s.n.] , 2006 9:3885–
3890.
[81] LI A, YAN Y, KAYAMA H. An enhanced denoise-and-forward relaying scheme
for fading channel with low computational complexity[J]. IEEE Signal Process-
ing Letters, 2008, 15:857–860.
[82] ZHAO Z, PENG M, DING Z, et al. Denoise-and-forward network coding for
two-way relay MIMO systems[J]. IEEE Transactions on Vehicular Technology,
2014, 63(2):775–788.
[83] NAZER B, GASTPAR M. Computing over multiple-access channels with con-
nections to wireless network coding[C]//Proc. of IEEE International Sympo-
sium on Information Theory. .[S.l.]: [s.n.] , 2006.
— 129 —
[84] WILSON M P, NARAYANAN K R, PFISTER H D, et al. Joint physical layer
coding and network coding for bidirectional relaying[J]. IEEE Transactions on
Information Theory, 2010, 56(11):5641–5654.
[85] LIM S H, KIM Y H, GAMAL A E, et al. Noisy network coding[J]. IEEE
Transactions on Information Theory, 2011, 57(5):3132 3152.
[86] AVESTIMEHR A S, DIGGAVI S N, TSE D N C. Wireless network information-
flow: A deterministic approach[J]. IEEE Transactions on Information Theory,
2011, 57(4):1872 1905.
[87] OZGUR A, DIGGAVI S N. Approximately achieving Gaussian relay network
capacity with lattice codes[C]//Proc. of IEEE International Symposium on In-
formation Theory. .[S.l.]: [s.n.] , 2010.
[88] FENG C, SILVA D, KSCHISCHANG F R. An algebraic approach to physical-
layer network coding[J]. IEEE Transaction on Information Theory, 2013.
[89] WEI L, CHEN W. Compute-and-Forward Network Coding Design over Multi-
Source Multi-Relay Channels[J]. IEEE Transactions on Wireless Communica-
tion, 2012, 11(9):3348–3357.
[90] NIESEN U, WHITING P. The degrees of freedom of compute-andforward[J].
IEEE Transactions on Information Theory, 2012, 58(8):5214 5232.
[91] ZHAN J, NAZER B, GASTPAR M, et al. MIMO compute-and-forward[C]//Proc.
of IEEE International Symposium on Information Theory. .[S.l.]: [s.n.] , 2009.
[92] BELFIORE J C, CASTRO M A V. Managing interference through space-time
codes, lattice reduction and network coding[C]//Proc. of IEEE Information The-
ory Workshop. .[S.l.]: [s.n.] , 2010.
[93] HERN B, NARAYANAN K R. Multilevel coding schemes for compute-and-
forward[C]//Proc. of IEEE International Symposium on Information Theory.
.[S.l.]: [s.n.] , 2011.
— 130 —
[94] ORDENTLICH O, ZHAN J, EREZ U, et al. Practical code design for compute-
and-forward[C]//Proc. of IEEE International Symposium on Information The-
ory. .[S.l.]: [s.n.] , 2011.
[95] FENG C, SILVA D, KSCHISCHANG F R. Lattice network coding via sig-
nal codes[C]//Proc. of IEEE International Symposium on Information Theory.
.[S.l.]: [s.n.] , 2011.
[96] BELFIORE J C. Lattice codes for the compute-and-forward protocol: The
flatness factor[C]//Proc. of IEEE Information Theory Workshop. .[S.l.]: [s.n.] ,
2011.
[97] YUNE T W, KIM D, IM G H. Opportunistic network-coded cooperative trans-
mission with demodulate-and-forward protocol in wireless channels[J]. IEEE
Transactions on Communications, 2011, 59(7):1791–1795.
[98] BLETSAS A, KHISTI A, REED D P, et al. A simple cooperative diversity
method based on network path selection[J]. IEEE Journal of Selected Areas
in Communications, 2006, 24(3):659–672.
[99] NGUYEN S L H, GHRAYEB A, AL-HABIAN G, et al. Mitigating error prop-
agation in two-way relay channels with network coding[J]. IEEE Transactions
on Wireless Communication, 2010, 9(11):3380–3390.
[100] PU W, LUO C, LI S, et al. Continuous network coding in wireless relay
networks[C]//Proc. IEEE INFOCOM. .[S.l.]: [s.n.] , 2008:1526–1534.
[101] YANG S, KOETTER R. Network coding over a noisy relay: a belief propagation
approach[C]//Proc. of IEEE International Symposium on Information Theory.
.[S.l.]: [s.n.] , 2007.
[102] WEI S, LI J, CHEN W, et al. Design of Generalized Analog Network Coding
for a Multiple-Access Relay Channel[J]. IEEE Transactions on Communica-
tions (Preprint), 2014.
— 131 —
[103] WEI S, LI J, CHEN W, et al. Wireless adaptive network coding strategy
in multiple-access relay channels[C]//Proc. IEEE International Conference on
Communication (ICC 2012). .[S.l.]: [s.n.] , 2012 9:4589–4594.
[104] MURALIDHARAN V T, RAJAN B S. Physical Layer Network Coding for the K-
User Multiple Access Relay Channel[J]. IEEE Transactions on Wireless Com-
munications, 2013, 12(6):3107–3119.
[105] GUAN W, LIU K J R. Diversity analysis of analog network coding with multi-
user interferences[J]. IEEE Transactions on Wireless Communication, 2013,
12(2):668–679.
[106] SIMON M K, ALOUINI M S. Digital Communication over Fading Chan-
nels[M].[S.l.]: Wiley-IEEE Press, 2004.
[107] ZHAO Q, ZHOU Z, LI J, et al. Joint semi-blind channel estimation and syn-
chronization in two way relay networks[J]. IEEE Transactions on Vehicular
Technology, 2014:1–18.
[108] JIANG B, GAO F, GAO X, et al. Channel estimation and training design for two-
way relay networks with power allocation[J]. IEEE Transactions on Wireless
Communications, 2010, 9(6):2022–2032.
[109] CRAIG J. A new, simple and exact result for calculating the probability of
error for two-dimensional signal constellations[C]//Military Communications
Conference, IEEE. .[S.l.]: [s.n.] , 1991 2:571–575.
[110] BROWN III D R, V. P H. Time-slotted round-trip carrier synchronization for
distributed beam forming[J]. IEEE Transactions on Signal Processing, 2008,
56(11):5630–5643.
[111] BERGER S, WITTNEBEN A. Impact of Noisy Carrier Phase Synchronization
on Linear Amplify-and-Forward Relaying[C]//IEEE Global Communications
Conference (IEEE Globecom 07). .[S.l.]: [s.n.] , 2007.
[112] VERDU S. Multiuser Detection[M].[S.l.]: Cambridge University Press, 1998.
— 132 —
[113] ANGHEL P A, KAVEH M. Exact symbol error probability of a Cooperative
network in a Rayleigh-fading environment[J]. IEEE Transactions on Wireless
Communications, 2004, 3(5):1416–1421.
[114] PENG A Y C, YOUSEFI S, KIM I M. On error analysis and distributed phase
steering for wireless network coding over fading channels[J]. IEEE Transac-
tions on Wireless Communication, 2009, 8(11):5639–5649.
[115] P. S, CHO S H. Probability of an arbitrary wedge-shaped region of the MPSK
system in the presence of quadrature error[J]. IEEE Communications Letters,
2005, 9(3):196–197.
[116] AZARIAN K, EL GAMAL H, SCHNITER P. On the achievable diversity-
multiplexing tradeoff in half-duplex cooperative channels[J]. IEEE TRANS-
ACTION ON INFORMATION THEORY, 2005, 51(12):4152–4172.
[117] WANG Y, QIN L, XIANG W. Generalized analysis on diversity-multiplexing
trade-off of relay protocols[J]. Journal of Applied Mathematics, 2013, 2:511–
517.
[118] R. N. Diversity-multiplexing tradeoff in the low-SNR regime[J]. IEEE Trans-
actions on Information Theory, 2006, 52(9):3965–3979.
[119] LIU Y, DHARMAWANSA P, MCKAY M R, et al. Finite-SNR diversity-
multiplexing trade-off of dual hop multiple-relay channels[J]. IEEE Transac-
tions on Communications, 2012, 60(5):1451–1463.
[120] STAUFFER E, OYMAN O, NARASIMHAN R, et al. Finite-SNR diversity-
multiplexing tradeoffs in fading relay channels[J]. IEEE Journal of Selected
Areas in Communications, 2007, 25(2):245–257.
[121] LOYKA S, LEVIN G. Diversity-multiplexing tradeoff in the low-SNR
regime[J]. IEEE Communications Letters, 2011, 15(5):542–544.
[122] GUAN W, LIU K J R. Mitigating error propagation for wireless network cod-
ing[J]. IEEE Transactions on Wireless Communication, 2012, 11(10):3632–
3643.
— 133 —
[123] NASRI A, SCHOBER R, UYSAL M. Performance and Optimization of
Network-Coded Cooperative Diversity Systems[J]. IEEE Transactions on Com-
munications, 2013, 61(3):1111–1122.
[124] ROUMY A, DECLERCQ D. Characterization and optimization of LDPC codes
for the 2-user Gaussian multiple access channel[J]. EURASIP Journal on Wire-
less Communications and Networking, 2007, 2007:074890.
[125] WORADIT K, QUEK T Q S, SUWANSANTISUK W, et al. Outage behavior of
selective relaying schemes[J]. IEEE Transactions on Wireless Communication,
2009, 8(8):3890–3895.
[126] FARHADI G, BEAULIEU N C. On the Outage and Error Probability of Amplify-
And-Forward Multi-Hop Diversity Transmission Systems[C]//Proc. IEEE Inter-
national Conference on Communication (ICC 2008). .[S.l.]: [s.n.] , 2008:3748–
3754.
[127] IKKI S S, AHMED M H. Performance analysis of adaptive decode-and-forward
cooperative diversity networks with best-relay selection[J]. IEEE Transactions
on Communications, 2010, 58(1):68–72.
[128] WOLDEGEBREAL D H, KARL H. Multiple-Access Relay Channel with
Network Coding and Non-Ideal Source-Relay Channels[C]//Proc. International
Conference on Wireless Communication Systems. .[S.l.]: [s.n.] , 2007:732–
736.
[129] NARASIMHAN R. Individual outage rate regions for fading multiple access
channels[C]//Proc. of IEEE International Symposium on Information Theory.
.[S.l.]: [s.n.] , 2007.
[130] KO Y, ALOUINI M S, SIMON M K. Outage probability of diversity systems
over generalized fading channels[J]. IEEE Transactions on Communications.
[131] SIMON M K, ALOUINI M S. Digital Communication Over Fading Channels: A
Unified Approach to Performance Analysis[M]. New York: Wiley Press, 2000.
— 134 —
[132] SUDEVALAYAM S, KULKARNI P. Energy harvesting sensor nodes: sur-
vey and implications[J]. IEEE Communications Surveys and Tutorials, 2011,
13(3):443–461.
[133] JIANG X, POLASTRE J, CULLER D. Perpetual Environmentally Powered Sen-
sor Networks[C]//Fourth International Symposium on Information Processing
in Sensor Networks. .[S.l.]: [s.n.] , 2005:463 468.
[134] TANEJA J, JEONG J, CULLER D. Design, Modeling, and Capacity Planning
for Micro-solar Power Sensor Networks[C]//Proc. 7th International Conference
on Information Processing in Sensor Networks. .[S.l.]: [s.n.] , 2008:407 418.
[135] RAGHUNATHAN V, KANSAL A, HSU J, et al. Design Considerations for
Solar Energy Harvesting Wireless Embedded Systems[C]//Fourth International
Symposium on Information Processing in Sensor Networks. .[S.l.]: [s.n.] ,
2005:457 462.
[136] PARK C, CHOU P. AmbiMax: Autonomous Energy Harvesting Platform for
Multi-Supply Wireless Sensor Nodes[C]//3rd Annual IEEE Communications
Society on Sensor and Ad Hoc Communications and Networks. .[S.l.]: [s.n.] ,
2006:168 177.
[137] PARADISO J A, FELDMEIER M. A Compact, Wireless, Self-Powered Pushbut-
ton Controller[C]//Proc. 3rd International Conference on Ubiquitous Comput-
ing. .[S.l.]: [s.n.] , 2001:299 304.
[138] KYMISSIS J, KENDALL C, PARADISO J, et al. Parasitic Power Harvesting
in Shoes[C]//Second International Symposium on Wearable Computers. .[S.l.]:
[s.n.] , 1998:132 139.
[139] STARNER T. Human-powered Wearable Computing[J]. IBM Systems Journal.,
1996, 35(3-4):618 629.
— 135 —
1985 7
2003 9 2007 7
2003 9 2007 7
2007 9 2009 7
2007 9 2009 7
ECE
2009 9 2014 12
2014
2014
2012
2011
2006
— 137 —
motivation-modeling-formulation-solution
2007
IEEE
LATEX
— 139 —
2009
SKYPE
A0903491
— 140 —
DC CMU
— 141 —
[1] Sha Wei, Jun Li, Wen Chen, Hang Su, Zihuai Lin, and Branka Vucetic, “Power
Adaptive Network Coding for a Non-orthogonal Multiple-Access Relay Chan-
nel”, IEEE Transactions on Communications, vol. 62, no. 3, pp. 872-887, Mar.
2014.
[2] Sha Wei, Jun Li, Wen Chen, Lizhong Zheng, and Hang Su, “Design of Gener-
alized Analog Network Coding for a Multiple-Access Relay Channel”, accepted
by IEEE Transactions on Communications, 2014.
[3] Sha Wei, Jun Li, and Wen Chen, “Network Coded Power Adaptation Scheme in
Non-orthogonal Multiple-Access Relay Channels” , IEEE International Confer-
ence on Communications (ICC), 2014.
[4] Sha Wei, Jun Li, Wen Chen, and Hang Su, “Wireless Adaptive Network Coding
Strategy in Multiple-Access Relay Channels.” IEEE International Conference on
Communications (ICC), 2012, pp.751-755.
[5] Sha Wei, Jun Li, and Hang Su, “Joint Orthogonal Coding and Modulation
Scheme for Soft Information in Bi-Directional Networks,” Wireless Communi-
cations, Networking and Mobile Computing (WiCOM), 7th International Con-
ference on , 2011, pp.1-4.
[6] (Best Paper Award.) Hang Su, Hua Yang, Shibao Zheng, Yawen Fan, and Sha
Wei, “Crowd Event Perception Based On Spatio-Temporal Viscous Fluid Field”,
International Conference on Advanced Video and Signal Based Surveillance
(AVSS), 2012, pp. 458-463.
— 143 —
![Vale of York MSA inquiry - Parameters plan€¦ · PARAMETERS PLAN : dKd > î ô ì ñ î ï ô ñ ñ í ì ñ î ó ô ñ ò î í ñ ï õ ò ñ: EKd W D µ u v } v K o À o ] v](https://img.pdfslide.tips/doc/110x75/5f913500bbb9f875b742ba9a/vale-of-york-msa-inquiry-parameters-plan-parameters-plan-dkd-.jpg)
![DESEMPENHO DO FRANCHISING 2017 - abf.com.br · ^d '/k^ /ed ze /ke >/ k ò ô 9 í õ 9 í ï 9 p ] } î p ] } ï p ] } ð ... z ^ ^dz e' /z ^ ek z ^/> î 9 ï 9 ñ 9 ñ 9 ñ 9 ò](https://img.pdfslide.tips/doc/110x75/5ba2a4ee09d3f2d14d8c57d1/desempenho-do-franchising-2017-abfcombr-d-k-ed-ze-ke-k-o-o-9.jpg)
![%ODGHQOLMVW · 0djd]lqhv /dqgholmnh 'djeodghq 2sodjh ] i o p } l i ñ í ñ x ô ï ï d p Ì ] v ñ í ñ x ô ï ï](https://img.pdfslide.tips/doc/110x75/5fbaecf701089f5228391c4f/odghqolmvw-0djdlqhv-dqgholmnh-djeodghq-2sodjh-i-o-p-l-i-x-.jpg)
![=s o µ K } µ v ] Ç } v } U K } v } K 8 l Z ] v o - LoopNet · 2019. 11. 27. · WZKW Zdz W,KdK^ í î ï K 8 ] Ç U ^ ] Á Á Á X Á ] X } u P v E u d ] o ñ ñ ñ X ñ ñ ñ](https://img.pdfslide.tips/doc/110x75/608ffc6030237f487a0f4e5f/s-o-k-v-v-u-k-v-k-8-l-z-v-o-loopnet-2019-11-27-wzkw.jpg)