Chapter 9. Multiple Access Techniques for Wireless Communications

Multiple Access (MA) 多“址”？够形象 多“接入”？涵义更广泛。

Why Multiple Access? Radio propagation-compare with conventional wire

communication. For multi-user AND multi-link communication

Broadcast – multiuser but it is not a MA

MA schemes are used to allow many users to share simultaneously a mount of radio spectrum.

MA must be done without severe degradation in the performance.(Capacity, BER, delay )

1

The three major conventional multiple access techniques are: FDMA, TDMA and CDMA.

Some recently used MA techniques are: SDMA, IDMA

Some random access techniques sometimes are also classified into Multiple Access Techniques. Packet radio (PR).

How to choose MA schemes ? –MA detail

2

9.1 Introduction Duplexing: allow the user to send simultaneously

information to BS and receive information from BS. Simplex system Semiduplexing

Frequency division duplexing (FDD): two distinct bands of frequencies for every user.

Time division duplexing (TDD): it uses time instead of frequency to provide both a forward and reverse link.

The forward link ：BS → mobile The reverse link: mobile→BS

3

In FDD, the frequency separation between forward and reverse channel is constant -- adjacent channel

The time separation between the forward and reverse time slot is small, then the transmission and reception of data appears simultaneous.

反向信道 前向信道频率

频率分隔

反向信道 前向信道时间

时间分隔

4

Tradeoffs between FDD and TDD:

FDD frequency allocation must be carefully

coordinated TDD No need for separate forward and reverse

frequency bands. time latency, --limited to short range access.

Some users are sensitive to propagation delays. Uplink overlap with downlink. 5

Narrowband Systems— bandwidth of a signal compared with the expected

coherence bandwidth of the channel. Wideband systems—

The transmission bandwidth of a signal is much larger than the coherence bandwidth of the channel.

6

Narrowband FDMA/FDD: radio spectrum is divided into narrowband channels. The channels are operated using FDD. A user is assigned a channel which is not shared by other users. AMPS narrowband TDMA/FDD or TDMA/TDD: radio channels allocated using FDD/TDD, and

each channel is shared using TDMA. GSM

7

不同无线通信系统中的多址技术

蜂窝移动通信系统 多址技术/双工方式

高级移动电话系统（AMPS） FDMA/FDD

全球移动通信系统GSM TDMA/FDD

美国数字蜂窝 USDC TDMA/FDD

日本数字蜂窝 PDC TDMA/FDD

CT2 无绳电话 FDMA/TDD

欧洲数字无绳电话(DECT) FDMA/TDD

美国窄带扩频 IS-95 CDMA/FDD

8

9.2 Frequency Division Multiple Access（FDMA）

Features to transmit simultaneously and continuously originally used in narrowband system the complexity is lower, need no equalization. however the cell site system costs are higher

(duplexers, costly bandpass filters, tight RF filtering). Many channels share the same antenna at BS at

the same time and maybe generates IM frequencies.

9

1 2mf nf+

信道1

频率

时间

代码

信道2

信道3

信道N

10

Capacity of FDMA

20

log (1 )PC WWN

= +

11

香农定理： FDMA情况下，每用户容量： 当 时，总容量不变 当 ，N个FDMA用户容量将随之用户数量上升。

( )20

20

log (1 )

log (1 )

useruser

userFDMA user

PWCN W N N

N PC N C WW N

= ⋅ +

⋅= ⋅ = ⋅ +

⋅

userP P N= FDMAC C=

userP P=

9.3 Time Division Multiple（TDMA） To transmit data in a buffer-and-burst

method,(Digital process), duplexers are not required (BS side) different users share bandwidth MAHO, idle slots can be used for monitoring TDMA have synchronization overhead. Users share a single carrier frequency with

non-overlapping time slots. Adaptive equalization is necessary(Why?) The number of time slots per frame depends

on modulation technique, available bandwidth, etc.

12

频率

代码

时隙

信道1信道2

信道3

信道N

时间 一个TDMA帧

头比特 信息 尾比特

时隙1 时隙2 时隙3 - - - - - 时隙N

尾比特 同步比特 信息数据 保护比特

13

Efficiency of TDMA：it is a percentage measure of payload to total transmitted data

( )1 100

OH r r t p t g r g

r t

r p

g

T f

f

f OH T

b N b N b N b N b

N Nb b

b

b T R

T R

b bη

= + + +

=

= − ×

每一帧的系统开销数：

：每一帧参考突发数，：每一帧业务突发数

：每一参考突发的比特数量，：每一时隙中每个头比特的开销

：每一保护时间间隔的等效比特数

每一帧总比特数为：

：帧长，：信息比特率

帧效率：％

14

一个TDMA帧

头比特 信息 尾比特

时隙1 时隙2 时隙3 - - - - - 时隙N

尾比特 同步比特 信息数据 保护比特

Number of channels in TDMA system：Multiplying the number of TDMA slots per channel by the number of channels available.

Example 9.3. A TDMA/FDD GSM system that uses 25MHz for the forward link,which is broken into radio channels of 200kHz. If 8 speech channels are supported on a single radio channel, and no guard band is assumed. Find the number of simultaneous users that can be accommodated in GSM.

( )2

:

tot

c

m B BN

Bm

−= 保护

每一个信道所能支持的最大TDMA用户数，

25 1000200 / 8

MHzNkHz

= =

15

Example9.4. If GSM uses a frame structure where each frame consists of 8 slots, and each time slot contains 156.25bits, and data is transmitted at 270.833kbps in the channel, find (1) the time duration of a bit, (2) the time duration of a slot, (3) the time duration of a frame, and (4) how long must a user occupying a single time slot wait between two successive transmissions.

1 1(1) 3.692270.833 /

(2) 156.25 0.577(3) 8 4.615

4.615

bb

slot b

f slot

T sR kbit s

T T msT T ms

ms

µ= = =

= == =

(4)用户必须等待 ，在一个新帧到来之后

才可以进行下一次发射。

16

Example9.5. If a normal GSM time slot consists of 6 training bits, 8.25 guard bits, 26 training bits, and two traffic bursts of 58 bits of data, find the frame efficiency.

6 8.25 26 2 58 156.258 156.25 1250

8 (6 8.25 26) 3223221 100 74.24%

1250

OH

f

b

P

+ + × =

× =

= × + =

= − × =

一个时隙有 ＋ 比特

一个帧有 比特

每帧的系统开销 ＋ 比特

帧效率

17

Capacity of TDMA

20

log (1 )PC WWN

= +

18

香农定理： TDMA情况下： 如果 ，那么 可见同等功率条件下，TDMA容量不变，每个用户的传输能

力有所下降，是因为所分得的时间缩短为1/N。如果一个时隙要达到所有时隙的吞吐量，那么

20

log (1 ) /useruser

PC W bitW N

= +⋅

秒

userP P= userC C=

,userC N C= 即

2 20 0

log (1 ) log (1 )

,

user

user

PP WWW N N W N

P P

+ = +⋅ ⋅

> 即增加功率，而如果调制等传输方式等不变，

那就只能通过增加带宽来增加容量

9.4 Spread Spectrum Multiple Access（SSMA）

It converts a narrowband signal to a wideband noise-like signal before transmission. （low power spectrum density, sicurity）

There are two main types of SSMA : FHMA DS-CDMA (it is also called CDMA).

19

9.4.1 Frequency Hopped Multiple Access（FHMA） The carrier frequencies vary in a pseudorandom fashion

within a wideband channel. Fast FH : hop rate > symbol rate Slow FH: hop rate< symbol rate FHMA Vs. FDMA:

At any point in time, a FH & FDMA signal only occupied a single, relative narrow channel.

FH signal changes channels at rapid intervals, while FDMA use a fixed bandwidth.

A fast FH may be thought of as an FDMA system which employs frequency diversity.

FHMA :constant envelope modulation. A FH system provides a level of security. Bluetooth

20

9.4.2 Direct Sequence spread spectrum ——Code Division Multiple Access （CDMA）

时间

信道1信道2信道3

信道N

频率

码

21

Transmitter performs PN codes modulation.

Receiver performs a time correlation operation to detect only the specific desired codeword.

All user use the same carrier frequency and may transmit simultaneously.

The features of CDMA including： Multipath fading may be reduced:

Chip length < delay spread RAKE receiver can be used. Frequency diversity(bandwidth>coherent bandwidth)

Since CDMA uses co-channel cells, it can use macroscopic spatial diversity to provide soft handoff.

Self-jamming and near-far problems exist in CDMA systems.

Power control is used in most CDMA implementations to combat near-far problem .

22

Capacity of CDMA： Capacity of a single CDMA user(according to

DS/SS principle)

N user total capacity

If ，then ，but ，So

23

20

log (1 ) ( )

useruser

PWCN W N N I

= +⋅ +

20

log (1 ) userCDMA user

N PC N C WW N NI

⋅= ⋅ = +

⋅ +

CDMAC C= 0I ≠

20

log (1 ) CDMAPC C W

W N< = +

⋅

0, userI P P N= =

Unlike TDMA or FDMA，CDMA has a soft capacity limit.

Use and

If , spectrum efficiency upper bound Else capacity is limited

24

20

2

0

2

0

log (1 ) ( ) ( 1)

log (1 )( 1)

ln( 1)

useruser

user

user user b

b user

user b

b user

PWCN W N N N P

NC NC ENW W N N E CW

NC E eNW N N E CW

σ

σ

σ

= +⋅ + −

= ++ −

≤ ⋅ ⋅+ −

02

202 2

( 1) ln

ln(ln ) ( 1) ln( 1)

b

b

N C N eE W

eC Ne N N eEW N

σ

σσ

+ ⋅ − ≤

≤ − − ≤ →∞−

0σ = →∞

ln(1 )x x+ ≤

1 Nσ ≈

9.4.3 Hybrid Spread Spectrum Techniques（HSS）

9.4.3.1 Hybrid FDMA/ CDMA（FCDMA） processing gain lower than original CDMA. Advantage is that the required bandwidth

need not be continuous. The capacity is the sum of the sub-spectra. TD-SCDMA multi-carrier CDMA2000 3x

宽带CDMA

窄带CDMA的频谱25

9.4.3.2 Hybrid DS/ FHMA DS-modulated signal whose center

frequency is made to hop periodically in a pseudorandom fashion.

Advantage is that they avoid the near-far effect.

However they are not adaptable to the soft handoff process.

信道中的码组传递 其他码组的可选信道

26

9.4.3.3 Time Division CDMA（TCDMA） Different spreading codes are assigned

to different cells. Within each cell, only one user is

allocated a particular time slot. When a handoff take place, the users’

spreading code is changed to that of the new cell.

It avoids the near-far effect.

27

9.4.3.4 Time Division Frequency Hopping（TDFH）

The subscriber can hop to a new frequency at the start of a new TDMA frame, thus avoiding a severe fade or erasure event on a particular channel.

This scheme also avoids CCI problems if two interfering BS transmitters are made to transmit on different frequencies at different times.

It can increase the capacity of GSM by several fold.（SLOW FH）

28

9.5 Space Division Multiple Access（SDMA）

SDMA controls the radiated energy for each user in space.

Sectorized antennas may be thought of as a primitive application of SDMA.

Adaptive antennas is used to simultaneously steer energy in the direction of many users at once and appear to be best suited for TDMA and CDMA BS architecture.

Increase the capacity (vs. TDMA, FDMA, CDMA)

29

9.5 Space Division Multiple Access（SDMA）

利用空间分割来区别不同的用户就称为空分复用。 如果利用空间分割来传送同一用户的相同数据，就称为分集传输。

容量

30

sy E Hs N= +

2 2( ) logr

HM

t

PC H I HHM σ

= + ⋅

31

9.6 Packet Radio（PR） Many users attempt to access a single channel in

an uncoordinated manner. PR MA is very easy to implement, but has low

spectral efficiency and induce delays. The users use a contention technique to transmit

on a common channel. Advantage: ability to serve a large number of

users with virtually no overhead. The performance can be evaluated by the

throughput(T) and the average delay(D). T is defined as the average number of messages

successfully transmitted per unit time.

32

9.6.1 Packet Radio Protocol To determine the throughput, it is

important to determine the vulnerable period Vp.

Vp is defined as the time interval during which the packets are susceptible to collision.

33

分组B 分组C

分组A

发射机1

发射机2

易损阶段 τ2时间

τ21 +t

一个分组时间τ

1t

Vp for a packet using ALOHA protocol

,

, Erlangs

Pr[ ] Pr[ ]

Pr( )!

n R

Poisson

R R

T R

PoissonR en

n

λ τ

λτ

λτ

−

=

= =

=

假设分组到达服从 分布，到达 率为 ， 是发射分组

所需要的时间 那么分组无线电的传输量或吞吐量为：

是归一化的信道业务量，单位：

规一化吞吐量为：

无碰撞 无碰撞

假设在一给定分组时间间隔内，用户产生n个分组的概率

为 分布，则

如果在一给定分组时间间隔内没有其它分组发射，那么

就假设这个分组发射成功，在这

Pr[ ] Pr[0] = -Re=

期间无碰撞的概率为：

无碰撞

34

9.6.1.1 Pure ALOHA It is a random access protocol used for data

transfer. The vulnerable period is double the packet

duration, The throughput is as follows:

9.6.1.2 Slotted ALOHA Time is divided into equal time slots of

length greater than the packet duration. Transmit a message only at the beginning

of a new time slot, avoids partial collisions. A greater delay will occur, the throughput

is T=Re-R.

( ) 222

Pr( ) ,at n=0, Re!

n RRR e

n Tn

−−= =

35

36

进入信

道业务量

9.6.2 Carrier Sense Multiple Access(CSMA) Protocols

By listening to channel before transmission, greater efficiencies may be achieved.

detection delay and propagation delay (cause conflict) are important parameters.

There exist several variations of the CSMA： 1-persistent CSMA：as soon as the channel

is idle, the terminal transmits its message with probability 1.

p- persistent CSMA: When a channel is idle, the packet is transmitted with probability p or in the next slot with 1-p. (for slotted channel)

37 ( )22 1 1p p+ − <

non- persistent CSMA: after receiving a NACK the terminal waits a random time before transmission of the packet.(WLAN)

CSMA/CD：a user monitors its transmission for collisions. If collision is detected, the transmission is

immediately aborted in midstream. User’s transmitter and receiver should support

l isten-while-talk operation. Or, for a single channel, by interrupting the

transmission to sense the channel. For duplex systems, a full duplex transceiver is

used.

38

Data sense multiple access (DSMA)：with a center to broadcast busy-idle message. Receiver broadcas data back on a reverse channel after successfully demodulating a forward control channel.

Each user attempts to detect a busy-idle message which interspread on the forward control channel.

If no users are transmitting on the reverse channel, a user is free to send a packet.

It is used in the CDPD cellular network.

39

40

归一化的进入信道业务量

9.6.3 Reservation Protocols 9.6.3.1 Reservation ALOHA A packet access scheme based on TDMA Certain packet slots are assigned with

priority, and it is possible for users to reserve slots for the transmission.

For high traffic conditions, it offers better throughput.

41

9.6.3.2 Packet Reservation Multiple Access（PRMA〕

PRMA uses a discrete packet time techniques similar to reservation ALOHA.

It combines the cyclical frame structure of TDMA in a manner that allows each TDMA time slot to carry either voice or data, where voice is given priority.

PRMA was proposed as a means of integrating bursty data and speech.

PRMA defines a frame structure, there are a fixed number of time slots designed as either “reserved” or “available”.

42

9.6.4 Capture Effect in Packet Radio PR techniques are based on contention. When used with FM or SS modulation, it is

possible for the strongest user to capture the intended receiver.

It offers both advantages and disadvantages. Many packets may survive despite collision. Hidden transmitter—strong transmitter may

make it impossible for the receiver to detect. A useful parameter--Capture ratio: the

minimum power ratio of an arriving packet, relative to other colliding packets.

43

通信类型 多址技术

分组、短消息 竞争协议

分组、长信息。大量用户 预留协议

分组、长信息、少量用户 固定 TDMA 预留信道和预留协议

数据流或确定的语音 FDMA、TDMA、CDMA

PR techniques support mobile transmitters sending bursty traffic in the form of data packets using random access. The MA techniques which should be used for different types of traffic conditions：

44

9.7 Capacity of Cellular Systems Channel capacity:

Maximum number of channels or users that can be provided in a fixed bandwidth. (CS)

Maximum bandwidth that can be provided.(PS) It is a parameter which measures

spectrum efficiency of a wireless system. It is determined by the required C/I and

the Bc.

45

Forward channel interference: at a MS receiver, it will come from the surrounding co-channel BS. D: the distance between two

co-channel cells, R: the cell radius. Q=D/R: co-channel reuse ratio.

46

Reverse channel interference: at a BS receiver, it will come from the subscriber units in the surrounding cells.

The radio capacity of a cellular system is defined as：

m=Bt/BcN (channels/cell) Bt: the total allocated

spectrum, Bc: channel bandwidth,

47

5

1

15

6 4

1416

2

3

12

13

29

30

31

32

7

18

17

33

9

10

1119

8

27

36

35

34 28

20

37

21

22

23

24

25

26

42

43

44

4547

46

49

48

38

39

40

41

When the above cellular structure is used,

Assuming maximum interference occurs when the mobile is at the cell edge d0=R.

(C/I)min is the minimum C/I for providing acceptable quality at receiver.

由前章所述

00

0 0

1

k

n

Mn

kk

dC n dI d

M

−

−

=

=

∑， 是服务小区中路径损耗指数， 是服务基站

到移动台的距离，最邻近的同信道小区个数为

--

min

2 2

2min

1 1 1

3 3

nnn

n

t t tn

cc c n

C R RI MD M D M Q

B B BmQB N M CB B

I

−

−

=

= = =

= =，则蜂窝系统容量为:

无线信道/小区

NQ 3=

48

( ) ( )( )

( )( )

2'

'min

min

2'

,

/ / /

4 /

t

cc c

eq c

eq

eq

c

ceq

B m

BC C B BI I B

C I C I C I

n C I

C I BC I B

=

如果和固定，则

=是特定系统的带宽，是不同系统的带宽

是相对于特定系统的不同系统的最小。

，对应于不同系统的，有：

＝

49

前向信道C/I由路损和拓扑结构决定。 例如：C/I上升，意味着接收性能变差，导致Q变大，那么只

有缩小单用户带宽，方可保证可支持的用户数不变。 窄带数字系统相对于窄带模拟系统，最小C/I下降，带来容

量增大。例如：The (C/I)min is abut 12dB for narrowband digital systems and 18dB for analog FM.

对于数据业务，无线容量可从单小区的带宽来衡量。

Example 9.7. Evaluate four different cellular radio standards, and choose the one with maximum capacity. n=4.

min

min

min

min

: 30 , ( / ) 18: 25 , ( / ) 14: 12.5 , ( / ) 2: 6.25 , ( / ) 9

c

c

c

c

systemA B kHz C I dBsystem B kHz C I dBsystemC B kHz C I dBsystem B kHz C I dB

= == == == =

B

D

( )( )( )

2

'min

'

'

'

'

6.25 ,

: 30 , ( / ) 18 20log 6.25 / 30 31.68

: 25 , ( / ) 14 20log 6.25 / 25 26

: 12.5 , ( / ) 2 20log 6.25 /12.5 8

: 6.25 ,

c

eq c

c eq

c eq

c eq

c

BC CkHzI I B

A B kHz C I dB

B kHz C I dB

B kHz C I dB

B kHz

= = − =

= = − =

= = − =

=

解：考虑系统带宽为=，则

系统

系统B

系统C

系统D ( )( / ) 9 20log 6.25 / 6.25 9eqC I dB

C

= + =

系统提供最大容量。50

In a digital cellular system, C/I can be expressed as:

In FDMA,C=EbRb，I=I0(Bt/M),when n=4,

In TDMA, C ’=EbR ’b，I ’=I0B ’

c， I 0 Represents the interference power/ Hz. 信号功率大M倍，干扰也大M倍。 事实上，载干比与信号功率没关系。 FDMA与TDMA容量相等。

b bb b

E RC E RI I= ， 每比特能量， 数据速率

min

23

t

t

BmB CM I

=

，无线信道/小区

51

Example 9.8. FDMA系统，三个信道，每个带宽10k、速率10k。TDMA系统，三个时隙，带宽30k，速率总共30kbps。两者载干比为：

说明两者相同的频谱效率 TDMA的峰值功率是FDMA单用户的峰值功率的3倍，但与

FDMA的总得峰值功率相等。

IkIBII

CERs

EREC

c

bbb

bb

330

331

103

0'

0'

4''

=⋅==

==⋅⋅

==

52

AMPS 和基于数字 TDMA 的蜂窝系统的比较 参数 AMPS GSM USDC PDC

带宽（MHz） 25 25 25 25 语音信道 833 1000 2500 3000 频率复用（簇大小） 7 4 或 3 7 或 4 4 或 3 信道/站址 119 250 或 333 357 或 625 429 或 750 通信量（爱尔兰/平方

公里） 11.9 27.7 或 40 41 或 74.8 50 或 90.8

容量增益 1.0 2.3 或 3.4 3.5 或 6.3 4.2 或 7.6

53

9.7.1 Capacity of Cellular CDMA CDMA is interference limited, while FDMA

and TDMA is bandwidth limited. Any interference reduction will cause a

directly increase in the capacity of CDMA. The link performance increases as the

number of users decreases. TDMA and FDMA reuse frequencies

depending on the isolation between cells, CDMA can reuse the entire spectrum for all cells.

For a single cell CDMA system: 1

( 1) 1PSNR

K P K= =

− −54

The SNR at the BS receiver:

这里的 是噪声干扰功率谱密度 The number of users that can access the

system is thus given as： When the number of users is large and

the system is interference limited rather than noise limited,

[ ]0

0

, 1( 1) ( 1)

b

b

W WPE R R RKN PEK P K P NW

ηηη

= = = + −− + − +

−+= PNE

RWKb

η0

1

'0

11sb

WR WK REN

αα

= +

， 是语音激活因子， 是处理增益

55

0N

9.7.2 Capacity of CDMA with Multiple Cells The amount of out-of-cell interference

determines the frequency reuse factor, f. FDMA/FDD systems, f=1/7. The f for a CDMA system on the reverse

link can be defined as：

0

0

0

,i ai

i

i

ai

NfN U N

NU iN i

=+∑

小区内用户的干扰，

第 个相邻小区的用户数，

第 个相邻小区内用户产生的平均干扰功率

56

Each adjacent cell may have a different number of users, and each out-of-cell user will offer a different level of interference depending on its exact transmitted power and location.

The variance of Nai can be computed using standard statistical techniques.

Concentric circle cellular geometry: Uses a recursive geometric technique to

determine how the propagation path loss impacts the frequency reuse of a CDMA system by considering the interference from both in-cell and out-of-cell users.

57

1θ

02d

3R

Adjacent

cell

02 dR +

02 dR −

Rdesiredcell

58

The area of the center cell of interest is ：

The area of the first surrounding layer of cells is A1. Each cell in the 1st surrounding layer have the same area A. there should be M1wedge-shaped cells.

The area of the ith surrounding layer is related to the number of cells within the layer by:

2 2 20A R d Rπ π π= − ≈

( )2 21 1

1 1

32

A R R M AM

π πθ π

= − =

=

1 1,i iA iM A iθ θ= =59

It is possible to consider the interference effects of just a single cell within the surrounding layer.

One can simply multiply the effects of a single cell by the number of cells within the surrounding layer. Since each cell contains the same area as the

center cell. Since each adjacent cell has the same

geometry and angular span as any other cell within the surrounding layer.

Since each cell within a particular layer has the same radial geometry to the center cell of interest.

60

It is often useful to consider the adjacent cell interference effects for various distributions of users within the interfering cells.

This allows one to determine worst case frequency reuse .

61

The interference layers to be broken into two sub-layers.

If K is the user density,

The particular geometry does not dramatically impact capacity predictions（users and the coverage area）.

( )( )( ) ( )( )

2 21 1 1 1

2 21 1 1 1

2 3

3 2 5

in

out

A M R R M A M

A M R R M A M

π π

π π

= − =

= − =

( ) ( )1 1 1 1 1 1

1 1

1 1

1 18 3 0

in in out out

in out

in out

U KA Kw A M Kw A Mw ww w

= = +

= =

= =

若 ， ，3/8内用户，5/8外用户,频率复用上限

若 ， ，全部为内用户，最坏情况

62

R

3R

外部区内部区

2/1θθ =

02 dR +

02 dR −

0dd ′

d

d

d ′

0=θ

2/1θθ −=

Using concentric circle geometry to find CDMA capacity

63

the in-cell interference power is simply given by：

In the adjacent cells, each subscriber is under PC within its own cell, and is a distance d’ from its own BS

The center cell from the jth user in the ith interfering cell can be given by：

( ) ( ) ( )

( ) ( ) ( )

2' 2 20 0

2' 2 20 0

sin 2 cos , 2 1 2

sin cos 2 , 2 2 1

i

i

d d R d d i R d i R d

d d d R d i R d d i R

θ θ

θ θ

= + − − − ≤ ≤ −

= + − − + ≤ ≤ −

( )0 0 01N P U P KA= − ≈

( ) ( ) ( ),

'0, , 0 , 0 0 0, , ,

i jn n ji j i j ai

i

NP r d N P d d d d N Uθ = = =

∑

0

0

,i ai

i

NfN U N

=+∑

64

f depending on the path loss exponent n and the distribution of users, while a single cell CDMA system offers ideal frequency reuse f=1.

65

d(km) n

频率复用效率

下限w1=3.0w2=0.0

六角形w1=1.38w2=0.78

上限w1=1.0w2=1.0

2

2

2

10

10

10

2

3

4

2

3

4

0.316

0.408

0.479

0.308

0.396

0.462

0.425

0.558

0.646

0.419

0.550

0.634

0.462

0.613

0.707

0.455

0.603

0.695

两种CDMA蜂窝系统反向信道的频率复用因子

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9.7.3 Capacity of SDMA For a single cell CDMA in AWGN, with perfect

PC and with omni-directional antennas used at BS,

Directive antennas can improve the reverse link in a single-cell CDMA systems.

The impact of multipath on SDMA is a topic of research.

3 , : number of users, N:spread factor1b

NP Q KK

= −

3 , : directivity of the antenna,3-10dB1b

DNP Q DK

= −

67

68

D=5.1dB, Pb=0.001, n=4, the flat top beam system will support 350 users, whereas, the omni-directional antenna will support only 100 users.

69