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Eindhoven University of TechnologyFaculty of Electrical EngineeringDivision of Telecommunication Technology and ElectromagneticsRadiocommunications Group

Performance of QPSK OFDM withand without channel/frequencyoffset estimation and equalization,and study of the interferencecause by RF Impairments.

By Andre M. J. Miranda.

Final Project - ERASMUS PROGRAMCarried out from March till July 2003Supervisors:Dr. ir. P.F.M. Smulders (TU/e)Graduation Professors:Dr. ir. P.F.M. Smulders (TU/e)Dr. Antonio Navarro (UA)Dr. Rui Luis Andrade Aguiar (UA)

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AcknowledgmentsThese last few months were a good experience through which I improved myknowledge, and I sincerely must thank all the people that made it possible. Specially, Iwould like to thank my project supervisor Dr. ir. P.F.M. Smulders, for generating a goodwork environment, for all the support given, and for receiving me as an Erasmusstudent. Also, I would like to express my gratitude for all the help and time disposed bymy Erasmus coordinators Dr. Antonio Navarro and Dr. Rui LUIs Andrade Aguiar.

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IndexO. Abstract....... 31. Introduction................................................................................................................ 4

1.1 OFDM - Basic scheme........ 41.2 Problems and possible solutions to them..... 51.3 RF impairments. 61.4 Channel............................................................................................................... 61.5 Channel estimation............... 71.6 Frequency offset estimation................................................................................. 8

2. Simulation 102.1 Characteristics of the transmitted signal. 102.2 Observation of the performance of the system without any type of estimation

and equalization 112.3 Implementation of channel estimation and equalization 122.4 Implementation of frequency offset estimation and equalization 142.5 RF impairments 162.5.1 IQ imbalance 162.5.2 Phase noise 182.5.3 Power amplifier non-linearities 192.6 Packet detection 203. Conclusions 224. Recommendations for future work 225. References 23Appendix 24

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Abstract

The OFDM modulation has been gaining interest and many practical uses in the lastyears. The responsible for this, is its great immunity to the interference of multipath andfading on the transmitted signal, and its spectral efficiency.In this report, a study on the vulnerabilities of an OFDM system to the channel andfrequency offset has been performed in the form of an implementation in MatLab.Solutions are proposed to make it more robust.The interference caused by RF impairments was analyzed and its substantialinfluence in the performance of the system was demonstrated, leading to theconclusion that good solutions have to be found and implemented.

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1. IntroductionWithin the radio communications discipline a great evolution is taking place currentlyalong with the demand of new services and integration of existing ones, increasing theneed for greater bandwidth and quality of service than what is available today to themobile user. Because when transmitting at higher data rate more bandwidth and moreaccurate hardware components are needed, this problem is not solved easily.A great obstacle to implement a high data rate WLAN is the phenomenon multipaththat, in conjunction with others interferences, degrade the performance of thecommunications systems by provoking frequency selective fading, Inter-CarrierInterference and Inter-Symbol Interference.In most systems an equalizer is used in the receiver to minimize the interferences ofthe channel in the signal. An obvious candidate that eliminates a need for complexequalizers or sector antennas is the Orthogonal Frequency Division Multiplexing(OFDM).OFDM is as a form of multicarrier modulation where its carrier spacing is carefullyselected (equal to the reciprocal of the useful symbol period) so that each subcarrier is

orthogonal to the subcarriers next to them. Doing so the sidebands of the individualcarriers can overlap and the signal still be received without adjacent carrierinterference. This approach improves the spectral efficiency, because the samenumber of subcarriers now occupies less bandwidth.

Figure 1 - OFDM spectrum.However, if the application is for mobile reception, the subcarrier spacing must be

large enough to make the Doppler shift negligible. If the intercarrier spacing 1/NT ischosen to be larger than the maximum Doppler frequency, the system will be relativelyinsensitive to the Doppler spread and the corresponding ICI.Having gained increasing interest, the OFDM is being used in Digital AudioBroadcasting (DAB), Digital Video Broadcasting-terrestrial (DVB-T), ADSL and 802.11astandards. It is also being investigated for high-speed wireless applications, as well asfor broadband digital communication on existing copper networks. One promisingfuture application is the use in 60 GHz high speed WLANs interconnected by fiberoptic.

1.1 OFDM - Basic schemeThe data to be transmitted, is first converted from serial to parallel and coded by aconvolutional encoder, which shall use the industry-standard generator polynomialsgo=1388 and g1=178 8 of rate 0=1/2.

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Increasing the number of parallel transmission channels reduces the data rate ofeach subcarrier, and that lengthens the symbol period leading to flat fading instead offrequency-selective fading. With flat fading channel equalization is very simple.The distribution of the data over many carriers means that fading will cause somebits to be received in error while others received correctly. By using an error-correctingcode, which adds extra bits at the transmitter, it is possible to correct many or all of thebits that were incorrectly received.Higher data rates can be achieved by employing "puncturing". This consists onomitting some off the encoded bits, reducing thus the number of transmitted bits andincreasing the coding rate (in the receiver side, a dummy "zero" metric is inserted inplace of the omitted bits before de Viterbi decoder, which corrects the errors).After "puncturing", data is grouped into x bits, each to form a complex number inresult of a specific modulation (into 2 bits and modulated by QPSK, in mostly all thisstudy). The modulation to be used in the OFDM system can be found analyzing thepower or spectrum efficiency required.Since this corresponds to the transmission of a large number of narrowbandcarriers, to avoid equal large number of modulators and filters at the transmitter, andcomplementary filters and demodulators at the receiver, it is desirable to use theInverse Fast Fourier Transform (IFFT) and Fast Fourier Transform (FFT), respectively.If the orthogonality of subchannels are maintained the individual subchannels can becompletely separated by the FFT at the receiver.Then, complex numbers are modulated in the baseband by the Inverse FFT (IFFT)and converted back to serial data for transmission.Next, a guard interval is inserted between symbols to avoid intersymbol interference(lSI), caused by multipath distortion, and this is true when the guard interval is longerthan the channel impulse response. This guard interval consists in an extension of thesignal itself, more precisely in a copy of the end of the symbol, and is usually calledcyclic prefix. The use of a cyclic prefix in the transmitted signal has the disadvantage ofrequiring more transmit energy.The discrete symbols are then converted to analog and low-pass filtered for RFupconversion. This step will not be done, since has no practical importance in thisstudy. All the impairments related with this step will be implemented with basebandmodels.The receiver performs the reciprocal process of the transmitter.

1.2 Problems and possible solutionsKnowing that the backbone of the OFDM is the orthogonality of the subcarriers,errors will occur when that property is lost. Several situations can occur that will disruptthe orthogonality:

Symbol time offset;Carrier frequency offset;Sampling frequency offset;Too much multipath (multipath component exceeding good time)As regards the later, the cyclic prefix is used to maintain orthogonality in a dispersivechannel, but symbol time, carrier frequency and sampling frequency offsets may induce

the loss of subcarrier orthogonality. The sensitivity to this offsets is due to the smallsubcarrier spacing. Unless compensated, they can limit the performance of an OFDMsystem because they cause inter-symbol interference (lSI) and inter-carrierinterference (ICI). With respect to symbol time offset, as long as the receiver capturesthe OFDM symbol starting inside the prefix, the OFDM symbol appears cyclic, andortogonality is maintained.

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In this paper, only the interference of the carrier frequency offset in the system willbe study and will be presented a solution to it. Observation and resolution of thesymbol time offset (packet detection) problem will be done, but in exclusive mademodel.Furthermore, in order to maintain the orthogonality between the subcarriers theamplifiers must be linear to not produce out-of-band emission.Being a sum of a large number of independent subcarriers, the OFOM signal willsuffer from large peak-to-average power ratios. This peaks cause out-of-band and inband interference because of power amplifier non-Iinearities. This demands from theamplifier a large power backoff and from the AOC and OAC, a large number ofbits/sample. Many solutions exist to solve this problem and they can be organized intothree classes: block coding, clip effect transformation and probabilistic.

1.3 RF impairmentsAnother source of signal distortion are the imperfections of the RF components, like

oscillator mismatches and amplifier non-linearities already mentioned above, andphase noise.A small mismatch between the oscillator frequencies of the transmitter and receiverswill produce a frequency offset at the receiver that compromises the orthogonalitybetween the subchannels. This degradation in the system performance increasesrapidly with the frequency offset and with the number of subcarriers. As the number ofsubcarriers gets bigger in a same portion of bandwidth, less will be the separationbetween the subcarriers and hence more effect will have the frequency offset.Radio frequency demodulation usually introduces phase noise acting as anunwanted phase modulation of the carrier wave. A possible solution, to solve phasenoise is the use of pilots, which can be utilized to track phase noise in thedemodulation. However, this is done under the penalty of reducing the payload datathroughput.Another source of distortion is the IQ Imbalance, which consist in a mismatchbetween the in-phase and quadrature modulator.

1.4 ChannelThe main problem with reception of radio signals is fading caused by the multipathphenomenon. Because after transmission, the signal can suffer many reflections

(reflections from terrain features such as trees, hills or mountains, or objects such aspeople, vehicles or buildings), the receiver will see many replications of the signalarriving at different times. These echoes cause lSI, and combined can produce fading.A solution could be usage of antenna arrays, but this is still not a mean streamtechnique.Considering a signal of a large bandwidth, some parts of it may suffer fromconstructive interference and be enhanced, whereas others may suffer from destructiveinterference and be attenuated, sometimes to the point of extinction. Frequencycomponents that are close together will suffer variations in signal strength that arestrongly correlated and this is helpful to measure this phenomenon.For a narrowband signal, distortion is usually minimized if the bandwidth is less thanthe correlation bandwidth of the channel, because all frequencies in the band areusually distorted in the same way (flat fading).The correlation bandwidth can be estimated by:

Bcl':; 1/0,

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where 0 is the RMS value of delay spread. Since ODFM divides the entire channelbandwidth into many narrow sub bands, the frequency response over each individualsub band is relatively flat.OFDM can randomize burst errors caused by Rayleigh fading (caused by thechannel) if interleaver is employed. This means that, instead of several adjacentsymbols being completely destroyed, many symbols will suffer only a slightly distortion.

1.5 Channel estimationThe channel deforms the transmitted signal, thus producing errors at the receiver. Ifthe channel response is known, one can use this information to correct the errors.An 802.11 a standard based Wireless LAN, is a burst communication system inwhich training symbols are used at the beginning of each burst. These training symbolsconsist of two long symbols with a guard interval, G12, and ten short symbols which canbe used to estimate the channel response. In this study the guard interval GI2 is notimplemented since the channel is not time dispersive, simplifying the introduction of the

preamble.

Figure 2 - OFDM preamble structure adopted by the IEEE 802.11 standardization group.A short OFDM training symbol consists of 12 subcarriers, which are modulated bythe elements of the sequence S:s = j(13i6) *{0,0,1+ j,O,O,O,-I- j,O,O,O,1 + j,O,O,O,-I- j,O,O,O,-I- j,O,O,O,1 + j,O,O,O,O,}-26,26 ( ) 0,0,0,-1- j,O,O,O,-I- j,O,O,O,1 + j,O,O,O,1 + j,O,O,O,1 + j,O,O,O,1 + j,O,O

where ~ ( 1 3 / 6) is to normalize the average power of the resulting OFDM symbol.A long training symbol consists of 53 subcarriers, which are modulated by theelements of the sequence L:

_ {1,1,-1 ,-1,1,1,-1,1, -1,1,1,1,1,1,1,-1 ,-1,1,1, -1,1, -1,1,1,1,1,0, }L-2626 -. 1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,1,1,1

If the burst (data packet) is short, which is the case for 802.11a WLAN, the channelcan be assumed static during the whole burst, and the channel estimated. The channelresponse varies during time so in each burst the channel response is calculated again.The channel estimation can be done in the frequency or in the time domain. It waschosen to implement the channel estimation in the frequency domain because thecosts are lower than in the time domain.The long training symbols allow an easy an efficient estimate of the channelfrequency response for all the subcarriers. Since the two long symbols are identical,the average of the received two, improves the channel estimate.After the FFT operation the received symbols can be expressed as

R I K = H K X K +WI K (1 ),

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, where R1,k is the I symbol received of the k subcarrier, Xk the transmitted trainingsymbols, Hkthe channel and Wi,k the additive noise.So the estimate can be found by doing the calculations:

[ R +R JK '= I,K 2 2,K X Kand the corrected transmitted symbol

R1 K '= H K '*R1 K, ,

1.6 Frequency offset estimation

(2)

(3)

Frequency offset resulting from mismatch of transmitter and receiver's oscillators, isother major problem in RF communications responsible for introducing errors. It is thendesired to eliminate its influence in the signal.This can be done, utilizing also the training symbols sent in each burst. It's importantto say that is possible to perform synchronization without using training symbols(reducing the overhead, increasing the data rate) and do it, just by utilizing theredundancy of the transmitted signal. The redundancy results from employing the cycleprefix in each symbol. The 802.11 a standard includes a preamble (with trainingsymbols) in each frame, so it's indifferent the usage of the cycle prefix in the estimationin terms of data rate. Since it's more simple the implementation using the two longtraining symbols than using the cycle prefix, the first method was chosen to estimatethe frequency offset.There are two possible ways to do so, in the time domain or in the frequencydomain. It was chosen the frequency domain estimation for reasons of simplicity.

Two consecutive symbols have the following relationR = R e j21r-f!>. (4)2,K I,K '

that reveals every subcarrier experiences the same phase shift, which is proportional tothe frequency offset. The frequency error can be then estimated form this phase shift:

, where z is given byf,..'= -1/27t L.z (5)

The frequency offset correction is not perfect and residual error tends to accumulateover samples. This residual error will cause orthogonality loss among subcarriers andthere will be phase factor to each symbol due to the residual error. This can beminimized utilizing the four pilot subcarriers, to estimate the phase factor due to theresidual error, for each data symbol and then compensate the carrier. Due to the lackof time this will not be implemented. The residual frequency offset will originate arotation on the constellation and consequently errors, depending on the size of the data

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packet. If the packet is short enough the next preamble will reset this residualfrequency offset, and no errors will occur.

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2. SimulationThe channel and RF impairments are responsible for errors detected at thereceiver. To study their effects on the transmitted data and the efficiency of thealgorithms used to correct the errors, simulations were made using Simulink (fromMatLab R13).The starting point of the simulation model ("OFDM_QPSK_De/ayChanne/.mdf') isshown in the figure below, where no channel estimation and frequency offsetestimation is made, and so, thus any type of equalization. During the study of thesystem, and the origin of the occurred errors, specific blocks were built andimplemented to accredit to the system the ability to detect and correct those errors,thus creating a more efficient system. The evolution steps suffered by the model arepresented in order throughout the report.A final model ("Synchronization.mdf') was achieved in the end of the study and isextensively described in Appendix A.

OFDM Radio LayerQPSK mode with 112 code rate . - - _ ~ : : i ; : ::: [=Trwwnl.t I I I . , . .

:':.. r 1-----,

p. . . .

Figure 3 - Initial system without any type estimation and equalization.All the system performance plots shown throughout the report, were obtained usingthe MatLab code "test.m" printed in Appendix C.

2.1 Characteristics of the transmitted signalThe simulations were all done with the same stream of bits. To create it, a blockcalled "Signal" was made so that later would be possible to introduce the preamble.The size of the packet was chosen so that the preamble would represent 2%. Packetsizes based on the real implementations can be easily used in the model.

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Decreasing the SNR below 31 dB the errors start to increase. So, in a multipathenvironment the minimum SNR that can be experienced without originating more errorsis 31 dB.

,,I I I I I-- -----T--------,---------,---------r--------r--------I I I II I I I II I I I II I I I II I I I II I I I II I I I II I I I I---- - - - ~ - - - - - - - - ~ - - - '_-. - - - ~ - - - - - - - - ~ - - - - - - - -I I I I II I I II I I I II I I I II I I I II I I I II I I I II I I I I._---- - ~ __ . _ - - - ~ - - - - - - - - - ~ - - - - - - - - ~ _ . _ - - - - - ~ - - - - - - - -I I I I II I I I II I I I II I I I II I I I I

I I I II I I I

I I I I I--------T - - - - - - - , - - - - - - - ~ - - - - - - - - r - - - - - - - - r - - - - - - - -I I I I II I I I II I I I II I I I II I I I II I I I I, I I I

Figure 5 - Performance of the system.The performance is so bad because there is no channel estimation implemented.

2.3 Implementation of channel estimation and equalizationTo become possible the estimation of the channel response, first of all, the preamblewith the required training symbols must be inserted between the data to be transmitted.So, each transmitted packet will have a preamble at the beginning and the datasymbols afterwards. Considering the channel response static over time, because thechannel in the simulation is, the size of the packet was chosen so that the preamblewould correspond to 2% of the packet. Otherwise the size of the packet should bechosen to have duration less than the time the channel remains the same.

Vert Cat

Add C'fcliePrefixPLCP Preamble Input Zero pad for OFDM

MatrixConcatenation

I - - / - - - - - - - - . JDI------+l

f--------+-----DSelectRows

MUltiportSelector

In

Figure 6 - Input of the preamble inside the OFDM block.One important aspect of the preamble is that the short symbols have higher ratethan the rest of the transmitted symbols. This became a difficult problem to solvebecause the limitations of the "Simulink". Without finding any solution, the approachtaken to continuing the study was maintain equal rate for all the symbols, thus everysymbol have the duration of 4e-6 seconds. Because of this incorrect implementation theuse of the short symbols in for any equalization was discarded.

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2.4 Implementation of frequency offset estimation and equalizationTo model frequency offset between the transmitter and the receiver, the basebandequivalent block "Phase/Frequency Offset" is put before the IFFT in the OFDM block,at the receiver.To observe the performance of the frequency offset estimation algorithm asimulation was run with, the same data stream, a 50KHz frequency offset was created,

an AWGN channel with SNR of 60 dB and multipath (one delay).First, a simulation without frequency offset equalization was made and afterwards, asimulation with frequency offset equalization.

Figure 9 - Constellation of the received signal without frequency offsetequalization, and channel equalization. Draw in persistent mode.As can be observed, the result of frequency offset is a rotation in the signalconstellation as expected. The loops observed in a multipath environment (figure 4b)),rotate in the clockwise direction due to the frequency offset.Analyzing the number of errors, 22240 errors (38.67%), the loss of orthogonalitybetween subcarriers is evident. The bit error rate (BER) is independent of the SNR fora fixed frequency offset.To correct the corrupted received signal, an implementation of equation (5) and (6)was done, as shown in the figure below.

Memory

Figure 10 - Block "Frequency Offset Estimation".After the offset has been estimated, in the block "Subsystem" in the figure above,each symbol is multiplied by the value present at the output of the block "FrequencyOffset Estimation", thus performing equalization.

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Figure 11 - Constellation of the received signal with frequency offsetequalization, and channel equalization. Draw in persistent mode.From the figure above, can be observed that the frequency estimation and

equalization is functioning, since the constellation is in part reconstructed. Thereconstruction is not perfect due to residual frequency offset. Analyzing also thenumber of errors, which is zero errors (reminding that the 7 errors in the simulation isdue to difficulties of simulink implementation), it can be said that the algorithm functionwell (it eliminated 22240 errors).Phase offset is also corrected by the algorithms if it is not equal or greater than 45The phase offset wouldn't arise any problem if differential modulation were used.

:::::: ::::: ~ ~ ~ ~ ~ ~ : ~ ~ ~ ~ ~ ~ ~ ~ ;~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ::::::;::::::i:::::::i::::::r-----t-:::::::::::r:::+:::::f::::::---.-- .--- .. - .. --.----,----- _... ------.------ .. ---- ~ - - - - - - - ... --_._- .. _--_., , . , " ", I , , , , , ,, , , , , I I ,_ _ _ _ _ _ J. . .. , .1. . . I . . _. I . . . . . . J L _. . . . . _ - _

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CP C1 C24 . .4Packet Detect C " i U ~ e Fll!quency

Offset EstinUltiel1Fine F,eque,toy Offset E

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c) d)Figure 14 - All constellations correspond to the transmitted signal.a) 1/0 amplitude imbalance of 3dB; b) 1/0 phase imbalance of 25c) I dc offset of 0.3 and 0 dc offset of -0.1; d) 10 imbalance with all the parameters.From the figures above the effects of IQ imbalance can be understood. Applying a 3dB amplitude imbalance, a gain of 3/2 dB is given to the in-phase component, and again of -3/2 dB to the quadrature component (figure 14a)). A phase imbalance of 25 isresponsible for an anti-clockwise rotation of the constellation by an equal angle (figure14b)). An I dc offset of 0.3 is responsible for a sum of 0.3 in the in-phase amplitude,and the Q dc offset of -0.1 for a sum of -0.1 in the quadrature amplitude (figure 14c)).Now introducing all this parameters at the same time, the constellation becomes asshown in the figure 14d).Running a simulation with these IQ imbalances and without any others interferences(channel and frequency offset), no errors are detected.Running a simulation again, adding multipath channel with SNR of 60 dB, theconstellation obtain is shown in the figure 15a) below.

a) b)Figure 15 - a) Received signal constellation; b) Constellation of the signal after equalization.Figure 15a) is to be compared to figure 4b), being the difference between them,

caused only by the IQ imbalance. The radius and center of the circles, originated by themultipath, are not the same. Observing figure 15b )and figure 16, it can be concludedthat the channel estimation and equalization don't function as it is supposed to, due tothe IQ Imbalance, resulting in 839 errors (1,46%).

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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

- -- -. - - -. - - - - - - . ~ ~ - ~ ~ ~ ~ ~ ~ ~ - - - - - - t - - - - - -- - - - - - - - -- -- -, , , , ., , , .I , , Figure 16 - Performance of the system with fa imbalance interference(channel equalization active).

The performance of the system, adding a frequency offset of 50KHz and activatingalso frequency offset compensation, can be observed from the figures below, to behighly degraded (27790 errors, 48,31%).

Figure 17 - a) Constellation of the la imbalanced signal without any equalization;b) Constellation of the la imbalanced signal after frequencyoffset and channel equalization.This result was expected because, since the channel estimation doesn't work well,

the performance of the offset estimation suffers the same fate.A solution to remove the effects of the IQ imbalance must be found andimplemented before any type of estimation and equalization.

2.5.2 Phase noiseThe phase noise is another RF impairment that also degrades the system, and can

be caused by a number of conditions, but is mostly originated by oscillators frequencyinstability. The appearance of phase noise in an oscillator is due to "thermal" and"flicker", or 1ff noise. It is best described in the frequency domain, where the spectraldensity is characterized by measuring the noise "sidebands" on either side of theoutput signal center frequency (dBcfHz at a given frequency offset from the carrier).

Figure 18a) shows its impact (-80dBc@10KHz) on the system, with multi pathchannel and SNR of 60dB (channel equalization active).

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a) b)Figure 18 - a) Constellation of the received signal after channel equalization;b) Constellation of the received signal after frequency offset and channel equalization,corrupted by noise (SNR 60dbB), multipath and frequency offset (50KHz).As can be observe the effect of phase noise is as expected since the phase of theconstellation points vary within a certain limit. Since the phase noise rotation is notequal or bigger than 45 the received data will not suffer any errors.Simulating again but adding frequency offset (50KHz), multipath channel with SNRequal to 60dB, and with frequency offset and channel equalization, the constellation ofthe received signal after equalization is shown in figure 18b). The algorithm of channelestimation and equalization functions well, removing the effect of the channel (seefigure 18b. The same is not true for the frequency offset estimation and equalizationalgorithm, which losses the efficiency (see figure 19) because of the phase noise (arotation in the constellation is observed), resulting in 26480 errors (46.03%).

Figure 19 - Performance of the system with phase noise(channel and frequency offset equalization active).A solution must be found and implemented in order to solve this problem.

2.5.3 Power amplifier non-IinearitiesThere are different ways of modeling the non-linearity of a system, but one of themost useful is the polynomial modeling. This type of modeling is a narrowbandapproximation of a real system, which is always affected by the signal bandwidth.Spectral components in four frequency bands, named dc, fundamental, 2ndharmonic and 3rd harmonic, are generated up to 3rd order non-Iinearities. Some of theunwanted spectral components, such as harmonics, and the dc band can be filtered

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out. For the 3rd order intermodulation (1M3) components that is impossible becausethey are very close to the carrier.AM-AM and AM-PM conversions are used to model the non-linearity of an amplifier.Non-linearities are characterized as changes in the fundamental signal.A simulation was run after adding the block "Cubic Polynomial", which models thePA non-Iinearities, with an IIP3 equal to 35dBm and a linear gain of 7dB. The graphicbelow shoes the dependence of the system performance on the AM/PM conversionparameter.

~ ~ ~ 1 ~ ~ 1 1 1 1 7 i l i r ~ 1 ~ 1 ~ ~ 1 1 i 1 ~ ~ 1 ~ 1 ~ 1 ~ ; 1 m ~ m ~ ~ n ~ ~ ~ T ~ ; ~ ~ ~ ~ 1 ~ 1 ~ 1

: : : : : : : : : ~ : : : : : : : : : :]:::::: : : : : ~ : : : : : : : : : ~ : : : : : : : : : :1::::: ::::: ~ : : : : : : : : :I , I I I---------.,----------,----------r---------.,---------..,----------r-----.-, I , ,I I , ,

Figure 20 - Dependence of the system performance on the AM/PM conversion.It is evident that for values greater than 6 degrees per dB errors are introduced inthe system. This means solutions that minimizes greatly the non-linearities in thesystem must be implemented.

2.6. Packet detectionThe packet detection is normally done during short training symbols, which havebeen design to help achieving this goal. The algorithm used for detection is mentionedin [4], the "delay and correlate algorithm", and being the first to be performed it musthave great accuracy so not to degrade the following synchronization algorithms.

Packet

A B

Figure 21 - Packet detection.The algorithm is based on two sliding windows through which the packet passes.When only noise is present in both windows, the energy ratio between A and B will beconstant. As soon as the packet starts to enter window A, the energy that it contains

starts to rise above the energy contained in B. When A has only the signal corrupted bynoise inside of it and B just noise, the energy ratio will be at maximum. In this instantthe packet beginning is clearly identified, but its beginning is in fact determined whenthe signal ratio rises above the threshold value Th.

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The packet detection was not simulated in the complete OFDM system (transmitterand receiver), but rather in apart simulation, because is integration in it became aproblem (simulink signal restrictions).

1In1

2Const. nt1

Figure 22 - Delay and correlate algorithm.

Figure 23 - Signal at the output of the above model.The peaks shown in the figure are originated by the cross-correlation of thepreamble because the training symbols are identical. Thus the beginning of eachpacket can be determined by the rising edge of each peak. The signal in figure 23 wasobtained running the simulink model "0FDM_PackeLDetection.mdf'. This model is

presented and extensively described in Appendix B.The bit error rate was calculated running the model IIPacket Detection.mdf', so thatthe analysis of the performance could be made directly in the stream of bits and not ina complex OFDM signal. The same stream used in all this study was sent, and noerrors were detected.

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3. ConclusionsThe OFDM modulation scheme is a promising way for achieving high bit data ratesin WLANs because of its efficient use of the available bandwidth and robustnessagainst multipath interference. The fact that it divides the data through many parallelsubcarriers results in an enlargement of the symbol period, reducing the sensitivity of

the system to delay spread, and also randomizes the burst errors originated by thechannel frequency fading.As seen in this study, the channel interference was greatly attenuated by eliminatingthe errors produced by the multipath phenomenon, and reducing the sensitivity of thesystem to the noise. More precisely, an improvement of 100% is made above a SNR of7 dB.The same can't be said about the performance of the frequency offset estimationand equalization. After introducing a frequency offset of 50KHz in the improved system,in spite the implementation of the synchronization algorithm it resulted in a 39 dB lossin the system performance. So, there is the need for a better frequency offsetestimator, using the short training symbols and/or the cycle prefix.It was also observed the major influence of the RF Impairments in the systemperformance. Good solutions are to be found and implemented to make the systemmore robust.

4. Recommendations for future workFinishing this study, it becomes evident that the first thing that should be done nextis to resolve the problem of short symbols rate implementation. Once resolved thisproblem, frequency offset estimation can be performed, with more accuracy, as well

packet detection (this one has an extra difficulty attached, because its integration in themain model "Synchronization.mdf', using only simulink, seams impossible).Having done that, the next step should be resolving the residual frequency offset.One possible way to do that is by using the four pilot carriers, included in the standardIEEE802.11 a, to track the carrier phase. Doing so, the phase could be perfectlycorrected if the channel estimation is accurate, which is very unlikely in practice (theestimation will have always some noise).The radio communications suffers from imperfection of the RF components, whicheffects are called RF impairments. In this report a study on the system performance ispresented when these impairments are present. The next step then recommended, isto implement a solution to each and every one of them.

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5. References[1]. OFDM as a possible modulation technique for multimedia applications in the range of mmwaves, Dusan Matiee.[2]. Performance Analysis of QPSK OFDM with Fading, Frequency Offset, and ChannelEstimation Error, Rafael Ballagas - Stanford University.[3]. Synchronization and Channel Estimation in OFDM Systems, Jan-Jaap van de Beek LuleaUniversity of Technology.[4]. OFDM Wireless LANs: A Theoretical and Practical Guide, Juha Heiskala and John Terry(Ph.D.).[5]. OFDM for Wireless Multimedia Communications, Chandra Athaudage - ARC SpecialResearch Center for Ultra-Broadband Information Networks.[6]. Synchronization in OFDM Systems, Daniel Landstrom - Lund University.[7]. Coarse Symbol Synchronization Algorithms for OFDM Systems in Multipath Channels,Donghoon Lee and Kyungwhoon Cheun.[8]. The performance of a packet mode OFDM modem for 5 GHz band high-data-rate wirelessLANs, Masato Mizoguchi, Kiyoshi Enomoto, Takeshi Onizawa, Tomoaki Kumagai and MasahiroMorikura - NTT Access Network Service Systems Laboratories.[9]. ML Estimation of Time and Frequency Offset in OFDM Systems, Jan-Jaap van de Beek,Magnus Sandell and Per Ola Borjesson.[10]. Time and Frequency Synchronization for Hiperlan/2, Anna Berno and Nicola Laurenti Universita di Padova.[11]. OFDM timing synchronization: Possibilities and Limits to the usage of Cycle Prefix forMaximum Likelyhood Estimation, Dusan Matic, Ton A.J.R.M. Coenen, Frits C. Schoute, RamjeePrasad - Delft University of Technology.[12]. Carrier Frequency Offset Estimation for OFDM-Based WLANs, Jian Li, Guoquing Liu andGeorgios B. Giannakis.[13]. IEEE P802.11 a/D7.0 (Supplement to IEEE Sid 802.11-1999)

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Appendix A"Synchronization.mdl"Model - Synchronization

Full Model Hierarchy1. Synchronization

1. Channel2. Channel & Frequency Offset Estimation and Equalization

1. Channel Estimation & Equalization1. Average

1. Buffer2. Memory

1. Enabled Subsystem2. Format Signal3. Gain

1. Normalize14. Memory

1. Enabled Subsystem2. Frequency Offset Estimation & Equalization

1. Frequency Offset Estimation1. Memory

1. Enabled Subsystem2. Offset Increment

1. Memory11. Enabled Subsystem

3. Preamble Remover1. Normalize

3. Denormalize4. Normalize5. OFDM Receiver6. OFDM Transmitter

1. PLCP Preamble Input1. Normalize2. Normalize1

2. Zero pad for OFDM7. Signal

Simulation ParameterSolverRelTolRefineMax OrderZero Cross

ValueFixed Step Discrete1e-315on

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System - SynchronizationOFDM radio layer

QPSK mode .....Hh 1 code rail'

Table 1. Convolutional Encoder Block Properties

...'.

NameConvolutional EncoderTable 2. Display Block Properties

trellispoly2trellis(7, [133 171])

resetNone

NameDisplay

Formatshort

Decimation1

Floatingoff

S amp le T im e-1

Table 3. E rror Rate Calculation Block PropertiesName N st delay cp mode subframe P Mo de W sN am e RsMode2 stopError Rate 34+96 2 Entire [] Port ErrorVec off offCalculation frameName numErr maxBitsError Rate 100 1e6CalculationTable 4. Insert Zero Block PropertiesNameInsert Zero

Insert Zero Vector[1 1 1 1 1 1]'

Table 5. Manual Switch Block PropertiesNameManual Switch

swo actiono

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Table 6. Puncture Block PropertiesNameP2 Puncture

Puncture Vector[1 1 1 1 1 1]'

Table 7. QPSK Demodulator Baseband Block PropertiesNameQPSK Demodulator Baseband

Out TypeBit

Table 8. QPSK Modulator Baseband Block PropertiesNameQPSK Modulator BasebandTable 9. Terminator Block PropertiesNameTerminator

InTypeBit

Table 10. To Workspace Block Properties

Name Variable Name Max Data Decimation Sample Time Save FormatPointsTo Workspace simoutl inf 1 -1 ArrayTable 11. Unipolar to Bipolar Converter Block PropertiesNameUnipolar to Bipolar ConverterTable 12. Viterbi Decoder Block PropertiesNameViterbiDecoder

trellispoly2trellis(7, [133171])

dectype nsdecb tbdepth opmode resetUnquantized 4 34 Continuous off

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System - Synchronization/Channel1 In1[aco:l]

AVVGN

[aco:ll

[aco:ll

-12.

[aco:l IInlegar Det3y

NameAWGNChannell

Table 1. AWGN Channel Block Propertiesseed Noise Mode------ 6789 Signal to noise ratio

(EslNo)Table 2. Inport Block Properties

EsNodB SNRdB Ps Tsym variance10 10 0.01 4e- 1

6/80

Narne Port PortDimensionsIn1 1 -1Table 3. Integer Delay Block Properties

Sample Time-1

Defined InAdd Cyclic Prefix

NameInteger Delay

delay1

ico reset-llopupNoneTable 4. Outport Block Properties

NameOut! Port Output When Disabled Initial Output1 held [] Used BySwitch

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Table 5. Sum Block PropertiesNarne Icon ShapeSum round

Inputs1++

Input Same DToff

Out Data Type ModeInherit via internal rule

System - Synchronization/Channel & Frequency Offset Estimation andEqualization

Table 1. Inport Block PropertiesNameInl

Port PortDimensions1 -1

Sample Time-1

Defined InRemove Pilots

Table 2.Manual Switch Block PropertiesNameManual SwitchManual Switch1Table 3. Outport Block PropertiesNarne Port Output When DisabledOut! 1 held

swo1

Initial Output[]

actionoo

Used ByMath Function

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Table 2. Delay Line Block PropertiesNameDelay Line

Table 3. Inport Block Properties

siz48

ica

NameInl


SampleTime-1

Defined InProduct1

Table 4. Outport Block PropertiesName Port Output When DisabledOut! 1 heldTable 5. Product Block Properties

Initial Output[]

Used ByProduct3

Name Inputs MultiplicationProduct! */ Element-wise(.*)

Input Same DToff

Out Data Type ModeSame as first input

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation & Equalization/Average/BufferHoriz.Caf

Mafrix.Sum

Mafrix.Co rrafenal io n

Table 1. Inport Block PropertiesNameInlIn2

Port PortDimensions1 -12 -1

Sample Time-1-1

Defined InProduct1Delay Line

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Table 2. Matrix Concatenation Block PropertiesNameMatrix Concatenation

Table 3. Matrix Sum Block PropertiesNameMatrix SumTable 4. Outport Block Properties

Num Inports2

DimRows

catMethodHorizontal

Narne Port Output When DisabledOutl I held

Initial Output[]

Used ByProduct!

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation & Equalization/Average/Memory-22

Pul5>BGenerator Integer Delay

~ ~ = = I " ' l n 'Enabled

S L b ~ e m

Table 1. Discrete Pulse Generator Block PropertiesName Pulse

TypePulse SampleGenerator based

Ampli tude Period PulseWidth

I 300 IPhaseDelayI I

SampleTime4e-6

VectorParamslDon


Port PortDimensionsI -I

SampleTime-1

Defined InMatrix Sum

Table 3. Integer Delay Block PropertiesNameInteger Delay

delay2

ico reset-popupNone32

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Table 4. Outport Block PropertiesNarne Port Output When DisabledOut1 1 held

Initial Output[]

Used ByProduct1

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation &Equalization/Average/MemorylEnabled Subsystem[TI]Enable

C D t : ! , ; [ 4 8 x ~ l l = = = = = = = = = . .~ C In1 Oul1

Table 1. Enable Port Block PropertiesName States When EnablingEnable resetTable 2. Inport Block Properties

Show Output Portoff

Zero Crosson

NameIn1

Port ~ o r t D i m e n s i o n s1 -1

SampleTime-1

Defined InMatrix Sum

Table 3. Outport Block PropertiesName Port Output When DisabledOut! 1 held

Initial Output[]

Used ByProduct1

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System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation & Equalization/Format Signal

-22IniegaT Delay

0.6 1------- 'Cor51anl1

11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,DSP

Co r51a nl2

Table 1. Constant Block PropertiesName Value VectorParamslD Out Data Type Mode ConRadixGroupConstant! 0.5 on Inherit from 'Constant value' Use specified scalingTable 2. DSP Constant Block PropertiesNarne Value Sample ModeDSP [1,1,1,1,1,1,1,1,1,1, DiscreteConstant 1,1,1,1,1,1,1,1,1,1,2 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]'

Discrete Output Continuous OutputFrame-based 4e-6

Name samp frame additional dataType wordLen udData fracBitsModeTime Period Params TypeDSP 4e-6 4e-6 on Inherit 16 sfix(16) Best precisionConstant from2 'Constantvalue'

Name numFracBits InterpretAslD Ts Frame based OutputDSPConstant2 15 -inf -inf -inf

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Table 3. Discrete Pulse Generator Block PropertiesNarne Pulse TypePulse SampleGenerator I based

Amplitude PeriodI 300

Pulse Width289

Phase DelayI I

Narne Sample TimePulse Generator I 4e-6Table 4. Inport Block Properties

Vector Params IDon

NameInl

Port PortDimensionsI -I

SampleTime-I

Defined InProduct3


delay2

ico reset-popupNoneTable 6. Outport Block PropertiesName Port Output When DisabledOutl I heldTable 7. Real Imag To Complex Block Properties

Initial Output[]

Used ByProduct2

NameReal-Imag to ComplexTable 8. Sum Block Properties

InputImag

Constant Parto

Name Icon ShapeSuml round

Inputs1+-

Input Same DToff


Table 9. Switch Block PropertiesName Criteria Threshold Input Same DT Out Data Type Mode Zero CrossSwitchI u2 > 0 off Inherit via internal onThreshold rule

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Prcx1JctJ

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation & Equalization/GainC D ~ ~ = = = = = = = = = = = = = = = t . . r x 1Inl ~ ~ = = = = = = J " ' l 1

Ouf1

11,...1,1,1,1,1,1,1,...1,...1,1,1,-1,1,...1DSP

OCtIslSl'l16 fien"1ClvePiols

Table 1. DSP Constant Block PropertiesNameDSPConstant6

Value Sample Mode Discrete Output Continuous Output[1,1,-1,-1,1,1,- Discrete Sample-based Sample-based1,1,-1,1,1,1,1,1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,1,1,1]'

Name Sample Frame AdditionalTime Period Params Data Type Word UdData FracBitsLen Type ModeDSPConstant6 4e-6 4e-6 on Inherit from 16 sfix(16) Best precision'Constantvalue'NameDSPConstant6

numFracBits InterpretAsID Ts Frame based Output15 -inf -inf -inf



Sample Time-1

Defined InProduct1

Table 3. Multiport Selector Block Properties

NameRemove Pilots rowsOrCols idxCellArrayRows [1:57:1921:2628:3335:4749:53] idxErrModeClip Index

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Table 4. Outport Block PropertiesName Port Output When DisabledOut! 1 held

Table 5. Product Block Properties

Initial Output[]

Used BySwitch1

Name Inputs MultiplicationProduct3 */ E1ement-wise(.*)

Input Same DToff


System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation & Equalization/Gain/Normalize!

Table 1. Gain Block PropertiesName GainGain1 l/sqrt(2)

MultiplicationElement-wise(K.*u)

Out Data Type ModeSame as input

Table 2. Inport Block PropertiesNarne Port PortDimensions

1 -1Table 3. Math Block Properties

Sample Time-1


NameMath Function OperatorconJ Output Signal TypeautoTable 4. Outport Block PropertiesName Port Output When Disabled

1 heldInitial Output[]

Used ByProduct3

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System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation & Equalization/Memory

Pul!;laGenerator

-22.Inlegar Deliilt

EnabledSubsystem

Table 1. Discrete Pulse Generator Block PropertiesName Pulse Type Amplitude Period Pulse Width Phase Delay SampleTimePulse Sample 1 300 2 10 4e-6Generator basedTable 2. Inport Block PropertiesName VectorParamslD Port PortDimensions Sample Time Defined InIn1 on 1 -1 -1 Product!

Table 3. Integer Delay Block PropertiesNarne delay icInteger Delay 2 0

reset-popupNone

Table 4. Outport Block PropertiesName Port Output WhenDisabledOut! 1 held

Initial Output[]

Used ByMatrix Concatenation,Delay Line

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Channel Estimation & Equalization/MemorylEnabledSubsystem[TI]Enable

Q J o d , ; [ 4 8 x ~ ' l ' = = = = = = = = = = = = = = = t I o ~ Q JIn1 Out1

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Table 1. Enable Port Block PropertiesNarne States When EnablingEnable resetTable 2. Inport Block Properties

Show Output Portoff

Zero Crosson

NameInl


SampleTime-I

Defined InProduct1

Table 3. Outport Block PropertiesName Port OutputWhen Disabled Initial OutputOutI I held []

Used ByMatrix Concatenation, DelayLine

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Frequency Offset Estimation & Equalization

FreCj UB ncy 01lselE51imalion 00n51anl3

2Oul2

-96 48xlZx

Produc11Inlegal Dat3y1

Table 1. Constant Block PropertiesName Value VectorParamslD Out Data Type Mode ConRadixGroupConstant3 I On Inherit from 'Constant value' Use specified scaling

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Table 2. Gain Block PropertiesNameGain1

Gaino



Table 3. Inport Block PropertiesNarne Port PortDimensionsIn1 1 -1In2 2 -1Table 4. Integer Delay Block Properties

Sample Time-1-1

Defined InRemove PilotsSwitch

NameInteger Delay1

delay96

Table 5. Outport Block PropertiesName Port OutputWhen DisabledOut! 1 HeldOut2 2 HeldOut3 3 HeldTable 6. Product Block Properties

Initial Output Used By[] Switch, Matrix Concatenation,

Delay Line, Product2[] Switch[] Switch, Gain1

Name Inputs MultiplicationProduct! ** Element-wise(.*)Table 7. Sum Block Properties

Input Same DToff


Name Icon ShapeSum Round

Inputs1++

Input Same DToff


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System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Frequency Offset Estimation & Equalization/FrequencyOffset Estimation

Table 1. Complex To Magnitude Angle Block PropertiesNameComplex to Magnitude-AngleTable 2. Constant Block Properties

OutputAngle

Name Value VectorParamslD Out Data Type Mode ConRadixGroupon Inherit from 'Constantvalue'Constant (1/(2*pi))

Constant3 (j*2*pi) on Inherit from 'Constantvalue'

Use specifiedscalingUse specifiedscaling

Table 3. Cumulative Sum Block PropertiesNameCumulative Sum

dimColumns

reset-popupNone

Table 4. Delay Line Block PropertiesNameDelay LineTable 5. Inport Block Properties

siz48

ico

NameIn l


SampleTime-1


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Table 6. Math Block PropertiesNameMath FunctionMath Function2

OperatorexpconJ

Output Signal Typeautoauto

Table 7. Outport Block PropertiesName Port OutputWhen DisabledOut1 1 heldTable 8. Product Block Properties

Initial Output[]

Used BySwitch, Gain1

Name InputsProduct 2Product2 **Product3 **

MultiplicationElement-wise(.*)Element-wise(.*)Element-wise(.*)

Input Same DToffoffoff

Out Data Type ModeSame as first inputSame as first inputSame as first input

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Frequency Offset Estimation & Equalization/FrequencyOffset EstimationlMemory

PuSsGenera10r

Erable;:lS u b ~ e m

Table 1. Discrete Pulse Generator Block PropertiesName Pulse Type Amplitude Period PulseWidth Phase Delay SampleTimePulse Sample 1 300 2 10 4e-6Generator basedTable 2. Inport Block PropertiesName Port VectorParamslD PortDimensions SampleTime Defined InIn1 1 on -1 -1 Remove Pilots

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Table 3. Outport Block PropertiesNarne Port Output When DisabledOut I I held

Initial Output Used By[] Delay Line, Product2

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Frequency Offset Estimation & Equalization/FrequencyOffset Estimation/Memory/Enabled Subsystem[TI]Erable

Q J - = [ 4 8 x = = = = ' l = = = = = = = = = . ~ Q JIn1 Ouf1

Table 1. Enable Port Block PropertiesNarne States When EnablingEnable resetTable 2. Inport Block PropertiesNarne Port PortDirnensionsInl I -1Table 3. Outport Block Properties

Show Output Portoff

SarnpleTirne-1

Zero Crosson


Name Port Output When DisabledOut! I held

Initial Output Used By[] Delay Line, Product2

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System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Frequency Offset Estimation & Equalization/FrequencyOffset Estimation/Offset Increment

) r - 11Oull

0.1,,)' I . . r -11[ -11 u"" ,Del")' Linel

~ r _ l l ...[ -11 '\+-11 + J[ - '1 [_1:

9 r4R>111[ 4 S " I ~(3,,;'

I l-"""'.l.L------Ilo41nl

Table 1. Delay Line Block PropertiesName siz icDelay Linel 48 oTable 2. Gain Block PropertiesName Gain Multiplication Out Data Type ModeGain 9 Element-wise(K.*u) Same as inputTable 3. Inport Block PropertiesName Port PortDimensions Sample Time Defined InInl 1 -1 -1 ProductTable 4. Outport Block PropertiesName Port OutputWhen Disabled Initial Output Used ByOut! 1 held [] Product3Table 5. Sum Block PropertiesName Icon Shape Inputs Input Same DT Out Data Type ModeSumSuml

roundround

1++1++

offoff

Inherit via internal ruleInherit via internal rule

44

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System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Frequency Offset Estimation & Equalization/FrequencyOffset Estimation/Offset Increment/Memoryl

Pul5aGenerator

):E==:!=:==JI't InlEnabledSubsys1em

Table 1. Discrete Pulse Generator Block PropertiesName Pulse Type Amplitude Period PulseWidth Phase Delay SampleTimePulse Sample 1 300 1 11 4e-6Generator basedTable 2. Inport Block PropertiesNameInl

Port VectorParamslD PortDimensions SampleTime Defined In1 on -1 -1 Product

Table 3. Outport Block PropertiesName Port Output When DisabledOut1 1 held

Initial Output[]

Used BySum, Gain

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Frequency Offset Estimation & Equalization/FrequencyOffset Estimation/Offset IncrementlMemoryl/Enabled Subsystem[TI]Enable

Q ) ~ [ 4 8 x ~ ' I = = = = = = = = = ...Q)In1 OLJt1

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Table 1. Enable Port Block PropertiesName States When EnablingEnable resetTable 2. Inport Block Properties

Show Output Portoff

Zero CrossOn

NameInl


SampleTime-1

Defined InProduct

Table 3. Outport Block PropertiesName Port Output When DisabledOutl 1 held

Initial Output[]

Used BySum, Gain

System - Synchronization/Channel & Frequency Offset Estimation andEqualization IPreamble Remover

-22

Imager Delay

0.5 1-------'Co nsIam1

Conslam2 Aaal-lma>l toCo rTF lax

Table 1. Constant Block PropertiesName Value VectorParamslD Out Data Type Mode ConRadixGroupConstant! 0.5 on Inherit from 'Constant value' Use specified scalingConstant2 I on Inherit from 'Constant value' Use specified scalingTable 2. Discrete Pulse Generator Block PropertiesNarne Pulse TypePulse SampleGenerator! based

Amplitude Period PulseWidth1 300 288

Phase Delay12

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NamePulseGenerator1

Sample Time4e-6

VectorParamslDon

Table 3. Inport Block PropertiesNameIn1


SampleTime-1

Defined InSwitch


delay2 o reset-popupNone


Initial Output[]

Used ByMath Function

Table 6. Real Imag To Complex Block PropertiesNameReal-Imag to ComplexTable 7. Su m Block Properties

InputReal

Constant Parto

NameSum1

Icon Shape Inputs Input Same DTround 1+- off


Table 8. Switch Block PropertiesName Criteria Threshold Input Same DT Out Data Type Mode Zero CrossSwitch1 u2> 0 off Inherit via internal onThreshold rule

System - Synchronization/Channel & Frequency Offset Estimation andEqualization /Preamble Remover/Normalize

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Gain1/sqrt(2)




1 -1Table 3. Math Block Properties

Sample Time-1

Defined InReal-Imag to Complex

NameMath Function

OperatorconJ

Output Signal Typeauto

Table 4. Outport Block PropertiesName Port OutputWhen Disabled

1 held

System - Synchronization/Denormalize

Initial Output[]

Used BySwitch1


Gainsqrt(10)



Table 2. Inport Block PropertiesName Port Port Dimensions

1 -1Sample Time-1

Defined InSwitch1

Table 3. Math Block Properties

NameMath Function OperatorconJ Output Signal Typeauto

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Table 4. Outport Block PropertiesName Port OutputWhen Disabled InitialOutput Used By

1 held [] M-PSK Demodulator Baseband

System - Synchronization/Normalize


GainlIsqrt(2)




1 -1

Table 3. Math Block Properties

Sample Time-1

Defined InM-PSK Modulator Baseband

NameMath Function

OperatorconJ


Table 4. Outport Block PropertiesName Port Output When Disabled Initial Output

1 hcld []

System - SynchronizationlOFDM Receiver

Used ByMultiport Selector

4Sill 1D ...Sole::ol DiIIIaIbN!s 2Pllobi Pial"RoSTlCl .....Rial"

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Table 1. FFf Block PropertiesNameFFT

Comp MethodTable lookup

Table OptSpeed

BitRevOrderoff

Table 2. Frame Status Conversion Block PropertiesNameFrame Status ConversionTable 3. Inport Block Properties

growRefPortoff

outframeFrame-based

NameReceived signal


SampleTime-1

Defined InSwitch

Table 4. Multiport Selector Block PropertiesNameRemovePilots

rowsOrCols idxCellArray idxErrModeRows {[1:5 7:1921:2628:3335:4749:53],[62034 Clip Index48]}

Table 5. Outport Block PropertiesName Port Output When DisabledData 1 heldPIlots 2 held

InitialOutput Used By[] Delay Line, Product2,Integer Delay1[] Terminator

Table 6. Selector Block PropertiesName Input Type Element Src Elements Row Src Rows Column SrcRemove zero- Vector Internal [39:64 Internal 1 Internalpadding and 1:27]reorderRemove Vector Internal [17:80] Internal 1 InternalCyclic Prefix

Name ColumnsRemove zero-padding and reorder IRemove Cyclic Prefix 1

Input Port Width6480

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System - Synchronization/OFDM Transmitter

.....

...-.M.llpllli.......

+------toI ......1 GIll

M1l1lx....-

Table 1. DSP Constant Block PropertiesName Value SampleMode Discrete continuousOutput Samp Frame Additional

Output Time Period ParamsDSP O+OiConstant Discrete Frame- Sample-based 4e-6 4e-6 offbasedName data wordL udDataT fracBitsM numF InterpretA Ts FramebasedOType en ype ode racBit slD utput

sDSP hiller 16Constant itfrom'Constantvalue

sfix(16) Best 15precIsIOn off 4e- on6

Table 2. Gain Block PropertiesNameGain

Gain-1



Table 3. IFFT Block PropertiesName CompMethodIFFT Table lookup

TableOpt BitRevOrderSpeed off

cs in SkipNorm modeoff off Complex

Table 4. Inport Block PropertiesNameIn


SampleTime-1

Defined InGain1

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Table 5. Matrix Concatenation Block PropertiesNameMatrix Concatenation

numInports11

catMethodVertical

Table 6. Multiport Selector Block PropertiesName rowsOrCols idxCeIIArray idxErrModeMultiport Selector Rows {I :5,6:18,19:24,25:30,31:43,44:48} Clip IndexTable 7. Outport Block PropertiesName Port Output When DisabledOut 1 held

Initial Output Used By[] Switch, Dynamic AWGN

Table 8. PN Sequence Generator Block PropertiesNamePN SequenceGenerator

poly[1 00 1 0001]

Table 9. Phase/Frequency Offset Block PropertiesNamePhase/ Frequency OffsetTable 10. Selector Block Properties

Freq Offseto

Phase Offseto

Name InputType Element Elements RowSrc Rows Column Columns InputPortSrc Src WidthAddCyclicPrefix

Vector Internal [49:64 Internal 1 Internal 1 641:64]

Table 11. Unipolar to Bipolar Converter Block PropertiesNameUnipolar to Bipolar Converter

M2

polarityNegative

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System - Synchronization/OFDM Transmitter/PLCP Preamble Input

CD . . . . . .

1,-1.1,1,1, I.D" 1,-1,-1,1.1,-1,1,-

CIln".ull:Z

Table 1. Abs Block PropertiesNameAbs

Zero Crosson

Table 2. Constant Block PropertiesName Value VectorParamslD Out Data Type Mode ConRadixGroupConstant 0.5 on Inherit from 'Constant value' Use specified scalingConstant! 0.5 on Inherit from 'Constant value' Use specified scalingConstant2 0.5 on Inherit from 'Constant value' Use specified scalingTable 3. DSP Constant Block PropertiesName Value Sample Discrete ContinuousMode Output Output

Discrete Frame- Sample-based basedDSP sqrt((13/6))* [0,0, 1+j,O,O,O,-IConstant2 j,O,O,O,1+j,O,O,O,-I-j,O,O,O,-Ij,O,O,O,1+j,O,O,O,O,O,O,O,-I-j ,0,0,0,-1j,O,O,O,1+j ,0,0,0,1+j,O,O,O,1+j,O,O,O,1+j,O,Or

DSP [1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,1,- Discrete Frame-Constant3 1,1,-1,1,1,1,1,0,1,-1,-1,1,1,-1,1,-1,1,-1,-1,- based1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,1,1,1]'

Samplebased

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Name Sample Frame Additional Data Word Ud Data FracBitsTime Period Params Type Len Type ModeDSP 4e-6 4e-6 off Inherit from 16 sfix(16) BestConstant2 'Constant precIsIOnvalue'DSP 4e-6 4e-6 on Inherit from 16 sfix(16) BestConstant3 'Constant precIsIOnvalue'Name Frac Bits Mode numFracBits InterpretAslD Ts FramebasedOutputDSP Best precision 15 -inf -inf -infConstant2DSP Best precision 15 -inf -inf -infConstant3Table 4. Discrete Pulse Generator Block PropertiesName Pulse Amplitude Period Pulse Phase Sample VectorType Width Delay Time ParamslDPulse Generator Sample 1 300 10 0 4e-6 onbasedPulse Generator1 Sample 1 300 2 10 4e-6 onbasedPulse Generator2 Sample 1 300 2 10 4e-6 onbasedTable 5. Gain Block PropertiesNameGain

Gaino MultiplicationElement-wise(K.*u) Out Data Type ModeSame as inputTable 6. Inport Block PropertiesName Port PortDimensionsIn2 1 -1Table 7. Outport Block Properties

Sample Time-1

Defined InMatrix Concatenation

Name Port OutputWhen DisabledOut! held

Initial Output[]

Used ByZero Pad

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Table 8. Real Imag To Complex Block PropertiesNameReal-Imag to ComplexTable 9. Sum Block Properties

InputReal

Constant Parto

Name Icon Shape Inputs Input Same DT Out Data Type ModeSum round 1+- off Inherit via internal ruleSuml round 1+- off Inherit via internal ruleSum3 round 1+- off Inherit via internal ruleTable 10. Switch Block PropertiesName Criteria Threshold Input Same DT Out Data Type Mode Zero CrossSwitch u2 > 0 off Inherit via internal rule onThresholdSwitch1 u2 > 0ThresholdSwitch2 u2 > 0Threshold

off

off

Inherit via internal rule onInherit via internal rule off

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System Synchronization/OFDM Transmitter/PLCP PreambleInput/Normalize

Table 1. Gain Block PropertiesName GainGain1 1/sqrt(2)



Table 2. Inport Block PropertiesName Port PortDimensions

1 -1Sample Time-1

Defined Inzoh

Table 3. Math Block PropertiesNameMath Function

Operatorcon]


Table 4. Outport Block PropertiesName Port OutputWhen Disabled

1 heldInitial Output[]

Used BySwitch

System Synchronization/OFDM Transmitter/PLCP PreambleInputlNormalizel


Gain1/sqrt(2)



Table 2. Inport Block PropertiesName Port PortDimensions

1 -1Sample Time-1

Defined Inzoh

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NameZero Pad

numOutCols1

trunc flagNone

System - Synchronization/Signal, . .------114D

S(Dp8

0.5 f--------- '

Con51ant

Berooulli 1:! l !o!!:! ! :==========M==;=::;=.:=111olBinaryBernoulli RandcrnBinaryGenarabr

Gain

48:1:1[48:1:1)

Table 1. Bernoulli Binary Generator Block PropertiesName P seed Ts Frame BasedBernoulli Random 0.5 1234567 4e-6/48 onBinary GeneratorTable 2. Constant Block Properties

Samp Per Frame orient48 off

Name Value VectorParamslD Out Data Type Mode ConRadixGroupConstant 0.5 on Inherit from 'Constant value' Use specified scalingTable 3. Discrete Pulse Generator Block PropertiesName Pulse

TypePulse SampleGenerator based

Amplitude Period Pulse PhaseWidth Delay

1 300 12 0SampleTime4e-6

VectorParamslDon

Table 4. Gain Block PropertiesNameGain

Gaino MultiplicationE1ement-wise(K.*u) Out Data Type ModeSame as input

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Table 5. Outport Block PropertiesName Port Output When DisabledSignal I held

Table 6. Sum Block Properties

Initial Output Used By[] Convolutional Encoder,

Error Rate Calculation

NameSum

Icon Shape Inputsround 1+-

Input Same DTOff


Table 7. Switch Block PropertiesNameSwitch

Criteria Threshold Input Same DTu2> 0 OffThreshold

Out Data Type ModeInherit via backpropagation

Zero Crosson

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Appendix B"Packet Detection.mdl"Model - Packet Detection

Full Model HierarchyI. Packet DetectionI . Frame Selection

2. Signal3. Start of Frame Detection4. auto-correlation

Simulation ParameterSolverRelTolRefineMaxOrderZero Cross

System - Packet Detection

"""""

ValueFixed Step Discretele-3I5on

o

""""' ..

.- " f--------H11i.. ~

."'"' .... -,.

1.t1b. . . . 1

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Table 1. AWGN Channel Block PropertiesEsNodBoise Mode

Signal to noise ratio 10(EslNo)

AWGN 1234ChannelName seed SNRdB Ps Tsym variance---------------------------10 1 4e-6/48 1Table 2. Constant Block PropertiesName Value VectorParamslD Out Data Type Mode ConRadixGroupConstant 0.2 on Inherit from 'Constant value' Use specified scalingTable 3. Display Block PropertiesName Format Decimation Floating Sample TimeDisplay1 short 1 off -1Table 4. Error Rate Calculation Block PropertiesNameError RateCalculation1Name numErr maxBitsError Rate 100 1e6Calculation1Table 5. Frame Status Conversion Block PropertiesName Grow Ref Port Out frameFrame Status Conversion off Sample-basedTable 6. Integer Delay Block PropertiesNameInteger Delay1Integer Delay2

delay9630

Table 7. Sum Block Properties

Name Icon Shape Inputs Input Same DT Out Data Type ModeSum round 1+- off Inherit via internal rule

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Table 8. Unbuffer Block PropertiesNameUnbufferUnbufferl

System - Packet Detection/Frame Selection[TI]

Enable

C D ' - - - - - - - - - - - - ~In1 Oul1

Table 1. Enable Port Block Properties

icoo

Name States When EnablingEnable reset

Table 2. Inport Block Properties

Show Output Portoff

Zero Crosson

NameIn1


SampleTime-1

Defined InInteger Delay1


System - Packet Detection/Signal

Pula!Generalor

Initial Output[]

Used ByUnbufferl

t:ww=J...ry-Be rnou iii f--""""--1I'1Binary

Ber nou iii RandomBinary Genel:8brGain

S W ~ c h,Sgnal

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Table 1. Bernoulli Binary Generator Block Properties

Bernoulli Random 0.5 20394875 4e-6/48 onBinary GeneratorName P seed Ts Frame Based SampPer Frame orient

48 off

Table 2. Discrete Pulse Generator Block PropertiesNarne Pulse Type Amplitude Period Pulse Phase Sample Vector

Width Delay Time ParamslDPulse Generator Sample based 1 100 30 0 4e-6 onTable 3. Gain Block PropertiesNameGain

Gaino MultiplicationElement-wise(K.*u) Out Data Type ModeSame as inputTable 4. Outport Block PropertiesName Port Output When DisabledSignal 1 heldTable 5. Switch Block Properties

Initial Output Used By[] Unbuffer, Integer Delayl

Name CriteriaSwitch u2 >Threshold

Threshold Input Same DT Out Data Type Mode Zero Crosso off Inherit via internal rule on

System - Packet Detection/Start of Frame DetectionQ J - - - - - - - - - - - I - m - - - - - - I ~

Flalay


Port PortDimensions-1

SampleTime-1

Defined InSum

Table 2. Outport Block PropertiesName Port OutputWhenDisabledOutl 1 held

InitialOutput[]

Used ByInteger Delay2

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Table 3. Relay Block PropertiesNarne On Switch Off Switch On OutputValue Value Value OffOutputValue Con RadixGroup ZeroCrossRelay -0.17 -0.175 1 o Usespecified

scalingon

System - Packet Detection/auto-correlation1

111

2

Table 1. Constant Block PropertiesName Value VectorParamslD Out Data Type Mode ConRadixGroupConstant! 2 on Inherit from 'Constant value' Use specified scalingTable 2. Inport Block PropertiesName Port PortDimensionsIn l 1 -1Table 3. Integer Delay Block Properties

Sample Time-1

Defined InDynamic AWGN

NameInteger DelayTable 4. Math Block Properties

delay48 o

reset-popupNone

Name Operator Output Signal TypeMath Function magnitudef\2 autoMath Functionl magnitudef\2 autoMath Function2 magnitudef\2 autoMath Function3 pow auto

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Appendix CThe following MatLab code, "test.m", is used to plot the dependence of the systemperformance on the signal to noise ratio value (SNR vs. BER). It can be easily changedto plot the dependence of the system performance on any other variable.To run the code a variable called SNR is placed in the field "SNR(dB)" of the blockAWGN Channel, and is necessary to save the model after. What the script will do is to

determine the bit error rate (BER) to each signal-to-noise ratio value dictated byvariable i. In the code, variable i define the study range of the SNR value, which is allinteger numbers from one to sixty."test.m"

for i=1:61SNR=i-1 ;sim('Synchronization',4*1200e-6);c1ose_system('Synchronization');a=size(simout1 );erros(i)=(simout1 (a(1 ),2)-7)/simout1 (a(1 ),3);erros2(i)=simout1 (a(1 ),2)-7;enddb=0:60;semilogy(db,erros,'r');axis=([O 60 101\-4 1]);grid on;xlabel('SNR(dB)');ylabel('BER');

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OFDM, QPSK