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# Mobile Comm Systems ECE 732

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This 56 page Class Notes was uploaded by Antonina Wuckert on Monday September 28, 2015. The Class Notes belongs to ECE 732 at George Mason University taught by Bernd-Peter Paris in Fall. Since its upload, it has received 83 views. For similar materials see /class/215013/ece-732-george-mason-university in ELECTRICAL AND COMPUTER ENGINEERING at George Mason University.

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Date Created: 09/28/15

Simulation of Wireless Communication Systems using MATLAB Dr BP Paris Dept Electrical and Comp Engineering George Mason University Fall 2007 Outline MATLAB Simulation Frequency Diversity WideBand Signals MATLAB Simulation gt Objective Simulate a simple communication system and estimate bit error rate gt System Characteristics gt BPSK modulation b E 1 71 with equal a priori probabilities Raised cosine pulses AWGN channel oversampled integrateanddump receiver frontend digital matched filter gt gt gt gt gt Measure Biterror rate as a function of ESNo and oversampling rate Z tinT A From Continuous to Discrete Time gt The system in the preceding diagram cannot be simulated immediately gt Main problem Most of the signals are continuoustime signals and cannot be represented in MATLAB gt Possible Remedies 1 Rely on Sampling Theorem and work with sampled versions of signals 2 Consider discretetime equivalent system gt The second alternative is preferred and will be pursued below Freq 7 Towards the DiscreteTime Equivalent System gt The shaded portion of the system has a discretetime input and a discretetime output gt Can be considered as a discretetime system gt Minor problem input and output operate at different rates Santpler rat is DiscreteTime Equivalent System gt The discretetime equivalent system gt is equivalent to the original system and gt contains only discretetime signals and components gt Input signal is upsampled by factor fsT to make input and output rates equal gt Insert fST 71 zeros between input samples Components of DiscreteTime Equivalent System gt Question What is the relationship between the components of the original and discretetime equivalent system Santpler N rat is Discretetime Equivalent Impulse Response gt To determine the impulse response hln of the discretetime equivalent system gt Set noise signal Nt to zero gt set input signal 3 to unit impulse signal 6M gt output signal is impulse response hin gt Procedure yields 1 n1TS bin i pt ma dt Ts quotTs gt For high sampling rates fST gtgt 1 the impulse response is closely approximated by sampling pt ht hlnl m pa h lnrs Discretetime Equivalent Impulse Response 2 15 05 TimeT Figure Discretetime Equivalent Impulse Response fsT 8 DiscreteTime Equivalent Noise gt To determine the properties of the additive noise Nn in the discretetime equivalent system gt Set input signal to zero gt let continuoustime noise be complex white Gaussian with power spectral density No gt output signal is discretetime equivalent noise gt Procedure yields The noise samples Nn gt are independent complex Gaussian random variables with gt zero mean an gt variance equal to NoTS Received Symbol Energy gt The last entity we will need from the continuoustime system is the received energy per symbol E5 gt Note that E5 is controlled by adjusting the gain A at the transmitter gt To determine E5 gt Set noise Nt to zero gt Transmit a single symbol b gt Compute the energy of the received signal RU gt Procedure yields Es0 A2lpfhfl2 or gt Here 73 denotes the variance of the source For BPSK gt For the system under consideration ES A2T Simulating Transmission of Symbols gt We are now in position to simulate the transmission of a sequence of symbols gt The MATLAB functions previously introduced will be used for that purpose gt We proceed in three steps 1 Establish parameters describing the system gt By parameterizing the simulation other scenarios are easily accommodated 2 Simulate discretetime equivalent system 3 Collect statistics from repeated simulation a on a Listing SimpIeSetParametersm This script sets a structure named Parameters to be used by the system simulator e a e Parameters construct structure of parameters to be passed to system simulator communications parameters e a a Signalitoinoise ratio Es N BPSK number of Symbols Parameters Alphabet Parameters Nsymbols l 1 1000 Parametersf 110000 symbol period ParameterslfsT 8 samples per s mbol ParametersEs l normalize received symbol energy to l ParametersEsOVerNO 6 0 discreteitime equivalent impulse response raised cosine pulse fsT ParameterslfsT tts 02fsTil 12 Parametershh fsT 1 r cos2pittssinpifsTpifsT sqrt23 Simulating the DiscreteTime Equivalent System gt The actual system simulation is carried out in MATLAB function MCSlmple which has the function signature below gt V V function The parameters set in the controlling script are passed as inputs The body of the function simulates the transmission of the signal and subsequent demodulation The number of incorrect decisions is determined and returned NumErrors Resultsstruct MCSlmple Parametersstruct Simulating the DiscreteTime Equivalent System gt The simulation of the discretetime equivalent system uses tOOIbOX functions Randomsymbols LinearModulation and addNoise A sqrtEsT transmitter gain EsEsOVerNO noise PSD complex noise NoiseVar NOTsfsT corresponding noise Variance NUTs Scale Ashhshh gain through signal chain simulate discreteitime equivalent system transmitter and channel Via toolbox functions Symbols Randomsymbols Nsymbols Alphabet Priors LinearModulation Symbols hh fsT if isrealSignal Sig l complexSignal ensure Signal is complexivalued Received addNoise NoiseVar Signal Digital Matched Filter gt The vector Received contains the noisy output samples from the analog frontend gt In a real system these samples would be processed by digital hardware to recover the transmitted bits gt Such digital hardware may be an ASIC FPGA or DSP chip gt The first function performed there is digital matched filtering gt This is a discretetime implementation of the matched filter discussed before gt The matched filter is the best possible processor for enhancing the signaltonoise ratio of the received signal Digital Matched Filter gt In our simulator the vector Received is passed through a discretetime matched filter and downsampled to the symbol rate gt The impulse response of the matched filter is the conjugate complex of the timereversed discretetime channel response hln Flln 5n MATLAB Code for Digital Matched Filter gt The signature line for the MATLAB function implementing the matched filter is function MFOut DMF Received Pulse fsT gt The body of the function is a direct implementation of the structure in the block diagram above convolve received Signal with conjugate complex of timeireversed pulse matched filter Temp conv Received conj fliplrPL1lse 9 down Sample at the end of each pulse period MFOut Temp lengthPulse 2 fsT 2 en DMF Input and Output Signal DMFtnput Ttme tT DM F Output TtmE tT IQScatter Plot of DMF Input and Output DMF tnput tmag Fart Reat Part DMF Output tmag Fart Slicer gt The final operation to be performed by the receiver is deciding which symbol was transmitted gt This function is performed by the slicer gt The operation of the slicer is best understood in terms of the lQscatter plot on the previous slide gt The red circles in the plot indicate the noisefree signal locations for each of the possibly transmitted signals gt For each output from the matched filter the slicer determines the nearest noisefree signal location gt The decision is made in favor of the symbol that corresponds to the noisefree signal nearest the matched filter output gt Some adjustments to the above procedure are needed when symbols are not equally likely MATLAB Function SimpleSlicer gt The procedure above is implemented in a function with signature function Decisions MSE Simpleslicer MFOut Alphabet Scale Loop over symbols to find symbol closest to MF output for kk llength Alphabet noiseifree signal location NoisefreeSig ScaleAlphabet kk a Euclidean distance between each observation and constellation po Dist abs MFOut NoisefreeSig find locations for which distance is smaller than previous best ChangedDec lSt lt MlnDlSt 9 stor new min distances and update decisions MinDist ChangedDec e is ChangedDec Decisions ChangedDec Alphabet kk Entire System gt The addition of functions for the digital matched filter completes the simulator for the communication system gt The functionality of the simulator is encapsulated in a function with signature function NumErrors Resultsstruct MCSlmple Parametersstruct gt The function simulates the transmission of a sequence of symbols and determines how many symbol errors occurred gt The operation of the simulator is controlled via the parameters passed in the input structure gt The body of the function is shown on the next slide it consists mainly of calls to functions in our toolbox on a Listing MCSimpIem ate discreteitime equivalent system annel via toolbox functions S mbols RandomSymbols NSymbols Alphabet Priors Signa LinearModulation Symbols hh fsT if isrealSignal Signal complexSignal ensure Signal is complexivalued en Received addNoise Signal NoiseVar digital matched filter and slicer MFOut DMF Received hh sT Decisions SimpleSlicer MFOutlNSymbols Alphabet Scale 6 Count errors NumErrors sum Decisions Symbols Monte Carlo Simulation gt The system simulator will be the work horse of the Monte Carlo simulation gt The objective of the Monte Carlo simulation is to estimate the symbol error rate our system can achieve gt The idea behind a Monte Carlo simulation is simple gt Simulate the system repeatedly gt for each simulation count the number of transmitted symbols and symbol errors gt estimate the symbol error rate as the ratio of the total number of observed errors and the total number of transmitted bits Monte Carlo Simulation gt The above suggests a relatively simple structure for a Monte Carlo simulator gt Inside a programming loop gt perform a system simulation and gt accumulate counts for the quantities of interest 43 while Done NumErrorskk NumErrorskk MCSlmple Parameters Numsymbolskk Numsymbolskk ParametersNSymbols compute Stop conditlo on 39 n e NumErrorskk gt MlnErrors ii Numsymbols kk gt Maxs Confidence Intervals gt Question How many times should the loop be executed gt Answer It depends gt on the desired level of accuracy confidence and gt most importantly on the symbol error rate gt Confidence Intervals gt Assume we form an estimate of the symbol error rate Pe as described above gt Then the true error rate P9 is hopefully close to our estimate gt Put differently we would like to be reasonably sure that the absolute difference We 7 P9 is small Confidence Intervals gt More specifically we want a high probability p0 eg pc 95 that lPe 7 Pei lt so gt The parameter so is called the confidence interval gt it depends on the confidence level pc the error probability P9 and the number of transmitted symbols N gt It can be shown that Pe1 7 P9 N I where 20 depends on the confidence level p0 gt Specifically 0zc 1 spa2 gt Example for pc 95 20 196 ScZc gt Question How is the number of simulations determined from the above considerations Choosing the Number of Simulations gt For a Monte Carlo simulation a stop criterion can be formulated from gt a desired confidence level pc and thus 20 gt an acceptable confidence interval so gt the error rate Pe gt Solving the equation for the confidence interval for N we obtain N Pe17 P9 zcsc2 gt A Monte Carlo simulation can be stopped after simulating N transmissions gt Example For pc 95 P9 10 3 and so 104 we find N z 400000 A Better StopCriterion gt When simulating communications systems the error rate is often very small gt Then it is desirable to specify the confidence interval as a fraction of the error rate gt The confidence interval has the form so we Pe eg we 01 for a 10 acceptable estimation error gt Inserting into the expression for N and rearranging terms Pe N 1 7 P9 201ch m zcocc2 gt Recognize that Pe N is the expected number of errors gt Interpretation Stop when the number of errors reaches 20040 2 gt Rule of thumb Simulate until 400 errors are found pc 95 0c 10 it to Listing MCSimpIeDriverm parameters delegated to script SimpleSetParameters SimpleSetParameters comms simulation parameters EsOverNOdB 02059 Maxsymbols le6 vary SNR between 0 and 9dB simulate at most 1000000 symbols a desired confidence level an size of confidence interval 1 95 ConfLeve ZValue Qinv liConfLevel 2 CoanntSize 0 l confidence interval size is 10 of estimate For the desired accuracy we need to ind this many errors MinErrors ZValueConflntSize AZ Verbose true control progress output simulation loops initialize loop variables NumErrors Numsymbols zeros zeros size size EsOverNOdB EsOverNOdB Listing MCSimpIeDriverm llength EsOVerNOdB a set ES 0 for this iteration ParametersEsOVerN0 B lin EsOVerNOdBkk rese st p condition for inner loop Done false progress output if Verbose disp sprintf EsNOHO3ngB EsOVerNOdB kk I end inner loop iterates until enough errors have been found while Done NumErrors kk NumErrors kk MCSimple Parameters Numsymbols kk e Numsymbols kk Parameters Nsymbols 9 Compute Stop condition Done NumErrors kk gt MinErrors Numsymbols kk gt MaXSymbol am 4 u m E 1 1 2 1 2 4 4 a 2mm 5E 335 Simulation Results Summary gt Introduced discretetime equivalent systems suitable for simulation in MATLAB gt Relationship between original continuoustime system and discretetime equivalent was established gt Digital postprocessing digital matched filter and slicer gt Monte Carlo simulation of a simple communication system was performed gt Close attention was paid to the accuracy of simulation results via confidence levels and intervals gt Derived simple rule of thumb for stopcriterion Where we are gt Laid out a structure for describing and analyzing communication systems in general and wireless systems in particular gt Saw a lot of MATLAB examples for modeling diverse aspects of such systems gt Conducted a simulation to estimate the error rate of a communication system and compared to theoretical results gt To do consider selected aspects of wireless communication systems in more detail including gt modulation and bandwidth gt wireless channels gt advanced techniques for wireless communications Outline MATLAB Simulation Frequency Diversity WideBand Signals Frequency Diversity through WideBand Signals gt We have seen above that narrowband systems do not have builtin diversity gt Narrowband signals are susceptible to have the entire signal affected by a deep fade gt In contrast wideband signals cover a bandwidth that is wider than the coherence bandwidth gt Benefit Only portions of the transmitted signal will be affected by deep fades frequencyselective fading gt Disadvantage Short symbol duration induces lSl receiver is more complex gt The benefits far outweigh the disadvantages and wideband signaling is used in most modern wireless systems Illustration Builtin Diversity of Wideband Signals gt We illustrate that wideband signals do provide diversity by means of a simple thought experiments gt Thought experiment gt Recall that in discrete time a multipath channel can be modeled by an FIR filter gt Assumefilter operates at symbol rate Ts gt The delay spread determines the number of taps L gt Our hypothetical system transmits one information symbol in every Lth symbol period and is silent in between gt At the receiver each transmission will produce L nonzero observations gt This is due to multipath gt Observation from consecutive symbols don t overlap no lSl gt Thus for each symbol we have L independent observations ie we have Lfold diversity Frequ Illustration Builtin Diversity of Wideband Signals gt We will demonstrate shortly that it is not necessary to leave gaps in the transmissions gt The point was merely to eliminate ISI gt Two insights from the thought experiment gt Wideband signals provide builtin diversity gt The receiver gets to look at multiple versions of the transmitted signal gt The order of diversity depends on the ratio of delay spread and symbol duration gt Equivalently on the ratio of signal bandwidth and coherence bandwidth gt We are looking for receivers that both exploit the builtin diversity and remove ISI gt Such receiver elements are called equalizers Equalization gt Equalization is obviously a very important and well researched problem gt Equalizers can be broadly classified into three categories 1 Linear Equalizers use an inverse filter to compensate for the variations in the frequency response gt Simple but not very effective with deep fades 2 Decision Feedback Equalizers attempt to reconstruct ISI from past symbol decisions gt Simple but have potential for error propagation 3 ML Sequence Estimation find the most likely sequence of symbols given the received signal gt Most powerful and robust but computationally complex Freciuentzw39 it Maximum Likelihood Sequence Estimation gt Maximum Likelihood Sequence Estimation provides the most powerful equalizers gt Unfortunately the computational complexity grows exponentially with the ratio of delay spread and symbol duration gt e with the number of taps in the discretetime equivalent FIR channel u Maximum Likelihood Sequence Estimation gt The principle behind MLSE is simple gt Given a received sequence of samples Rln eg matched filter outputs an gt a model for the output of the multipath channel fln sln hln where gt sin denotes the symbol sequence and gt hn denotes the discretetime channel impulse response ie the channel taps gt Find the sequence of information symbol sln that minimizes 02 lrln 7 sln hlnllz ln to Equaltalicm l Maximum Likelihood Sequence Estimation gt The criterion N 02 erln 7 sln hlnllz n gt performs diversity combining via sln hlnl and gt removes ISI gt The minimization of the above metric is difficult because it is a discrete optimization problem gt The symbols sln are from a discrete alphabet gt A computationally efficient algorithm exists to solve the minimization problem gt The Viterbi Algorithm gt The toolbox contains an implementation of the Viterbi Algorithm in function Va MATLAB Simulation gt A Monte Carlo simulation of a wideband signal with an equalizer is conducted gt to illustrate that diversity gains are possible and gt to measure the symbol error rate gt As before the Monte Carlo simulation is broken into gt set simulation parameter script VASetParameters gt simulation control script MCVADerer and gt system simulation function MCVA MATLAB Simulation System Parameters on Parameters Parameters Parameters Parameters Parameters Parameters Parameters Parameters Parameters channel Parameters Parameters Parameters Listing VASetParametersm T lle6 fsT 8 Es l EsOVerNO 6 Alphabet l 1 NSymbols 500 TrainLoc TrainLength TrainingSeq ChannelParams tux fd 3 L 6 floor ParametersNSymbols2 a 40 r Randomsymbols Par P symbol iod samples per symbol normalize received symbol energy to l Signalitoinoise ratio ESN0 BPSK number of Symbols per frame quot location of t ametersTrainLength arametersAlphabet 05 05 channel model Dopp er channel e e a order MATLAB Simulation gt The first step in the system simulation is the simulation of the transmitter functionality gt This is identical to the narrowband case except that the baud rate is 1 MHZ and 500 symbols are transmitted per frame gt There are 40 training symbols Listing MCVAm transmitter and channel Via toolbox functions Infosymbols Randomsymbols Nsymbols Alphabet Priors insert training sequence Symbols InfosymbolslTrainLoc TrainingSeq Infosymbols TrainLoclend 46 linear modulation 3 Signal A LinearModulation Symbols hh fsT MATLAB Simulation gt The channel is simulated without spatial diversity gt To focus on the frequency diversity gained by wideband signaling gt The channel simulation invokes the timevarying multipath simulator and the AWGN function timeivarying multiipath channels and additive noise Received SimulateCOSTChannel Signal ChannelParams f5 51 Received addNoise Received NoiseVar MATLAB Simulation m N gt The receiver proceeds as follows gt Digital matched filtering with the pulse shape followed by downsampling to 2 samples per symbol gt Estimation of the coefficients of the FIR channel model gt Equalization with the Viterbi algorithm followed by removal of the training sequence MFOut DMF fSTZ Received hh channel estimation MFOutTraining MFOut 2TrainLocl ChannelEst EstChannel 2TrainLocTrainLength L MFOutTraining TrainingSeq VA over MFOut using ChannelEst Decisions Va MFOut ChannelEst Alphabet 2 a strip training sequence and possible extra symbols TrainLocTrainLength Decisions TrainLocl Channel Estimation gt Channel Estimate F1 S S 1 S r where gt S is a Toeplitz matrix constructed from the training sequence and gt r is the corresponding received signal TrainingSPS zerosl lengthReceiVed TrainingSPS l 2 SpS end Training 5 make into a Toepliz matrix Such that TH is Convolution TrainMatrix toeplitz TrainingSPS Trainingl zerosl Orderil co ChannelEst Received conj TrainMatrix invTrainMatrix TrainMatrix 5 Emma Figure Symbol Error Rate with Viterbi Equalizer over Multipath Fading Channel Rayleigh channels with transmitter diversity shown for comparison Baud rate 1MHZ Delay spread z 2145 Conclusions gt The simulation indicates that the wideband system with equalizer achieves a diversity gain similar to a system with transmitter diversity of order 2 gt The ratio of delay spread to symbol rate is 2 gt comparison to systems with transmitter diversity is appropriate as the total average power in the channel taps is normalized to 1 gt Performance at very low SNR suffers probably from inaccurate estimates gt Higher gains can be achieved by increasing bandwidth gt This incurs more complexity in the equalizer and gt potential problems due to a larger number of channel coefficients to be estimated gt Alternatively this technique can be combined with additional diversity techniques eg spatial diversity Frequeruw More Ways to Create Diversity gt A quick look at three additional ways to create and exploit diversity 1 Time diversity 2 Frequency Diversity through OFDM 3 Multiantenna systems MIMO Time Diversity gt Time diversity is created by sending information multiple times in different frames gt This is often done through coding and interleaving gt This technique relies on the channel to change sufficiently between transmissions gt The channels coherence time should be much smaller than the time between transmissions gt If this condition cannot be met eg for slowmoving mobiles frequency hopping can be used to ensure that the channel changes sufficiently gt The diversity gain is at most equal to the number of timeslots used for repeating information gt Time diversity can be easily combined with frequency diversity as discussed above gt The combined diversity gain is the product of the individual diversity gains OFDM gt OFDM has received a lot of interest recently gt OFDM can elegantly combine the benefits of narrowband signals and wideband signals gt Like for narrowband signaling an equalizer is not required merely the gain for each subcarier is needed gt Very lowcomplexity receivers gt OFDM signals are inherently wideband frequency diversity is easily achieved by repeating information really coding and interleaving on widely separated subcarriers gt Bandwidth is not limited by complexity of equalizer gt High signal bandwidth to coherence bandwidth is possible high diversity MIMO y We have already seen that multiple antennas at the receiver can provide both diversity and array gain gt The diversity gain ensures that the likelihood that there is no good channel from transmitter to receiver is small gt The array gain exploits the benefits from observing the transmitted energy multiple times It the system is equipped with multiple transmitter antennas then the number of channels equals the product of the number of antennas V gt Very high diversity Recently it has been found that multiple streams can be transmitted in parallel to achieve high data rates gt Multiplexing gain The combination of multiantenna techniques and OFDM appears particularly promising V V

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