MULTICARRIER MODULATION FOR WIMAX:SIMULATION RESULTS OF MODULE-1

NARESH KUMAR.T (07EC6314)

CONETENTS PAGE NO:

OFDM SYMBOL GENERATION 2-5

CODING SCHEME IMPLEMENTATION 5-7

EQUALIZER IMPLEMENTATION 8-10

ISI SIMULATION WITH VARYING 10-11GUARD FRACTION

FADING CHANNEL CHARACTERISTICS 11-13

SUBCARRIER SPACING EFFECTON RECEIVER PERFORMACE 13-14

SUB CARRIER /SUB CHANNEL ALLOCATION STRATERGY 14-15

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PROJECT SIMULATION RESULTS:1.OFDM SYMBOL GENERATION:BLOCK SCHEMATIC :

MATLAB CODE:clc;clear all;close all;Tu=64e-6; %useful OFDM symbol periodT=Tu/256; %baseband elementary periodFS=256; %IFFT/FFT lengthq=10; %carrier period to elementary period ratiofc=q*1/T; %carrier frequencyRs=4*fc; %simulation periodt=0:1/Rs:Tu/2;%Data generator M=192;a=-1+2*round(rand(M,1))+i*(-1+2*round(rand(M,1)));A=length(a);info=zeros(FS,1);info(1:(A/2)) = [ a(1:(A/2)).']; %Zero paddinginfo((FS-((A/2)-1)):FS) = [ a(((A/2)+1):A).'];%Subcarriers generation carriers=FS.*ifft(info,FS);%cyclic prefix insertion pl=FS*(1/8); li=length(carriers); z=zeros((pl+li),1); for i=1:1:li z(pl+i)=carriers(i); end for i=1:1:pl z(i:pl)=carriers((li-pl+i):li); endtt=0:T/2:Tu;figure(1);subplot(211);stem(tt(1:20),real(z(1:20)));subplot(212);stem(tt(1:20),imag(z(1:20)));% D/A simulationL = length(z);chips = [z.';zeros((2*q)-1,L)];

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p=1/Rs:1/Rs:T/2;g=ones(length(p),1); %pulse shapefigure(3);stem(p,g);dummy=conv(g,chips(:));u=[dummy(1:length(t))];figure(4);subplot(211);plot(t(1:400),real(u(1:400)));subplot(212);plot(t(1:400),imag(u(1:400)));[b,a] = butter(13,1/20); %reconstruction filter[H,F] = FREQZ(b,a,FS,Rs);figure(6);plot(F,20*log10(abs(H)));uoft = filter(b,a,u); %baseband signal figure(7);subplot(211);plot(t(80:480),real(uoft(80:480)));subplot(212);plot(t(80:480),imag(uoft(80:480)));%Upconverters_tilde=(uoft.').*exp(1*j*2*pi*fc*t);s=real(s_tilde); %passband signal figure(9);plot(t(80:480),s(80:480));%********RECEIVER DESIGN***************%r_tilde=exp(-1*j*2*pi*fc*t).*s; %down convertionfigure(10);subplot(211);plot(t,real(r_tilde));axis([0e-7 100e-7 -60 60]);grid on;subplot(212);plot(t,imag(r_tilde));axis([0e-7 100e-7 -100 150]);[B,AA] = butter(13,1/2);r_info=2*filter(B,AA,r_tilde); %LOw pass filtered outputfigure(11);subplot(211);plot(t,real(r_info));axis([0 100e-7 -60 60]);grid on;figure(11);subplot(212);plot(t,imag(r_info));axis([0 100e-7 -100 150]);length(r_info)grid on;%r_data=(r_info(1:(2*q):length(t)));r_data=real(r_info(1:(2*q):length(t)))+j*imag(r_info(1:(2*q):length(t)));figure(12);subplot(211);stem(tt(1:30),(real(r_data(2:31))));axis([0.375e-6 30e-7 -40 40]);grid on;subplot(212);stem(tt(1:30),(imag(r_data(1:30))));axis([0.375e-6 30e-7 -40 40]);grid on;

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%FFTinfo_2N=(1/FS)*fft(r_data,L);%removal of cyclic prefixinfo_2N=info_2N((pl+1):length(info_2N));length(info_2N)info_h=[info_2N(1:A/2) info_2N((FS-((A/2)-1)):FS)];figure(13)grid on;plot(info_h((1:A)),'*');title('info Received Constellation')

INPUT SEQUENCE:

FILTERED O/P BUTTERWORTH:

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PASSBAND SIGNAL:

RECEIVED SEQUENCE;

O/P:

CODING SCHEMES IMPLEMENTATIONS:QPSK:clc;clear;g=input('enter the bit stream:');l=length(g);if(rem(l,2)~=0); error('please insert a vector divisible by 2');end t=0:(1/99):1;

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cp=[];sp=[];mod=[];mod1=[];bit=[];for n=1:2:length(g); if g(n)==0 && g(n+1)==1; inph=(1/sqrt(2))*ones(1,100); qph=-(1/sqrt(2))*ones(1,100); data=[zeros(1,50) ones(1,50)]; elseif g(n)==0 && g(n+1)==0; inph=-(1/sqrt(2))*ones(1,100); qph=-(1/sqrt(2))*ones(1,100); data=[zeros(1,50) zeros(1,50)]; elseif g(n)==1 && g(n+1)==0; inph=-(1/sqrt(2))*ones(1,100); qph=(1/sqrt(2))*ones(1,100); data=[ones(1,50) zeros(1,50)]; elseif g(n)==1 && g(n+1)==1; inph=(1/sqrt(2))*ones(1,100); qph=(1/sqrt(2))*ones(1,100); data=[ones(1,50) ones(1,50)]; end f=10*10^6; c=cos(2*pi*f*t); s=sin(2*pi*f*t); cp=[cp inph]; sp=[sp qph]; mod=[mod c]; mod1=[mod1 s]; bit=[bit data];endbpsk=cp.*mod+sp.*mod1;subplot(2,1,1);plot(bit,'LineWidth',1.5);grid on;title('Binary Signal')axis([0 50*length(g) -1.5 1.5]); subplot(2,1,2);plot(bpsk,'LineWidth',1.5);grid on;title('QPSK modulation')axis([0 50*length(g) -1.5 1.5]);

RESULTS:enter the bit stream:[1 0 0 1 1 0 1 0]

5. study effect of varying sub carrier spacing on receiver performance : Complex envelope of the transmitted OFDM signal for a given OFDM Symbol, sampled with sampling frequency fs=B;

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with .n=0,1,2,…N-1;This symbol is actually extended with a Time Guard in order to cope with multipath delay spread, as explained in Section II. For the sake of simplicity, we will not consider this prefix since it is eliminated in the receiver. Assuming that the channel is flat, the signal is only affected by phase noise at the receiver the received signal is Orthogonal Frequency Division Demultiplexed (OFDD) by means of a Discrete Fourier Transform.

In order to separate the signal and noise terms, let us suppose that is small, so that In this case, the demultiplexed signal is:

Thus we have an error term for each sub-carrier which results from some combination of all of them and is added to the useful signal. Let us analyze more deeply this noise contribution:

1) Common Phase Error: for (r=k)

We have a common error added to every sub-carrier that is proportional to its value multiplied by a complex number that is a rotation of the constellation. This angle results from an average of phase noise:

This average implies low frequencies of phase noise spectrum up to, that is the inter-carrier spacing. Since it is constant for all sub-carriers, it can be corrected by some kind of phase rotation.

This term corresponds to the summation of the information of the other sub-carriers each multiplied by some complex number which comes from an

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average of phase noise with a spectral shift. The result is also a complex number that is added to each sub-carrier’s useful signal and has the appearance of Gaussian noise. It is normally known as inter-carrier interference.

1. When the ratio between the phase noise bandwidth and he OFDM inter-carrier spacing is small, it comes out from that the common phase error dominates over the inter-carrier interference (ICI). Since this error can be corrected together with the channel effects [9], the symbol error rate after correction is much lower than before as

2. On the other hand, as this ratio approaches unity, that is, the phase noise bandwidth becomes closer to the inter-carrier spacing value, the inter-carrier interference increases and the correction capabilities decrease.

3.If it is greater than 1, then symbol error rate after correction can be equal to that obtained before correction or even worse if the chosen phase correctingScheme fails due to the presence of noise.

2. ADAPTIVE RESOURCE ALLOCATION STRATERGIES TO COMBAT THE EFFECT OF FADING ENVIRONMENTS:

We consider uncoded transmission over a synchronous flat fading multiple-access (uplink) OFDM discretetime system with N users and L sub-carriers (referred to as sub-bands) for each user. The signal received at timen is given by:

where xi,j(n) denotes the transmitted symbol, si,j the spreading sequence, wi,j(n) the additive Gaussian noise and hi,j (n) the stationary and ergodic channel gain corresponding to User i in sub-band j. The hi,j (n) are assumedto be i.i.d., and to result from a combination of fast (assumedRayleigh) fading and slow fading. Equivalently,

hi,j results from the product of a fast fade rid(n) and a slow fade hi,j(n). We assume ri,j(n) to be unit mean. Equivalently, hi,j(n) is the short-term mean ofhi,j(n) (hence the symbol hi,j for the slow fade). We assume that hi,j(n) is known perfectly at the transmitter and receiver at time n. Note that, with appropriate scaling, we may assume that the noise variance is unity.The short-term means hi,j (n) for each user and each sub-band are fed back fromthe base-station to all the users in the system. Since most OFDM systems in use today use the conventional matched filter receiver, we assume the same

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for our OFDMA system, with one matched filter for every Spreading sequence si,j. We assume that any two spreading Sequences have a constant cross correlation given by PWe.

Now characterize the constraints imposed on this system by practical requirements. The power of each User i is required not to exceed p on average, where the average is over the composite fading distribution hi,j (n). Constructing a matrix H(n) whose (i, j)th element is hi,j(n) and denoting the power of User i in sub-channel j by Pi,j ,we have EH cj”=, Pi,j = p for 1 5 i 5 N.First, we analyze the MC-CDMA system given with one sub-band per user, i.e with L = 1. This is equivalent to a synchronous ofdma system without inter-symbol interference (ISI). There are three well known techniques for dynamic rate adaptation OFDM systems: multi-code, multi-bit Rate and variable constellation size methods, which are explained in [9]. To maintain continuity with previous sections, we focus on variable-constellation size schemes in this paper. In a variable constellation size scheme, each user is assigned a single spreading sequence.

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