BIT ERROR RATE OF COHERENT CP-OFDM SYSTEM OPERATING OVER A RAYLEIGH FADING CHANNEL

SYSTEM SPECIFICATIONS:

1) 128 subcarriers

2   BPSK modulation

3)  10 tap Rayleigh fading channel with exponential PDP

4)  Cyclic prefix length of 32 to avoid Inter-block interference

5)  Coherent receiver

MATLAB CODE:

clc;

clear all;

close all;

k=0;

snr= -5:2:11;

snrn=power(10,snr/10);

a=1;

for j=1:20

    wf(1,j)=1./exp(j-1);                   %EXPONENTIAL POWER DELAY PROFILE

end

for SNR=-5:2:11

    k=k+1;

    error=0;

    for chnlno=1:power(10,3)

        msgbits=randint(1,128);                           % 128 SUBCARRIERS

        for i=1:length(msgbits)

            if msgbits(i)==0

                s(i)=a;

            else

                s(i)=-a;

            end

        end                                              %BPSK MAPPING DONE

       

        xi=ifft(s);

        for i=97:128

            cp(i-96)=xi(i);                                  % 32 LENGTH CP

        end

        x=horzcat(cp,xi);                              %CYCLIC PREFIX ADDED

       

        hi=((1/sqrt(2))*randn(20,2));

        for j=1:20

            hi2(1,j)=hi(j,1)+sqrt(-1)*hi(j,2);             % 10 TAP CHANNEL

        end

        h=(wf).*(hi2);

       

        ynn=conv(x,h);     

       

        sigmasqr=(1)/(2*(power(10,(SNR/10))));

        noisei=(sigmasqr)*randn(length(ynn),2);

       

        for j=1:length(ynn)

            noise(1,j)=noisei(j,1)+sqrt(-1)*noisei(j,2);

        end

       

        y=ynn+noise;

       

        for i=33:160

            yh(i-32)=y(i);                           %CYCLIC PREFIX REMOVED

        end

       

        Yeq=(fft(yh))./(fft(h,128));

        yeq=ifft(Yeq);

        yi=fft(yeq);

       

        for i=1:128

            if real(yi(i)>0)

                mh(i)=0;

            else

                mh(i)=1;

            end

        end

       

        for i=1:128

            if mh(i)==msgbits(i)

                error=error+0;

            else

                error=error+1;

            end

        end

    end

    BER(k)=error/(128*power(10,4));

end

figure(1);

semilogy(snr,BER,'linewidth',1.5);

xlabel('SNR IN dB ------>');

ylabel('BER');

title('BER PERFORMANCE OF A CP-OFDM SYSTEM');

grid;

SNR Vs BER CURVE:

SOME PHILOSOPHY:

1)  BER curve almost in sync with that of a single carrier system operating over Rayleigh flat fading channel (as expected).

2)  Do not expect waterfall curve for BER in Rayleigh fading channels. BER plot will always be a straight line in high SNR regime. Slope can be improved using diversity (time, frequency, space).

3)  To make OFDM achieve frequency diversity, you have to code across subcarriers instead of coding across time. Coding across time alone results in high latency since OFDM symbol duration is pretty high. Typical systems code across both subcarriers and time in order to achieve same diversity with lesser latency (as compared to coding just across time).

4)  While coding across subcarriers, keep in mind that not all parallel channels are uncorrelated. You need to determine the minimum frequency spacing for uncorrelatedness before you code. Otherwise, you will not get full diversity.