In BER SIMULATION of BPSK IN RAYLEIGH FADING ENVIRONMENT when I place h=sqrt(1/2​)*(randn+j​*randn) before while loop I don't get any curve and total BER result why is that ?

clear

EbN0dB_vector=0:2:20

Eb=1;

for snr_i=1:length(EbN0dB_vector);

EbN0dB=EbN0dB_vector(snr_i);

EbN0=10.^(EbN0dB/10)

N0=Eb/EbN0;

sym_cnt=0

err_cnt=0

h=sqrt(1/2)*(randn+j*randn);

while err_cnt<500

s=sqrt(Eb)*sign(rand-0.5) ;

n=sqrt(N0/2)*(randn+j*randn);

r=h*s + n;

D=r*exp(-j*angle(h));

s_hat=sign(real(D));

if s_hat~=s

err_cnt=err_cnt+1;

end

sym_cnt=sym_cnt+1;

end

BER(snr_i)=err_cnt/sym_cnt

end

figure

semilogy(EbN0dB_vector, BER)%y in logarithm scale

xlabel('E_b/N_0 [dB]')

ylabel('BER')

grid

%Get result upto this

BER =

0.0543 0.0001 0.0057 0.0008 0.0007 0.0031 0.0049

Answer 1

[Shashi Kiran]

Hi Mashrur,

I understand that you are encountering an issue of not getting the complete Bit Error Rate (BER) results for all Signal to Noise Ratio (SNR) values when you place the channel matrix (h) before the while loop in your code.

This occurs because, placing channel matrix h outside the loop results in a constant channel for all symbols, simulating a slow fading scenario (Constant Channel Effect).

• If the channel is poor, errors accumulate quickly, ending the loop sooner.
• If the channel is good, it takes longer to reach the error threshold, causing the program to run continuously, as you observed.

To simulate fast fading, generate h inside the loop so the channel changes for each symbol. This approach offers a more robust and realistic evaluation of system performance across varying conditions.

Here is how the code can be modified to simulate a fast fading scenario:

clear;
EbN0dB_vector = 0:2:20;
Eb = 1;
BER = zeros(1, length(EbN0dB_vector)); % Pre-allocate BER array

for snr_i = 1:length(EbN0dB_vector)
    EbN0dB = EbN0dB_vector(snr_i);
    EbN0 = 10^(EbN0dB / 10);
    N0 = Eb / EbN0;
    sym_cnt = 0;
    err_cnt = 0;
    while err_cnt < 500
        % Generate a random BPSK symbol
        s = sqrt(Eb) * (2 * (rand > 0.5) - 1); 
        
        % Rayleigh fading channel
        h = (1/sqrt(2)) * (randn + 1i * randn);
        
        % AWGN noise
        n = sqrt(N0/2) * (randn + 1i * randn);
        
        % Received signal
        r = h * s + n;
        
        % Coherent detection
        D = r * exp(-1i * angle(h));
        
        % Decision
        s_hat = sign(real(D));
        
        % Error counting
        if s_hat ~= s
            err_cnt = err_cnt + 1;
        end
        
        sym_cnt = sym_cnt + 1;
    end
    
    % Calculate BER
    BER(snr_i) = err_cnt / sym_cnt;
end
disp(BER);

    0.1465    0.1067    0.0777    0.0538    0.0336    0.0240    0.0150    0.0098    0.0060    0.0037    0.0025

% Plotting
figure;
semilogy(EbN0dB_vector, BER, 'b-o'); % Plot with blue circles
xlabel('E_b/N_0 [dB]');
ylabel('BER');
title('BER vs E_b/N_0 for BPSK over Rayleigh Channel');
grid on;

Hope this helps.