mewthturn
Newbie level 3
MATLAB : need help for BER and SNR plot for QAM modulation and demodulation
i am currently creating a code where the signal vector will be segmented out to a certain amount of bits and i will add noise to it and demodulation and get the BER. But my BER vs SNR plot graph looks very wierd to how a normal BER vs SNR graph should look like. I would appreciate if someone can tell me what is wrong with my code or something I am lacking, thank you.
Here is the code:
i am currently creating a code where the signal vector will be segmented out to a certain amount of bits and i will add noise to it and demodulation and get the BER. But my BER vs SNR plot graph looks very wierd to how a normal BER vs SNR graph should look like. I would appreciate if someone can tell me what is wrong with my code or something I am lacking, thank you.
Here is the code:
Code:
%% QAM-[Modulation,Demodulation,Bit Error Rate]
%% (1)Setup
a = 4; % A variable to make sure it is in [2^]
N = 4; % Number of antennas in Receieve and Transmit ends
M = 2^a; % M-ary QAM in base 2 / Size of bit for signal constellation points
k = log2(M); % Number of bits per symbol
n = 20; % Number of bits to process
oo=1;
snr=1:5; % snr in dB
%% (2)Signal Source
% Create a binary data stream as a column vector.
binary = randi([0 1],n,k); % Random binary data stream
de = bi2de(binary,'left-msb'); % Convert binary to decimal values
%% (4)Modulation
qammodulation = modem.qammod(M); % Modulation type with value 'M'
sym = modulate(qammodulation,de); % Modulate using h-type \ showing where the points are located
%sym=step(zz1,de) for soft decision of generalqammod
%% (5)Normalization : setting Es and Eb to 1
% to obtain E==1 : integral of (abs(signal))^2 dt
b = zeros(n,1); % Creating a vector with 'n' amount of rows
for o = 1:(length(binary)) % For 'o' amount of loops running to length of binary
b(o) = (1/(abs(sym(o))))*sym(o); % Each index of 'b' takes in the value of the function 4qam
% Modulated vector = b
end
Es=1;Eb=1; % due to normalization
%% (6)Miscellaneous
% Standard distribution matrix of N antena
H = (1/sqrt(2))*(randn(N) + 1i*randn(N)); % H to be a matrix of mean=0,variance=1 and complex
% 1/sqrt(2) due to (var=1) + (var=1) and normalisation is absolute rms
y = zeros(N,1); % y = output vector
s = zeros(N,1); % s = signal vector
zfnns = zeros(N,1); % new s with 0 noise interference with Gzf
zfns = zeros(N,1); % new s with noise interference with Gzf
nns = zeros(N,1); % new s with 0 noise interference and direct inverse
ns = zeros(N,1); % new s with noise interference with direct inverse
tx = zeros(N*k,1); % tx = transmit vector
%% (7)Loop for Segmentation of 'k' bits matrix into vector
io = 1; jo = 1; ko = 1;
while (ko<=M)
tx(ko) = binary(io,jo);
ko = (ko + 1);
jo = mod( (jo + 1),(k + 1) );
if jo == 0
io = io + 1;
jo = 1;
end
end
%% (8)Segmentation of Signal Vector(s) to wanted dimension with 'N' amount of Transmitted and Received antenna(s)
x=zeros((length(snr)),(n/k));
ja=1;
while ja<=length(snr)
i = 1;
j = N;
oo=1;
while((i<=(n-(N-1)))&&(j<=(n)))
SNR=10^((snr(ja))/10); % Changing from Decibels
No = Es/SNR; % Noise power
meanofnoise = 0; % Expected Value of Noise vector to be zero
sigma_2 = No; % Variance not zero
sigma = sqrt(sigma_2); % Standard deviation
s(1:N)=b(i:j); % Segmentation of vectors out to wanted amount
i = i + N;
j = j+ N;
y(1:N) = H*s ; % Output : y = H*s
%adding y with noise
noise = normrnd(meanofnoise,sigma,N,1)+1i*normrnd(meanofnoise,sigma,N,1);
ynoise=y+noise;
vec_length = length(noise);
Cn = zeros(vec_length);
for r = 1:vec_length
Cn(r,r) = var(noise); % Creating Covariance Matrix with diagonal element of noise variance
% and has zero mean due to Stochastic Independent
end;
%% (9)Filter Matrix
G = pinv(H); % Due to zero noise ; HG = I
Gzf = inv(conj(H'))*(inv(Cn))*(inv(Cn)); % Zero Forcing Filter Matrix
nns(1:N) = G*y; % noiseless inverse
ns(1:N) = G*ynoise; % noise inverse
zfnns(1:N) = Gzf*y; % noiseless Gzf
zfns(1:N) = Gzf*ynoise; % noise Gzf
%% (10)Demodulation
% Demodulate signal using M-QAM.
qamdemodulation = modem.qamdemod(qammodulation);
desym = demodulate(qamdemodulation,ynoise);
% Decimal values to binary using toolbox
dectobit = comm.IntegerToBit(k);
%
rx = step(dectobit,desym);
%% (11)BER Computation of each atenna of 'N' amount
% Comparsion of [ 't' which is the amount/type of bits transmitted ] &
% & [ 'r' which is the amount/type of bits received ] to obtain the number of error(s) % the bit error rate.
er = comm.ErrorRate; % Toolbox that creates an error rate calculator System object
bit_error_rate = step(er,tx,rx); % Computes the error
BER = bit_error_rate(1); % Bit Error Rate per 'N' amount of atenna bits
errors = bit_error_rate(2); % Number of Errors per 'N' amount of atenna bits
x(ja,oo:oo)=errors;
% alternate way%[nubmer_of_errors,bit_error_rate] = biterr(tx,rx);
oo=oo+1;
end
ja=ja+1;
end
%% (12)Transmitted Signal
ytx = s;
%% (13)Received Signal
yrx = ynoise;
%% (14)Total Bit Error Rate
c1=zeros(length(snr),1);
m=length(snr)*(k*N); %total bits per snr
%total no.of different snr * no. of bits to represent 1 symbol * no. of atennas
c=1;
while c<=length(snr)
c1(c)=sum(x(c,:)); %total errors per snr
c=c+1;
end
ber=c1/m; %dividing total error by total bits gives BER
%% Scatter Plot
% Create scatter plot of noisy signal and transmitted signal on the same axes.
h = scatterplot(yrx(1:N),1,0,'b.');
hold on;
scatterplot(ytx(1:N),1,0,'k*',h);
title('Received Signal');
legend('Received Signal','Signal Constellation, What was transmitted');
axis([-5 5 -5 5]); % axis parameters.
hold off;
%% BER vs SNR
figure;
loglog(snr,ber);
title('log graph of SNR vs BER');
xlabel('BER');
ylabel('SNR');
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