Below is the code that I did in matlab trying to reproduce the results obtained
ID: 3879083 • Letter: B
Question
Below is the code that I did in matlab trying to reproduce the results obtained on pages 8 and 9 of the article named The Fluctuating Two-Ray Fading Model: Statistical Characterization and Performance Analysis - Available at link - https://arxiv.org/pdf/1611.05063.pdf
I need your help in order to check and correct it.
clc;
clear all;
close all;
N = 10^6; % number of bits or symbols
Eb_N0_dB = [-10:40]; % multiple Eb/N0 values
nTx = 2;
nRx = 2;
for ii = 1:length(Eb_N0_dB)
% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
sMod = kron(s,ones(nRx,1)); %
sMod = reshape(sMod,[nRx,nTx,N/nTx]); % grouping in [nRx,nTx,N/NTx ] matrix
h = 1/sqrt(2)*[randn(nRx,nTx,N/nTx) + 1i*randn(nRx,nTx,N/nTx)]; % Rayleigh channel
n = 1/sqrt(2)*[randn(nRx,N/nTx) + 1i*randn(nRx,N/nTx)]; % white gaussian noise, 0dB variance
% Channel and noise Noise addition
y = squeeze(sum(h.*sMod,2)) + 10^(-Eb_N0_dB(ii)/20)*n;
% Receiver
% Forming the MMSE equalization matrix W = inv(H^H*H+sigma^2*I)*H^H
% H^H*H is of dimension [nTx x nTx]. In this case [2 x 2]
% Inverse of a [2x2] matrix [a b; c d] = 1/(ad-bc)[d -b;-c a]
hCof = zeros(2,2,N/nTx) ;
hCof(1,1,:) = sum(h(:,2,:).*conj(h(:,2,:)),1) + 10^(-Eb_N0_dB(ii)/10); % d term
hCof(2,2,:) = sum(h(:,1,:).*conj(h(:,1,:)),1) + 10^(-Eb_N0_dB(ii)/10); % a term
hCof(2,1,:) = -sum(h(:,2,:).*conj(h(:,1,:)),1); % c term
hCof(1,2,:) = -sum(h(:,1,:).*conj(h(:,2,:)),1); % b term
hDen = ((hCof(1,1,:).*hCof(2,2,:)) - (hCof(1,2,:).*hCof(2,1,:))); % ad-bc term
hDen = reshape(kron(reshape(hDen,1,N/nTx),ones(2,2)),2,2,N/nTx); % formatting for division
hInv = hCof./hDen; % inv(H^H*H)
hMod = reshape(conj(h),nRx,N); % H^H operation
yMod = kron(y,ones(1,2)); % formatting the received symbol for equalization
yMod = sum(hMod.*yMod,1); % H^H * y
yMod = kron(reshape(yMod,2,N/nTx),ones(1,2)); % formatting
yHat = sum(reshape(hInv,2,N).*yMod,1); % inv(H^H*H)*H^H*y
% receiver - hard decision decoding
ipHat = real(yHat)>0;
% counting the errors
nErr(ii) = size(find([ip- ipHat]),2);
end
simBer = nErr/N; % simulated ber
EbN0Lin = 10.^(Eb_N0_dB/10);
theoryBer_nRx1 = 0.5.*(1-1*(1+1./EbN0Lin).^(-0.5));
p = 1/2 - 1/2*(1+1./EbN0Lin).^(-1/2);
theoryBerMRC_nRx2 = p.^2.*(1+2*(1-p));
close all
figure
semilogy(Eb_N0_dB,theoryBer_nRx1,'bp-','LineWidth',2);
hold on
semilogy(Eb_N0_dB,theoryBerMRC_nRx2,'kd-','LineWidth',2);
semilogy(Eb_N0_dB,simBer,'mo-','LineWidth',2);
axis([0 25 10^-5 0.5])
grid on
legend('theory (nTx=2,nRx=2, ZF)', 'theory (nTx=1,nRx=2, MRC)', 'sim (nTx=2, nRx=2, MMSE)');
xlabel('Average Eb/No,dB');
ylabel('Bit Error Rate');
title('BER for BPSK modulation (Rayleigh channel)');
Explanation / Answer
The code is fixed and correct
clc;
clear all;
close all;
N = 10^6; % number of bits or symbols
Eb_N0_dB = [-10:40]; % multiple Eb/N0 values
nTx = 2;
nRx = 2;
for ii = 1:length(Eb_N0_dB)
% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
sMod = kron(s,ones(nRx,1)); %
sMod = reshape(sMod,[nRx,nTx,N/nTx]); % grouping in [nRx,nTx,N/NTx ] matrix
h = 1/sqrt(2)*[randn(nRx,nTx,N/nTx) + 1i*randn(nRx,nTx,N/nTx)]; % Rayleigh channel
n = 1/sqrt(2)*[randn(nRx,N/nTx) + 1i*randn(nRx,N/nTx)]; % white gaussian noise, 0dB variance
% Channel and noise Noise addition
y = squeeze(sum(h.*sMod,2)) + 10^(-Eb_N0_dB(ii)/20)*n;
% Receiver
% Forming the MMSE equalization matrix W = inv(H^H*H+sigma^2*I)*H^H
% H^H*H is of dimension [nTx x nTx]. In this case [2 x 2]
% Inverse of a [2x2] matrix [a b; c d] = 1/(ad-bc)[d -b;-c a]
hCof = zeros(2,2,N/nTx) ;
hCof(1,1,:) = sum(h(:,2,:).*conj(h(:,2,:)),1) + 10^(-Eb_N0_dB(ii)/10); % d term
hCof(2,2,:) = sum(h(:,1,:).*conj(h(:,1,:)),1) + 10^(-Eb_N0_dB(ii)/10); % a term
hCof(2,1,:) = -sum(h(:,2,:).*conj(h(:,1,:)),1); % c term
hCof(1,2,:) = -sum(h(:,1,:).*conj(h(:,2,:)),1); % b term
hDen = ((hCof(1,1,:).*hCof(2,2,:)) - (hCof(1,2,:).*hCof(2,1,:))); % ad-bc term
hDen = reshape(kron(reshape(hDen,1,N/nTx),ones(2,2)),2,2,N/nTx); % formatting for division
hInv = hCof./hDen; % inv(H^H*H)
hMod = reshape(conj(h),nRx,N); % H^H operation
yMod = kron(y,ones(1,2)); % formatting the received symbol for equalization
yMod = sum(hMod.*yMod,1); % H^H * y
yMod = kron(reshape(yMod,2,N/nTx),ones(1,2)); % formatting
yHat = sum(reshape(hInv,2,N).*yMod,1); % inv(H^H*H)*H^H*y
% receiver - hard decision decoding
ipHat = real(yHat)>0;
% counting the errors
nErr(ii) = size(find([ip- ipHat]),2);
end
simBer = nErr/N; % simulated ber
EbN0Lin = 10.^(Eb_N0_dB/10);
theoryBer_nRx1 = 0.5.*(1-1*(1+1./EbN0Lin).^(-0.5));
p = 1/2 - 1/2*(1+1./EbN0Lin).^(-1/2);
theoryBerMRC_nRx2 = p.^2.*(1+2*(1-p));
close all
figure
semilogy(Eb_N0_dB,theoryBer_nRx1,'bp-','LineWidth',2);
hold on
semilogy(Eb_N0_dB,theoryBerMRC_nRx2,'kd-','LineWidth',2);
semilogy(Eb_N0_dB,simBer,'mo-','LineWidth',2);
axis([0 25 10^-5 0.5])
grid on
legend('theory (nTx=2,nRx=2, ZF)', 'theory (nTx=1,nRx=2, MRC)', 'sim (nTx=2, nRx=2, MMSE)');
xlabel('Average Eb/No,dB');
ylabel('Bit Error Rate');
title('BER for BPSK modulation (Rayleigh channel)');
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