%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% All rights reserved by Krishna Pillai, http://www.dsplog.com
% The file may not be re-distributed without explicit authorization
% from Krishna Pillai.
% Checked for proper operation with Octave Version 3.0.0
% Author : Krishna Pillai
% Email : krishna@dsplog.com
% Version : 1.0
% Date : 23rd October 2008
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Script for computing the BER for BPSK modulation in a
% Rayleigh fading channel with 2 Tx, 2Rx MIMO channel
% Zero Forcing equalization
clear
N = 10^6; % number of bits or symbols
Eb_N0_dB = [0:25]; % 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
iq=randn(1,N)>0.5;
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
sq=-2*iq+1;
s=s-j*sq;
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) + j*randn(nRx,nTx,N/nTx)]; % Rayleigh channel ？？？
n = 1/sqrt(2)*[randn(nRx,N/nTx) + j*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;% 注意这里是点乘，对应位直接乘，不是矩阵乘法
%squeeze删去大小为1的孤维
% B = sum(A,dim) %sum(x,2)表示矩阵x的横向相加，求每行的和，结果是列向量。
% 沿着A的每一维计算总和用指定标量dim，dim是一个从1到N 的整数值，其中N是A的维数。
% dim为1就是计算A的每一列的总和，2计算A的每一行的总和，以此类推。
%B=squeeze(A) 在这里应该是指sum(h.*sMod)是第三维是N/nTx 现在把他转换为第二维是N/nTx，第三维不见了。这样才可以跟噪声相加
%返回和矩阵A相同元素但所有单一维都移除的矩阵B，单一维是满足size(A,dim)=1的维。
%squeeze命令对二维数组是不起作用的;
%如果A是一行或列向量或一标量(1*1)值，则B=A
% Receiver
% Forming the Zero Forcing equalization matrix W = inv(H^H*H)*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); % d term 现在是1*N/2矩阵
hCof(2,2,:) = sum(h(:,1,:).*conj(h(:,1,:)),1); % 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 共轭 %2*2*N/2变成2*N矩阵
%ZC = conj(Z)
%返回Z中元素的复共轭值
yMod = kron(y,ones(1,2)); % formatting the received symbol for equalization
% Y = ones(m,n) 或 Y = ones([m n])
% 返回元素都为1的m*n矩阵，m和n都为标量
yMod = sum(hMod.*yMod,1); % H^H * y 先点乘，再行相加，成行向量 N
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 这里对应 （3）？
% receiver - hard decision decoding
ipHat = real(yHat)>0;
iqHat = imag(yHat)>0;
% counting the errors
nErr(ii) = size(find([ip- ipHat]),2); %ind = find(X) 返回非零元的下标
nErrq(ii)=size(find([iq- iqHat]),2); %A的第二维的大小,如M*N size(A，2)返回N
end
simBer = (nErrq+nErr)/(2*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);
%semilogy(X1,Y1,...,Xn,Yn)
%Xn和Yn是成对出现的.
%如果Xn或Yn其中一个为矩阵其他为向量且向量维数与矩阵的维数(行或列)相匹配，semilogy则按照匹配的方向分解矩阵并画图。
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=1,nRx=1)', 'theory (nTx=1,nRx=2, MRC)', 'sim (nTx=2, nRx=2, ZF)');
xlabel('Average Eb/No,dB');
ylabel('Bit Error Rate');
title('BER for QPSK modulation with 2x2 MIMO and ZF equalizer (Rayleigh channel)');
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