CCS - simulation of Nt = Nr MIMO systems' capacity
1 % MATLAB script for Illustrative Problem 11.7 2 3 SNR_dB = 0:5:20; SNR = 10.^(SNR_dB/10); 4 L = length(SNR); 5 % Initialization: 6 C1 = zeros(1,L); C2 = zeros(1,L); C3 = zeros(1,L); 7 % Capacity Calculations: 8 echo off; 9 for i = 1:L 10 % Nt = Nr = N = 1: 11 C1(i) = quadgk(@(x)log2(1 + SNR(i)*x).*exp(-x),0,inf); 12 % Nt = Nr = N = 2: 13 C2(i) = quad2d(@(x,y)(log2(1 + SNR(i)*x/2)+log2(1 + SNR(i)*y/2))/2.*... 14 exp(-x-y).*(x-y).^2,0,1000,0,1000); 15 % Nt = Nr = N = 3: 16 C3(i) = triplequad(@(x,y,z)(log2(1 + SNR(i)*x/3)+log2(1 + SNR(i)*y/3)+log2(1 + SNR(i)*z/3))/... 17 24.*exp(-x-y-z).*((x-y).*(x-z).*(y-z)).^2,0,10,0,10,0,10); 18 end 19 echo on; 20 % Plot the results: 21 plot(SNR_dB,C1,'-*',SNR_dB,C2,'-o',SNR_dB,C3,'-s') 22 axis([0 20 0 25]) 23 legend('Nt = Nr = 1','Nt = Nr = 2','Nt = Nr = 4') 24 xlabel('Average SNR (dB)','fontsize',10) 25 ylabel('Capacity (bps/Hz)','fontsize',10)
Simulation Result
Conclusion
We observe that at high SNRs, the capacity of the (Ny,NR) = (4, 4) MIMO system is approximately four times the capacity of the (1, 1) system.
Thus, at high SNRs, the capacity increases linearly with the number of antenna pairs when the channel is spatially white.
Reference,
1. <<Contemporary Communication System using MATLAB>> - John G. Proakis
