MIMO预编码

%---------------------------------------------------------------------- % Optimization program to find the transmit covariance matrix that achieves % the ergodic capacity of a MIMO channel given the channel mean and transmit % correlation matrices. The program then calculates the mutual information % using the covariance matrix that maximizes Jensen's upper bound on % the average mutual information, and compares that with the capacity itself. % %---------------------------------------------------------------------- % Author: Mai Vu % Date: Mar 02, 2004 % Modified: Apr 19, 2004 % %---------------------------------------------------------------------- % INPUT: The channel mean and transmit correlation matrices % The program either takes inputs from channel_file, or generates the % matrices arbitrarily. % % OUTPUT: It saves the results in save_file, which includes: % - The channel parameters: mean H0, transmit correlation Rt, SNR % - The optimal transmit covariance matrix: Q_opt, x_opt (the % vectorized form of Q_opt) % - The channel ergodic capacity: mi_opt % - Optimality gap (a bound on the gap between the numerical % solution and the true capacity): fgap_opt % - The mutual information obtained using the input covariance matrix % which is optimal for the Jensen bound: mutual_jen_fw % - The mutual information with iid equal power input: mutual_equal % % The program also produces two graph files: % - graph_mi_file: plots the capacity and the other two mutual % information curves % - graph_eig_file: plots the input power distribution (i.e. the % eigenvalue of the transmit covariance matrix) for the three % cases: optimal, Jensen bound and equal power. % % PARAMETERS: % N: Number of transmit antennas % M: Number of receive antennas % NSAMPLE: number of channel samples used in each Monte-Carlo simulation % SNR_dB: input signal to noise ratio in dB % K: Rician K factor % random_data: 0 means generate random channel mean and correlation matrices % 1 means take input from channel_file % spec_case: 0 means channel has both mean and tx corr % 1 means channel has zero mean % 2 means channel has no transmit correlation % file_version: file version % channel_file: input mat file for channel parameters (.mat) % save_file: output mat file (.mat) % graph_mi_file: output graph file (.eps) % graph_eig_file: output graph file (.eps) %---------------------------------------------------------------------- clear all; close all; clc; disp('Initializing...'); %--------------------PARAMETERS-------------------- % change these parameters to run different simulations N = 4; % number of Tx antennas M = 4; % number of Rx antennas NSAMPLE = 10000; SNR_dB = [-10:5:15]; % SNR in dB K = 5; % channel K factor random_data = 0; % generate random channel mean and correlation matrices spec_case = 0; % 1 is no mean, 2 is no tx corr % setting up various file names if spec_case == 1 suffix = 'corr'; elseif spec_case == 2 suffix = 'mean'; else suffix = 'both'; end file_version = 'a'; channel_file = ['mutual_mimo_channel_4_4_', file_version]; save_file = ['opt_mutual_mimo_', suffix, '_', file_version]; graph_mi_file = ['mutual_mimo_compare_', suffix, '_', file_version, '.eps']; graph_eig_file = ['eigval_cov_compare_', suffix, '_', file_version, '.eps']; %--------------------PROGRAM-------------------- I = eye(N); SNR = 10.^(SNR_dB/10); % use the test data or create random channel statistics if random_data Rt_half = randn(N,N) + j*randn(N,N); Rt = Rt_half*Rt_half'; Rt = Rt/(K+1); H0 = randn(M,N) + j*randn(M,N); H0 = H0/norm(H0, 'fro')*sqrt(K*M*N/(K+1)); else load(channel_file); [M N] = size(H0); end if (spec_case == 2) % check for mean only case Rt = I*real(trace(Rt))/N; % this is to retain the same K factor elseif (spec_case == 1) % check for correlation only case Rt = Rt/trace(Rt)*N; % full correlation H0 = zeros(M,N); end Rt_sqrt = sqrtm(Rt); % Jensen upper bound waterfill matrix S0 = (H0'*H0 + M*Rt); [U lambda] = eig(S0); lambda = real(diag(lambda)); % mutual information at the initial input covariance matrix % for k=1:length(SNR_db) % fval_init(k) = mutual_mimo_func(M,N,H0,Rt_sqrt,gamma(k),Q,NSAMPLE,I); % end disp('Optimizing the average mutual information...'); [x_opt, Q_opt, fval_opt, fgap_opt] = mutual_mimo_opt(H0, Rt, M, N, SNR_dB); lambda_equal = ones(N,1)/N; disp('Calculating Jensen''s upper bound on the average mutual information...'); for k = 1:length(SNR_dB) disp([' SNR = ', num2str(SNR_dB(k)), 'dB']); lambda_jen_wf(:,k) = waterfill(SNR(k), lambda); mutual_jen_wf(k) = ... - mutual_mimo_func_diag(M,N,H0*U,U'*Rt_sqrt*U,... SNR(k),lambda_jen_wf(:,k),NSAMPLE,I); mutual_equal(k) = ... - mutual_mimo_func_diag(M,N,H0,Rt_sqrt,... SNR(k),lambda_equal,NSAMPLE,I); if (size(x_opt,1) > N) lambda_opt(:,k) = eig(Q_opt(:,:,k)); else lambda_opt(:,k) = x_opt(:,k); end end mi_opt = -fval_opt; %--------------------SAVE AND DISPLAY RESULTS-------------------- % save data and plot graphs save(save_file, 'H0', 'Rt', 'SNR_dB', 'x_opt', 'Q_opt', 'mi_opt', 'fgap_opt', ... 'lambda_jen_wf', 'mutual_jen_wf', 'mutual_equal'); disp('________________________'); disp('Optimization successful.'); disp(' The optimum covariance matrix is in Q_opt'); disp(' The optimum power allocation is in lambda_opt'); disp(' The ergodic capacity is in mi_opt'); figure; plot(SNR_dB, mi_opt/log(2), 'r'); hold on; plot(SNR_dB, mutual_jen_wf/log(2), '-.'); plot(SNR_dB, mutual_equal/log(2), 'g:'); xlabel('SNR in dB'); ylabel('Mutual information (bps/Hz)'); legend('Ergodic capacity', 'MI w/Jensen cov', 'MI w/equal power',2); saveas(gcf, graph_mi_file, 'psc2'); figure; fig_leg(:, 1) = plot(SNR_dB, lambda_opt, 'r'); hold on; fig_leg(:, 2) = plot(SNR_dB, lambda_jen_wf, 'b--'); fig_leg(:, 3) = plot(SNR_dB, lambda_equal*ones(1, length(SNR_dB)), 'g:'); xlabel('SNR in dB'); ylabel('Eigenvalues of the transmit covariance matrix'); legend(fig_leg(1, :), 'Optimum power', 'Jensen power', 'Equal power',1); saveas(gcf, graph_eig_file, 'psc2');