mutual_mimo_deri_diag.m

实现mimo预编码环境中容量的所有计算,包括不同的准则

function [fgrad_mean, fhess_mean, fmutual_mean] = ...
    mutual_mimo_deri_diag(M, N, H0, Rt_sqrt, gamma, lambda, NSAMPLE, I)
  
%------------------------------------------------------------
% Function to calculate the gradient and Hessian for diagonal covariance
% matrix case.
%
% Author: Mai Vu
% Date: 12/1/2003
% Revised: 04/12/2004
%------------------------------------------------------------

%------------------------------------------------------------
% INPUTS
%   M: number of receive antennas
%   N: number of transmit antennas
%   H0: channel mean
%   Rt_sqrt: square root of transmit correlation
%   gamma: SNR
%   lambda: the previous transmit covariance matrix eigenvalues
%   NSAMPLE: number of samples used in Monte-Carlo simulation
%   I: identity matrix of size NxN
%
% THE PROBLEM
%
%   The unknown covariance matrix Q is diagonalized using the optimum U,
%   hence the number of unknowns is only N, which are the eigenvalues lambda
%   of Q.
%   
%   Objective function
%     f = -E[logdet(I + SQ)] = -E[logdet(I + U'SU diag(lambda))]
%     where  S = H'*H
%            H = H0 + Hw*Rt_sqrt
%   This function calculates the gradient and Hessian of f wrt lambda.
%
% OUTPUTS
%   fgrad_mean: average gradient
%   fhess_mean: average Hessian
%   fmutual_mean: average mutual information
%
%------------------------------------------------------------

% create the variables
fgrad = zeros(N,1);
fhess = zeros(N,N);
fmutual = 0;

% generate the sample set of channels
H = (randn(M,N,NSAMPLE) + j*randn(M,N,NSAMPLE))/sqrt(2);

% calculate the gradient and the Hessian
for k=1:NSAMPLE
  H_k = H0 + H(:,:,k)*Rt_sqrt;
  S_k = gamma*H_k'*H_k;
  P = I + S_k*diag(lambda);
  fmutual = fmutual - real(log(det(P)));
  
  Y = inv(P);
  Z = Y*S_k;
  fgrad = fgrad - real(diag(Z));
  
  fhess = fhess + abs(Z).^2;
end

% take sample mean
fgrad_mean = fgrad/NSAMPLE;
fhess_mean = fhess/NSAMPLE;
fmutual_mean = fmutual/NSAMPLE;