add AIR stuff from TUM

minor changes here and there

Libs/mutual information rate TUM/mi_cg.m

@@ -0,0 +1,104 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Copyright (c) 2019 Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
+% Institute for Communications Engineering (LNT)
+% Technical University of Munich, Germany
+% www.lnt.ei.tum.de
+%
+% All rights reserved.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 
+% Permission is hereby granted, free of charge, to any person obtaining a
+% copy of this software and associated documentation files (the
+% "Software"), to deal in the Software without restriction, including
+% without limitation the rights to use, copy, modify, merge, publish,
+% distribute, sublicense, and/or sell copies of the Software, and to permit
+% persons to whom the Software is furnished to do so, subject to the
+% following conditions:
+% 
+% The above copyright notice and this permission notice shall be included
+% in all copies or substantial portions of the Software.
+% 
+% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+% OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+% MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
+% NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+% DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+% OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
+% USE OR OTHER DEALINGS IN THE SOFTWARE.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%% example_mi_cg_complex_16qam.m %%%%%%%%%%%%%%%%%%%%%%
+%
+% Example usage of the function mi_cg to numerically compute mutual
+% information between two complex sequences. This file simulates a
+% one-dimensional complex AWGN channel with 16-QAM constellation for
+% different SNRs, and then plots the achievable rate, which is equal to two
+% times the 4-PAM curve of Fig. 1 of [1]. 
+%
+% Note that using mi_cg with complex sequences assumes that the channel
+% model q(Y|X) is circularly symmetric for a given X=x (i.e., that the
+% received clouds are circular). This is not the case in a channel with
+% phase noise: see example_it_mi_cg.m for an example of how to deal with
+% non-circularly-symmetric channels.
+%
+% [1] G. David Forney and Gottfried Ungerboeck, "Modulation and Coding for
+% Linear Gaussian Channels", IEEE Trans. Inf. Theory vol. 44, no. 6, pp.
+% 2384-2415, October 1998 
+%
+% Technische Universitaet Muenchen - Lehrstuhl fuer Nachrichtentechnik
+% Date: 12.12.2019
+% Author: Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+clear;
+close all;
+
+%%% Simulation parameters
+M_QAM=16; % QAM size
+var_w=1; % noise variance
+SNR_dB_values=(-5):2:25; % SNR values in dB
+N=8000; % number of Monte-Carlo points
+
+%%% Derived parameters
+n_SNR=length(SNR_dB_values);
+SNR_values=10.^(SNR_dB_values/10);
+
+%%% Generation of QAM constellation with power 1
+M_PAM=sqrt(M_QAM); % number of points per real dimension
+X_1d=-(M_PAM-1)+2*(0:(M_PAM-1)); % generate PAM
+X=X_1d+1i*X_1d.'; % transform to QAM
+X=X(:).'*sqrt(3/2/(M_QAM-1)); % set to unit power
+
+%%% Uniformly choose transmit indices
+idx_tx=randi(M_QAM, [1, N]);
+
+%%% AWGN noise
+w=sqrt(var_w/2)*(randn([1, N])+1i*randn([1, N]));
+
+%%% Loop over the SNR values
+MI_awgn=zeros(1, n_SNR);
+for i_SNR=1:n_SNR
+    % transmitted points
+    
+    s=sqrt(SNR_values(i_SNR)*var_w)*X(:, idx_tx);
+    
+    % AWGN channel
+    r_awgn = s+w;
+    
+    % Compute MI
+    MI_awgn(i_SNR)=air(X, r_awgn, idx_tx);
+    % The following also works but is slower: MI_awgn(i_SNR)=air(s, r_awgn);
+end
+
+
+I_shannon=log2(1+SNR_values);
+
+figure;
+plot(SNR_dB_values, I_shannon, '-', 'DisplayName', 'log_2 (1+SNR)');
+hold on;
+plot(SNR_dB_values, MI_awgn, '--', 'DisplayName', [num2str(M_QAM) '-QAM, AWGN']);
+hold off;
+xlabel('SNR (dB)'); ylabel('Achievable rate (bits/complex dimension)');
+title(['Achievable rate of ' num2str(M_QAM) '-QAM in AWGN']);
+legend('Location', 'NorthWest');