-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathSingleMC_SNR_randomDOA.m
379 lines (319 loc) · 15.5 KB
/
SingleMC_SNR_randomDOA.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
% Version 5.12: (03/13/2024)
% written by Yongsung Park
% Yongsung Park & Peter Gerstoft
% MPL/SIO/UCSD
% noiselab.ucsd.edu
% Citation
% C. F. Mecklenbräuker, P. Gerstoft, E. Ollila, and Y. Park, “Robust and Sparse M-Estimation of DOA,” Signal Process. 220, 109461 (2024).
% https://doi.org/10.1016/j.sigpro.2024.109461
% C. F. Mecklenbräuker, P. Gerstoft, and E. Ollila, “DOA M-estimation using sparse bayesian learning,” in Proc. IEEE ICASSP (2022), pp. 4933–4937.
% https://doi.org/10.1109/ICASSP43922.2022.9746740
% Sparse Bayesian learning is available.
% P. Gerstoft, C. F. Mecklenbräuker, A. Xenaki, and S. Nannuru, “Multi-snapshot sparse Bayesian learning for DOA,” IEEE Signal Process. Lett. 23(10) (2016).
% https://doi.org/10.1109/LSP.2016.2598550
%%
clear; clc;
close all;
dbstop if error;
% rng(777)
addpath([cd,'/_common'])
% addpath(['../_common'])
% SNRs = 30:-3:-9;
% NmonteCarlo = 100;
% Number_of_DOAs = 2 ;
% function errorDOAcutoff, threshold = 10 [deg.]
% save results: DOAs & errors; struct('theta',theta(Ilocs),'error',DoA_error);
% findpeaks for error calculation, 'Npeaks', Number_of_DOAs "+ 2", minPeakSeparation: 5[deg.] (=5/dphi points)
for iModel = 1:3
%% Noise model
if iModel == 1
model = 'Gaussian'; nu_model_string = '';
elseif iModel == 2
model = 'Complex-Student'; nu_model = 2.1; nu_model_string = '2p1';
elseif iModel == 3
model = 'epscont'; epsilon_model = 0.05; lambda_model = 10.0; nu_model_string = 'epsilon=5e-2_lambda=10';
noise_enhancement = (1-epsilon_model) + epsilon_model*lambda_model^2;
end
%% Environment parameters
freq = 2.0E+03; % frequency (Hz)
c0 = 343; % speed of sound (m/s) in dry air at 20°C
lambda = c0/freq; % wavelength (m)
wavenum= 2*pi/lambda;% wave number (rad/m)
%% Array configuration
antenna_array.type = 'ULA'; % or 'UCA'
switch(antenna_array.type)
case 'ULA' % definition of uniform linear array geometry
theta = 0.0; % irrelevant elevation angle of incoming wave [degrees]
antenna_array.N = 20; % no. of sensors in ULA
antenna_array.d = 0.5; % sensor spacing of ULA measured in wavelengths
for n=0:(antenna_array.N-1)
antenna_array.x(n+1) = n * antenna_array.d * lambda;
antenna_array.y(n+1) = 0.0;
antenna_array.z(n+1) = 0.0;
end
% array steering matrix of size N x M for all azimuth, the elevation is irrelevant.
% M = 181; % standard dictionary, 1 deg azimuth resolution
% M = 361; % standard dictionary, .5 deg azimuth resolution
M = 18001; % high resolution dictionary, 0.01 deg azimuth resolution
dphi=180/(M-1);
phi_vec = [-90:dphi:90];
case 'UCA' % definition of uniform circular array geometry
theta = 30.0; % elevation angle of incoming wave [degrees]
antenna_array.N = 8; % no. of antenna elements in UCA
antenna_array.radius = 0.05; % 5cm radius == 10cm diameter
for n=0:(antenna_array.N-1)
phi = 2*pi*n / antenna_array.N; % polar angle of n-th sensor coordinates [rad]
antenna_array.x(n+1) = antenna_array.radius * cos(phi);
antenna_array.y(n+1) = antenna_array.radius * sin(phi);
antenna_array.z(n+1) = 0.0;
end
antenna_array.d = norm([antenna_array.x(2) - antenna_array.x(1);
antenna_array.y(2) - antenna_array.y(1);
antenna_array.z(2) - antenna_array.z(1);
]) / lambda; % sensor spacing of UCA measured in wavelengths
% array steering matrix of size N x M for all azimuth at one single elevation theta (degrees)
M = 361;
dphi=360/(M-1);
phi_vec = [-180:dphi:180]; % sweep over all azimuth angles (degrees)
end
% Design/steering matrix (Sensing matrix)
sensingMatrix = zeros(antenna_array.N,M);
sensingMatrixD = zeros(antenna_array.N,M); %-- CRB-YP
for m=1:M
kvec = wavenum * [sind(phi_vec(m))*cosd(theta);cosd(phi_vec(m))*cosd(theta);sind(theta)];
kvecD = wavenum * [cosd(phi_vec(m))*cosd(theta);-sind(phi_vec(m))*cosd(theta);sind(theta)];
sensingMatrix(:,m) = exp(-1j * kvec.' * [antenna_array.x;antenna_array.y;antenna_array.z]); % normalization to |a_n|=1 or ||a||_2^2 = N.
sensingMatrixD(:,m) = (-1j * kvecD.' * [antenna_array.x;antenna_array.y;antenna_array.z])...
.* exp(-1j * kvec.' * [antenna_array.x;antenna_array.y;antenna_array.z]); % normalization to |a_n|=1 or ||a||_2^2 = N.
end
%% Number of sensors / grid-points / snapshots
Nsensor = antenna_array.N; % number of sensors
Ntheta = M; % number of angular-search grid
Nsnapshot = 25; % number of snapshots
%% Simulation parameters
% noise standard deviation sigma
SNRs = 36:-3:-6;
% SNRs = 30:-3:-9;
% SNRs = [50;45;40];
% SNR = SNRs(6);
% SNR = [14.9081800077602]; % dB
Number_of_DOAs = 1;
NmonteCarlo = 250;
LSnapshot = Nsnapshot;
% LSnapshot = Nsnapshot * NmonteCarlo; % Number of array data vector observations "Large"
%% loop over various SNR levels
for isnr = 6 %1:length(SNRs)
% for isnr = 1:length(SNRs)
% rng('default') % YP: We need to be careful where to set 'rng'
rng(1,'twister')
SNR = SNRs(isnr);
% evaluate SBL
options = SBLSet;
options.Nsource = Number_of_DOAs;
% options.gamma_range=10^-3;
options.convergenceMu = 1;
errorDOAseparation = 1; % [deg.]
errorDOAsepP = floor(errorDOAseparation/dphi) - 1;
errorDOApeak = Number_of_DOAs + 2;
errCut = 10; % Maximum RMSE cut-off.
% obtain active indices --------------------------%
options.activeIndices = 1;
options.activeIndRepN = 10;
options.convergence.min_iteration = options.activeIndRepN;
%-------------------------------------------------%
for n_monteCarlo = 1
% for n_monteCarlo = 1:NmonteCarlo % parfor loop over snapshot realizations
disp(' ')
disp(['SNR',num2str(SNR),'#Sim : ',num2str(n_monteCarlo)])
% number of sources
x_src = ones(Number_of_DOAs,1);
DOA_src = floor(asind(gen_bs(sind(-75), sind(75), Number_of_DOAs, asin(2/Nsensor))));
DOA_MC(:,n_monteCarlo) = DOA_src;
% Steering vectors for true sources
for k=1:Number_of_DOAs
m_src(k) = find(phi_vec == DOA_src(k));
end
a_src = sensingMatrix(:,m_src);
% Noise modeling
sigma = 1 * norm(a_src*x_src,'fro') / (10^(SNR/20));
% SNR_gen = 10*log10(norm(a_src*x_src,'fro')^2 ./ (sigma.^2));
% % check the generated SNR
switch(model)
case 'Laplace-like'
[y,xAmp] = generate_signal(a_src,x_src,Nsensor,LSnapshot,Number_of_DOAs,...
sigma,model);
case 'Gaussian'
[y,xAmp] = generate_signal(a_src,x_src,Nsensor,LSnapshot,Number_of_DOAs,...
sigma,model);
case 'epscont'
[y,xAmp] = generate_signal(a_src,x_src,Nsensor,LSnapshot,Number_of_DOAs,...
sigma,model,epsilon_model,lambda_model);
case 'Complex-Student' % method in Ollila & Koivunen, PIMRC 2003
[y,xAmp] = generate_signal(a_src,x_src,Nsensor,LSnapshot,Number_of_DOAs,...
sigma,model,nu_model);
case 'Heteroscedastic'
[y,xAmp] = generate_signal(a_src,x_src,Nsensor,LSnapshot,Number_of_DOAs,...
sigma,model);
otherwise
error(['unknown model ', model]);
end
Y = y;
% Y = y(:,(n_monteCarlo-1)*Nsnapshot+(1:Nsnapshot));
%% CRB-YP Van Trees Book Eq.(8.106) & (8.110)
XAMP = xAmp;
% XAMP = xAmp(:,(n_monteCarlo-1)*Nsnapshot+(1:Nsnapshot));
vanTreeV = sensingMatrix(:,m_src);
vanTreeD = sensingMatrixD(:,m_src); % D Eq.(8.100)
vanTreeSf = diag(diag(XAMP*XAMP'/Nsnapshot)); % S_f
Pn = sigma^2;
% H Eq.(8.101) where P_V Eq.(8.96)
H = vanTreeD'...
*(eye(Nsensor) - vanTreeV/(vanTreeV'*vanTreeV)*vanTreeV')...
*vanTreeD;
% Eq.(8.110)
CRBa = real(H .* (vanTreeSf.'));
CRBa = eye(size(XAMP,1)) / CRBa * (Pn / Nsnapshot / 2);
if exist('outputsCRBa','var')==0, outputsCRBa = []; end
outputsCRBa = [outputsCRBa;mean(diag(CRBa))];
% Eq.(8.106)
CRBaux1 = vanTreeV' * vanTreeV * (vanTreeSf / Pn);
CRBaux2 = eye(size(XAMP,1)) / ( eye(size(XAMP,1)) + CRBaux1 );
CRB = real( vanTreeSf * (CRBaux2 * CRBaux1) .* (H.') );
CRB = eye(size(XAMP,1)) / CRB * (Pn / Nsnapshot / 2);
if exist('outputsCRBd','var')==0, outputsCRBd = []; end
outputsCRBd = [outputsCRBd;mean(diag(CRB))];
%% Gaussian
loss_param = inf;
[gammaInd81,report81] = SBL_v5p12(sensingMatrix, Y, 'SBL-G', loss_param, options, errorDOApeak, errorDOAsepP);
%% MVT
loss_param = 2.1;
[gammaInd82,report82] = SBL_v5p12(sensingMatrix, Y, 'SBL-T', loss_param, options, errorDOApeak, errorDOAsepP);
%% Huber
loss_param = 0.9;
[gammaInd83,report83] = SBL_v5p12(sensingMatrix, Y, 'SBL-H', loss_param, options, errorDOApeak, errorDOAsepP);
%% Tyler's
loss_param = Nsensor;
[gammaInd84,report84] = SBL_v5p12(sensingMatrix, Y, 'SBL-Tyl', loss_param, options, errorDOApeak, errorDOAsepP);
%% Results
disp([' ']), disp([' '])
if iModel == 1
disp(['Gaussian array data model'])
elseif iModel == 2
disp(['MVT array data model'])
elseif iModel == 3
disp(['\epsilon-contaminated array data model'])
end
disp([' '])
DoA_error = errorDOAcutoff(phi_vec(gammaInd81),DOA_src,errCut);
disp(['RMSE Gaussian-loss models (-G) : ',num2str(sqrt(mean(power(DoA_error,2))))])
if exist('outputsSBLv5p12G','var')==0, outputsSBLv5p12G = []; end
outputSBLv5p12G = struct('theta',phi_vec(gammaInd81),'error',DoA_error,'itr',report81.results.iteration_L1);
outputsSBLv5p12G = [outputsSBLv5p12G; outputSBLv5p12G];
DoA_error = errorDOAcutoff(phi_vec(gammaInd82),DOA_src,errCut);
disp(['RMSE MVT-loss models (-T) : ',num2str(sqrt(mean(power(DoA_error,2))))])
if exist('outputsSBLv5p12T','var')==0, outputsSBLv5p12T = []; end
outputSBLv5p12T = struct('theta',phi_vec(gammaInd82),'error',DoA_error,'itr',report82.results.iteration_L1);
outputsSBLv5p12T = [outputsSBLv5p12T; outputSBLv5p12T];
DoA_error = errorDOAcutoff(phi_vec(gammaInd83),DOA_src,errCut);
disp(['RMSE Huber-loss models (-H) : ',num2str(sqrt(mean(power(DoA_error,2))))])
if exist('outputsSBLv5p12H','var')==0, outputsSBLv5p12H = []; end
outputSBLv5p12H = struct('theta',phi_vec(gammaInd83),'error',DoA_error,'itr',report83.results.iteration_L1);
outputsSBLv5p12H = [outputsSBLv5p12H; outputSBLv5p12H];
DoA_error = errorDOAcutoff(phi_vec(gammaInd84),DOA_src,errCut);
disp(['RMSE Tyler-loss models (-Tyl) : ',num2str(sqrt(mean(power(DoA_error,2))))])
if exist('outputsSBLv5p12Tyl','var')==0, outputsSBLv5p12Tyl = []; end
outputSBLv5p12Tyl = struct('theta',phi_vec(gammaInd84),'error',DoA_error,'itr',report84.results.iteration_L1);
outputsSBLv5p12Tyl = [outputsSBLv5p12Tyl; outputSBLv5p12Tyl];
end % end of the for-loop
% saveCharVar = who('outputs*');
% saveChar = ['save([ ''p12rand_'', model(1), ''mode_'', ''s'', num2str(Number_of_DOAs), ''MC'' , num2str(NmonteCarlo) , ''SNRn'' , num2str(isnr) ], ''SNRs'' , ''NmonteCarlo'' '];
% for ichar = 1:numel(saveCharVar)
% saveChar = [saveChar,',''',char(saveCharVar{ichar}),''''];
% end
% saveChar = [saveChar,');'];
% eval(saveChar)
%
% if isnr > 1
% delete( [ 'p12rand_', model(1), 'mode_', 's', num2str(Number_of_DOAs), 'MC' , num2str(NmonteCarlo) , 'SNRn' , num2str(isnr-1), '.mat' ] )
% end
end % end of for isnr=1:length(sigma_vec) loop
end
%%
rmpath([cd,'/_common'])
% rmpath(['../_common'])
%% End------------------------------------------------------------------------------------------------------------------------ %%
%% Signal generation
function [receivedSignal,s_src] = generate_signal(a_src,x_src,Nsensor,LSnapshot,Number_of_DOAs,...
sigma,model,model_param1,model_param2)
% function to generate sensor observations
if strcmpi(model,'Laplace-like')
if 0
% deterministric source
receivedSignal = laplacelike_rand(a_src*x_src, sigma, Nsensor, LSnapshot);
else
% stochastic source
error('laplacelike_rand for stochastic source not yet implemented')
end
elseif (strcmpi(model,'Gaussian') || isempty(model) )
noise_realization = sigma * complex(randn(Nsensor,LSnapshot),randn(Nsensor,LSnapshot))/sqrt(2);
if 0
% deterministric source
receivedSignal = (a_src * x_src * ones(1,LSnapshot)) + noise_realization;
else
% stochastic source
s_src = x_src .* complex(randn(Number_of_DOAs,LSnapshot),randn(Number_of_DOAs,LSnapshot))/sqrt(2 * Number_of_DOAs);
receivedSignal = ( a_src * s_src ) + noise_realization;
end
elseif (strcmpi(model,'epscont') || isempty(model) )
if nargin < 9
epsilon_model = 0.05; lambda_model = 10.0;
else
epsilon_model = model_param1; lambda_model = model_param2;
end
noise_realization = epscont(Nsensor,LSnapshot,sigma,epsilon_model, 0.0,lambda_model);
%old: noise_realization = epscont_old(Nsensor * LSnapshot, epsilon_model, 0.0, lambda_model, sigma);
%old: noise_realization = reshape(noise_realization, Nsensor, LSnapshot);
if 0
% deterministric source
receivedSignal = (a_src * x_src * ones(1,LSnapshot)) + noise_realization;
else
% stochastic source
s_src = x_src .* complex(randn(Number_of_DOAs,LSnapshot),randn(Number_of_DOAs,LSnapshot))/sqrt(2 * Number_of_DOAs);
receivedSignal = ( a_src * s_src ) + noise_realization;
end
elseif (strcmpi(model,'Complex-Student') || isempty(model) ) % method in Ollila & Koivunen, PIMRC 2003
if nargin < 8
nu_model = 2.1;
else
nu_model = model_param1;
end
noise_realization = sigma * complex(randn(Nsensor,LSnapshot),randn(Nsensor,LSnapshot))/sqrt(2);
if 0
% deterministric source
receivedSignal = (a_src * x_src * ones(1,LSnapshot)) + noise_realization;
else
% stochastic source
s_src = x_src .* complex(randn(Number_of_DOAs,LSnapshot),randn(Number_of_DOAs,LSnapshot))/sqrt(2 * Number_of_DOAs);
receivedSignal = ( a_src * s_src ) + noise_realization;
end
% nu_model = 5, % choose number of degrees of freedom of chi^2 distribution
s = ones(Nsensor, 1) * chi2rnd(nu_model * ones(1, LSnapshot));
receivedSignal = receivedSignal ./ sqrt(s/nu_model);
elseif (strcmpi(model,'Heteroscedastic') || isempty(model) )
noise_realization = sigma * complex(randn(Nsensor,LSnapshot),randn(Nsensor,LSnapshot))/sqrt(2);
std_dev = 10.^(-1.0+2.0*rand(Nsensor,LSnapshot));
std_dev = std_dev/sqrt(sum(sum(std_dev.^2))/(Nsensor*LSnapshot));
if 0
% deterministric source
receivedSignal = (a_src * x_src * ones(1,LSnapshot)) + std_dev .* noise_realization;
else
% stochastic source
s_src = x_src .* complex(randn(Number_of_DOAs,LSnapshot),randn(Number_of_DOAs,LSnapshot))/sqrt(2 * Number_of_DOAs);
receivedSignal = ( a_src * s_src ) + std_dev .* noise_realization;
end
else
error(['please specify noise model as a string equal to Laplace-like, ...' ...
'Gaussian, epscont, Complex-Student or Heteroscedastic\n']);
end
end