Encoding fix + more experiments.

array/mra_1d.m

@@ -10,9 +10,9 @@
 %   design - An array design struct.
 %References:
 %   [1] M. Ishiguro, "Minimum redundancy linear arrays for a large number
-%       of antennas," Radio Sci., vol. 15, no. 6, pp. 1163–1170, Nov. 1980.
+%       of antennas," Radio Sci., vol. 15, no. 6, pp. 1163-1170, Nov. 1980.
 %   [2] A. Moffet, "Minimum-redundancy linear arrays," IEEE Transactions
-%       on Antennas and Propagation, vol. 16, no. 2, pp. 172–175,
+%       on Antennas and Propagation, vol. 16, no. 2, pp. 172-175,
 %       Mar. 1968.
 
 if d <= 0 || ~isreal(d)

estimator/music_1d.m

@@ -30,7 +30,7 @@
 %Reference:
 %   [1] R. Schmidt, "Multiple emitter location and signal parameter
 %       estimation," IEEE Transactions on Antennas and Propagation,
-%       vol. 34, no. 3, pp. 276–280, Mar. 1986.
+%       vol. 34, no. 3, pp. 276-280, Mar. 1986.
 unit = 'radian';
 refine_estimates = false;
 for ii = 1:2:nargin-5

estimator/sn_sorte.m

@@ -7,7 +7,7 @@
 %Reference:
 %   [1] Z. He, A. Cichocke, S. Xie, and K. Choi, "Detecting the number of
 %       clusters in n-way probabilistic clustering," IEEE Trans. Pattern
-%       Anal. Mach. Intell., vol. 32, pp. 2006–2021, Nov. 2010.
+%       Anal. Mach. Intell., vol. 32, pp. 2006-2021, Nov. 2010.
 n = length(l);
 if l < 2
     error('At least two eigenvalues required.');

examples/experiments/coarrays_music_crb/sim_mse_same_coarray.m

@@ -0,0 +1,66 @@
+% This script demonstrate that even if several sparse linear arrays
+% share the same virtual ULA, they exhibit different performances under
+% different SNR settings and different numbers of sources.
+% This script will produce results similar to Fig. 1 in the following
+% paper:
+% * M. Wang, Z. Zhang, and A. Nehorai, "Performance analysis of
+%   coarray-based MUSIC and the Cramér-Rao bound," in 2017 IEEE
+%   International Conference on Acoustics, Speech and Signal Processing
+%   (ICASSP), 2017, pp. 3061-3065.
+
+
+clear(); close all;
+
+wavelength = 1; % normalized wavelength
+d_0 = wavelength / 2;
+designs = {...
+    design_array_1d('nested', [5  6], d_0, 'Nested (5, 6)') ...
+    design_array_1d('nested', [2 12], d_0, 'Nested (2, 12)') ...
+    design_array_1d('nested', [3  9], d_0, 'Nested (3, 9)') ...
+    design_array_1d('nested', [1 18], d_0, 'Nested (1, 18)') ...
+};
+n_designs = length(designs);
+
+power_source = 1;
+n_snaphots = 1000;
+
+n_grid = 20;
+SNRs = linspace(-10, 20, n_grid);
+
+doas1 = linspace(-pi/3, pi/3, 8);
+
+MSEs_SNR_ana1 = zeros(n_designs, n_grid);
+for dd = 1:n_designs
+    design = designs{dd};
+    A = steering_matrix(design, wavelength, doas1);
+    for ii = 1:n_grid
+        power_noise = power_source*10^(-SNRs(ii)/10);
+        MSEs_SNR_ana1(dd, ii) = mean(ecov_coarray_music_1d(design, wavelength, ...
+                doas1, power_source, power_noise, n_snaphots, 'DiagonalsOnly'));
+    end
+end
+
+doas2 = linspace(-pi/3, pi/3, 20);
+
+MSEs_SNR_ana2 = zeros(n_designs, n_grid);
+for dd = 1:n_designs
+    design = designs{dd};
+    A = steering_matrix(design, wavelength, doas2);
+    for ii = 1:n_grid
+        power_noise = power_source*10^(-SNRs(ii)/10);
+        MSEs_SNR_ana2(dd, ii) = mean(ecov_coarray_music_1d(design, wavelength, ...
+                doas2, power_source, power_noise, n_snaphots, 'DiagonalsOnly'));
+    end
+end
+
+figure;
+subplot(1,2,1);
+semilogy(SNRs, rad2deg(sqrt(MSEs_SNR_ana1)));
+xlabel('SNR (dB)'); ylabel('RMSE (deg)'); grid on;
+legend(arrayfun(@(x) x{1}.name, designs, 'UniformOutput', false));
+title(sprintf('K = %d', length(doas1)));
+subplot(1,2,2);
+semilogy(SNRs, rad2deg(sqrt(MSEs_SNR_ana2)));
+xlabel('SNR (dB)'); ylabel('RMSE (deg)'); grid on;
+legend(arrayfun(@(x) x{1}.name, designs, 'UniformOutput', false));
+title(sprintf('K = %d', length(doas2)));

performance/crb_general_det_1d.m

@@ -13,7 +13,7 @@
 %   [1] P. Stoica and A. Nehorai, "Performance study of conditional and
 %       unconditional direction-of-arrival estimation," IEEE Transactions
 %       on Acoustics, Speech and Signal Processing, vol. 38, no. 10,
-%       pp. 1783–1795, Oct. 1990.
+%       pp. 1783-1795, Oct. 1990.
 if design.dim ~= 1
     error('1D array expected.');
 end

performance/crb_general_sto_1d.m

@@ -15,7 +15,7 @@
 % [1] P. Stoica and A. Nehorai, "Performance study of conditional and
 %     unconditional direction-of-arrival estimation," IEEE Transactions on
 %     Acoustics, Speech and Signal Processing, vol. 38, no. 10,
-%     pp. 1783–1795, Oct. 1990.
+%     pp. 1783-1795, Oct. 1990.
 if design.dim ~= 1
     error('1D array expected.');
 end

performance/ecov_music_1d.m

@@ -19,10 +19,10 @@
 %   [1] P. Stoica and A. Nehorai, "MUSIC, maximum likelihood, and
 %       Cramer-Rao bound: further results and comparisons," IEEE
 %       Transactions on Acoustics, Speech and Signal Processing, vol. 38,
-%       no. 12, pp. 2140–2150, Dec. 1990.
+%       no. 12, pp. 2140-2150, Dec. 1990.
 %   [2] P. Stoica and A. Nehorai, "MUSIC, maximum likelihood, and
 %       Cramer-Rao bound," IEEE Transactions on Acoustics, Speech and
-%       Signal Processing, vol. 37, no. 5, pp. 720–741, May 1989.
+%       Signal Processing, vol. 37, no. 5, pp. 720-741, May 1989.
 if design.dim ~= 1
     error('1D array expected.');
 end

utils/logdeth.m

@@ -0,0 +1,14 @@
+function v = logdeth(A, force_hermitian)
+%LOGDETH Log-determinant function for Hermitian symmetric matrices. This
+%function uses Cholesky decomposition. If the decomposition fails, inf will be
+%returned. This input matrix is assumed Hermitian.
+if nargin == 1 || force_hermitian
+    A = 0.5*(A+A');
+end
+[R, p] = chol(A);
+if p > 0
+    v = inf;
+else
+    v = sum(log(diag(R))) * 2;
+end
+end