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FigPLCMetrics.m
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FigPLCMetrics.m
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% NMSE[dB] and MAE yielded by various nonlinear filters in the context of
% powerline communications. Figure 9.
%
% Reference:
%
% [1] Ramirez, J., & Paredes, J. (2016). Recursive Weighted Myriad Based
% Filters and their Optimizations. IEEE Transactions on Signal
% Processing, 64(15), 4027-4039.
%
% Author:
% Juan Marcos Ramirez, M.S.
% Universidad de Los Andes, Merida, Venezuela
% email: juanra@ula.ve, juanmarcos26@gmail.com
%
% Date:
% September, 2016
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;
close all;
disp('---------------------------------------');
disp('This routine could take several minutes');
disp('---------------------------------------');
%% Add Paths
addpath('RecursiveMyriadFilters/');
addpath('OthersNonlinearFilters/');
%% Training Stage
alpha = 0.6:0.1:1.9;
dispersion = 0.01.^alpha;
trials = 10;
kd = sqrt(alpha./(2-alpha)).*(dispersion.^(1./alpha));
for jj = 1:length(alpha)
disp(['Characteristic Exponent (alpha): ' num2str(alpha(jj))])
tic;
symbols = sign(randn(200,1)).*randi(2,200,1);
so = [];
for ii = 1:length(symbols)
so = [so symbols(ii)*ones(1,50)];
end
s1 = so + astable(1,10000,alpha(jj),0,dispersion(jj),0);
u = 0.001;
if alpha(jj) ~= 2
kd = sqrt(alpha(jj)/(2-alpha(jj)))*(dispersion(jj)^(1/alpha(jj)));
else
kd = sqrt(1.93/(2-1.93))*(dispersion(jj)^(1/1.925));
end
K1f = kd;
K2f = kd*25;
Kf = kd;
% Adaptive recursive weighted myriad filter (RWMy filter)
M = 8; N = 4;
g = (1/(M+N))*ones(1,M);
h = (1/(M+N))*ones(1,N);
[g2,h2,e2] = adaptiveRWMy(s1,so,g,h,K1f,K2f,u);
% Adaptive recursive hybrid myriad filter (RHMy filter)
[g4,h4] = adaptiveRHMy(s1,so,g,h,Kf,u);
%% Test Stage
disp(['Number of realizations: ' num2str(trials)])
for kk = 1:trials
disp(['Iteration: ' num2str(kk)]);
symbols = sign(randn(20,1)).*randi(2,20,1);
so = [];
for ii = 1:length(symbols)
so = [so symbols(ii)*ones(1,50)];
end
s1 = so + astable(1,1000,alpha(jj),0,dispersion(jj),0);
W = N + M;
y0 = zeros(size(s1));
y1 = zeros(size(s1));
z0 = zeros(size(s1));
z1 = zeros(size(s1));
z3 = zeros(size(s1));
z4 = zeros(size(s1));
for ii = W:length(s1);
window = s1(ii - W + 1:ii);
y0(ii) = median(window);
y1(ii) = weightedMyriadFPSII(window,ones(1,W),K1f);
z0(ii) = ITM(window,1);
z1(ii) = ITTM(window,3);
z3(ii) = MeridianFilter(window, 1);
z4(ii) = MGCFilter(window, 0.756, 0.896);
end
% Recursive Weighted Myriad Filter on the chirp signal
y2 = rwmyFilter(s1,g2,h2,K1f,K2f);
% Recursive Hybrid Myriad Filter on the chirp signal
y4 = rhmyFilter(s1,g4,h4,Kf);
MAE(kk,1) = mean(abs(so(102:899) - z0(105:902)));
MAE(kk,2) = mean(abs(so(102:899) - z1(105:902)));
MAE(kk,3) = mean(abs(so(102:899) - y0(107:904)));
MAE(kk,4) = mean(abs(so(102:899) - y1(107:904)));
MAE(kk,5) = mean(abs(so(102:899) - z3(107:904)));
MAE(kk,6) = mean(abs(so(102:899) - z4(107:904)));
MAE(kk,7) = mean(abs(so(102:899) - y2(103:900)));
MAE(kk,8) = mean(abs(so(102:899) - y4(103:900)));
NMSE(kk,1) = 10 * log10(mean((so(102:899) - z0(105:902)).^2)/mean(so(101:900).^2));
NMSE(kk,2) = 10 * log10(mean((so(102:899) - z1(105:902)).^2)/mean(so(101:900).^2));
NMSE(kk,3) = 10 * log10(mean((so(102:899) - y0(107:904)).^2)/mean(so(101:900).^2));
NMSE(kk,4) = 10 * log10(mean((so(102:899) - y1(107:904)).^2)/mean(so(101:900).^2));
NMSE(kk,5) = 10 * log10(mean((so(102:899) - z3(107:904)).^2)/mean(so(101:900).^2));
NMSE(kk,6) = 10 * log10(mean((so(102:899) - z4(107:904)).^2)/mean(so(101:900).^2));
NMSE(kk,7) = 10 * log10(mean((so(102:899) - y2(103:900)).^2)/mean(so(101:900).^2));
NMSE(kk,8) = 10 * log10(mean((so(102:899) - y4(103:900)).^2)/mean(so(101:900).^2));
end
mae_mean(:,jj) = mean(MAE)';
nmse_mean(:,jj) = mean(NMSE)';
toc;
disp('---------------------------------------');
end
%% Diplay Results
subplot(121);
plot(alpha,nmse_mean(3:8,:)','LineWidth',2);
ylabel('NMSE[dB]'), xlabel('Characteristic Exponent');
legend('Median','Myriad','Meridian','M-GC','RWMy','RHMy');
subplot(122);
plot(alpha,mae_mean(3:8,:)','LineWidth',2);
ylabel('MAE'), xlabel('Characteristic Exponent');
legend('Median','Myriad','Meridian','M-GC','RWMy','RHMy');