gary_code.rar_MOD_coded modulation _gary

%% Incorporating Gray Coding % This example,aims to solve the following % problem: % Modify the modulation example (COMMDOC_MOD) so that it uses % a Gray-coded signal constellation. %% Setup % Define parameters. M = 16; % Size of signal constellation k = log2(M); % Number of bits per symbol n = 3e4; % Number of bits to process nsamp = 1; % Oversampling rate %% Signal Source % Create a binary data stream as a column vector. x = randint(n,1); % Random binary data stream %% Bit-to-Symbol Mapping % Convert the bits in x into k-bit symbols, using % Gray coding. % A. Define a vector for mapping bits to symbols using % Gray coding. The vector is specific to the arrangement % of points in a 16-QAM constellation. mapping = [0 1 3 2 4 5 7 6 12 13 15 14 8 9 11 10].'; % B. Do ordinary binary-to-decimal mapping. xsym = bi2de(reshape(x,k,length(x)/k).','left-msb'); % C. Map from binary coding to Gray coding. xsym = mapping(xsym+1); %% Modulation % Modulate using 16-QAM. y = modulate(modem.qammod(M),xsym); %% Transmitted Signal ytx = y; %% Channel % Send signal over an AWGN channel. EbNo = 10; % In dB snr = EbNo + 10*log10(k) - 10*log10(nsamp); ynoisy = awgn(ytx,snr,'measured'); %% Received Signal yrx = ynoisy; %% Scatter Plot % Create scatter plot of noisy signal and transmitted % signal on the same axes. h = scatterplot(yrx(1:nsamp*5e3),nsamp,0,'g.'); hold on; scatterplot(ytx(1:5e3),1,0,'k*',h); title('Received Signal'); legend('Received Signal','Signal Constellation'); axis([-5 5 -5 5]); % Set axis ranges. hold off; %% Demodulation % Demodulate signal using 16-QAM. zsym = demodulate(modem.qamdemod(M),yrx); %% Symbol-to-Bit Mapping % Undo the bit-to-symbol mapping performed earlier. % A. Define a vector that inverts the mapping operation. [dummy demapping] = sort(mapping); % Initially, demapping has values between 1 and M. % Subtract 1 to obtain values between 0 and M-1. demapping = demapping - 1; % B. Map between Gray and binary coding. zsym = demapping(zsym+1); % C. Do ordinary decimal-to-binary mapping. z = de2bi(zsym,'left-msb'); % Convert z from a matrix to a vector. z = reshape(z.',prod(size(z)),1); %% BER Computation % Compare x and z to obtain the number of errors and % the bit error rate. [number_of_errors,bit_error_rate] = biterr(x,z)