Question

I need star 16 QAM Modulator and demodulator design matlab code

Please suggest me how to make the code. The sample constellation diagram given below.
I want to make the code for this constellation with different ring radius.

Sample Constellation Points

Answer 1

Here‘s an example Matlab script that does Star-16-QAM mapping with Gray mapping, models an AWGN channel and does the decision and demapping. The bit error rate (BER) is also calculated. I’ll shortly explaing how it works.

First, we create a random bit sequence with ‘0’ and ‘1’ occuring with equal probability. The radius of the inner and outer circle of the constellation diagram are also defined.

% Random bit sequence
numberOfBits = 1e5;
x = rand(1, numberOfBits);
x( x < 0.5 ) = 0;
x( x >= 0.5 ) = 1;

% Radius of inner and outer circle
r1 = 1;
r2 = 2;

In the next step we define the mapping table that maps an integer index number to a complex symbol. This is done in such a way, that two neighbouring symbols only differ in one bit. This is called Gray mapping.

% Define mapping table applying Gray mapping
mappingTable(1) = r1 * exp(1i* 0);
mappingTable(2) = r1 * exp(1i* pi/4);
mappingTable(3) = r1 * exp(1i* 3*pi/4);
mappingTable(4) = r1 * exp(1i* pi/2);
mappingTable(5) = r1 * exp(1i* 7*pi/4);
mappingTable(6) = r1 * exp(1i* 3*pi/2);
mappingTable(7) = r1 * exp(1i* pi);
mappingTable(8) = r1 * exp(1i* 5*pi/4);
mappingTable(9:16) = mappingTable(1:8) ./ r1 .* r2;

Now for each block of 4 bits we calculate the symbol index and look up the according complex symbol in our mapping table.

if mod(numberOfBits, 4) ~= 0
    error('numberOfBits must be a multiple of 4.');
end
mappedSymbols = zeros(1, numberOfBits / 4);

% Map bits to symbols
for i = 1:4:length(x)

    symbolBits = x(i:i+3);

    symbolIndex = 2^3 * symbolBits(1) + 2^2 * symbolBits(2) + 2^1 * symbolBits(3) + 2^0 * symbolBits(4);

    % Mapping
    mappedSymbols((i - 1)/4 + 1) = mappingTable( symbolIndex + 1);
end

In a practical communication system the real and imaginary part of the complex symbols will now be converted to an analog signal (with an impulse shaper) and be modulated onto a radio frequency carrier. Here, we assume that D/A and A/D conversion as well as modulation and demodulation are ideal, so that we don’t need to model it. Furthermore, the channel is assumed to be ideal, i.e. flat in the frequency domain. However, we will consider noise by adding white Gaussian noise. Note that the noise power is equally distributed on the real and imaginary part of the signal.

% Add white Gaussian noise
snr = 20; % signal-to-noise ratio in dB
meanSignalPower = (r1^2 + r2^2)/2;
snr_lin = 10^(snr/10); % linear scale
meanNoisePower = meanSignalPower ./ snr_lin;
receivedSignal = mappedSymbols + randn(1, length(mappedSymbols)) * sqrt(meanNoisePower/2) +...
    1i * randn(1, length(mappedSymbols)) * sqrt(meanNoisePower/2);

Finally, for each received symbol, we determine the constellation point with the minimum distance and convert the symbol index back to a sequence of bits.

% Decision and demapping
receivedBits = zeros(1, numberOfBits / 4);
for i = 1:length(receivedSignal)
  [mindiff minIndex] = min(receivedSignal(i) - mappingTable);
  symbolIndex = minIndex - 1;
  bitString = dec2bin(symbolIndex, 4);
  receivedBits((i-1)*4 + 1) = str2double(bitString(1));
  receivedBits((i-1)*4 + 2) = str2double(bitString(2));
  receivedBits((i-1)*4 + 3) = str2double(bitString(3));
  receivedBits((i-1)*4 + 4) = str2double(bitString(4));
end

Of course, we’re interested in the number of bit errors:

numberOfBitErrors = nnz( x - receivedBits );
ber = numberOfBitErrors / numberOfBits; % bit error rate
disp(['SNR: ' num2str(snr) ' dB']);
disp(['Bit error rate (BER): ' num2str(ber)]);

And plotting transmitted and received signal yields the typical constellation diagram:

figure;
plot( real(receivedSignal), imag(receivedSignal), '.'); hold on;
absLim = max( max(real(receivedSignal)), max(imag(receivedSignal)));
xyLimits = [-absLim*1.1 absLim*1.1];
xlim( xyLimits );
ylim( xyLimits );
plot( real(mappedSymbols), imag(mappedSymbols), '.r'); hold off;
xlim( xyLimits );
ylim( xyLimits );
xlabel('real part');
ylabel('imaginary part');
legend('received', 'transmitted');

I uploaded the complete source code in a whole: http://pastebin.com/MDcVLZhh