How to Correct 64-QAM Constellation Rotation After Free Space Channel Using phased.FreeSpace?

Question

Jakub 2025-6-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2177545-how-to-correct-64-qam-constellation-rotation-after-free-space-channel-using-phased-freespace

回答： Jaskirat 2025-6-11

When I transmit a 64-QAM signal through a free-space channel using phased.FreeSpace, the resulting constellation at the receiver appears rotated due to a carrier phase offset. I attempted to correct this using comm.CarrierSynchronizer, but the constellation still remains misaligned.

How can I accurately estimate and correct this phase rotation to recover the original symbol alignment?

clear; clc; close all;
%% Parameters
M = 64; k = log2(M); fs = 1e7; fc = 2e9;
numData = 6000; 
%% Generate data symbols and original bitstream
dataBits = randi([0 1], numData * k, 1);
dataSymbols = bit2int(dataBits, k, true);
figure;
stairs(dataSymbols(1:100))
% Modulate
modulated = qammod(dataSymbols, M, 'UnitAveragePower', true);
t = (0:length(modulated)-1)' / fs;
%% Plot Original Constellation
figure; scatterplot(modulated);
title('Original 64-QAM Constellation');
%% Plot original I/Q waveform
figure;
subplot(2,1,1); plot(t*1e6, real(modulated)); title('Tx I (Real)');
xlabel('Time (microseconds)'); ylabel('Amplitude'); grid on;
subplot(2,1,2); plot(t*1e6, imag(modulated)); title('Tx Q (Imag)');
xlabel('Time (microseconds)'); ylabel('Amplitude'); grid on;
%% Transmit over Passband with Phase Offset
tx_passband = modulated .* exp(1j * 2 * pi * fc * t);
fsChannel = phased.FreeSpace(...
    'SampleRate', fs, ...
    'PropagationSpeed', physconst('LightSpeed'), ...
    'OperatingFrequency', fc, ...
    'TwoWayPropagation', false);
txloc = [0;0;0]; rxloc = [100;0;0];
rx_signal = fsChannel(tx_passband, txloc, rxloc, [0;0;0], [0;0;0]);
%% Downconvert
rx_mixed = rx_signal .* exp(-1j * 2 * pi * fc * t);
% Plot received waveform
figure;
subplot(2,1,1); plot(t*1e6, real(rx_mixed)); title('Rx I (Real) Before Correction');
xlabel('Time (microseconds)'); ylabel('Amplitude'); grid on;
subplot(2,1,2); plot(t*1e6, imag(rx_mixed)); title('Rx Q (Imag) Before Correction');
xlabel('Time (microseconds)'); ylabel('Amplitude'); grid on;
%% Constellation before correction
figure; scatterplot(rx_mixed); title('Rx Constellation Before Phase Correction');
%% Phase estimation and correction
csync = comm.CarrierSynchronizer( ...
    'Modulation', 'QAM', ...
    'SamplesPerSymbol', 1, ...
    'DampingFactor', 1, ...
    'NormalizedLoopBandwidth', 0.01);
[rx_corrected, phEst] = csync(rx_mixed);
figure; scatterplot(rx_corrected); title('After CarrierSynchronizer');
figure; plot(phEst); title('CarrierSynchronizer Phase Estimate');
xlabel('Sample'); ylabel('Phase (rad)');
%% Plot corrected waveform
figure;
subplot(2,1,1); plot(t*1e6, real(rx_corrected)); title('Rx I (Real) After Correction');
xlabel('Time (microseconds)'); ylabel('Amplitude'); grid on;
subplot(2,1,2); plot(t*1e6, imag(rx_corrected)); title('Rx Q (Imag) After Correction');
xlabel('Time (microseconds)'); ylabel('Amplitude'); grid on;
%% Plot constellation after correction
figure; scatterplot(rx_corrected); title('Rx Constellation After Phase Correction');
%% Demodulate
demodulated = qamdemod(rx_corrected, M, 'UnitAveragePower', true);
% Convert to bitstream
rxBits = int2bit(demodulated, k, true);
%% Plot bitstream comparison
figure;
subplot(2,1,1); stairs(dataBits(1:200)); title('Original Bitstream (First 200 bits)');
xlabel('Bit Index'); ylabel('Bit'); ylim([-0.5 1.5]); grid on;
subplot(2,1,2); stairs(rxBits(1:200)); title('Received Bitstream (First 200 bits)');
xlabel('Bit Index'); ylabel('Bit'); ylim([-0.5 1.5]); grid on;
%% BER Calculation
bitErrors = sum(rxBits ~= dataBits(1:length(rxBits)));
BER = bitErrors / length(rxBits);
fprintf('BER: %.5f (%d bit errors)\n', BER, bitErrors);

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Answer 1

Jaskirat 2025-6-11

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2177545-how-to-correct-64-qam-constellation-rotation-after-free-space-channel-using-phased-freespace#answer_1566275

Hi @Jakub,

I understand you want to estimate and correct the phase offset.

This can be done by using the “comm.CoarseFrequencyCompensator” object to correct frequency offset, followed by fine-tuning the correction using carrier synchronization.

You can refer to the following example for more details:

https://www.mathworks.com/help//releases/R2021a/comm/ug/correct-frequency-offset-qam-using-coarse-and-fine-synchronization.html

You can also refer to the following documentation to learn more about comm.CoarseFrequencyCompensator:

https://www.mathworks.com/help/comm/ref/comm.coarsefrequencycompensator-system-object.html

Hope this helps!