QPSK Constellation over an AWGN Channel for Inter-Robot Communication in a Swarm

Project info

• Field of studyRobotics and Mechatronics
• LevelDoctoral dissertation (S3)
• Method typeCommunications and Forecasting
• Estimated build time± 7 working days
• Toolspskmod, pskdemod, awgn, berawgn (Communications Toolbox)
• PriceUS$34 - US$225

Research goal

Analyse the error vector magnitude using QPSK constellation analysis and examine its sensitivity to the signal-to-noise ratio and the inter-robot distance.

Variables

Example result

• 9.878Es/N0 (dB)
• 31.838EVM (%)
• 9.941MER (dB)
• 0.001Measured SER
• 0.002Theoretical SER
• 3000Symbols

At Es/N0 of 9.9 dB the QPSK constellation shows an EVM of 31.8% and MER of 9.9 dB with a measured symbol error rate Error vector magnitude of 0.0010 (theory 0.0018) over 3000 symbols.

Computed from illustrative synthetic data, not from a real study.

About QPSK Constellation over an AWGN Channel

A QPSK simulation over an AWGN channel shows a constellation diagram spread by noise and measures SER or EVM. It is used to understand the effect of SNR on modulation quality and to validate transmitter-receiver designs.

Steps

1. 1Generate random symbols and modulate QPSK with pskmod
2. 2Convert Eb/N0 to SNR per symbol
3. 3Add AWGN noise
4. 4Demodulate and compute SER and BER
5. 5Compute EVM from the received constellation
6. 6Plot constellations at several SNRs and compare with theory

Assumptions to check

• AWGN channel and perfect synchronisation
• Gray mapping so one symbol error is generally one bit error
• Enough symbols for stable error statistics

Reading and reporting the results

Show constellations at several SNRs and report BER, SER, and EVM against theory. Explain how constellation spread relates to error probability.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(7);
M = 4;  k = log2(M);
N = 2e5;
signal_to_noise_ratio = [2 6 10];                                  % Eb/N0 in dB
error_vector_magnitude = zeros(size(signal_to_noise_ratio));                        % simulated BER
sym = randi([0 M-1], N, 1);
tx = pskmod(sym, M, pi/4, 'gray');

figure;
for i = 1:numel(signal_to_noise_ratio)
    snr = signal_to_noise_ratio(i) + 10*log10(k);                  % Es/N0 in dB
    rx = awgn(tx, snr, 'measured');
    rsym = pskdemod(rx, M, pi/4, 'gray');
    [~, ser] = symerr(sym, rsym);
    [~, error_vector_magnitude(i)] = biterr(sym, rsym, k);
    evm = 100 * sqrt(mean(abs(rx - tx).^2) / mean(abs(tx).^2));
    fprintf('Eb/N0 = %2d dB: SER = %.2e, BER = %.2e (theory %.2e), EVM = %.1f %%\n', ...
        signal_to_noise_ratio(i), ser, error_vector_magnitude(i), berawgn(signal_to_noise_ratio(i), 'psk', M, 'nondiff'), evm);
    subplot(1, 3, i);
    plot(real(rx(1:2000)), imag(rx(1:2000)), '.'); axis square; grid on;
    title(sprintf('Eb/N0 = %d dB', signal_to_noise_ratio(i))); xlabel('In-phase'); ylabel('Quadrature');
end

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions