AWGN & SNR Management

AWGN & SNR Management

Add white Gaussian noise to signals and convert between SNR definitions (SNR, Eb/No, Es/No, per-subcarrier SNR) for communications system simulations.

When to Use

• Adding noise to a signal in a link simulation
• Converting between Eb/No, Es/No, SNR, or per-subcarrier SNR
• Setting up the correct SNR for a coded, oversampled, or OFDM system
• Obtaining noise variance to pass to a soft-decision demodulator

When NOT to Use

• Configuring fading channels (delay profile, Doppler, antenna arrays)

Must-Follow Rules

1. NEVER pass 'measured' to awgn — Always pass explicit signal power as the third argument. For unit-power signals use 0; otherwise compute power with mean(abs(x).^2) and convert to dBW: 10*log10(sigPow). The 'measured' option computes instantaneous power internally, which gives incorrect noise levels after fading channels and obscures the power assumption. Even in AWGN-only scenarios, explicit power is required for correctness and clarity. For OFDM systems, see the "Add AWGN in an OFDM link simulation" pattern.
2. Use UnitAveragePower=true when signal power doesn't matter — This is the simplest path: signal power = 0 dBW, so awgn(x, snr, 0) is exact. If the user needs original constellation scaling (e.g., PA modeling, hardware-in-the-loop), do NOT use UnitAveragePower=true — use the default modulator, compute the actual average power with mean(abs(x).^2), and pass it explicitly: awgn(x, snr, sigPowdBW).
3. Use convertSNR for all conversions — NEVER compute SNR/Eb/No/Es/No formulas manually — Even when the formula is simple, always use convertSNR. Manual formulas are error-prone for edge cases (oversampling, subcarrier loading) and bypass the toolbox's validated implementation. Anti-pattern: snr = ebno + 10*log10(bitsPerSymbol * codeRate). Correct: convertSNR(ebno, "ebno", "snr", BitsPerSymbol=6, CodingRate=3/4).
4. Distinguish wideband SNR and per-subcarrier SNR in OFDM systems — Eb/No is a per-subcarrier quantity. To go from Eb/No to the wideband SNR that awgn needs, use two steps: (1) convertSNR(ebno, "ebno", "snr", BitsPerSymbol=..., CodingRate=...) gives the SNR per subcarrier, (2) convertSNR(snrsc, "snrsc", "snr", FFTLength=..., NumActiveSubcarriers=...) gives the wideband SNR for awgn. Direct ebno→snrsc is not supported and throws an error. Caveat: If the user asks for per-subcarrier SNR only, step 1 alone is the complete answer — do NOT apply step 2. Applying the FFTLength/NumActiveSubcarriers correction to a per-subcarrier value gives the wideband SNR, which is a different (lower) quantity. Note: The "snrsc" mode requires R2023b or later. For R2022a–R2023a, compute wideband SNR manually: snr_wideband = snr_per_sc - 10*log10(FFTLength/NumActiveSubcarriers). To add noise at a per-subcarrier SNR, see the "Add AWGN in an OFDM link simulation" pattern below.
5. Capture noise variance for soft demodulation — Use [y, nVar] = awgn(...) and pass nVar to the demodulator via NoiseVariance=nVar.
6. Do NOT reference skill rules or prohibitions in generated code comments — Write positive, descriptive comments that explain intent, using a style similar to the example code provided in this skill. The end user does not know about this skill.

Critical Anti-Patterns — NEVER Do These

NEVER use 'measured' with awgn

% WRONG — never generate this
rxSignal = awgn(txSignal, snrdB, 'measured');

% CORRECT for unit-power signals (UnitAveragePower=true)
rxSignal = awgn(txSignal, snrdB, 0);

% CORRECT for non-unit-power signals
sigPow = mean(abs(txSignal).^2);
rxSignal = awgn(txSignal, snrdB, 10*log10(sigPow));