OFDM System Design

When To Use

Use this skill when the user wants to build a custom (non-standard) OFDM transmitter/receiver, configure subcarrier allocation, add noise to OFDM signals, equalize OFDM through fading channels, implement synchronization, or add LDPC coding.

When Not To Use

Do NOT use this skill for standards-specific OFDM (use 5G Toolbox for 5G NR, WLAN Toolbox for Wi-Fi, LTE Toolbox for 4G/LTE, Bluetooth Toolbox for Bluetooth, Satellite Communications Toolbox for satellite links).

GATE — Ask Before Coding

If the user's request does not specify or unambiguously imply ALL of the following, STOP and ask before generating any code. Present unclear items as a numbered list and ask whether the user wants to: (a) specify values, (b) have you derive them from other constraints (e.g., CP from delay spread, SCS from Doppler), or (c) use typical defaults. Do not assume defaults. Do not proceed until the user responds.

1. OFDM parameters — FFT size, CP length, subcarrier spacing, subcarrier allocation
2. Channel model — AWGN only, fading with perfect CSI, or fading with pilot-based estimation
3. Pilots — needed for channel estimation or phase tracking?
4. Coding — uncoded, or coded with a specific rate?
5. Synchronization — perfect sync, or include timing/CFO estimation?

Must-Follow Rules

1. ALWAYS use `ofdmmod`/`ofdmdemod` — NEVER implement OFDM by directly calling `ifft`/`fft` — The functions handle CP insertion/removal, ifftshift/fftshift for centered-frequency ordering, and pilot/null subcarrier management. Direct IFFT/FFT gets subcarrier mapping wrong (silent error). Input is [nDataSC × nSym] for SISO. Output is a time-domain column vector. Note: sync preambles (e.g., Schmidl-Cox) that require DFT-order subcarrier mapping may use ifft directly, since ofdmmod applies ifftshift which changes the even/odd bin assignment. Windowing: ofdmmod does not support windowing. For raised cosine windowing, use comm.OFDMModulator for the transmitter only (always use ofdmdemod function for demodulation). See references/ofdm-system-guide.md for capability comparison.

1. Always use a `symOffset` variable in `ofdmdemod` — when passing nullidx (5th arg), symOffset must be explicitly provided as the 4th arg. The default symOffset value is cpLen (skip entire CP). Note: cpLen/2 is more robust when timing synchronization is imperfect.

1. Use explicit signal power in `awgn`, NEVER `'measured'` or `0` — ofdmmod output power is NOT 1W. It equals nActiveSC / nFFT^2 due to MATLAB's 1/N IFFT normalization. Using awgn(x, snr, 0) adds far too much noise. Compute sigPow = 10*log10(nActiveSC / nFFT^2) once before any loop — it is a constant determined by OFDM parameters.

1. Use `ofdmChannelResponse` for frequency-domain channel response — do NOT compute H = fft(h, nFFT) directly. ofdmmod uses ifftshift internally, so direct FFT-based channel responses have wrong subcarrier mapping. Pass the result to ofdmEqualize for equalization.

1. When deriving OFDM parameters from physical specs, show the computation with comments — do not just state the values. Show how you calculate subcarrier spacing, FFT size, CP length, sample rate, guard subcarriers, etc. from bandwidth, delay spread, and Doppler spread. Add comments explaining each derivation step.

1. Check MATLAB version before using version-gated APIs — Functions like ofdmChannelEstimate, ofdmPilotConfig (R2026a), and ldpcPCM (R2025a) are not available on older releases. Unless the user specifically asks for code compatible with a previous version, call version('-release') to get the current MATLAB release, then choose the appropriate API path.

Key Functions

Subcarrier Allocation

Subcarrier indices use centered-frequency ordering: index 1 = most negative frequency, index nFFT/2 + 1 = DC, index nFFT = most positive frequency.

Rules for subcarrier indices:

• nullIdx and pilotIdx must be vectors of 1-based integers in [1, nFFT]
• They must not overlap
• DC subcarrier = nFFT/2 + 1 (always null it)
• ofdmmod input X has size [nDataSC x nSym] — null and pilot subcarriers are excluded
• ofdmdemod output has size [nDataSC x nSym] — nulls stripped, pilots returned separately

Example (WiFi-like 64-FFT):

nullIdx = [1:6, 33, 60:64].';  % 12 nulls (6 lower guard + DC + 5 upper guard)
pilotIdx = [12; 26; 40; 54];   % 4 pilots
nActiveSC = nFFT - length(nullIdx);                    % 52 (data + pilots)
nDataSC   = nFFT - length(nullIdx) - length(pilotIdx); % 48

Basic OFDM Tx/Rx (AWGN)

% Parameters
nFFT = 64;  cpLen = 16;
nullIdx = [1:6, 33, 60:64].';  % 12 nulls
nActiveSC = nFFT - length(nullIdx);  % 52
nDataSC = nActiveSC;  % no pilots
M = 4;  % QPSK
nSym = 100;
snr_sc = 10;  % dB, per-subcarrier SNR

% Transmit
data = randi([0 M-1], nDataSC, nSym);
modData = pskmod(data, M, InputType="integer");
txSig = ofdmmod(modData, nFFT, cpLen, nullIdx);

% SNR conversion and noise
sigPow = 10*log10(nActiveSC / nFFT^2);  % OFDM signal power (dBW)
snr_wb = convertSNR(snr_sc, "snrsc", "snr", ...
    FFTLength=nFFT, NumActiveSubcarriers=nActiveSC);
rxSig = awgn(txSig, snr_wb, sigPow);

% Receive
symOffset = cpLen;
rxData = ofdmdemod(rxSig, nFFT, cpLen, symOffset, nullIdx);
demodData = pskdemod(rxData, M, OutputType="integer");
[numErr, ber] = biterr(data(:), demodData(:));

SNR Handling for OFDM

SNR per subcarrier (SNR_sc) is the standard noise reference for OFDM simulations. If you need other noise metrics — Eb/No for theoretical BER comparison, or wideband SNR for awgn — use convertSNR to derive them from SNR_sc. See matlab-add-awgn for full convertSNR patterns and awgn usage.

For theoretical BER: convert SNR_sc to Eb/No via convertSNR(snr_sc, "snr", "ebno", BitsPerSymbol=log2(M)), then call berawgn(ebno, 'qam', M). Do NOT pass SNR_sc directly to berawgn or use it as Eb/No in erfc/qfunc closed-form expressions — SNR_sc ≠ Eb/No.

OFDM-specific points (beyond what the AWGN skill covers):

• Signal power = 10*log10(nActiveSC / nFFT^2) dBW — due to MATLAB's 1/N IFFT normalization
• `nActiveSC` includes data AND pilot subcarriers
• Always capture noise variance from `awgn`'s second output: [rxSig, nVar] = awgn(...). Do NOT compute noise variance manually from SNR formula — use the value awgn returns to stay in sync with its internal rounding.
• Noise variance after `ofdmdemod` scales by nFFT: nVar_sc = nVar * nFFT (FFT sums N terms)
• `convertSNR` "snr" type = per-subcarrier SNR when converting from Eb/No or Es/No (each OFDM subcarrier carries one symbol). To convert per-subcarrier SNR to wideband SNR (for awgn), use convertSNR(snr_sc, "snrsc", "snr", FFTLength=nFFT, NumActiveSubcarriers=nActiveSC).

Critical Gotchas

awgn(x, snr, 0) is WRONG for OFDM

OFDM signal power depends on nActiveSC and nFFT, not 1W.

% WRONG — assumes unit power (adds ~19 dB too much noise for 64-FFT)
rxSig = awgn(txSig, snr_wb, 0);

% CORRECT — explicit power, capture noise variance
sigPow = 10*log10(nActiveSC / nFFT^2);
[rxSig, nVar] = awgn(txSig, snr_wb, sigPow);

symOffset is required in ofdmdemod

symOffset = cpLen;  % skip entire CP (or cpLen/2 for imperfect timing)
rxData = ofdmdemod(rxSig, nFFT, cpLen, symOffset, nullIdx);

Modulator/demodulator input must be a column vector for single-stream

All Communications Toolbox modulators (qammod, pskmod, etc.) process by columns — each column is an independent channel/stream. For single-stream OFDM, always pass bits or integers as a column vector:

% WRONG — [nSym x k] matrix: each column is treated as a separate stream
txData = reshape(txBits, nBitsPerSym, []).';
txSymbols = qammod(txData, M, InputType="bit", UnitAveragePower=true);

% CORRECT — column vector in, then reshape output to OFDM grid
txSymbols = qammod(txBits, M, InputType="bit", UnitAveragePower=true);
txSymbols = reshape(txSymbols, nActiveSC, nSym);

Use multiple columns only when modulating independent MIMO streams or parallel codewords simultaneously.

DC subcarrier index

DC = nFFT/2 + 1. For nFFT=64, DC is index 33. Always include it in nullIdx.

ofdmEqualize hEst dimensions

With default DataFormat="3-D", hEst dimensions are:

• [nSC × NS × NR] — static: same estimate applied to all OFDM symbols
• [(nSC*nSym) × NS × NR] — time-varying: per-symbol estimates collapsed into first dimension

Passing [nSC × nSym] directly is wrong — dim 2 is read as NS, not nSym:

% WRONG — hEst [nSC x nSym] misinterpreted as [nSC x NS=nSym]
eqData = ofdmEqualize(rxData, hEst_per_sym, nVar);

% CORRECT — collapse first dim to (nSC*nSym), keep stream/antenna dims
eqData = ofdmEqualize(rxData, reshape(hEst_per_sym, [], Ns, Nr), nVar);

OFDM with Pilots

To insert pilots, pass pilotIdx and pilot symbols as additional arguments to ofdmmod/ofdmdemod. Signal power is based on nActiveSC (data + pilots), not nDataSC alone.

See references/ofdm-pilots-and-estimation.md for the full pilot insertion example.

Pilot-Based Channel Estimation (R2026a)

Use ofdmPilotConfig + ofdmChannelEstimate for pilot-based channel estimation without perfect CSI. If you have not already checked, get the current MATLAB version before deciding between the R2026a workflow and the pre-R2026a manual LS approach.

The ofdmChannelEstimate workflow differs from the legacy pilotIdx approach:

• `nullIdx` contains only guard bands (NOT DC) — DC becomes an active-grid position that you zero out manually.
• No `pilotIdx` argument to ofdmmod/ofdmdemod — build a full [nActiveSC x nSym] grid with data, pilots, and DC=0, then pass it directly.
• Pilot locations come from `ofdmPilotConfig`, not from function arguments.
• `rxSym` is 3-D: [nActiveSC x nSym x nRx] — add the receive-antenna dimension even for SISO.

See references/ofdm-pilots-and-estimation.md for complete code examples.

OFDM over Fading Channels

Two approaches for channel equalization:

1. Perfect CSI (R2023a) — use ofdmChannelResponse with path gains from comm.RayleighChannel (requires PathGainsOutputPort=true). Get pathFilters from info(channel).ChannelFilterCoefficients. Pass H(:) to ofdmEqualize for time-varying SISO.

1. Pilot-based estimation (R2026a) — use ofdmPilotConfig + ofdmChannelEstimate.

Both approaches use ofdmEqualize with Algorithm="mmse" for final equalization. Always use explicit signal power in awgn (not 'measured') — fading changes the instantaneous power.

See references/ofdm-fading-channel.md for channel configuration (Rayleigh/Rician, Doppler, 3GPP profiles, ofdmEqualize dimensions).

Fading Channel Setup

Configure comm.RayleighChannel or comm.RicianChannel with PathGainsOutputPort=true. Key rules:

• Always set SampleRate (default is 1 Hz)
• Maximum path delay must be < CP duration: max(PathDelays) < cpLen/SampleRate
• Compute Doppler from velocity: fd = (velocity * carrierFreq) / physconst('LightSpeed')

See references/ofdm-fading-channel.md for full setup, 3GPP profiles, and quasi-static fading.

Synchronization

Pipeline: Coarse timing → CFO estimation → CFO correction → Fine timing → OFDM demod → Phase tracking

Key rules:

• Use frequencyOffset for CFO application/correction (not manual exp(-1j*2*pi*...))
• Use timingEstimate for cross-correlation timing detection
• Always unwrap pilot phase estimates before applying correction across symbols

See references/ofdm-synchronization.md for Schmidl-Cox, CP-based timing, Zadoff-Chu preambles, and complete Rx example.

LDPC Coding

Key rules:

• Use ldpcEncode/ldpcDecode with config objects (NOT removed comm.LDPCEncoder/comm.LDPCDecoder)
• Create config from parity check matrix only: H = ldpcPCM(648, 324); encCfg = ldpcEncoderConfig(H); decCfg = ldpcDecoderConfig(H). Do NOT pass scalars or Name-Value pairs — ldpcEncoderConfig(648), ldpcEncoderConfig(648, 1/2), and ldpcDecoderConfig(BlockLength=648) all error. If you have not already checked, get the current MATLAB version to decide between ldpcPCM (R2025a+) and ldpcQuasiCyclicMatrix (R2021b+).
• Include CodingRate in convertSNR when computing Eb/No for coded systems
• Pass NoiseVariance to demodulators, such as qamdemod, for proper LLR scaling; scale to frequency domain: nVar_sc = nVar * nFFT
• Use OutputType="approxllr" for LLR computation

See references/ofdm-ldpc-coding.md for OFDM+LDPC workflow and multi-codeword framing.

Advanced Features

See references/ofdm-system-guide.md for:

• Variable CP length — per-symbol CP via row vector cpLens
• Common OFDM configurations — WiFi-like, LTE-like, 5G-like parameter sets
• SNR conversion — see matlab-add-awgn skill for all convertSNR patterns
• Noise variance for soft demodulation — scaling after ofdmdemod

Cross-References

• `matlab-add-awgn` — when you need to add noise and calculate SNR conversions, use this skill. It covers all convertSNR patterns, awgn usage, and noise variance capture.

Reference Loading

Load references/ofdm-pilots-and-estimation.md when the user asks about pilot insertion, pilot-based channel estimation (R2026a ofdmChannelEstimate), or pre-R2026a LS estimation.

Load references/ofdm-fading-channel.md when the user asks about fading channel configuration, Rayleigh/Rician setup, Doppler calculation, 3GPP delay profiles, or ofdmEqualize dimension handling.

Load references/ofdm-synchronization.md when the user asks about timing synchronization, CFO estimation/correction, Schmidl-Cox, preamble design, or pilot-based phase tracking.

Load references/ofdm-ldpc-coding.md when the user asks about LDPC coding, forward error correction, ldpcEncode/ldpcDecode, NoiseVariance for soft decoding, or coded BER simulations.

Load references/ofdm-system-guide.md when the user asks about SNR conversion details, common OFDM configurations, noise variance for soft demodulation, or variable CP length.

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