OFDM ISAC waveform design for a monostatic SISO radar-communications system operating at 3.5 GHz with 30.72 MHz bandwidth (1024 subcarriers, 30 kHz spacing). The pilot fraction alpha - the allocation of subcarriers between Zadoff-Chu radar pilots and QAM data - controls the sensing-vs-throughput tradeoff.
The symbolic analysis derives the cross-ambiguity function, Cramér-Rao bound on range estimation, and Shannon throughput as closed-form expressions in alpha and the waveform parameters. These are converted to function handles via matlabFunction, producing a Pareto frontier that maps the full design space without Monte Carlo sweeps or repeated simulation. Scalar design parameters (ZC sequence length, root index, subcarrier allocations) are extracted via double at two operating points and fed directly into waveform generation, spectral analysis, range-Doppler processing, and pilot-based equalization with EVM measurement, validating the symbolic predictions against the numerical results.
Symbolic declaration of the signal model: N subcarriers, pilot fraction alpha, subcarrier spacing Delta_f, frame structure with M OFDM symbols.
Derive the frequency-domain and time-domain ambiguity functions as closed-form Dirichlet kernels via symsum and simplify. The resulting expressions give range and Doppler resolution as explicit functions of the design parameters.
Shannon throughput and spectral efficiency as symbolic functions of alpha, using the same signal model.
Derive the Cramér-Rao bound on range estimation from the radar SNR expression (diff, simplify). Both the CRB and the throughput are now closed-form functions of alpha. Convert them to callable function handles with matlabFunction and subs, evaluate at a concrete design point (1024 subcarriers, 30 kHz spacing, 3.5 GHz carrier), and plot the Pareto frontier.
Zadoff-Chu sequences require prime length and a coprime root index. Given a desired pilot count K = alpha * N, find the nearest valid length with prevprime and nextprime, verify the root with gcd, and confirm ideal periodic autocorrelation both symbolically (symsum) and numerically (zadoffChuSeq from Communications Toolbox™).
Extract scalar parameters via double and function handles via matlabFunction at two operating points: sensing-heavy (alpha = 0.75) and comms-heavy (alpha = 0.25). Generate OFDM ISAC waveforms using ofdmmod, qammod, and zadoffChuSeq (Communications Toolbox), with per-symbol pseudo-random pilot scrambling to flatten the power spectrum.
Measure the power spectral density of both waveforms with pwelch and hamming (Signal Processing Toolbox™) and overlay the symbolically-predicted occupied bandwidth.
Simulate a single target (150 m, 30 m/s). The OFDM radar processor divides the received pilot subcarriers by the known transmitted pilots, then applies IFFT (range) and FFT (Doppler). The resulting range-Doppler maps are shown with the symbolic resolution cell overlaid.
The pilot subcarriers also serve as channel estimates for the communications receiver. Per-symbol channel estimation on the pilots is interpolated to the data subcarriers (interp1) and used to equalize the Doppler-induced phase rotation. EVM is measured with comm.EVM (Communications Toolbox) at both operating points: the sensing-heavy design equalizes better because the denser pilot grid produces more accurate interpolation.
- MATLAB® R2024b or later
- Symbolic Math Toolbox™
- Communications Toolbox
- Signal Processing Toolbox
- Open MATLAB and navigate to this directory
- Open
ISACWaveformDesign.mas a Live Script - Run section by section, or run all — the example is self-contained
| File | Description |
|---|---|
ISACWaveformDesign.m |
Main example (Live Script). Full workflow from symbolic derivation through waveform validation. |
For a full system-level MIMO-OFDM ISAC simulation building on these concepts, see Integrated Sensing and Communication II: Communication-Centric Approach Using MIMO-OFDM.