Multiuser MIMO-AFDM Beamforming for ISAC in Doubly Dispersive Channels

Integrated sensing and communication (ISAC) in high-mobility channels requires waveform and beamforming designs that are robust to delay-Doppler dispersion. With this in mind, in this paper we study a monostatic multiuser multiple-input multiple-output (MIMO) affine frequency division multiplexing (AFDM) downlink system. We develop a discrete affine Fourier transform (DAFT)-domain model that preserves Doppler-induced inter-bin coupling and derive a data-aided delay-Doppler detector. The expected matched-bin detector signal-to-noise ratio (SNR) is shown to be proportional to a transmit-covariance beampattern, which leads to a detector-SNR-based sector-illumination constraint. The resulting sensing-constrained weighted sum-rate maximization problem is solved using a combined weighted minimum mean squared error (WMMSE) and majorization-minimization (MM) formulation. Simulations show that the proposed AFDM design outperforms its orthogonal frequency division multiplexing (OFDM) counterpart in terms of the rate-sensing tradeoff, robustness to Doppler, and delay-Doppler sensing quality.