Low-Complexity Minimum BER Precoder Design for ISAC Systems: A Delay-Doppler Perspective

Orthogonal time frequency space (OTFS) modulation is anticipated to be a promising candidate for supporting integrated sensing and communications (ISAC) systems, which is considered as a pivotal technique for realizing next-generation wireless networks. In this paper, we develop a minimum bit error rate (BER) precoder design for an OTFS-based ISAC system. In particular, the BER minimization problem takes into account the maximum available transmission power budget and the required sensing performance. Unlike previous studies that focused on ISAC in the time-frequency (TF) domain, we devise the precoder from the perspective of the delay-Doppler (DD) domain by exploiting the equivalent DD domain channel. The DD domain channel generally tends to be sparse and quasi-static, which is conducive to a low-complexity ISAC system design. To address the non-convex optimization design problem, we resort to optimizing the lower bound of the derived average BER by adopting Jensen's inequality. Subsequently, the formulated problem is decoupled into two independent sub-problems via singular value decomposition (SVD) methodology. We then theoretically analyze the feasibility conditions of the proposed problem and present a low-complexity iterative solution via leveraging the Lagrangian duality approach. Simulation results verify the effectiveness of our proposed precoder compared to the benchmark schemes and reveal the interplay between sensing and communication for dual-functional precoder design, indicating a trade-off where transmission efficiency is sacrificed for increasing transmission reliability and sensing accuracy.