Integrated sensing and communications (ISAC) is a spectrum-sharing paradigm that allows different users to jointly utilize and access the crowded electromagnetic spectrum. In this context, intelligent reflecting surfaces (IRSs) have lately emerged as an enabler for non-line-of-sight (NLoS) ISAC. Prior IRS-aided ISAC studies assume passive surfaces and rely on the continuous-valued phase-shift model. In practice, the phase-shifts are quantized. Moreover, recent research has shown substantial performance benefits with active IRS. In this paper, we include these characteristics in our IRS-aided ISAC model to maximize the receive radar and communications signal-to-noise ratios (SNR) subjected to a unimodular IRS phase-shift vector and power budget. The resulting optimization is a highly non-convex unimodular quartic optimization problem. We tackle this problem via a bi-quadratic transformation to split the design into two quadratic sub-problems that are solved using the power iteration method. The proposed approach employs the M-ary unimodular sequence design via relaxed power method-like iteration (MaRLI) to design the quantized phase-shifts. Numerical experiments employ continuous-valued phase shifts as a benchmark and demonstrate that our active-IRS-aided ISAC design with MaRLI converges to a higher value of SNR with an increase in the number of IRS quantization bits.

翻译：集成感知与通信（ISAC）是一种频谱共享范式，允许多用户联合利用和接入日益拥挤的电磁频谱。在此背景下，智能反射表面（IRS）近期成为实现非视距（NLoS）ISAC的关键技术。现有IRS辅助的ISAC研究通常假设被动表面，并依赖于连续值相位模型，而实际应用中相位是量化的。此外，最新研究表明，主动式IRS具有显著的性能优势。本文将上述特性纳入IRS辅助ISAC模型，在满足IRS单位模相位向量与功率预算约束下，最大化接收雷达与通信的信噪比（SNR）。由此产生的优化问题是一个高度非凸的单位模四次优化问题。我们通过双二次变换将该问题分解为两个二次子问题，并采用迭代幂法求解。所提方法利用基于松弛幂法迭代的M元单位模序列设计（MaRLI）来生成量化相位。数值实验以连续值相位作为基准，结果表明：随着IRS量化比特数的增加，基于MaRLI的主动式IRS辅助ISAC设计能够收敛至更高的SNR值。