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 via a bi-quadratic transformation to split the problem 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. As expected, numerical experiments demonstrate that our active IRS-ISAC system design with MaRLI converges to a higher value of SNR when we increase 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，允许不同用户共同利用和接入拥挤的电磁频谱。在此背景下，智能超表面（IRS）近期成为非视距（NLoS）ISAC的关键使能技术。此前基于IRS的ISAC研究均假设采用无源表面，并依赖连续值相移模型。而实际中，相移是量化的。此外，最新研究表明有源IRS可带来显著的性能增益。本文将这些特性纳入所提IRS辅助的ISAC模型中，以在满足单模IRS相移向量和功率预算约束下最大化雷达和通信接收信噪比（SNR）。由此产生的优化问题是一个高度非凸的单模四阶优化问题。我们通过双二次变换将其分解为两个二次子问题，并利用幂迭代法求解。所提方法采用基于松弛幂迭代类方法的M元单模序列设计（MaRLI）来设计量化相移。数值实验表明，随着IRS量化比特数增加，采用MaRLI的有源IRS-ISAC系统设计可收敛至更高SNR值，结果符合预期。