Uplink integrated sensing and communication (ISAC) systems have recently emerged as a promising research direction, enabling simultaneous uplink signal detection and target sensing. {In this paper, we propose the flexible projection (FP)-type receiver that unifies the projection-type receiver and the successive interference cancellation (SIC)-type receiver by using a flexible tradeoff factor to adapt to dynamically changing uplink ISAC scenarios.} The FP-type receiver addresses the joint signal detection and target response estimation problem through two coordinated phases: 1) Communication signal detection using a reconstructed signal whose composition is controlled by the tradeoff factor, followed by 2) Target response estimation performed through subtraction of the detected communication signal from the received signal. With adjustable tradeoff factors, the FP-type receiver can balance the enhancement of the signal-to-interference-plus-noise ratio (SINR) with the reduction of correlation in the reconstructed signal for communication signal detection. The pairwise error probability (PEP) expressions are analyzed for both the maximum likelihood (ML) and the zero-forcing (ZF) detectors, revealing that the optimal tradeoff factor should be determined based on the adopted detection algorithm and the relative power of the sensing and communication (S\&C) signals. A homotopy optimization framework is first applied for the FP-type receiver with a fixed tradeoff factor. This framework is then extended to develop the dynamic flexible projection (DFP)-type receiver, which iteratively adjusts the tradeoff factor for improved algorithm performance and environmental adaptability. Finally, we show that the length of the jointly processed signal should scale with the antenna size to fully unleash the potential of the uplink ISAC receiver.

翻译：上行集成感知与通信（ISAC）系统近期已成为一个极具前景的研究方向，它能够同时实现上行信号检测与目标感知。本文提出柔性投影（FP）型接收机，该接收机通过引入柔性折衷因子，将投影型接收机与逐次干扰消除（SIC）型接收机统一起来，以适应动态变化的上行ISAC场景。FP型接收机通过两个协调阶段解决联合信号检测与目标响应估计问题：1）利用由折衷因子控制构成的恢复信号进行通信信号检测；2）通过从接收信号中减去检测到的通信信号来估计目标响应。通过可调的折衷因子，FP型接收机能够在提升信干噪比（SINR）与降低通信信号检测所用的恢复信号相关性之间取得平衡。针对最大似然（ML）检测器与迫零（ZF）检测器，本文分析了其成对错误概率（PEP）表达式，揭示了最优折衷因子应基于所采用的检测算法以及感知与通信（S&C）信号的相对功率来确定。首先针对固定折衷因子的FP型接收机应用同伦优化框架，随后将该框架扩展至动态柔性投影（DFP）型接收机，通过迭代调整折衷因子以提升算法性能与场景适应性。最后，本文指出联合处理信号的长度应与天线数量成比例扩展，以充分释放上行ISAC接收机的潜力。