A Unified KLD Framework for Duplexity and Deployment Paradigms in Cell-Free mMIMO-ISAC

Abstract

This paper presents a comparative study of four potential operating configurations for distributed cell-free massive multiple-input multiple-output (CF-mMIMO) ISAC, spanning separated (SE) and shared (SH) access point (AP) deployment with half-duplex (HD) and full-duplex (FD) paradigms. The system comprises distributed APs serving multiple downlink (DL) and uplink (UL) users while simultaneously detecting radar targets. The configurations incorporate realistic impairments at the AP receivers: residual self-interference (SI) from transmit--receive leakage under FD operation, imperfect interference cancellation (IC) of the known radar and DL waveforms due to channel-estimation errors, and environmental clutter. To establish a common analytical scale for communication and sensing, the Kullback--Leibler divergence (KLD) is adopted as a unifying measure that represents both subsystems in comparable quantities, thereby enabling consistent comparison between error-rate and detection metrics. A generalised likelihood ratio test (GLRT) framework is developed, yielding closed-form expressions that link the KLD to the detection probability. Our results confirm the derived KLD-to-symbol error rate (SER) and KLD-to-detection links: with adequate SI suppression and IC quality, FD attains substantial communication gains over HD while preserving strong radar detection, and SH deployment raises both communication and radar performance through its larger effective aperture, though its radar gain then depends on cancellation quality, which SE deployment avoids by isolating the subsystems. These trends persist under imperfect channel state information (CSI) and sensing estimation, and a complexity analysis attributes the SH deployment and FD gains to a higher per-configuration processing cost, yielding deployment guidelines and quantitative design thresholds for next-generation CF-mMIMO ISAC systems.