How to Proactively Monitor Untrusted Communications with Cell-Free Massive MIMO?

This paper studies a cell-free massive multiple-input multiple-output (CF-mMIMO) proactive monitoring system in which multiple multi-antenna monitoring nodes (MNs) are assigned to either observe the transmissions from an untrusted transmitter (UT) or to jam the reception at the untrusted receiver (UR). We propose an effective channel state information (CSI) acquisition scheme for the monitoring system. In our approach, the MNs leverage the pilot signals transmitted during the uplink and downlink phases of the untrusted link and estimate the effective channels corresponding to the UT and UR via a minimum mean-squared error (MMSE) estimation scheme. We derive new spectral efficiency (SE) expressions for the untrusted link and the monitoring system. For the latter, the SE is derived for two CSI availability cases at the central processing unit (CPU); namely case-1: imperfect CSI knowledge at both MNs and CPU, case-2: imperfect CSI knowledge at the MNs and no CSI knowledge at the CPU. To improve the monitoring performance, we propose a novel joint mode assignment and jamming power control optimization method to maximize the monitoring success probability (MSP) based on the Bayesian optimization framework. Numerical results show that (a) our CF-mMIMO proactive monitoring system relying on the proposed CSI acquisition and optimization approach significantly outperforms the considered benchmarks; (b) the MSP performance of our CF-mMIMO proactive monitoring system is greater than 0.8, regardless of the number of antennas at the untrusted nodes or the precoding scheme for the untrusted transmission link.