Energy Efficiency for Massive MIMO Integrated Sensing and Communication Systems

This paper explores the energy efficiency (EE) of integrated sensing and communication (ISAC) systems employing massive multiple-input multiple-output (mMIMO) techniques to leverage spatial beamforming gains for both communication and sensing. We focus on an mMIMO-ISAC system operating in an orthogonal frequency-division multiplexing setting with a uniform planar array, zero-forcing downlink transmission, and mono-static radar sensing to exploit multi-carrier channel diversity. By deriving closed-form expressions for the achievable communication rate and Cram\'er-Rao bounds (CRBs), we are able to determine the overall EE in closed-form. A power allocation problem is then formulated to maximize the system's EE by balancing communication and sensing efficiency while satisfying communication rate requirements and CRB constraints. Through a detailed analysis of CRB properties, we reformulate the problem into a more manageable form and leverage Dinkelbach's and successive convex approximation (SCA) techniques to develop an efficient iterative algorithm. A novel initialization strategy is also proposed to ensure high-quality feasible starting points for the iterative optimization process. Extensive simulations demonstrate the significant performance improvement of the proposed approach over baseline approaches. Results further reveal that as communication spectral efficiency rises, the influence of sensing EE on the overall system EE becomes more pronounced, even in sensing-dominated scenarios. Specifically, in the high $\omega$ regime of $2 \times 10^{-3}$, we observe a 16.7\% reduction in overall EE when spectral efficiency increases from $4$ to $8$ bps/Hz, despite the system being sensing-dominated.