Massive MIMO ISAC Under Target-Angle Uncertainty: CRLB Outage Analysis and Robust Resource Allocation

Abstract

In integrated sensing and communications (ISAC), the same spectral and hardware resources are shared for two functionalities. Most ISAC designs assume perfect target-angle information neglecting angle estimation errors, which introduce steering-vector mismatches, degrade sensing accuracy, and may invalidate deterministic sensing guarantees. This paper investigates monostatic massive multiple-input-multiple-output (MIMO) ISAC systems under imperfect target-angle estimates. We derive closed-form expressions for the Cram\'er-Rao lower bounds (CRLBs) of target azimuth and elevation estimates in the presence of angle uncertainty. We characterize the cumulative distribution functions and outage probabilities of the CRLBs under Gaussian, generalized uniform, and von Mises angle-error models. Our analysis reveals that, in the small-error regime, the CRLBs increase quadratically with the angle errors due to transmit steering-vector mismatch. To ensure reliable sensing, we propose a robust power allocation framework that jointly optimizes pilot training and communications/sensing transmission powers to maximize the communications sum rate while satisfying CRLB outage constraints. The resulting nonconvex problem is solved using an alternating-optimization algorithm based on successive convex approximation. Numerical results validate the developed analysis and show that the proposed robust design reduces azimuth and elevation CRLB outage probabilities by up to $60\%$ compared with conventional non-robust schemes. It attains up to $45\%$ higher sum rates than the non-robust design under strict CRLB thresholds.