On the Trade-off Between Angle of Arrival and Symbol Estimation in Bistatic ISAC Systems Using Unitary Signaling

Previous works in array processing have proposed two types of snapshot models for the angle of arrival (AoA) estimation problem in multi-antenna systems. The deterministic model assumes that the source waveforms are non-random, while the random sensor noise is white Gaussian with a known covariance matrix. The stochastic model assumes that both the waveforms and the noise are zero-mean Gaussian. Interestingly, the performance of these two models have rarely been compared in integrated sensing and communication (ISAC) systems. Therefore, in this paper, we consider the uplink of a bistatic ISAC system that uses unitary constant envelope signaling and pilot-based channel estimation while transmitting a sensing signal simultaneously with the communication signals. The base station uses both the pilot and data signals to estimate the angle of a passive source and the transmitted data symbol by an active (connected) user equipment device. For this system, we derive the classical Cramér-Rao bound for unbiased estimators of the AoA and the transmitted symbol, along with the Bayesian Cramér-Rao bound, which bounds the error of all estimators. We also derive the ISAC-aware minimum mean squared error receiver for both the deterministic and stochastic models. We study the trade-off between sensing and communication under the deterministic and stochastic waveform assumptions. Specifically, we show that the fundamental trade-off between sensing and communication power allocations is expressed differently in the deterministic and stochastic models and argue that the results serve as basic considerations when designing pilot and sensing signals for ISAC systems.