MIMO Sensing Beamforming Design with Low-Resolution Transceivers

Adopting low-resolution hardware at transceivers in multi-input multi-output (MIMO) sensing systems can substantially reduce hardware costs and power consumption. This motivates us to study MIMO sensing systems with hardware constraints, specifically phase-only analog transmit antennas and low-resolution receive antennas. This paper adopts a Bayesian approach and aims to design low-complexity algorithms for the MIMO sensing beamforming problem while leveraging prior information about the target at each sensing stage. We formulate the problem of minimizing the Bayesian Cramér-Rao lower bound (BCRLB) for estimating a parameter of interest, and show that it has the structure of a weighted sum-of-ratios problem. For the case where the phase shifters at transmit antennas are continuous, we propose a novel linear transform that can transform a fractional function into a linear function. In this way, the original problem is turned into a sequence of sub-problems that can be solved in closed-form in each step with linear complexity in the number of antennas, making the iterative optimization process highly efficient. When the phase shifters are discrete, we propose a penalty-based convex-hull relaxation algorithm, which provides better performance than directly quantizing the solution of the continuous case, but at the cost of increased computational complexity. Numerical results demonstrate the effectiveness of the proposed algorithms.