Unified ISAC Pareto Boundary Based on Mutual Information and Minimum Mean-Square Error Estimation

The performance of multiple-input multiple-output (MIMO) integrated sensing and communication systems (ISAC) can be evaluated from the perspectives of information theory and estimation theory to provide more fundamental insights. In this paper, we study the relationship between mutual information (MI) and minimum mean square error (MMSE) by characterizing the Pareto boundary for a general ISAC scenario, a dual-functional BS simultaneously estimates the target response matrix while communicating with a user. First, optimization problems are formulated to achieve MI Pareto boundary and MMSE Pareto boundary, respectively. Then, we show that under the same maximum transmit power constraint and set of transmit filters, MI Pareto bounary can be transformed to MMSE Pareto boundary with optimized MSE-weights in ISAC with colored Gaussian noise. Subsequently, based on unified MI and MMSE performance, we propose Data-dependent alternate algorithm (DDA) to obtain the MI Pareto boundary with colored Gaussian noise. In order to reduce complexity, we propose Data-independent alternate algorithm (DIA) when noise degenerates into white Gaussian noise. Finally, simulation results show DDA almost achieves the MI Pareto boundary with colored Gaussian noise and DIA achieves almost the same performance as DDA with white Gaussian noise at a lower cost to implement.