A Unified MI–KLD Framework for Multi-User MIMO ISAC: Normalized Achievable Region and Asymptotic Analysis

This paper establishes an information-theoretic framework for multi-user multi-target multiple-input multiple-output (MIMO) integrated sensing and communication systems under Gaussian signaling and treating-interference-as-noise (TIN) decoding. The analysis characterizes communication performance via weighted sum mutual information (MI) and sensing performance via weighted sum Kullback–Leibler divergence (KLD). To resolve the dimensional heterogeneity of these metrics, a normalization methodology based on single-functionality baselines is introduced. This approach maps the performance utilities onto a dimensionless unit square and defines the normalized achievable region as a compact and convex deterministic inner bound. Fixed-strategy low signal-to-noise ratio (SNR) trajectories are characterized through asymptotic analysis under the fixed-baseline convention. In the low-SNR regime, the linear scaling of MI and the quadratic scaling of KLD drive fixed-strategy tradeoff trajectories to become tangent to the communication axis near the origin. In the high-SNR regime, independent precoding that ignores cross-functional interference is shown to exhibit an asymptotic efficiency collapse in the normalized domain under interference saturation, implying that suppressing the projected leakage order is necessary within the specified persistent-overlap fixed-direction regime. For algorithmic construction, an alternating optimization algorithm based on the minorization-maximization principle is developed to compute scalarized operating points through an implemented rank-one multiple-input single-output block approximation with an objective safeguard. This implementation integrates a sensing-priced weighted minimum mean-square error update with a closed-form sensing covariance refinement and uses the objective safeguard to preserve monotonicity of the accepted objective sequence. Numerical results corroborate the theoretical scaling laws and illustrate improved normalized performance over the independent precoding baseline in the simulated interference-limited settings.