Common-Rate Constrained Cramér–Rao Bound Minimization for Multicast MIMO ISAC

Abstract

We study Cramér–Rao bound (CRB) minimization under common-rate and power constraints for the multicast MIMO downlink. Under a covariance-matched nonparametric extended-target model, the trace CRB equals <inline-formula><tex-math notation="LaTeX">$c\,\text{tr}(\mathbf {S}^{-1})$</tex-math></inline-formula> and is attained by the least-squares estimator, so it is also the attainable total MSE of an unbiased estimator. We develop a two-block consensus alternating direction method of multipliers (ADMM) solver, termed ADMM-LDP, that splits the received covariances and combines an exact spectral log-det projection with a trace-inverse/power proximal step. Each iteration reduces to eigendecompositions and scalar root-finding. Numerical results show close agreement with the interior-point reference, competitive runtime, and tractability up to <inline-formula><tex-math notation="LaTeX">$N_{t}=64$</tex-math></inline-formula>.