Multi-terminal joint transceiver design for MIMO systems with contaminated source and individual power constraint

This paper considers optimal transceiver design for a multi-terminal multi-inputmulti-output (MIMO) system, where L sensors wirelessly communicate individually-contaminated observations of the same source to the fusion center. The constraint that each sensor has individual power cap significantly complicates the non-convex optimization problem, and the optimal (linear) precoding and postcoding are not previously known. Using the signal-to-noise-ratio (SNR) as the performance metric, and employing the alternative minimization approach, we decompose the original problem into multiple subproblems that will run iteratively. The key results include the development of a closed-form solution to the optimal postcoder given the precoders, and the development of a closed-form solution for the ε-optimal precoders given the postcoder. The former is achieved via eigenvalue decomposition, and the latter is achieved by bounding the optimal solutions from above and from below, designing a series of fast-converging bisection search, and developing the closed-form analytical solution for each search. The convergence and the complexity of the proposed algorithm is analyzed and simulations are provided to confirm the efficiency of our proposal.