  This paper investigates the transceiver design problem in a noisy-sensing
noisy-transmission multi-input multi-output (MIMO) wireless sensor network.
Consider a cluster-based network, where multiple sensors scattering across
several clusters will first send their noisy observations to their respective
cluster-heads (CH), who will then forward the data to one common fusion center
(FC). The cluster-heads and the fusion center collectively form a coherent-sum
multiple access channel (MAC) that is affected by fading and additive noise.
Our goal is to jointly design the linear transceivers at the CHs and the FC to
maximize the signal-to-noise ratio (SNR) of the recovered signal. We develop
three iterative block coordinated ascent (BCA) algorithms: 2-block BCA based on
semidefinite relaxation (SDR) and rank reduction via randomization or solving
linear equations, 2-block BCA based on iterative second-order cone programming
(SOCP), and multi-block BCA that lends itself to efficient closed-form
solutions in specific but important scenarios. We show that all of these
methods optimize SNR very well but each has different efficiency
characteristics that are tailored for different network setups. Convergence
analysis is carried out and extensive numerical results are presented to
confirm our findings.
