Optimal transmission codebook design in fading channels for the decentralized estimation in wireless sensor networks

In this paper, we design the near optimal transmission codebook for decentralized estimation in wireless sensor networks with uniform quantizations and digital communications over orthogonal Rayleigh fading channels. We start from deriving the maximum likelihood estimator (MLE) for arbitrary transmission codebook with known and unknown channel state information (CSI) at the fusion center (FC). Because the MLE is not a convex problem in the system we considered, it is not trivial to obtain an analytical expression of either its mean square error or Cramer-Rao lower bound (CRLB). By analyzing the likelihood function, we convert the optimal transmission codebook design minimizing the CRLB to a two-stage optimization problem, where the problem in each stages is convex. It is shown that the estimation accuracy with our designed codebooks and MLE is superior to that with available transmission schemes. The proposed codebook suggests that the sensors should use orthogonal codes to transmit different observations for unknown CSI, while the optimal codebook for known CSI is not orthogonal.