  Optimal and suboptimal decentralized estimators in wireless sensor networks
(WSNs) over orthogonal multiple-access fading channels are studied in this
paper. Considering multiple-bit quantization before digital transmission, we
develop maximum likelihood estimators (MLEs) with both known and unknown
channel state information (CSI). When training symbols are available, we derive
a MLE that is a special case of the MLE with unknown CSI. It implicitly uses
the training symbols to estimate the channel coefficients and exploits the
estimated CSI in an optimal way. To reduce the computational complexity, we
propose suboptimal estimators. These estimators exploit both signal and data
level redundant information to improve the estimation performance. The proposed
MLEs reduce to traditional fusion based or diversity based estimators when
communications or observations are perfect. By introducing a general message
function, the proposed estimators can be applied when various analog or digital
transmission schemes are used. The simulations show that the estimators using
digital communications with multiple-bit quantization outperform the estimator
using analog-and-forwarding transmission in fading channels. When considering
the total bandwidth and energy constraints, the MLE using multiple-bit
quantization is superior to that using binary quantization at medium and high
observation signal-to-noise ratio levels.
