Estimation Over Deterministic Multiaccess Channels

We study the problem of communicating sensor readings over a Gaussian multiaccess (MAC) channel. We focus on the scenario that each sensor observes a single random variable, and transmits it using certain signaling in a shared channel. The objective is the design of channel waveforms (i.e., signal constellation) to facilitate the estimation of field parameters from the channel output. We propose a new approach named Histogram-Delivering Multiple Access (HDMA). In case of symmetric channel gains, it is shown that the HDMA is asymptotically optimal in the limit of large number of sensors. In particular, we show that the HDMA together with a variant of the maximum-likelihood estimator achieves the Cramer-Rao lower bound asymptotically. We then compare the performance of HDMA with other approaches that allocate orthogonal channels to sensors such as TDMA.