Estimation Over Multiaccess Channels

We study the problem of communicating sensor readings over a Gaussian multiaccess 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., the signal constellation) to facilitate the estimation of field parameters from the channel output. In case of symmetric channel gains, it is shown that Pulse Position Modulation (PPM) (i.e., simultaneous transmission of pulses timed according to the sensed data) is asymptotically optimal in the limit of large number of sensors. In particular, we show that the PPM together with a variant of the maximum-likelihood estimator achieves the Cramer-Rao bound asymptotically. We then extend the asymptotic analysis of PPM to fading channels, and compare the performance of PPM with other approaches that allocate orthogonal channels to sensors such as TDMA.