Converse bounds on modulation-Estimation performance for the Gaussian multiple-access channel

Ünsal, Ayse; Knopp, Raymond; Merhav, Neri
IEEE Transactions on Information Theory, Vol. 64, N°2, February 2018

This paper focuses on the problem of separately modulating and jointly estimating two independent continuousvalued parameters sent over a Gaussian multiple-access channel (MAC) under the mean square error (MSE) criterion without bandwidth constraints. To this end, we first improve an existing lower bound on the MSE that is obtained using the parameter modulation-estimation techniques for the single-user additive white Gaussian noise (AWGN) channel [1]. As for the main contribution of this work, this improved modulation-estimation analysis is generalized to the model of the two-user Gaussian MAC. We present outer bounds to the achievable region in the plane of the MSE's of the two user parameters, which provides a trade-off between the MSE's, where we used zero-rate lower bounds on the error probability of Gaussian channels by Shannon [2] and Polyanskiy et al. [3]. Numerical results showed that, the multiuser adaptation of the zero-rate lower bound by Polyanskiy et al. provides a tighter overall lower bound on the MSE pairs than the classical Shannon bound. In addition, we introduced upper bounds on the MSE exponents, namely, the exponential decay rates of these MSE's in the asymptotic regime of long blocks, that could make use of any bound on the error exponent of a single-user AWGN channel. The obtained results are numerically evaluated for three different bounds on the reliability function of the Gaussian channel. It is shown that the adaptation of the reliability function by Ashikhmin et al. [4] to the MAC provides a significantly tighter characterization than Shannon's spherepacking bound and the divergence bound [5]¹.

Communication systems
Eurecom Ref:
© 2017 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.