Encoder and decoder design for signal estimation

Abstract

Abstract-In this paper, we study the joint design of optimal linear encoders and decoders for filtering and transmission of a signal over an additive Gaussian noise channel subject to a real-time constraint. The objective is to minimize the variance of the estimation error at the receiving end. The design problem is nonconvex, but it is shown that a global optimum can be found by solving a related two-stage problem. The first stage consists of a mixed H 2 and H 1 norm minimization problem, where the H 2 norm corresponds to the error variance in a corresponding WienerKolmogorov filtering problem and the H 1 norm is induced by the channel noise. The second stage consists of a spectral factorization. The results are illustrated by a numerical example.

A framework for linear control over channels with signal-to-noise ratio constraints

“…The problem considered in [11] is actually a special case of the problem studied here. This also holds for the estimation problem considered in [12].…”

“…It will now be demonstrated that the estimation problem considered in [12] and the control problem considered in [11] are special cases of the problem in this paper.…”

“…Since G yu = 0, we can let N = 0, M = 1, U = 0 and V = 1. Then Q = K and the corresponding functional to minimize is, just as in [12],…”

An approach to stationary state estimation with missing data

“…where Px L and P wL are the stationary covariances of the auxiliary signalsx L and w L in Figure 3, and P q is the variance of the auxiliary noise source q. Lemma 1 shows that solving Problem 1 amounts to solving an optimal control problem subject to an equality SNR constraint (see also [6], [32]- [34]). We now exploit this fact and solve Problem 1 in two stages.…”

Enhanced Adaptive Modulation and Coding (AMC) Technique Using ILDPCA Coders for MIMO Systems

“…are used [5].However the exact number of environmental parameters like signal energy, noise variance, channel state information and other subtle factors like quantization error, made it hard to tune the transmission parameters optimally (even near optimal) [4]. Erik Johannesson et al [6] proposed the joint design of an optimal linear MIMO encoderdecoder pair of parallel Gaussian channels that can be formulated as a convex optimization problem followed by a matrix spectral factorization. It concentrated on a mixed norm minimization problem, in which the relative weight of the two norms is determined by the maximum transmission power.…”