Signal Estimation Over Channels with SNR Constraints and Feedback

We consider the problem of designing optimal linear encoders and decoders for estimation and transmission of a signal over an analog communication channel with additive noise and a signal-to-noise ratio (SNR) constraint. The objective is to minimize the variance of the estimation error at the receiving end, subject to a real-time constraint. It has been previously shown that, for channels without feedback, a solution can be obtained by solving a mixed norm minimization problem and performing a spectral factorization, see Johannesson et al. (2010b). In this paper, these results are extended to the case when the encoder has access to feedback from the channel output. This results in improved performance, which is demonstrated by a numerical example.