Robust MIMO Equalization for Non-Parametric Channel Model Uncertainty

Abstract

In this paper, three MIMO robust equalization problems are considered for non-parametric classes of channel models defined by weighted or balls (of frequency-responses) and performance criteria based on (variance) or norms of error signals. The approach pursued here centers on characterizing the worst-case performance of candidate equalizers, or upper bounds on it, by means of dual Lagrangian functionals. Then, for linearly parametrized, finite-dimensional classes of candidate equalizers, the corresponding robust equalization problems are converted into semi-definite linear programming problems for which approximate solutions can be effectively computed. A simple numerical example is presented, involving model uncertainty and error-variance performance, to illustrate, for various levels of uncertainty, the changes in the worst-case performances of the nominally optimal equalizer and of the one, in a specific linear class, which minimizes the worst-case error variance.

Robust Equalizer for Multicell Massive MIMO Uplink With Channel Model Uncertainty

“…Further, to obtain (3), we do not have to make assumptions about the channel model. That's why we can design the robust equalizer with channel model uncertainty, which is similar as in [13]. From the point of the physical insight, we just acquire and employ the least information that the channel estimation provides.…”

“…According to the literature on the worst-case method of robust design [8]- [13], the principle is to minimize the MSE in the estimation of x for the worst H satisfying Lemma 1. The MSE between x andx in (6) is…”

“…In (12), F is not invertible due to the existence of pilot contamination, which distinguishes it from the conventional robust design problems in other literature [9]- [13].…”

“…This completes the proof. Note that Theorem 1 enables us to convert the complex and constrained min-max problem into an unconstrained optimization problem, based on which we derive the optimality conditions and provide several methods to compute a solution to problem (13) in the next section.…”

“…Further, these works obtain the robust MIMO equalizer for the case that the bound on the Frobenius norm of the channel matrix error is perfectly known. On the other hand, [13] generally studies the robust MIMO equalizer for the weighted channel matrix error based on both the Frobenius norm and the l-∞ norm. However, pilot contamination disables the computation of the exact bound on the Frobenius norm or the l-∞ norm of the channel matrix error.…”