Training sequence design for MIMO channels: an application-oriented approach

Abstract

In this paper, the problem of training optimization for estimating a multiple-input multiple-output (MIMO) flat fading channel in the presence of spatially and temporally correlated Gaussian noise is studied in an application-oriented setup. So far, the problem of MIMO channel estimation has mostly been treated within the context of minimizing the mean square error (MSE) of the channel estimate subject to various constraints, such as an upper bound on the available training energy. We introduce a more general framework for the task of training sequence design in MIMO systems, which can treat not only the minimization of channel estimator's MSE but also the optimization of a final performance metric of interest related to the use of the channel estimate in the communication system. First, we show that the proposed framework can be used to minimize the training energy budget subject to a quality constraint on the MSE of the channel estimator. A deterministic version of the 'dual' problem is also provided. We then focus on four specific applications, where the training sequence can be optimized with respect to the classical channel estimation MSE, a weighted channel estimation MSE and the MSE of the equalization error due to the use of an equalizer at the receiver or an appropriate linear precoder at the transmitter. In this way, the intended use of the channel estimate is explicitly accounted for. The superiority of the proposed designs over existing methods is demonstrated via numerical simulations.

Algorithmic solutions for pilot design optimization in arbitrarily correlated scenarios

“…As is shown in [11], this cost metric can often be well approximated by a quadratic expression of the form…”

“…An approach proposed in [10,11] is to define an ellipsoidal confidence region for which the probability is easy to calculate, D = {h H C −1 MSEh ≤ 1 2 χ 2 α (2NtNr)} 1 and replace the constraint Pr[J(h) ≤ 1/γ] = α by the tighter constraint that J(h) ≤ 1/γ for allh ∈ D. As shown in [11], the resulting pilot design problem can be written as…”

“…2.1 have been analyzed in [11]. Under the assumptions (12) and the additional assumptions Iadm = I T T ⊗ IQ, it is possible to convert the converse (minimizing P 2 F given c) confidence region formulation (11) into a convex problem with closed-form solution.…”

“…However, depending on how the channel estimate will be used, it is not necessarily optimal to aim for a minimal channel estimate MMSE. Instead, we follow [11] and consider an end performance metric M (Ĥ) of the equalizer or precoder or whatever application the channel estimate is intended for and define our cost metric as the difference in end performance between using the channel estimate and using the true channel,…”

“…Inspired by the system identification literature, such as [10], the recent paper [11] shows how to incorporate the application in the pilot design, using a cost function that reflects the impact of the channel estimation error on the end performance. Two main strategies are proposed, one related to the average performance and one related to the probability that the performance is good enough.…”