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.
Highlights
An important factor in the performance of multiple antenna systems is the accuracy of the channel state information (CSI) [1]
CSI is primarily used at the receiver side for purposes of coherent or semicoherent detection, but it can be used at the transmitter side, e.g., for precoding and adaptive modulation
We assume that RR = SR, since the high SNR expressions for Iadm in the context of minimum mean square error (MMSE) channel equalization in Appendix 1 indicate that IT = I for this application and according to Theorem 5 the optimal training corresponds to the optimal training for channel estimation in [8]
Summary
An important factor in the performance of multiple antenna systems is the accuracy of the channel state information (CSI) [1]. We study two uses of the channel estimate: channel equalization at the receiver using a minimum mean square error (MMSE) equalizer and channel inversion (zero-forcing precoding) at the transmitter, and derive the corresponding optimal training signals for each case. The novelty of this paper is on introducing the application-oriented framework as the appropriate context for training sequence design in communication systems To this end, Hermitian form-like approximations of performance metrics are addressed here because they usually are good approximations of many performance metrics of interest, as well as for simplicity purposes and comprehensiveness of presentation. This paper is organized as follows: Section 2 introduces the basic MIMO received signal model and specific assumptions on the structure of channel and noise covariance matrices.
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