Correlation Matching Approaches for Blind OSTBC Channel Estimation

In this paper, the problem of blind channel estimation under orthogonal space-time block coded (OSTBC) transmissions is solved by minimizing some distance measure between the theoretical and estimated correlation matrices of the observations. Specifically, the minimization of the Euclidean distance and the Kullback-Leibler divergence leads, respectively, to the Euclidean correlation matching (ECM) and Kullback correlation matching (KCM) criteria. The proposed techniques exploit the knowledge of the source correlation matrix to unambiguously recover the multiple-input multiple-output (MIMO) channel. Furthermore, due to the orthogonality properties of OSTBCs, both the ECM and KCM criteria result in closed form solutions. In particular, the channel estimate is given by the principal eigenvector of a matrix, which is obtained from the estimated correlation matrix of the observations modified by the code matrices and a set of weights. In the ECM case, the weights are fixed and equal to the eigenvalues of the source correlation matrix, whereas the KCM weights depend on both the signal-to-noise ratio (SNR) and the source eigenvalues. Additionally, we show that the proposed approaches are equivalent in the low SNR regime, whereas in the high SNR regime the KCM criterion is asymptotically equivalent to the relaxed blind maximum-likelihood (ML) decoder. Finally, the performance of the proposed criteria is illustrated by means of some numerical examples.