Gaussian maximum-likelihood channel estimation with short training sequences

Abstract

Abstract-In this paper, we address the problem of identifying convolutive channels using a Gaussian maximum-likelihood (ML) approach when short training sequences (possibly shorter than the channel impulse-response length) are periodically inserted in the transmitted signal. We consider the case where the channel is quasi-static (i.e., the sampling period is several orders of magnitude smaller than the coherence time of the channel). Several training sequences can thus be used in order to produce the channel estimate. The proposed method can be classified as semiblind and exploits all channel-output samples containing contributions from the training sequences (including those containing contributions from the unknown surrounding data symbols). Experimental results show that the proposed method closely approaches the Cramer-Rao bound and outperforms existing trainingbased methods (which solely exploit the channel-output samples containing contributions from the training sequences only). Existing semiblind ML methods are tested as well and appear to be outperformed by the proposed method in the considered context. A major advantage of the proposed approach is its computational complexity, which is significantly lower than that of existing semiblind methods.Index Terms-Block transmission, maximum-likelihood (ML) estimation, stationary multipath channel, training sequence.

Shifted Known Symbol Padding for Efficient Data Communication in a WLAN Context

“…Describing the system with a circulant channel matrix is highly desirable as it allows for the use of low-complexity frequency-domain equalizers relying on the diagonalization properties of circulant matrices. However, when the padded sequences are used for channel estimation purposes, the use of non-constant training sequences, i.e., t k = t l , ∀k = l, largely improves the quality of the channel estimates, irrespective of the estimation method that is used [8]. More specifically, the Cramer-Rao bound (CRB) analysis presented in [8] indicates that the channel modeling error tends to zero when there exists an exact solution to the channel estimation problem in the noiseless case.…”

“…However, when the padded sequences are used for channel estimation purposes, the use of non-constant training sequences, i.e., t k = t l , ∀k = l, largely improves the quality of the channel estimates, irrespective of the estimation method that is used [8]. More specifically, the Cramer-Rao bound (CRB) analysis presented in [8] indicates that the channel modeling error tends to zero when there exists an exact solution to the channel estimation problem in the noiseless case. When no exact solution exists in the noiseless case, an error floor appears.…”

“…When constant training sequences are used, this happens only when N t ≥ 2L + 1. But even when the channel order L is sufficiently small to guarantee identifiability for non-constant as well as constant training sequences, the first always outperforms the latter [8].…”

“…For KSP systems, no training symbols are inserted and the channel estimate relies solely on the knowledge of the padded sequences. The channel estimates are obtained from the Gaussian ML method proposed in [8] considering 50 blocks of data symbols. We consider short padded sequences (N t = 8, which corresponds to the optional short CP length).…”

“…These padded sequences can be exploited for time and frequency synchronization [4][5][6], channel estimation [7,8] or direct equalizer design [9]. However, KSP does not simultaneously allow for low-complexity frequency-domain equalization and accurate channel estimation.…”