LMMSE channel estimation in OFDM context: a review

Abstract

International audienceLinear minimum mean square error (LMMSE) is by definition the optimal channel estimator in the sense of meansquare error criterion, but its practical application is limited by its high complexity. Furthermore, the LMMSE estimation methodrequires the knowledge of both the channel and the noise statistics, which are a priori unknown at the receiver. A wide range oftechniques are proposed in the literature in order to overcome these two drawbacks. In this study, the authors give an overviewof the LMMSE-based channel estimation in an orthogonal frequency division multiplexing (OFDM) context. A didactic reminderconcerning the basics of LMMSE estimation and its performance is provided, and a survey of techniques of the literature, whichenable the practical application of LMMSE and the reduction of its complexity, is presented in both single-input single-output andmultiple-input multiple-output contexts. Finally, some perspectives are provided, in particular the application of the LMMSEestimator to flexible waveforms beyond OFDM

Uplink Channel Estimation and Equalization in NB-IoT System

“…Another observation is that perfect channel estimation outperforms LMMSE+MMSE of more than 1 dB. However, we can notice in papers such as [11] that LMMSE is very close to perfect estimation. The reason is that we are using SC-FDMA contrarily to [11] where OFDM is considered.…”

“…As a prerequisite to channel estimation, it is noteworthy that Y p can be rewritten as Y p = X p H p + W p , where X p is the diagonal matrix containing the elements of X p , and H p is the vector containing the frequency response of the channel. From this, we derive the expression of the channel estimate using LS and LMMSE methods, such as presented in [8]- [11]. a) Least Square (LS): LS method is based on the minimization of the cost function J LS = Y p − X p H p 2 , which yields to:…”

“…where D is a matrix whose expression is given below. The minimization of J LM M SE with respect to D finally leads to (see [11] for details):…”

Effects of imperfect channel sensing and estimation on the performance of cognitive radio systems

“…Most of the used algorithms are based on the LS and LMMSE algorithms. The LMMSE performs better than the LS but at the cost of more computational complexity . For the purpose of comparison, we first discuss the LS and LMMSE algorithms.…”

“…The LMMSE estimator of the channel exploits the channel frequency correlation optimally in terms of the MSE but with a little practical value because of its computational complexity. The LMMSE estimate of h (minimizing for all possible linear estimators ) is given by where …”