Abstract
This article presents an iterative minimum mean square error- (MMSE-) based method for the joint estimation of signal-to-noise ratio (SNR) and frequency-selective channel in an orthogonal frequency division multiplexing (OFDM) context. We estimate the SNR thanks to the MMSE criterion and the channel frequency response by means of the linear MMSE (LMMSE). As each estimation requires the other one to be performed, the proposed algorithm is iterative. In this article, a realistic case is considered; i.e., the channel covariance matrix used in LMMSE is supposed to be totally unknown at the receiver and must be estimated. We will theoretically prove that the algorithm converges for a relevantly chosen initialization value. Furthermore simulations show that the algorithm quickly converges to a solution that is close to the one in which the covariance matrix is perfectly known. Compared to existing SNR estimation methods, the algorithm improves the trade-off between the number of required pilots and the SNR estimation quality.
Highlights
The multipath channel and the additive noise are two important sources of distortion in wireless communication systems
At the transmitter, the time-reversal method [2] can be performed, thanks to the channel impulse response. Many algorithms such as the linear minimum mean square error (MMSE) (LMMSE) channel estimation [3] or the turbo-decoder [4] require the knowledge of the signalto-noise ratio (SNR), and an accurate channel state information (CSI) allows to perform a simple one-tap equalization in orthogonal frequency division multiplexing (OFDM) systems
The SNR is estimated, thanks to the MMSE noise variance estimation combined with the second moment order of the signal, and the channel, thanks to the LMMSE method
Summary
The multipath channel and the additive noise are two important sources of distortion in wireless communication systems. The iterative expectation maximization (EM) algorithm [27,28] has been developed so that the ML estimator is an appropriate tool in frequency-selective channels when the observed data are not complete, i.e., when the size of the observation is smaller than the vector to be estimated An adaptation of this algorithm for both channel and noise estimation is presented in [29,30], and joint iterative EM data detection and recursive channel tracking are proposed in [31]. In [34], we proposed an MMSE-based iterative algorithm for both SNR and channel estimations It was a theoretical approach, in which the channel covariance matrix was supposed to be known at the receiver.
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