Digital Compensation for Analog Front-Ends: A New Approach to Wireless Transceiver Design

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ML Channel Estimator

The channel equalization methods integrated in most of the digital communication systems usually rely on the knowledge of the channel impulse response. Pilot symbols are often interleaved in the data symbols based on which the channel impulse response can be estimated. A matrix model is typically built that links the channel impulse response vector h of size L to the observed vector of samples r of size N_r:

in which of size N_r × L is a matrix composed of the transmitted pilot symbols and n of size N_r is the additive noise composed of independent Gaussian elements of variance .

The ML estimate of the channel impulse response vector h is selected such that:

where the second equality has been obtained by taking the expression of the noise probability into account. After optimization, the ML estimate is given by Deneire et al. (2003) and Kay (1993):

where ...