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

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MMSE Linear Detector

A usual problem in the design of a digital communication system is to estimate a vector of symbols d of size N_d transmitted at one side of the link based on the observation of a vector of samples r of size N_r received at the other side of the link. The received vector is typically a channel distorted version of the transmitted vector plus an additive Gaussian noise, so that:

in which of size N_r × N_d models the channel distortion and n of size N_r is the additive noise. The rank of the matrix should be at least equal to N_d. When a linear joint detector of size N_d × N_r is applied on the received signal (A1) in order to estimate the transmitted symbols, the expression of the estimated vector is:

and the prediction error vector is defined as:

The linear MMSE detector is designed to minimize the variance of the symbol estimation errors, or equivalently the diagonal ...