MMSE decision feedback equalizer from channel estimate

In digital radio transmission over frequency selective channels, the minimum mean-square error decision feedback equalizer (MMSE-DFE) is widely recognized as an efficient equalization scheme. In order to compute the coefficients of the feedforward and feedback filters of the MMSE-DFE, both the channel impulse response (CIR) and the variance of the noise have to be estimated. The estimate of the CIR is usually performed by the standard least-square method, where a known training sequence is employed. Then, the estimated CIR is used to evaluate the variance of the noise. The use of the two above estimates for MMSE-DFE is studied. In particular, an unbiased estimate of the variance of the noise is described.