Determinant maximizing cost function impulse response shortening for discrete multitone transceivers

A new criterion is proposed for solving the problem of channel shortening in multicarrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In N. Al-Dahir and J. M. Cioffi (1996) a new criterion for partially equalizing severe ISI channels to reduce the cyclic prefix overhead of the discrete multitone transceiver (DMT), assuming a fixed transmission bandwidth, is introduced. Due to specific constrained (unit morm constraint on the target impulse response (TIR)) in their method, the freedom to choose optimum vector (TIR) is reduced. Better results can be obtained by avoiding the unit norm constraint on the target impulse response (TIR). We change the cost function proposed in N. Al-Dahir and J. M. Cioffi (1996) to the cost function of determining the maximum of a determinant subject to linear matrix inequality (LMI) and quadratic constraint and solve the resulting optimization problem. Usefulness of the proposed method is shown with the help of simulations.