Partial imaginary precursor cancelling in DFE for BPSK and GMSK modulations

This paper examines the effect of partial imaginary precursor cancelling on the performance of a system which uses a DFE and employs a one dimensional modulation. As opposed to QAM, BPSK or GMSK (after proper manipulations) require minimization of the mean square (MS) of the error real part only. Therefore, a lower MSE is achieved if the DFE coefficients are computed taking this fact into account, by trying to minimize as few imaginary precursors as possible. However, this introduces a delay by the imaginary part of the feedback filter (FBF) which is no longer causal. In this paper we investigate the influence of the length of imaginary precursor cancelling on system performance, and its effect on carrier phase tracking. The equations for the computation of the DFE coefficients for none or partially cancelled imaginary precursors are derived and performance on GMSK channels is presented.