Decoding of severely filtered modulation codes using the (M, L) algorithm

The problem of decoding data in the presence of infinite-duration intersymbol interference that is caused by severe channel filtering is considered. Filtered continuous phase modulations (CPM) are the particular object of study. A state-variable approach is used for defining the decoder tree. Maximum likelihood sequence estimation requires exhaustive tree searching, which is restricted by using the ( M, L) algorithm since this approach does not require that the channel intersymbol interference be finite. After briefly describing the (M, L) algorithm, the authors motivate the problem of equalization of infinite-impulse-response channels by considering the performance of a discrete-time single-pole channel filtering a binary input sequence. The state variable description of a linear system is used to analyze the filtered modulation. The state of the filtered modulation for a given input modulation is used to define the tree structure of the filtered signal upon which the (M, L) algorithm operates. The minimum signal space distance results for several filtered CPM schemes are then summarized. Extensive simulation results are presented, and comparisons to the optimal performance are made