Cochannel Receivers for CPM Signals Based Upon the Laurent Representation

In this paper, we develop optimum and suboptimum receivers for jointly detecting two cochannel continuous phase modulated (CPM) signals. These receivers are based upon Laurent's representation of binary CPM as the sum of a nite number of pulse amplitude modulated signals. We also provide a review of the Laurent representation and its application to the design of optimum and suboptimum single-channel receivers. 1 Introduction Cochannel interference, which occurs when two or more signals share the same spectral and temporal channels , is a major obstacle to high quality speech and data transmission in mobile radio systems 1, 2]. In a recent paper 3], we investigated a single-sensor technique for jointly detecting two cochannel CPM signals. The result was the development of the joint maximum likelihood sequence estimation (JMLSE) receiver based upon the conventional representation of CPM 4]. It was shown that this receiver performed well under certain conditions even when the power separation between the signals was negligible. One of the major drawbacks with this receiver, however, is its high degree of complexity. In an eeort to simplify the receiver and provide new perspectives on the joint detector, we have investigated the use of the Laurent representation 5] for binary CPM in developing both optimum and suboptimum cochannel receivers. In 5], Laurent showed that a binary CPM signal can be exactly represented as the sum of K pulse amplitude modulated (PAM) signals. The Laurent representation is a generalization of the interpretation of MSK-type signals (i.e., binary CPM with modulation index 1=2) as the sum of time and phase shifted PAM signals 6, 7]. For example, it is well known that MSK can be represented as an ooset-QPSK signal in which the pulse shape is a half-cycle sinusoid with period four times the bit duration. There are three main advantages of the Laurent representation. First, it provides for easy calculation of the autocorrelation and power spectrum of CPM signals. Second, it provides for easy inclusion of channel eeects in the expression for an LTI-ltered CPM signal. Third, and more important to the discussion in this paper, it provides a straightforward method of accurately approximating CPM signals using only a subset of the K PAM components in the exact representation. Kaleh employed the representation to develop the optimum maximum likelihood sequence estimation (MLSE) receiver for a single CPM signal in additive white Gaussian noise. It was pointed out that this optimum receiver …