In 1986, Laurent showed that binary continuous phase modulated (CPM) signals can be decomposed into pulse amplitude modulated (PAM) waveforms. This result, later extended to multilevel CPM signals by Mengali and Morelli, has attracted much attention, especially for the design of simplified receivers. The paper proceeds from the premise that the decomposition into PAM waveforms is not unique, and follows a systemtheory approach that leads to a natural formulation. First, the CPM modulator is represented by a nonlinear part (encoder) followed by a linear part (bank of PAM modulators).The two parts are then rearranged with the aim of obtaining real-valued continuous PAM waveforms and to reduce their number. Several classes of decompositions arise with this approach, each of which admits an infinite number of different decompositions of the same CPM signal, among which the Laurent and MengaliMorelli results appear as special cases. Throughout the paper, a systematic use is made of the Kronecker product, which appears to be the natural tool for dealing with CPM decompositions and for expressing results in a very simple form.

A system-theory approach to decompose CPM signals into PAM waveforms

Continuous phase modulation (CPM) is a power and bandwidth efficient modulation scheme used in cellular, personal, and satellite communications among other applications. If the modulation index of the CPM waveform used by the transmitter is unavailable at the receiver, serious performance degradation may occur. This paper investigates the problem of modulation index estimation for partial response continuous phase modulation schemes. Specifically, we propose two novel estimators for the CPM signal observed in an additive white Gaussian noise channel. A non-data aided method of moments (MoM) estimator based upon the fourth-order cumulants and a data-aided best linear unbiased estimator (BLUE) based upon an approximate linear phase model of the received CPM signal have been proposed. Modified Cramer–Rao lower bound is derived for the partial response CPM schemes to assess the performance of the estimators. We also perform numerical simulations to compare the mean-squared error (MSE) performance of the proposed MoM and BLUE estimators with previously proposed estimators in the literature. It is shown that the MoM estimator exhibits good MSE performance at low signal-to-noise ratio (SNR) while the BLUE estimator performs very well at high SNRs. Moreover, the proposed estimators have lower complexity than existing methods and are based upon non-iterative algorithms.

Estimation of Modulation Index for Partial Response CPM Signal

This paper deals with the spectral analysis of multi-h continuous phase modulation (CPM) signals. A new solution to the problem is obtained by identifying an inner hidden Markov model in the CPM signal, which can be accomplished by expressing the modulator as the cascade of a sequential machine (SM), and a bank of PAM modulators. An in-depth study of the resulting Markov chain shows that it is both cyclostationary and reducible, and proper tools are identified to address these peculiarities. As a result, the multi-h CPM spectrum is expressed as a combination of Fourier transforms of portions of a CPM signal, thus allowing an efficient numerical evaluation through fast Fourier transforms (FFTs).

New Results on the Spectral Analysis of Multi-h CPM Signals

A continuous phase modulation (CPM) is specified by the size M of the input alphabet, the modulation index h, the phase response /spl phi/(t) and the duration LT of the active part of /spl phi/(t). The integer L indicates the memory and, roughly, the complexity of a CPM system. In this contribution we show that a CPM with an arbitrary memory L is equivalent to a CPM with a unitary memory and a bigger alphabet with size L(M - 1) + 1. The assumption is that the phase response /spl phi/(t) is "separable", a requirement verified in some practical implementations. We discuss some consequences of this equivalence on modulator and demodulator structure.

An equivalence principle for separable CPM signals

Continuous phase modulation (CPM) is a power and bandwidth efficient modulation yet the receiver complexity is usually too high. Therefore, receiver complexity reduction techniques become very important. Among the complexity reduction techniques, the PAM decomposition approach for CPM signals have recently gained much attention, due to its effectiveness and excellent BER performance. The PAM decomposition approach decomposes CPM signals into a set of PAM waveforms and employs only significant part of the PAM waveforms to design receiver. More recently, a PAM waveforms reduction method for a special class of CPM signals, which have the so-called separable phase property, enables the CPM to be reformulated as an correlatively encoded equivalent CPM scheme, such that the equivalent CPM can be represented as less PAM waveforms than the original CPM. Nevertheless, most of the known CPM family does not satisfy the separable phase property. This paper proposes a new class of CPM with phase separable property. It is found that the new class of CPM can reduce the number of filters to 25 percent of the MLSD receiver required. Moreover, the bandwidth and power efficiency of this new set of CPM are very close to the conventional CPM and sometimes are even better.

A novel class of continuous-phase modulation (CPM) with separable phase property

This letter proposes a new pulse amplitude modulation decomposition of continuous phase modulation (CPM) signals under the constraint of phase response separability. The separability condition is met by a broad class of CPM signals, including full-response signals. We show that the proposed decomposition has minimal cardinality of N/sub c/=L(M-1), where M is the alphabet size and L is the CPM memory length. The cardinality increases linearly with L, while previous proposed decompositions have cardinalities M/sup L/-M/sup L-1/, which grow exponentially with L.

G. Cariolaro

Papers

Minimal PAM decompositions of CPM signals with separable phase