Properties of a Class of Signaling Waveforms for Digital Phase Modulation

This paper is concerned with the performance of partially coherent digital phase modulation (DPM) systems employing a class of binary signaling waveforms containing a zero crossing within each bit period. The class of waveforms includes the Manchester II bit code and sinusoidal bit code as well as an infinite number of other nonrectangular bit shapes. We wish to study the tradeoff between the RF bandwidth and the probability of bit error as a function of bit shape. The equation describing the RF power spectrum for these DPM signals is obtained using a two-dimensional Fourier transform technique and is shown to contain both continuous and discrete terms. The spectra are evaluated numerically for a typical bit rate showing the effect of different bit shapes. An original technique is presented for including the effects of modulation interference on the extraction of the carrier-phase reference from these DPM signals using a partially coherent phase-locked-loop receiver. The expression for the is obtained for the class of signals and is a function of the phase deviation angle and the modulation interference. This expression is evaluated numerically to obtain sets of curves that show the optimal phase deviation angles for five members of the class. The tradeoff between the RF bandwidth and the is given by a curve that indicates the increase in for a reduction in RF bandwidth as a function of the bit shape.