On the Selection of a Two-Dimensional Signal Constellation in the Presence of Phase Jitter and Gaussian Noise

A very attractive modulation format for coherent high-speed data transmission is the family of suppressed-carrier, two-dimensional signal constellations of which quadrature amplitude modulation (QAM) and combined amplitude and phase modulation (AM-PM) are two examples. In this paper we wall consider using this more general signal format, which is equivalent to the arbitrary placement of a discrete number of signal points in the plane, subject only to a peak or average power constraint. The object will be to mitigate the major statistical transmission impairments encountered on the voice-grade telephone channel, such as carrier frequency offset, carrier phase jitter, and additive noise. Our attention is focused on constellations of 16 points, since this seems to be the largest constellation which is practical for the typical telephone channel. However, the techniques we develop are applicable to constellations of arbitrary size. The placing of signal points in the plane is a long-standing problem that has received considerable attention in the past. Previous investigations 1-3 have considered the signal evaluation and design problem in the presence of Gaussian noise alone and within the framework of a particular structure such as combined amplitude and phase modulation. When Gaussian noise is the only transmission impairment, it is well known that at high signal-to-noise ratios ( > 2 5 dB) the signal points should be placed as far apart from each other as possible (the circle-packing problem).