NASA NTRS1985
Traditionally symmetric, multiple phase-shift-keyed (MPSK) signal constellations, i.e., those with uniformly spaced signal points around the circle, have been used for both uncoded and coded systems. Although symmetric MPSK signal constellations are optimum for systems with no coding, the same is not necessarily true for coded systems. This appears to show that by designing the signal constellations to be asymmetric, one can, in many instances, obtain a significant performance improvement over the traditional symmetric MPSK constellations combined with trellis coding. The joint design of n/(n + 1) trellis codes and asymmetric 2 sup n + 1 - point MPSK is considered, which has a unity bandwidth expansion relative to uncoded 2 sup n-point symmetric MPSK. The asymptotic performance gains due to coding and asymmetry are evaluated in terms of the minimum free Euclidean distance free of the trellis. A comparison of the maximum value of this performance measure with the minimum distance d sub min of the uncoded system is an indication of the maximum reduction in required E sub b/N sub O that can be achieved for arbitrarily small system bit-error rates. It is to be emphasized that the introduction of asymmetry into the signal set does not effect the bandwidth of power requirements of the system; hence, the above-mentioned improvements in performance come at little or no cost. MPSK signal sets in coded systems appear in the work of Divsalar.