Showing papers on "Constellation diagram published in 1974"

Optimization of Two-Dimensional Signal Constellations in the Presence of Gaussian Noise

Abstract: A considerable amount of literature exists on the problem of selecting an efficient set of N digital signals with in-phase and quadrature components for use in a suppressed carrier data transmission system. However, the signal constellation which minimizes the probability of error in Gaussian noise, under an average power constraint, has not been determined when the number of signals is greater than two. In this paper an asymptotic (large signal-to-noise ratio) expression, of the minimum distance type, is derived for the error rate. Using this expression, a gradient-search procedure, which is initiated from several randomly chosen N -point arrays, converges in each case to a locally optimum constellation. The algorithm incorporates a radial contraction technique to meet the average signal power constraint. The best solutions are described for several values of N and compared with well-known signal formats. As an example, the best locally optimum 16-point constellation shows an advantage of about 0.5 dB in signal-signal-to-noise ratio over quadrature amplitude modulation. The locally optimum constellations are the vertices of a trellis of (almost) equilateral triangles. As N \rightarrow \infty , it is rigorously proved in the Appendix that the optimum constellations tend toward an equilateral structure, and become uniformly distributed in a circle.

Combined scrambler-encoder for multilevel digital data

Abstract: A high-speed digital data transmission system combines quadrature amplitude modulation with scrambling-descrambling, differential amplitude coding-decoding, and Gray-to-rotational coding-decoding of multilevel data symbols channeled at baseband, i.e., including frequencies extending down to zero, onto parallel bit streams with a minimization of error multiplication. Scrambling and descrambling facilitate timing recovery and equalizer adjustment. Differential and rotational encoding and decoding compensate for phase ambiguities in the signal constellation, i.e., points on a space diagram representative of the tips of multilevel symbol vectors.