Abstract: An improved constellation pruning and partial Gray coding method for generating constellations that are transmitted by a transmitter. The approximate symbol error rate (SER) for each possible subconstellation is first determined. Then, each of the subconstellations are scaled in terms of power so that each subconstellation has the same symbol error rate. Then, the subconstellation that requires the least amount of power to generate is selected as the pruned constellation for use by the transmitter. After the pruned constellation is determined, it is then coded a single time, and this coded pruned constellation is used by the transmitter.

Abstract: This disclosure describes an electronic support measures (ESM) system for estimating the angle of arrival of a signal which impinges on an array of antennas configured in a straight line. The antennas in the array are spaced such that the distances from the interior antennas to one of the end antennas—in terms of units of a reference length &xgr;—are relatively prime. The system does not require a priori knowledge of the signal radio frequency. In order to enhance the computational efficiency and ability of the system, a Diophantine processing algorithm is utilized. The set of antenna spacings is selected based upon minimizing the probability that this algorithm produces an ambiguity error in the estimated angle of arrival. The computational efficiency of the system is improved relative to current systems, as it requires only N2 real multiplications, where N+1 is the number of antennas in the array.