Clarification of interference power assignment in "capacity of large array receivers for deep-space communications in the presence of interference"

Abstract

The assignment of interference power in the Numerical Results section of the paper entitled “Capacity of Large Array Receivers for Deep-Space Communications in the Presence of Interference” (IEEE Transactions on Communications, February 2008, pp. 194-200) is on a perantenna basis, whereas the received signal power is defined in terms of the entire array. The reason for this normalization is that the signal source is a distant spacecraft, hence appears as a point source to both the individual antenna elements and to the entire array. This means that the signal power remains constant over the entire spacecraft trajectory (ignoring atmospheric attenuation), hence a single value can be assigned for each plot. This however is not the case for interference power collected from nearby extended sources (such as Mars) that are resolved by the array, because the effective shape of the array beam is determined by the projection of the array layout onto the source direction vector, which is a function of time. Therefore, the interference power collected by the array varies over the spacecraft trajectory, but remains constant for the antenna elements that do not resolve the interference: hence it is more convenient to assign interference power on a perantenna basis. In particular, we should emphasize that in the text describing Fig. 2b in the Numerical Results section, the interference power per antenna is set equal to the source power over the array, hence the total interference power collected by the array is N times that of the signal power, where N is the number of antenna elements. Similarly, the summed interference power per antenna in Fig. 3a is nominally one fifth of the signal power. Although not discussed specifically in the text, this same normalization was used to compute the array capacity results of Figs. 4a and 4b.