Saddle-Point Approximation for M-ary Phase-Shift Keying with Adjacent Satellite Interference

The problem of adjacent satellite interference, which is basically one of co-channel interference, has received extensive attention in terms of exact computation methods1"15 and bounds.6"9 In spite of this, system designers still often treat the interference as additive Gaussian noise, even though this has been shown to be very pessimistic2,4 for lower error rates (10" '). The reason for this is that the exact methods are too difficult to use and the simple bounds are not tight enough for large signal-to-noise ratios (i.e., low error rates). As a result, the communication system is overspecified and the geosynchronous orbit, a limited natural resource, is not used efficiently. In this paper, we describe a saddle-point method10,11 which is both simple to use and accurate for evaluating adjacent satellite interference. After defining the problem in Section II, we derive the saddlepoint approximation from the Fourier inversion integral representation of the error probability in Section III. To illustrate the accuracy of the approximation, we consider the uplink error performance of a QPSK 1139