An Analysis of an Overlaid DPSK-FH Spread Spectrum Communication System

The large bandwidth requirements of current spread spectrum systems combined with a scarcity of available frequency allocations has created the need for systems to share spectral resources. The term "overlay" is generally used to describe the operation of a spread spectrum system collocated, both spectrally and geographically, with more conventional narrow band systems. In this paper we consider the operation of a differential phase-shift-keyed frequency hopped system in the presence of a large number of narrow band signals. Certain aspects of the spread spectrum system considered are designed to increase both its performance and compatibility with the narrow band system. The result of the analysis is an n-fold integral equation for the bit error probability, the dimensionality of the integral being equal to the number of hops in a user's pseudorandom pattern. While neither direct nor numerical evaluation are feasible, very tight bounds (both upper and lower) are derived using a very elegant result on multivariate Gaussian quadrant probabilities. The results suggest that, under the conditions assumed, the spread spectrum system could operate with very good performance even if every time slot in a user's hopping pattern were exposed to a narrow band interfering signal comparable in power to that of the desired transmission.