Spread Spectrum Performance Analysis in Arbitrary Interference

Abstract

An important application of spread spectrum modulation is to provide interference immune communications. Generally, the approach to system performkce analysis will assume a host of various interference situations with the hope the results give wide applicability, while, based on the concept and properties of pseudo-random spreading waveforms, it is possible to rid the analysis of artificial or restricting interference assumptions and obtain completely general performance bounds.

Maximin performance of binary-input channels with uncertain noise distributions

“…Lemma 5 permits a simplified analysis using Lagrange multiplier techniques even in cases where the divergence constraint is not necessarily active in the optimization problem (3).…”

“…Assume by contradiction that there exist two distinct solutions and for (3). Since the divergence constraint is assumed to be active, Consider the candidate pdf By convexity of the feasible set, is a feasible candidate, and performs as least as well as and by the noted concavity of the objective function (2).…”

“…The form of (29) reveals that the second moment of is strictly greater than for any strictly positive divergence tolerance, implying by uniqueness that as expected. Now consider the new candidate pdf for (3) given by where and is chosen small enough so that the second moment of is no greater than By strict convexity of the divergence measure, , rendering a feasible solution for (3). Concavity of the objective function then implies that demonstrating sub-optimality of and providing the desired contradiction.…”

“…Most often, a peak or average power constraint is imposed on the noise or interference and a worst case distribution is sought, either for guaranteed performance quantification [3]- [13] or in the context of a zerosum game formulation between communicator and jammer [14], [15]. Worst case performance for power-constrained interference in a direct-sequence spread spectrum (DS/SSc) system with Gaussian background noise and linear matchedfilter detector is considered in [3], with an extension to nonlinear detection considered in [4] for large spreading gain.…”

Worst-case error probability of a spread-spectrum system in energy-limited interference

“…Note that the energy constraint (4) implies that satisfies (a.s.) (9) is the signal-to-interference power ratio. Hence, the worst-case probability of error for all interfering signals satisfying (4) is where Note that this probability will not be changed by restricting the supremum to deterministic sequences , i.e., (10) To see this, observe that the right side of (10) is clearly a lower bound to since deterministic sequences are a particular case of random sequences. Conversely, it is also an upper bound for because it is greater than or equal to for every outcome that satisfies .…”