Determining system parameters for optimal performance of hybrid DS/FFH spread-spectrum

In recent years there has been great interest in using hybrid spread-spectrum (HSS) techniques for commercial applications in addition to their inherent uses in military communications because they accommodate high data rates with high link integrity, even in the presence of significant multipath effects and interfering signals. A highly useful form of this transmission technique for many types of command, control, and sensing applications is the specific code-related combination of standard direct sequence (DS) modulation with 'fast' frequency hopping (FFH), denoted hybrid DS/FFH, wherein multiple frequency hops occur within a single data-bit time. However, the optimum parameter sets for specific HSS applications have not been examined heretofore in the literature. In this paper, an optimization approach is formulated that maximizes the hybrid DS/FFH communication system performance in terms of biterror probability and solves for the resulting system design parameters. The optimization objective function is non-convex and can be solved by applying the Karush-Kuhn-Tucker conditions. Specific system design parameters of interest are the length of the DS code sequence, number of frequency-hopping channels, number of channels corrupted by wide-band jamming, and number of hops per bit. The proposed formulation takes into account the effects from wide- and partial-band jamming, multiuser interference, and/or varying degrees of Rayleigh and Rician multipath fading. Numerical results are used to illustrate the method's viability.