Multiple-Access Capability of Frequency-Hopped Spread-Spectrum Revisited: An Exact Analysis of the Effect of Unequal Power Levels.

Abstract

In this paper we present a new method for the evaluation of the probability of error of uncoded frequency-hopped spread-spectrum multiple-access (FH/SSMA) communications. For systems with binary FSK modulation the method provides an accurate approximation and a tight upper bound to the bit error probability; for systems with m-ary FSK modulation it provides tight upper bounds to the symbol error probability. This method relies on the integration of the product of the characteristic function of the envelope of the branch of the BFSK demodulator, which carries the desired signal, and of the derivative of the characteristic function of the envelope of the other branch; it can achieve any desirable accuracy and the computational effort required for its evaluation grows linearly with the number of interfering users. In the M-ary case tight upper bounds based on the union bound and the results of the binary case are derived. The new method allows us to quantify accurately the effect of unequal power levels on the otheruser interference for the first time. Comparison of the multiple-access capability of FH/SS systems as predicted by the bounds available in the literature and by the new method indicates that FH/SS systems without error-control can support (at a given error rate) considerably many more simultaneous users than previously thought when the relative received powers of the users are not significantly different. This trend is amplified further for systems with error-control. Our results indicate that the FH/SSMA systems also suffer from the near-far problem although less seriously than the direct-sequence SSMA systems.