Diversity combining considerations for incoherent frequency hopping multiple access systems

On the detection of a class of fast frequency-hopped multiple access signals

“…Suppose (Hz) is the hopping bandwidth and the channel spacing is Hz, then the channel (tone) number available for hopping is given by (1) where is the integer part of and is usually larger than . In this paper, however, we will only consider the case of , for such a system yields a spectral efficiency higher than those having other frequency structures of [6].…”

“…2, it can be expressed as (5) where the random phases result from the noncoherent frequency hopper. Furthermore, , is a set of basis waveforms defined by (6) is the signal power, is the average signal energy per chip, and otherwise.…”

“…In general, there are two methods to resolve this kind of ambiguity. One is to use soft-decision schemes [6] while the other uses the information of the other users' addresses to eliminate the faulty entries in the receiver's T-F matrix. The first approach is studied in the following two sections while one alternative to the second approach will be presented in Section V.…”

“…By invoking the approximation that are i.i.d. [3]- [6] and following a procedure similar to that presented in [3] and [6], we can show that the (nearly) optimal noncoherent Bayes' decision rule is given by Accept the hypothesis that the th tone was transmitted if (14) It can be shown that is the squared magnitude of the complex random variable , which is given by (15) where is given by (11); complex conjugate of defined by (6); , , and components contributed by the desired signal, the th interferer and AWGN, respectively. In particular, is a zero-mean complex Gaussian r.v.…”

“…Earlier analysis on noncoherent frequency-hopped multiple access (FHMA) systems [1]- [6] assume that: 1) a single-stage detector is employed by the receiver and 2) random memoryless FH patterns (users' addresses) are used. Moreover, except for [3], they also assume that a chip(hop)-synchronous mode is maintained, i.e., all users switch their carrier frequencies simultaneously.…”