Frequency-Hopping, Multiple-Access, Phase-Shift-Keying System Performance in a Rayleigh Fading Environment

Abstract

Recently, various Frequency‐Hopping, Multiple‐Access (fhma) schemes have been proposed as alternatives to frequency‐division (fdma) techniques for guarding against interference from other users and multipath fading in transmitting digitized speech in mobile radio. While the advantage of frequency diversity against fading is well known, the system degradation of frame‐asynchronous fhma‐psk due to interference from other users and fading has not been studied, except by modeling the interference as additive white Gaussian noise (awgn). In this paper, we analyze the performance of two fhma‐psk systems in a Rayleigh fading environment. We assume that the interferers' addresses are assigned at random and derive expressions for the union upper bound on the bit error rate (Pb) for U users, each assigned N frequencies, i.e., N chips. As an example, we consider transmitting digitized speech (R = 31.25 kb/s) over the mobile radio channel (bandwidth W = 20 MHz), using orthogonal coding of rate r = 5/32 (N = 32). For the differentially coherent fhma‐psk case, the number of users in a two‐way radio system is limited to 26 by the performance of the mobile‐to‐base link, which corresponds to an equivalent bandwidth of 770 kHz per user.

Multistage multiuser detection for FHMA

“…The variable " is an unknown, strictly positive value which is a function of the energy, delay and phase of the colliding users as well as a function of the energy, proximity to the frequency i, delay and phase of the other users and the noise. When we assume no noise and no interferering sidelobes, the expected value of " across the phase becomes P j2S" 1 4 (A j (l) jk ) 2 where S " is the set of users present at that location and (l) jk is the fraction of time (normalized by T) that the jth user's chip overlaps the kth user's lth time slot. Ideally, the value of E aj would be 1 4 (A j (l) jk ) 2 .…”

“…When we assume no noise and no interferering sidelobes, the expected value of " across the phase becomes P j2S" 1 4 (A j (l) jk ) 2 where S " is the set of users present at that location and (l) jk is the fraction of time (normalized by T) that the jth user's chip overlaps the kth user's lth time slot. Ideally, the value of E aj would be 1 4 (A j (l) jk ) 2 . Unfortunately, this value is corrupted by the noise and the sidelobes of other asynchronous interferers.…”

Land mobile radio systems - A tutorial exposition

“…A comparison of average number of usable "channels" per cell for FH-DPSK and FM systems showed that they do not differ greatly. In [38], it is noted that no error occurs if the transmission is frame synchronous (which is possible for base to mobile communications), and for frame-asynchronous mobile to base communications, a good. [34].…”