Residue Number System Arithmetic Based Parallel Communication Scheme Using Orthogonal Signaling: Part II-Multipath Fading Channels

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Description/Abstract

A novel signaling scheme is presented, where a set of orthogonal signals is transmitted in parallel. The signals are selected according to the so-called residue number system (RNS). Hence the system is essentially a multiple code parallel communication scheme using high-modulation alphabets. It is demonstrated that the system performance can be substantially improved by exploiting a number of advantageous properties of the RNS arithmetic. The model treated in Part I of this paper is extended here to account for the effects of the multipath Rayleigh fading channel when using noncoherent demodulation. Diversity reception techniques with equal gain combining (EGC) or selection combining (SC) are concerned. The related performance is evaluated for both nonredundant and redundant RNS-based orthogonal signaling. Interleaving and forward error-correction techniques are introduced for enhancing the system’s bit error rate (BER) performance. The concept of concatenated coding with a Reed–Solomon (RS) code as the outer code and a redundant RNS code as the inner code is presented, and the performance of the proposed concatenated code is evaluated. Expressions of the error probability for the above-mentioned scenarios are presented, and the associated BER performance is evaluated numerically with respect to specific system parameters. Without concatenated coding, coding gains up to 8.5 or 11 dB are achieved at a BER of $10^{-6}$ using the lowest reliability dropping technique of Part I and one or two redundant moduli, respectively. The BER is substantially higher than that over the additive white Gaussian noise channel reported in Part I. With the aid of RS coding, an additional 7.5-dB coding gain is achieved. Index Terms—Code-division multiple access (CDMA), concatenated coding, forward error correction, joint demodulation/decoding, $M$-ary orthogonal signaling, redundant residue number system (RNS).