Performance Analysis of RS Coded DS-CDMA Using Noncoherent M-ary Orthogonal Modulation over Multipath Fading Channels

Lie-Liang Yang and Lajos Hanzo

Department of Electronics and Computer Science,
University of Southampton, SO17 1BJ, UK.
Tel: +44 1703 593125, Fax: +44 1703 593045
Email: lly@ecs.soton.ac.uk lh@ecs.soton.ac.uk

Abstract:

In this contribution we investigate the performance of Reed-Solomon (RS) coded Direct-Sequence Code-Division Multiple-Access (DS-CDMA) using noncoherent $M$-ary orthogonal modulation over multipath Rayleigh fading channels. `Errors-and-erasures' RS decoding is considered, where erasures are declared based on the proposed low-complexity, low-delay erasure insertion scheme, namely the joint Maximum Output and Ratio Threshold Test (MOR-TT). The joint two-dimensional (2D) Probability Density Functions (PDF) of the maximum and the ratio associated with MOR-TT are derived, conditioned on both the correct detection and erroneous detection of M-ary symbols. These PDFs give us an insight into the characteristics of the joint MOR-TT, and provide us with necessary and sufficient conditions for investigating the performance of `errors-and-erasures' RS decoding using the proposed MOR-TT erasure insertion scheme. Furthermore, in this contribution, two classes of diversity reception techniques suitable for noncoherent M-ary detection are invoked, namely Equal Gain Combining (EGC) or Selection Combining (SC) and their related performance is evaluated for both uncoded and coded DS-CDMA systems. The performance of the proposed MOR-TT technique is compared to that of two low-complexity, low-delay erasure insertion schemes, namely the Ratio Threshold Test (RTT) and the Output Threshold Test (OTT). Furthermore, the performance of `errors-and-erasures' decoding employing the MOR-TT is compared to that of `error-correction-only' decoding. The numerical results show that, when using `errors-and-erasures' decoding, RS codes of a given code rate can achieve a significantly higher coding gain than without erasure information, and that the MOR-TT technique outperforms both the RTT and the OTT techniques.

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