An Alternative Statistical Characterization of TWDP Fading Model

TL;DR

This paper improves the statistical characterization of the TWDP fading model by proposing a physically justified parameterization, deriving exact series expressions for PDF, CDF, and MGF, and providing the first explicit ASEP formula for M-ary PSK.

Contribution

It introduces a new physically meaningful parameterization of TWDP, derives exact series-based statistical expressions, and presents the first explicit ASEP formula for M-ary PSK in TWDP fading.

Findings

Exact infinite-series PDF and CDF derived.

New MGF suitable for performance analysis obtained.

Explicit ASEP expression for M-ary PSK in TWDP fading provided.

Abstract

Two-wave with diffuse power (TWDP) is one of the most promising models for description of small-scale fading effects in emerging wireless networks. However, its current statistical characterization has several fundamental issues. Primarily, conventional TWDP parameterization is not in accordance with the model's underlying physical mechanisms. In addition, available TWDP expressions for PDF, CDF, and MGF are given either in integral or approximate forms, or as mathematically untractable closed-form expressions. Consequently, the existing TWDP statistical characterization does not allow accurate evaluation of system performance (such as error and outage probability) in all fading conditions for most modulation and diversity techniques. In this paper, the existing statistical characterization of the TWDP fading model is improved by overcoming some of the noticed issues. In this regard, physically justified TWDP parameterization is proposed and used for further calculations. Additionally, exact infinite-series PDF and CDF are introduced. Based on these expressions, the exact MGF of the SNR is derived in form suitable for mathematical manipulations. The applicability of the proposed MGF for derivation of the exact average symbol error probability (ASEP) is demonstrated with the example of M-ary PSK modulation. Therefore, in this paper, M-ary PSK ASEP is derived as an explicit expression for the first time in the literature. The derived expression is further simplified for large SNR values in order to obtain a closed-form asymptotic ASEP, which is shown to be applicable for SNR > 20 dB. All proposed expressions are verified by Monte Carlo simulation in a variety of TWDP fading conditions.