Nakagami's Approximation for Distribution of Signal Envelope in TWDP Channel
Keywords:mobile communication, two-beam channel with scattering, small-scale fading, envelope distribution, Nakagami’s distribution
Problem statement. With the development of radio communication technologies, especially mobile, the choice of radio channel models is playing an increasingly important role. In this paper, one of the currently popular models is considered, namely, a Two-Wave radio propagation with Diffuse Power scattering, which is abbreviated in the literature as TWDP. For this model, both exact and approximate expressions for the Probability Density Function (PDF) and the Cumulative Distribution Function (CDF) of the signal envelope are known. However, their common disadvantage is the high complexity in terms of practical application. In this regard, this paper considers the possibility of a much simpler approximation of the PDF and CDF of a signal envelope based on the Nakagami’s distribution.
Method development. The approximation of distributions by the Nakagami method comes down to the calculation of the second and fourth moments of a signal envelope at a channel output. Such calculations are performed in the paper, which allows to represent the specified moments as functions of two parameters of the TWDP channel: the K-factor and Δ-parameter depending from the ratio of beams amplitudes.
Analysis of the approximation errors. Errors were estimated by comparing the calculations for the PDF and CDF as per exact formulas and calculations using the Nakagami approximation. In parallel, calculations were also carried out as per the approximation formulas known in the literature. The analysis showed that the Nakagami method gives errors in the calculation of the CDF that are acceptable for practical needs in all ranges of parameters values K and Δ. At the same time, the accuracy of the PDF approximation in comparison with other known methods was not very satisfactory.
Conclusions. Studies carried out in this paper have confirmed the possibility of approximating the CDF of the signal envelope in the TWDP channel by the Nakagami distribution. However, the results of such approximation for the PDF were less satisfactory. The usefulness of the obtained results for the interpretation of the data of field experiments is also noted.
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