This paper investigates the performance of selection combining (SC) diversity in dual-hop cooperative networks under double Rice fading channels. Expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the SC output fading processes are first investigated. The obtained quantities are in the form of finite and semi-infinite range integrals, which can be easily computed using numerical tools. For the PDF, CDF, and LCR statistics corresponding approximate solutions are determined using the Laplace method's of integration. The PDF and CDF are then applied to derive exact and approximate solutions for the average symbol error probability (SEP) of non-coherent M-ary differential phase-shift keying (M-DPSK) modulation. Moreover, results corresponding to the special cases of mixed Rayleigh×Rice and double Rayleigh fading channels are extracted. The validity of the derived expressions and the accuracy of the approximations have been checked by using computer simulations. The results can be useful in the performance assessment of mobile-to-mobile (M2M) communications with dual-hop cooperative SC diversity and millimeter wave (mmWave) bands where, in general, the line-of-sight (LOS) propagation arises. INDEX TERMSDouble Rice fading, selection combining (SC) diversity, dual-hop cooperative system, level-crossing rate (LCR), average duration of fades (ADF), symbol error probability (SEP), M-ary differential phase-shift keying (M-DPSK) modulation.
This paper studies the statistical properties of selective combining (SC) diversity schemes over double Nakagami-m fading channels. It is assumed that all diversity branches follow independent and identically distributed (i.i.d.) double Nakagami-m fading processes, where the serial concatenated Nakagami-m processes making up the double Nakagami-m fading branches are assumed to be independent, but not necessarily identically distributed. Starting from already known statistics on double Nakagami-m processes, analytical expressions are derived for the cumulative distribution function (CDF), probability distribution function (PDF), level-crossing rate (LCR), and average duration of fades (ADF) of SC diversity schemes. A general expression is derived for the moments of the instantaneous signalto-noise ratio (SNR). By using the general expression, we study the mean SNR, amount of fading (AoF), and the diversity gain. The derived expressions include also the corresponding results for double Rayleigh, double one-sided Gaussian, and one-sided Gaussian×Rayleigh channels as special cases. A good agreement is observed between theory and simulation, which confirms the validity of the obtained analytical expressions.Index Terms-Double Nakagami-m fading, selective combining diversity, level-crossing rate, average duration of fades, amount of fading, diversity gain.
This paper investigates the statistical properties of selection combining (SC) cooperative diversity over double Rice narrow-band fading channels under the transparent or amplifyand-forward (AF) strategy. It is assumed that the source, the destination, and relay stations are all equipped with single antenna. The Doppler power spectral density, associated with each of the double Rice fading processes, is considered to be symmetrical about the carrier frequency. Under the above conditions, analytical integral expressions are derived for the probability density function (PDF) and the cumulative distribution function (CDF) of the SC fading envelopes. Also, expressions for the level crossing rate (LCR) as well as the average duration of fades (ADF) are determined. For some cases, the integral expressions are shown to be approximated using the Laplace's method of integration. The approximations are verified to be accurate when the number of relay stations is large. The obtained results include those corresponding to the double Rayleigh and combined Rayleigh×Rice models as special cases of the double Rice fading channel. The validity of all the presented theoretical results are checked by computer simulations.Index Terms-Double Rice fading channels, selection combining (SC) cooperative diversity, probability density function (PDF), cumulative distribution function (CDF), level crossing rate (LCR), average duration of fades (ADF).
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