New results for Shannon capacity over generalized multipath fading channels with MRC diversity

EURASIP Journal on Wireless Communications and Networking, Nov 2012

In this article, we investigate the Shannon capacity for L-branch maximal combining ratio (MRC) over generalized multipath fading channel. We derive closed-form expressions of the maximal spectral efficiency over Rayleigh, Rician, Nakagami-m, and Weibull multipath fading channel under flat fading conditions. The results are expressed in terms of Meijer G-functions, which can be evaluated numerically using mathematical tools such as Mathematica and Maple. We show, in particular, that the more the number L increases, the larger the Shannon capacity is. We deduce that four branches are sufficient in several cases to mitigate the fading effect and the channel model will approaches the one of AWGN.

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New results for Shannon capacity over generalized multipath fading channels with MRC diversity

Faissal El Bouanani 1 Hussain Ben-Azza 0 Mostafa Belkasmi 1 0 ENSAM, Mekne`s, Morocco 1 ENSIAS, Mohammed V-Souissi University , Rabat, Morocco In this article, we investigate the Shannon capacity for L-branch maximal combining ratio (MRC) over generalized multipath fading channel. We derive closed-form expressions of the maximal spectral efficiency over Rayleigh, Rician, Nakagami-m, and Weibull multipath fading channel under flat fading conditions. The results are expressed in terms of Meijer G-functions, which can be evaluated numerically using mathematical tools such as Mathematica and Maple. We show, in particular, that the more the number L increases, the larger the Shannon capacity is. We deduce that four branches are sufficient in several cases to mitigate the fading effect and the channel model will approaches the one of AWGN. - Introduction The channel capacity is an important parameter in the design of any communication system. It provides an upper bound of maximum transmission rate in a given channel. In 1948, Shannon derived the AWGN channel capacity [1,2]. Recently, in wireless mobile communication system, the diversity techniques have been used to combat multipath fading and multiuser interference [3]. In last years, several articles have been published regarding the Shannon capacity of fading channels with various important diversity schemes, such as maximum ratio combining (MRC), postdetection equal gain combining (EGC), and selective combining (SC), in terms of generalized special functions. The capacity with MRC in correlated Rayleigh fading in terms of Poisson distribution and Exponential integral was obtained in [4,5]. In [6,7], an expression of the capacity of single branch receivers operating over Rician, Nakagami-m, and Weibull fading channel was obtained in term of Meijer G-function. Some statistics properties, such as the probability density function (PDF) and the cumulative distribution function, of *Correspondence: 1ENSIAS, Mohammed V-Souissi University, Rabat, Morocco Full list of author information is available at the end of the article the instantaneous signal-to-noise ratio (SNR) per symbol at the output of MRC receiver in correlated Nakagamim fading was derived in terms of Foxs H and Gamma functions [8] in [9,10]. A statistical analysis for the capacity over Nakagami-m fading with MRC/SC/switch and stay combining (SSC) in terms of Meijer G-function was presented in [11]. In [12], the capacity expressions of correlated Nakagami-m fading with sual-branch MRC, EGC, SC, and SSC were obtained in terms of Gamma function. Expressions for the capacity of generalized fading channel with MRC/EGC for MIMO/SISO systems based on moment generating function (MGF) approach was obtained in terms of Foxs H and Meijer functions [13,14]. Recently, a novel expression for the BER of modulations and Shannon capacity over generalized-K and Nakagamim fading channels in terms of Meijer G-function and its generalization [15] was investigated in [16,17]. The equivalent channel model of a multipath fading channel using a MRC Rake receiver and flat fading has been approximated by a fading channel with fading amplitude is a square root of a sum of a square amplitude of each fading [18,19]. The equivalent channel model in DSCDMA system with MRC-Rake receiver was investigated in [18]. In this article, we present novel closed-form and analytical expressions, in terms of Meijer G-function, for the ergodic Shannon capacity for L-branch MRC-Rake receiver over Rician, Rayleigh, Nakagami-m, and simple approximation for Weibull multipath fading channel in the non-frequency selective channels case. We generalize for L-branch MRC the capacity expression given for single path case (L = 1) in [6,7]. All the results are validated by numerical Monte Carlo simulations. The study include both DS-CDMA system and no-spreading system cases. This article is structured as follows. In Section Channel model, the equivalent channel models of both DS-CDMA communication system and system without spreading using a Rake receiver is introduced. In Section Channel capacity, the closed-form expression of the channel capacity for multipath fading channel (case of Rayleigh, Rice, Nakagami-m, and Weibull) is derived. The main results are summarized and some conclusions are given in Section Conclusion. For the convenience of the reader, an short appendix is added, regarding Meijer G-function. Channel model In this section, we present the equivalent channel model of communication systems using coherent MRC receiver in both system without spreading and Direct spread spectrum system (DS-CDMA). System with MRC diversity Consider MRC diversity systems in flat fading environment. Let xi, yi, bi be the i th transmitted symbol, i th combined received symbol, i th zero-mean, N0/2-variance Gaussian noise added, N0 is the noise power spectral density, hil be the fading amplitude corresponding to the ith symbol and the l th antenna, assumed (...truncated)


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Faissal El Bouanani, Hussain Ben-Azza. New results for Shannon capacity over generalized multipath fading channels with MRC diversity, EURASIP Journal on Wireless Communications and Networking, 2012, pp. 336, Volume 2012, Issue 1, DOI: 10.1186/1687-1499-2012-336