WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. (2012) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.2332 RESEARCH ARTICLE Closed-form expressions for the average channel capacity of the ˛– fading model under different adaptive transmission protocols Amer M. Magableh 1 * and Mustafa M. Matalgah 2 1 Electrical Engineering Department, Jordan University of Science and Technology, Irbid, 22110, Jordan 2 Department of Electrical Engineering—Center for Wireless Communications, University of Mississippi, University, Oxford, MS 38677, U.S.A. ABSTRACT In this paper,we consider a small-scale multipath fading channel following the ˛– generalized fading model distribu- tion.We first derive an expression for the amount of fading (AF ) for this channel model to show the generalization attribute of this fading model recently reported in the literature. Then, we derive closed-form expressions for the average channel capacity considering this channel distribution under different adaptive transmission protocols, namely the simultaneous power and rate adaptation protocol, the optimal rate adaptation with fixed power protocol, and the channel inversion with fixed-rate protocol. All the obtained expressions are in closed-form and general expressions that can reduce to other channel capacity expressions that are well-known and to some others that are not known for Rayleigh, Nakagami-m, and Weibull, as special cases. The derived expressions in this paper are new and have not been previously reported in the literature. Copyright © 2012 John Wiley & Sons, Ltd. KEYWORDS ˛– fading model; amount of fading; channel capacity; multipath fading; adaptive transmission protocols; optimal SNR cutoff *Correspondence Amer M. Magableh, Electrical Engineering Department, Jordan University of Science and Technology, Irbid, 22110, Jordan. E-mail: ammagableh@just.edu.jo 1. INTRODUCTION Wireless communication transmission over multipath fad- ing channels undergoes signal degradation due to signal envelope random variation behaviors. Different distribu- tions have been considered in the literature to model these signal envelope variations such as Rayleigh, Nakagami-m, and Weibull [1]. Recently, the ˛– distribution has been proposed to model the small-scale fading variations, in which most of the other well-known channel models can be derived from it, as special cases [2]. The level-crossing rate, the average fade duration, and the joint statistics of the correlated ˛– random variables were obtained in [3]. Whereas in [4] and [5], an expression was derived for the multivariate ˛– joint probability density function (PDF) in infinite series form. Most recently, results for the outage probability, the moment generating function, and the bit error probability in the ˛– fading channel were derived in [6]. In this paper, we consider this generalized fad- ing model, and we derive further performance metrics that have not been reported before, which are crucial and important for any wireless communication system. The first performance measure we consider is the amount of fading (also known in statistics as the squared coefficient of variations), which was first defined in [7] reflecting the severity level of the fading channel. In the second part, which is the main contribution of the paper, we con- sider different adaptive transmission protocols and derive closed-form expressions for the average channel capacity under these transmission protocols considering the ˛– channel model. As special cases of the ˛– model, the obtained expressions can reduce to other expressions that represent the average channel capacity of other well-known channel models (Rayleigh, Nakagami-m, and Weibull) that some of which exactly match previously published results and some others generalize previously published ones, and some are new and have not been previously reported in the literature, as will be explained throughout the paper. The channel capacity is an important performance metric for any wireless communication system, which can be defined as the upper bound on the amount of informa- tion that can be reliably transmitted over a noisy wireless Copyright © 2012 John Wiley & Sons, Ltd.