Published in IET Communications Received on 1st November 2009 Revised on 3rd May 2010 doi: 10.1049/iet-com.2009.0703 ISSN 1751-8628 Error probability performance and ergodic capacity of L-branch switched and examine combining in Weibull fading channels A.M. Magableh 1 M.M. Matalgah 2 1 Department of Electrical Engineering, Jordan University of Science and Technology, Irbid 22110, Jordan 2 Department of Electrical Engineering - Center for Wireless Communications, The University of Mississippi, MS 38677, USA E-mail: mustafa@olemiss.edu Abstract: In this study, we consider a switched and examine combining (SEC) diversity scheme over independent and identically distributed (i.i.d.) L-branch Weibull fading channels and evaluate its performance in terms of ergodic capacity and the bit error rate (BER) for a class of coherent modulation schemes. The authors use the probability density function (pdf) of the effective signal-to-noise ratio (SNR) at the output of the SEC combiner in evaluating the BER and ergodic capacity for the considered model. The results are presented in closed-form expressions that are shown to generalise some special cases that are known in the literature. The general expressions are also shown to reduce to some other novel cases that are not reported in the literature. Numerical results and simulations are provided to verify the derived expressions. 1 Introduction In wireless communication systems, multi-path fading can cause serious difficulties in signal detection at the receiver. To mitigate this type of signal degradation, diversity combining techniques can be employed at the receiver side. In diversity combining, two or more identical replicas of the same information-bearing signal are efficiently combined to increase the overall received signal-to-noise- ratio (SNR) [1, 2]. Many diversity schemes have been developed to effectively extract the overall SNR from received signal replicas over different paths. There are four main diversity combining techniques known in the literature: maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switching combining [1–4]. The first two combining schemes require all or some of the channel state information (CSI) to be available, and therefore extra hardware is required at the receiver, which results in an increase in the overall receiver’s structure complexity. On the other hand, SC is considered to be simpler than the first two schemes in terms of structure complexity, but it still requires monitoring the SNR all the time to select the branch with the highest SNR. Unlike the SC, the switching combining scheme selects a particular branch and switches to another one when its SNR drops below a predetermined threshold [1]. Switched and examine combining (SEC) is another combining scheme that has been considered in the recent literature [3] and [5]. In SEC, the received multi-path signals are combined in such a way that if the selected current path is not of an acceptable SNR, the combiner will examine all the other received paths and select the one that satisfies the required SNR [1, 3]. Furthermore, SEC adds the benefit of having additional paths, especially when they are independent and identically distributed (i.i.d.) or equi- correlated and identically distributed, which is not considered in the switch and stay combining (SSC) scheme. In the SSC, the receiver switches between the best two branches out of L branches, that is, adding any other branch does not improve the SSC performance unless the new branch is better than at least one of the best two ones. On the other hand, the SEC performance always improves by adding any new branch regardless of its conditions. Consequently, SEC incurs a trade-off between system performance and receiver structure complexity [3, 5]. Particularly, in [3–5], the bit error rates (BERs) for different coherent techniques were studied in multi-branch switched diversity combining, including SEC. In [4, 5], the moment generating function (MGF) has been used to derive the error rates over Nakagami-m channel model with switched diversity combining, whereas in [3], the probability density function (pdf) approach has been used to obtain the BER in the SEC diversity scheme for different modulation techniques over a Nakagami-m fading channel model for integer values of m. The ergodic capacity for an independent and identically distributed (i.i.d.) Nakagami-m channel with different power allocation schemes was derived in [6], and the capacity for a non-i.i.d. Nakagami-m channel was derived in [7]. In [8, 9], the capacity of the generalised channel model employing the SSC scheme was studied. The Weibull distribution has been considered to model the experimental data better than other statistical models [10–12]. Moreover, the Weibull fading model is a general IET Commun., 2011, Vol. 5, Iss. 9, pp. 1173–1181 1173 doi: 10.1049/iet-com.2009.0703 & The Institution of Engineering and Technology 2011 www.ietdl.org