IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 5, MAY 2008 1963 Cooperative Diversity over Log-Normal Fading Channels: Performance Analysis and Optimization Majid Safari, Student Member, IEEE, and Murat Uysal, Senior Member, IEEE Abstract— Although there has been a growing interest on cooperative diversity, the current literature is mainly limited to the results obtained for Rayleigh, Rician, or Nakagami fading channels. In this paper, we investigate the performance of cooperative diversity schemes over log-normal fading channels which provide an accurate channel model for indoor wireless environments. We focus on single-relay cooperative networks with amplify-and-forward relaying and consider three TDMA-based cooperation protocols which correspond to distributed implemen- tations of MIMO (multi-input multi-output), SIMO (single-input multi-output), and MISO (multi-input single-output) schemes. For each protocol under consideration, we derive upper bounds on pairwise error probability over log-normal channels and quantify the diversity advantages. Based on the minimization of a union bound on the bit error rate performance, we further formulate optimal power allocation schemes which demonstrate significant performance gains over their counterparts with equal power allocation. Index Terms— Cooperative diversity, distributed space-time codes, pairwise error probability, power allocation, log-normal fading. I. I NTRODUCTION A major impairment in wireless channels is the multipath- induced fading which causes random fluctuations in the received signal level. For a typical mobile wireless channel in urban areas where there is no line of sight propagation and the number of scatters is considerably large, the application of central limit theory indicates that the complex fading channel coefficient can be modeled with two quadrature components which are zero-mean Gaussian random processes. As a result, the amplitude of the fading envelope follows a Rayleigh distribution. In terms of error rate performance, Rayleigh fading converts the exponential dependency of the bit error rate on the signal-to-noise ratio (SNR) for the classical additive white Gaussian noise (AWGN) channel into an approximately inverse linear one, resulting in a large SNR penalty. Diversity techniques are widely adopted in wireless com- munication systems as a counter-measure to fading effects providing redundancy across independently faded diversity branches. Deployment of multiple transmit and/or receive antennas realizes the advantages of spatial diversity. Through the use of suitably designed space-time codes [1]–[3], diversity Manuscript received April 12, 2007; revised October 19, 2007; accepted November 9, 2007. The associate editor coordinating the review of this paper and approving it for publication was J. Andrews. This paper was presented in part at the 10th Canadian Workshop on Information Theory (CWIT07), Edmonton, Alberta, Canada, June 2007. The work of M. Uysal is supported in part by a Natural Sciences and Engineering Research Council of Canada (NSERC) Special Research Opportunity Grant (SROPJ305821-05). The authors are with the Department of Electrical and Computer Engi- neering, University of Waterloo, Waterloo, ON, N2L3G1, Canada (e-mail: m3safari@uwaterloo.ca, muysal@ece.uwaterloo.ca). Digital Object Identifier 10.1109/TWC.2008.070393. and/or multiplexing gains can be achieved at no cost in terms of transmission time and bandwidth expansion. An alternative form of spatial diversity, referred as ”cooper- ative diversity” [4]–[9], has been recently proposed to realize diversity advantages in a distributed manner. In this technique, spatial diversity gain is extracted by creating virtual antenna arrays through cooperating users. In their pioneering work [6], Laneman et al. have proposed a two-phase cooperation protocol which is able to extract the full spatial diversity. In the first phase (i.e., broadcasting phase), the source transmits to the destination and relay terminals. In the second phase (i.e., relaying phase), the relays transmit their received sig- nals to the destination using either orthogonal sub-channels (repetition based cooperative diversity) or the same sub- channel (space-time coded cooperative diversity). The receiver coherently combines the received signals over two phase durations realizing receive diversity in a distributed manner. In [8], Nabar et al. have established a unified framework for user cooperation protocols in single-relay wireless networks. They propose three TDMA (time division multiple access)- based cooperation protocols so-called Protocol I, Protocol II, and Protocol III which realize distributed MIMO (multi-input multi-output), SIMO (single-input multi-output) and MISO (multi-input single-output) configurations, respectively. Pro- tocol II coincides with Laneman et.al.’s cooperation protocol proposed in [6]. Protocol I differs from Protocol II in the sense that the source terminal continues transmission in the relaying phase and it has been recently shown in [10] that this protocol is optimal in terms of diversity-multiplexing trade-off. Although there has been a growing interest on cooperative diversity, the current literature is mainly limited to the results obtained for Rayleigh, Rician, or Nakagami fading channels. These channel models accurately capture the characteristics of outdoor wireless channels, however log-normal fading is found to be a better fit for indoor radio propagation environments [11]–[14]. It has been demonstrated through empirical fading channel measurements that short-term and long-term fading effects tend to get mixed in indoor wireless channels and the log-normal statistics tend to dominate, and therefore, describe the distribution of the channel coefficient. The performance of receive antenna diversity in log-normal fading channels has been studied in [15], [16]. In [15], Alouini and Simon have derived outage probability and amount of fading for maximal- ratio combining, selection combining, and switch-and-stay combining schemes assuming the deployment of two receive antennas. In [16], Piboongungon and Aalo have derived the outage probability for selection combining with more than two receive antennas. 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