IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 2, FEBRUARY 2001 303 Simple and Accurate Methods for Outage Analysis in Cellular Mobile Radio Systems—A Unified Approach A. Annamalai, Member, IEEE, C. Tellambura, Member, IEEE, and Vijay K. Bhargava, Fellow, IEEE Abstract—Two unified expressions for computing the refined outage criterion (which considers the receiver noise) in cellular mobile radio systems are derived using the Laplace and Fourier inversion formulas. Since these expressions do not impose any re- strictions on the signal statistics while being easy to program, they provide a powerful tool for outage analysis over generalized fading channels. We also assess compatibility and applicability of previ- ously published approaches that treat noise as cochannel interfer- ence (noise-limited model) or consider a minimum detectable re- ceiver signal threshold and receiver noise. The outage probability in an interference-limited case can be evaluated directly by setting the minimum power threshold to zero. The analysis of correlated interferers is presented. Results are also developed for a random number of interferers. Several new closed-form expressions for the outage probability are also derived. Some previous studies have suggested approximating Rician desired signal statistics by a Nak- agami- model (with positive integer fading severity index) to cir- cumvent the difficulty in evaluating the outage in Rician fading. The suitability of this approximation is examined by comparing the outage performance under these two fading conditions. Sur- prisingly, some basic results for Nakagami- channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami- approximation model. However, similar approx- imation for the interferer signals is valid. Index Terms—Cochannel interference, fading channels, land mobile cellular radio systems. I. INTRODUCTION I N CELLULAR radio engineering, the system designers are frequently required to evaluate the probability of outage, which is a useful statistical measure of the radio link perfor- mance in the presence of cochannel interference (CCI) [1]–[12]. Development of mathematical tools for outage analysis has re- ceived a lot of attention during the past two decades—since the deployment of the cellular architecture in the early 1980s for Paper approved by K. B. Letaief, the Editor for Wireless Systems of the IEEE Communications Society. Manuscript received February 2, 1999; revised April 28, 2000. This work was supported in part by a Strategic Project Grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada and by Telus Mobility. This paper was presented in part at the IEEE International Conference on Communications, Vancouver, BC, Canada, June 1999. A. Annamalai is with the Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Alexandria, VA 22314 USA (e-mail: annamalai@vt.edu). C. Tellambura is with the School of Computer Science and Software Engineering, Monash University, Clayton, Vic. 3168 Australia (e-mail: chintha@dgs.monash.edu.au). V. K. Bhargava is with the Department of Electrical and Computer Engi- neering, University of Victoria, Victoria, BC V8W 3P6 Canada (e-mail: bhar- gava@engr.uvic.ca). Publisher Item Identifier S 0090-6778(01)01299-5. commercial mobile radio systems. Several commonly used def- initions of the outage exist. In its simplest version, the outage is the probability that the ratio of the desired signal power to the total interference power falls below a given threshold that de- pends on the modulation type and other system design require- ments. More refined definitions take into consideration additive noise levels and minimum signal requirements. Despite many years of research, closed-form expressions for the probability of outage (even for the simplest defini- tion) do not exist for some fading channel models because of the lack of a simple expression for the probability den- sity function (pdf) of a sum of interfering signals. For ex- ample, the pdf of a sum of unequal Rician signal powers is not available in closed form. Similarly, the pdf of a sum of unequal Nakagami signal powers with noninteger fading severity indices is not available in simple, closed form. As a result, many previous studies make restrictive assumptions and approximations (e.g., Nakagami fading index limited to integer values, statistically equal interferers, a Rician vari- able approximated by a Nakagami variable and so on). Al- though the assumption that all the received signals (both de- sired and undesired) have the same statistical characteristics is quite reasonable for medium and large cell systems, its validity for pico- and microcellular systems is questionable. This is because an undesired signal from a distant cochannel cell may well be modeled by Rayleigh statistics but Rayleigh fading assumption may not hold for the desired signal since a line-of-sight path is likely to exist in a microcell. Therefore, it is evident that different statistics are needed to characterize the desired user signal and the interfering signals in a micro- or picocellular radio systems. A simple yet general numerical technique for computing the outage seem useful and attractive to address the problem on hand. However, a general unified expression for computing the outage (simple and refined criterion) where the system designer can simply plug in the required fading channel models with ar- bitrary parameters has not been developed previously. This is the main contribution of this paper. Our numerical technique is very easy to compute and handles arbitrary fading models, as well as both simple and refined definitions of the outage are considered. We also derive exact closed-form formulas for some special cases. These formulas are reported because they are new to the best of the authors’ knowledge. The literature on outage analysis is extensive (see references in [1]–[3]). Closed-form expressions for outage in Nakagami fading is derived in [2] for integer fading parameters. Results 0090–6778/01$10.00 © 2001 IEEE Authorized licensed use limited to: UNIVERSITY OF ALBERTA. Downloaded on December 22, 2009 at 18:49 from IEEE Xplore. Restrictions apply. "©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."