On the Capacity of Spectrum Sharing Systems in Generalized Fading Scenarios Daniel Benevides da Costa † and Ugo Silva Dias ‡ † Federal University of Ceara (UFC) Computer Engineering Sobral, CE, Brazil Email: danielbcosta@ieee.org ‡ University of Brasilia (UnB) Department of Electrical Engineering Brasilia, DF, Brazil Email: ugodias@ieee.org Abstract— Spectrum sharing concepts have been widely employed in the design of practical systems with the aim to im- prove the utilization efficiency of the radio spectrum. Motivated by this, a comprehensive capacity study of spectrum sharing systems undergoing α-μ fading is performed in this paper. More specifically, assuming identical fading parameters, a closed-form expression for the delay-limited capacity is derived. In addition, based on the power allocation related to the outage capacity, a closed-form expression for the corresponding minimum outage probability is attained. Guidelines on how the ergodic capacity can be evaluated are also presented. Numerical plots are shown in order to investigate the effect of the fading parameters in the system capacity. Index Terms— Capacity analysis, cognitive radio, generalized fading scenarios, spectrum sharing. I. I NTRODUCTION As the demand for additional bandwidth continues to in- crease, spectrum policy makers and communication technolo- gists are seeking solutions for the apparent spectrum scarcity [1], [2]. Meanwhile, measurement studies have shown that the licensed spectrum is relatively unused across many time and frequency slots [3]. To solve the problem of spectrum scarcity and spectrum underutilization, cognitive radio technology has arisen as a promising solution due to its ability to rapidly and autonomously adapt operating parameters to changing requirements and conditions. Recently [4]–[6], fundamental capacity limits of spectrum sharing systems in AWGN and traditional fading environments (Rayleigh and Nakagami-m) were addressed. However, works investigating the capacity of spectrum sharing systems in generalized fading scenarios, in which the traditional models do not fit very well, still lack in the literature. In [7], a general physical fading model, namely the α-µ fading model, has been proposed which considers a signal composed by clusters of multipath waves propa- gating in a nonhomogeneous environment. The distribution associated with this fading model embraces as special cases important other distributions, such as Nakagami-m, Weibull and Rayleigh. (Therefore, the Negative Exponential, One- Sided Gaussian, and Rayleigh are also special cases of it). As its names implies, the α-µ distribution is written in terms of two physical parameters, namely α and µ. Roughly speaking, the parameter α is related to the non-linearity of the environment, whereas the parameter µ is associated to the number of multipath clusters. In addition, the flexibility of the α-µ distribution renders it adaptable to situations in which neither of these other aforementioned distributions yield good fit [7]. In this paper, assuming an α-µ fading scenario, closed- form expressions for the minimum outage probability (closely related to the outage capacity) and delay-limited capacity (DLC) of cognitive radio systems subject to interference power constraints are derived. The study of these metrics finds applicability in the performance analysis of systems that carry delay-sensitive applications. Guidelines are also presented in order to evaluate the ergodic capacity under the average and the peak interference power constraints. Numerical results are shown and the influence of the fading parameters on the capacity is discussed. To the best of the authors’ knowledge, this is the first time that the capacity of spectrum sharing systems in α-µ fading channels is considered, reported and investigated in the literature. The remainder of this paper is structured as follows. In Section II, the system model is briefly introduced. Section III investigates the capacity of the system model under study. More specifically, the outage capacity and the delay-limited capacity are analyzed assuming a peak interference power constraint and an average interference power constraint, re- spectively. The ergodic capacity is also examined in this section and guidelines on how this metric can be evaluated are provided. Section IV shows some numerical results along with insightful discussions and Section V concludes this Letter.