1054 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 3, MARCH 2010 Effective Capacity of Delay-Constrained Cognitive Radio in Nakagami Fading Channels Leila Musavian, Member, IEEE, and Sonia Aïssa, Senior Member, IEEE Abstract—In this paper, we consider coexistence of secondary and primary users who share particular portions of the spectrum and propose a delay-constrained power and rate allocation scheme for the secondary user link. Secondary users are allowed to access the spectrum occupied by a primary user subject to satisfying interference-power limitations imposed by the primary user. Applying this limitation, we obtain the maximum arrival- rate supported by the secondary channel in Nakagami- block- fading environment subject to satisfying a given statistical delay quality-of-service (QoS) constraint. In this respect, we derive the optimal rate and power adaptation policy that maximizes the effective capacity of the channel, and provide closed-form expressions for the power allocation and the effective capacity. In addition, we obtain closed-form expressions for the expenditure- power that is required at the secondary transmitter to achieve the above-mentioned capacity metric. Moreover, for comparison purposes, we consider two widely deployed power allocation strategies, namely, optimal power and rate allocation (opra) and channel inversion with fixed rate (cifr), and investigate the effective capacity of the channel under these power transmission techniques. Numerical simulations are conducted to corroborate our theoretical results. Index Terms—Cognitive radio, effective capacity, delay QoS constraint, interference-power constraint, power allocation. I. I NTRODUCTION R ECENT advances in spectrum-sharing techniques have enabled different wireless communications technologies to coexist and cooperate towards achieving a better gain from the limited spectrum resources. A major trend in this regard started when spectrum utilization measurements showed that most of the allocated spectrum experiences low utilization [1]. In fact, the spectrum regulatory bodies have traditionally granted license for spectrum utilization with compulsory and detailed transmission guidelines, and allocated proper guard bands between neighboring frequency bands to avoid mu- tual interference. This conservative approach has left non- negligible parts of the spectrum to be inefficiently utilized. On the other hand, this century’s growth of wireless applications and demands have caused the frequency allocation table for wireless services to become oversaturated. These key obser- vations motivated the concept of cognitive radio (CR), which Manuscript received September 17, 2008; revised August 12, 2009; ac- cepted September 24, 2009. The associate editor coordinating the review of this paper and approving it for publication was M. Guizani. L. Musavian is with the Advanced Signal Processing Group, Loughborough University, UK (e-mail: l.musavian@lboro.ac.uk). S. Aïssa is with INRS-EMT, University of Quebec, Montreal, QC, Canada (e-mail: aissa@emt.inrs.ca). This work was supported by a Discovery Grant (DG) from the Natural Sciences and Engineering Research Council (NSERC) of Canada. Part of this work is published in the proceedings of IEEE Globecom’08. Digital Object Identifier 10.1109/TWC.2010.03.081253 offers a tremendous potential for improving the utilization of the radio spectrum. There are different spectrum-sharing approaches suggested for cognitive radios, e.g., interweave and underlay. In the interweave scheme, secondary users utilize the spectrum when the primary user is not transmitting in that particular frequency band, whereas in the underlay approach, secondary users share the spectrum with the primary user such that the transmission of the former does not harmfully affect the communications process of the latter. Each of these schemes is characterized by its own challenges and benefits. In the interweave scheme, the secondary users need to sense the primary user’s activity and to respond to challenges such as the hidden primary node problem. In the underlay scheme, on the other hand, information about the channel gains between the secondary and primary users is required so that the secondary user can adapt its transmission parameters to the channel changes in order to satisfy the primary interference requirements. In either of the proposed schemes, there are, indeed, critical doubts on the capability of CR networks in satisfying the QoS requirements of cognitive users. In fact, CR is required to determine the spectrum band allocation that meets the QoS requirements for different users with various applica- tions. QoS guarantees play a critical role in next-generation wireless networks, e.g., in systems that carry real-time or delay-sensitive applications, it is required to ensure that the delay adheres to the service requirements. Indeed, it is of paramount importance to investigate the performance of CR under heterogenous QoS requirements of different users. Com- prehensive overviews of the challenges of CR, policy issues and fundamental limits have been published in the literature, e.g., [2]–[7]. Recently, several approaches have been introduced to satisfy the QoS requirements for heterogenous applications. Among them, adaptive power and rate allocation has been shown to be a strong tool for maximizing the channel spectral efficiency [8]. In this regard, two of the very well-known and widely used schemes are the optimum power and rate allocation (opra) and total channel inversion with fixed-rate (cifr) schemes. The opra technique achieves the maximum long-term rate of the channel while in contrast cifr technique achieves the maximum constant-rate of the channel. From the information theory point-of-view, opra achieves a higher capacity compared to cifr and remains a better choice in terms of spectral efficiency. However, the benefit of opra lays on sacrificing delay and complexity and, as such, in systems with delay-limited applications opra does not seem to be a good choice. 1536-1276/10$25.00 c ⃝ 2010 IEEE