2272 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 12, DECEMBER 2013 Outage Analysis of Spectrum Sharing Cognitive DF Relay Networks Using Outdated CSI Kamel Tourki, Khalid A. Qaraqe, and Mohamed M. Abdallah Abstract—We investigate the effect of the outdated channel state information (CSI) on the secondary relay-aided network’s performance. We carry out the analysis of the outage probability as well as the diversity order of the secondary network (SN) considering three key constraints: 1) maximum transmit power at the secondary transmitter, 2) peak interference power at the primary receiver, and 3) outdated CSI at the secondary- to-primary and secondary-to-secondary links. The performance results show that the relay cluster position, the imperfect CSI of the interference links and of the second hop are the key optimization factors. We show that the correlation coefficient of the second hop link is the key optimization parameter of the diversity order. Index Terms—Cognitive relay networks, Outdated CSI, Outage analysis. I. I NTRODUCTION C OGNITIVE radio (CR) is an emerging technique which is proposed to improve the wireless spectrum resources utilization efficiency. Recently, it was shown that introducing relays in spectrum sharing CNs can boost the quality of service (QoS) [1]–[6]. Involving a single relay, the impact of the primary transmitter (PT) on the CRN was investigated in [4], [7]. In particular, the authors in [4] considered the maximum transmit power and several primary transmitters (PTs) and receivers (PRs). However, all the aforementioned works assumed perfect channel state information (CSI) for all involved links. Recently, by neglecting the direct link and the transmit power limitation at the secondary transmitter (ST), the authors in [5] and [6] carried out the outage probability of the secondary system when the CSI of the ST-PR and the selected relay-PR interference channel links are assumed to be imperfect. In this letter, we address the outage performance of the secondary network (SN) assuming outdated CSI 1 and consid- ering the maximum transmit power constraint at the ST as well as the peak interference power at the primary receiver (PR). We derive the outage probability expression as well as the generalized diversity order. We confirm the results via simulations, and show that the relay cluster position and the correlation coefficients of the interference and second hop links are the key optimization factors of the diversity. Manuscript received July 24, 2013. The associate editor coordinating the review of this letter and approving it for publication was T. Q. Duong. This publication was made possible by NPRP grant ♯ 5-250-2-087 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. The authors are with the ECEN Program, Texas A&M University at Qatar. The corresponding author is K. Tourki (e-mail: kamel.tourki@qatar.tamu.edu). Digital Object Identifier 10.1109/LCOMM.2013.110413.131698 1 We assume imperfect CSI knowledge of the secondary transmitting nodes to the PR, and the second hop links. II. SYSTEM MODEL Consider a SN consisting of the ST, a receiver (SR), and a cluster of K potential relays, coexisting with a primary network (PN) consisting of a PT and a PR, where each node is equipped with a single antenna and each relay operates in DF mode. We denote h ij the coefficients of the channels between a transmitter i and a receiver j , modeled as flat fading and Rayleigh distributed with variances λ ij 2 . We assume that the relays are close to each other and forming a cluster and accordingly, we assume that λ sr = λ sk , λ rs = λ ks and λ rp = λ kp for all k. As a relay-aided system, the SN adopts a dual-hop trans- mission consisting of two distinct phases. In the first phase, the ST broadcasts its data to the SR and the relays where the successful decoding relays form a decoding set referred to as C . In the second phase, only one relay r is selected according to r = arg max k∈C ( |h ks | 2 ) to assist the ST transmission. We consider that the interference at the PR inflicted by the ST and r during the first and second phase, respectively, should not exceed a given maximum tolerable level I. However under realistic considerations, due to several fac- tors such as the mobility and feedback delay, the outdated CSI (denoted as h ij ) used for the power allocation as well as for the opportunistic relay selection may differ from the actual values referred to as g ij , giving g s(r)p = ρ s(r) h s(r)p +  1 - ρ 2 s(r) w s(r) and g rs = ρ 2 h rs +  1 - ρ 2 2 w 2 , where w s(r) and w 2 are circularly symmetric complex Gaussian random variables (RV) having the same variance as RV h s(r)p and h rs , respectively; ρ s(r) (ρ 2 ) is the correlation coefficient between g s(r)p and h s(r)p (g rs and h rs ). It follows that, a power margin η should be introduced to limit the probability that the inflicted interference at the PR exceeding I remains less than a predefined value ǫ, such that Pr  η i I |h ip | 2 |g ip | 2 > I  ≤ ǫ, i = s, r. (1) Considering the equality in (1), and using [8, Eq. (2.264.5) and Eq. (2.264.6)], the power margin can be given after some manipulations as [9] η i = - 1 + (1 - 2ρ 2 i )((2ǫ - 1)) 2 (2ǫ - 1) 2 - 1 - 1 - 2ǫ  (1 - ρ 2 i )(1 - ρ 2 i (2ǫ - 1) 2 ) 2ǫ(1 - ǫ) ,i = s, r (2) Furthermore, the secondary transmissions coming from the ST (P s ) and eventually from r (P r ) are constrained by a 2 i ∈{s, k, r} and j ∈{s, k, r, p}. When i = s (j = s) it refers to the ST (SR) and p stands for the PR. However, k and r stand for the k th relay and the selected relay, respectively. 1089-7798/13$31.00 c  2013 IEEE