Throughput Analysis Using Eigenvalue Based Spectrum Sensing Under Noise Uncertainty Ayse Kortun, Tharm Ratnarajah and Mathini Sellathurai Queen’s University Belfast Queen’s Road, Queen’s Island, Belfast Ying-Chang Liang and Yonghong Zeng Institute for Infocomm Research A*STAR, Singapore Abstract—The essential tradeoff between sensing capability and achievable throughput of the secondary network is one of the active research topics for researchers working on cognitive radio. In this paper, noise uncertainty which has a great impact on sensing methods is taken into account in the maximization of throughput using eigenvalue based spectrum sensing schemes. This issue has not been tackled in the throughput associated studies before. First, the theoretical and empirical distributions of the decision statistics and the detection performances for eigenvalue based sensing techniques are studied in the presence of noise uncertainty. The computed detection probabilities of maximum- minimum eigenvalue (MME) detector and maximum eigenvalue detector (MED) are compared with the most widely used energy detector (ED). Then, in the light of the obtained results, the throughput of the secondary network is maximized in order to find out the sensing duration for each scheme using multiple receive antennas. It is shown that, under low signal to noise ratio (SNR) regime, the designed sensing slot duration achieves the best sensing throughput tradeoff. Index Terms—Cognitive radio, spectrum sensing, eigenvalue- based detection, sensing-throughput tradeoff. I. I NTRODUCTION It is surely known that, spectrum sensing constitutes the backbone of the cognitive radio and it is crucial to the throughput of secondary networks as well. This is because the sensing techniques used directly affect the throughput of these networks. As a result of this, in order to achieve higher throughput, many researchers have been aiming for designing better sensing schemes in terms of a higher detection performance. Several studies have recently examined optimization prob- lems from different perspectives in the context of through- put maximization in multi-band scenarios [1], [2]. In [1], a nonconvex weighted throughput maximization problem is proposed in order to maximize the weighted sum of secondary users throughputs. The bilevel optimization and monotonic programming methods are utilized to solve the problem. Sensing-throughput tradeoff problem using sequential sensing algorithm is examined in [2]. The developed sequential sensing scheme based formulation is studied both for single cognitive radio and multiple cooperating cognitive radios. In [3], k-out- of-N fusion scheme is used for cooperative sensing. In this study, the sensing time and the k value that maximize the secondary users’ throughput are obtained. In [4], the sensing duration is designed in order to achieve optimum throughput. The effect of the cooperation overhead on the throughput of the secondary network is observed in [5]. It is shown that, the throughput decreases as the number of cooperating users increase. The common consideration of all of the mentioned studies is that the throughput optimizations are studied based on the energy detection and the noise uncertainty which is one of the challenges in spectrum sensing is not taken into consideration. In this paper, different from all these studies, the throughput of the secondary user is maximized using the eigenvalue based sensing techniques in the presence of noise uncertainty which is not tackled before. Note that, the structure of the throughput optimization formulation given in this paper is based on the framework provided in study [4]. However, in the presented work in this paper, MME, MED and ED sensing algorithms are used in designing the sensing duration to maximize the throughput for the secondary network. Moreover, noise uncertainty is taken into consideration while optimizing the secondary network throughput using the complex Gaussian signal. Above all, multi receiver antennas are used in this study. The probability of false alarm and the probability of detec- tion are essential information for throughput calculation. Thus, distribution of the decision test statistics in the presence and in the absence of the primary signal has to be known. The distribution of decision statistics for eigenvalue-based sensing techniques can be quantified using some results provided by random matrix theory. Recently, threshold formulations of MME and MED based on the exact test (decision) statistics distributions are derived in some studies [6]- [8]. It is shown that the proposed exact thresholds achieve better performance as compared to the asymptotic threshold which assumes infinite number of antennas and signal samples. However, the calculation of exact threshold becomes complicated as the number of samples increase. So, alternative asymptotic thresholds for MME and MED techniques are derived for any fixed number of antennas and large number of samples in [9]. A practical cognitive radio system can only have limited number of antennas while using a large number of samples for sensing. So, this is a realistic assumption and the computational complexity is less than the exact approaches. Because of this, the results of this study are integrated into the throughput optimization studied in this paper. This paper is organized as follows. Section II briefly presents the system model and the considered noise uncer- tainty model. The formulation of detection and false alarm probabilities in the absence and in the presence of noise 978-1-4577-1379-8/12/$26.00 ©2012 IEEE 395