2696 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 62, NO. 8, AUGUST 2014 Optimal Sequential Channel Estimation and Probing for Multiband Cognitive Radio Systems Raied Caromi, Student Member, IEEE, Seshadri Mohan, Member, IEEE, and Lifeng Lai, Member, IEEE Abstract—In this paper, we propose a novel sequential channel estimation approach for multiband cognitive radio (CR) systems. We introduce a general model and test two scenarios of practical interest. The two scenarios are as follows: 1) CR users optimally estimate all the available bands; and 2) CR users find one good channel with a large gain. In particular, we use a sequential search in which the CR users estimate the available channels one by one. During the search, the CR users determine whether to terminate the current channel estimation process and switch to the next channel based on the training symbols received so far. Our objective is to design a switch function, an estimator, and a stopping rule that minimize a combination of estimation time and error. For the multiband estimation scenario, we show that the optimal rule is to find the optimal number of symbols required for each channel in a joint optimization problem. For the good channel search problem, we show that the optimal decision rules that minimize a properly chosen cost function have a simple structure. In particular, both the termination and switching rules are threshold based. Numerical results are provided to illustrate the effectiveness of the proposed algorithms. Index Terms—Channel estimation, channel probing, cognitive radio, good channel search, multiband, optimal stopping, sequen- tial analysis, spectrum sharing. I. I NTRODUCTION I NCREASING the spectrum efficiency was the motivating principle for developing cognitive radio (CR) technology. Besides the high accuracy requirements for spectrum sensing, sensing delay forms a major factor in the development of spectrum sensing algorithms. This is mainly due to the fact that if less time is spent in sensing the spectrum, then more time will be available for transmission. Numerous spectrum sensing algorithms have been proposed in the literature, for example, [3]–[6], to quickly identify one or more free chan- nels. Various approaches have been developed to not only incorporate efficient spectrum sensing techniques but also to Manuscript received October 26, 2013; revised April 8, 2014 and June 10, 2014; accepted June 14, 2014. Date of publication June 24, 2014; date of current version August 20, 2014. The work of L. Lai was supported by the National Science Foundation under Grant DMS-12-65663. This paper was presented in part at the Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, November 2012, and in part at the Conference on Information Sciences and Systems (CISS), Princeton, NJ, USA, March 2012. The associate editor coordinating the review of this paper and approving it for publication was E. G. Larsson. R. Caromi and S. Mohan are with the Department of Systems Engineering, University of Arkansas at Little Rock, Little Rock, AR 72204 USA (e-mail: rmcaromi@ualr.edu; sxmohan@ualr.edu). L. Lai is with the Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609-2280 USA (e-mail: llai@wpi.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCOMM.2014.2332452 improve the throughput of the CR system. In [7], the problem of energy allocation is studied for opportunistic spectrum ac- cess (OSA) using a multiarmed bandit framework to optimally allocate energy for sensing, probing, and data transmission. The problem of channel probing and transmission scheduling for OSA is also studied in [8]. Specifically, optimal strategies are studied to decide which channels to probe and in what order. Different approaches have been considered in the literature in order to choose a good channel that maximizes the throughput. For example, [9]–[12] demonstrate that the order in which the channels are sensed influences the throughput and that an optimal order of sensing the channels improves the throughput performance. In [5], a sensing framework is developed to opti- mally utilize the sensing time between the secondary users with the objective of maximizing the network throughput. Another approach is proposed in [13] to select a channel and a relay based on location information and channel usage statistics. It is important to take into account the channel quality during the spectrum sensing process to improve the throughput efficiency of multiband CR [14]–[18]. In particular, [14], [15] propose sensing and probing models to improve the CR throughput, while [17] and [18] study different scenarios to improve the quality of service (QoS) by solving an optimization problem to select a better channel. Most of the current CR research efforts focus on multiband detection under different sensing strategies to maximize the throughput [19], [20]. The optimal power allocation problem is studied in [21] and [22] with the goal of maximizing the overall CR performance. While the field of spectrum sensing has been extensively studied, the topic of channel estimation for cognitive radios has not received much attention. Among limited existing literature on the channel estimation problem for cognitive radios, [23] proposes a sequential policy to evaluate the channel parameters in order to maximize the estimator’s asymptotic efficiency. The problem of optimally placing sensing times over a time window is studied in [24]. The authors focus on obtaining the best possible estimates of the parameters of an on-off renewal channel. The focus of our paper 1 is on how to arrive at an optimal trade-off strategy between the channel estimation quality and the time left for useful data transmission. After the cognitive radios detect some channels to be free, they need to estimate the channel gain between them before they can start transmitting data. One would like the channel gain estimate to be as accurate as possible. However, this may degrade the overall throughput performance since more time is needed for the estimation process to obtain highly accurate channel gain 1 The results in this paper partially appear in [1], [2]. 0090-6778 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.