Iterative Grid Search for RSS-Based Emitter Localization Suzan Üreten, Abbas Yongaço˘ glu, Emil Petriu School of Electrical Engineering and Computer Science 800 King Edward Ave. University of Ottawa Ottawa, ON K1N 6N5 Email: suret057@uottawa.ca Abstract—In this paper, we present a reduced complexity iter- ative grid-search technique for locating non-cooperating primary emitters in cognitive radio networks using received signal strength (RSS) measurements. The technique is based on dividing the search space into a smaller number of candidate subregions, selecting the best candidate that minimizes a cost function and re- peating the process iteratively over the selections. We evaluate the performance of the proposed algorithm in independent shadowing scenarios and show that the performance closely approaches to that of the full search, particularly at small shadowing spread values with significantly reduced computational complexity. We also look at the performance of our algorithm when the initial search space is specified based on two different data-aided approaches using sensor measurements. Our simulation results show that the data-aided initialization schemes do not provide performance improvement over blind initialization. I. I NTRODUCTION Flexible radio technologies that enable opportunistic access to unused spectrum have been a focal point of recent research in addressing spectrum shortage problem. Opportunistic radio systems are expected to adhere to spectrum regulations in the region they are deployed and they should avoid harmful interference to primary spectrum holders in their exclusive region. Primary exclusive region is the area within which opportunistic users are not allowed to transmit [1]. Predicting primary exclusive region of a primary emitter requires the knowledge of primary emitter’s location and its transmit power, which in most cases are not readily available due to non- cooperative nature of primary networks. Emitter localization problem in general has been consid- ered extensively in the literature; see for example [2] for an overview of localization techniques. Localization may be accomplished via many techniques, such as received signal strength (RSS), time of arrival (TOA), time difference of arrival (TDOA) and angle of arrival (AOA). Although TOA and TDOA are generally more accurate, RSS based techniques are often of interest as they require simpler hardware. The challenge of RSS based localization is due to numerous factors affecting the energy decay between the transmitter and emitter such as shadowing, multipath, path loss exponent estimation errors, geometric configuration of the nodes and antenna orientation. Despite having several sources of error, RSS based techniques are expected to perform satisfactorily when a large number of spatially separated sensors are employed. The literature on RSS based emitter localization has been on developing efficient algorithms for accurate location es- timation. Among the others, maximum-likelihood estimation (MLE) method offers an attractive approach for the local- ization problems since it is asymptotically efficient, unbiased and it does not require prior information [3],[4]. In fact, it has been shown that MLE method achieves the Cramer-Rao lower bound (CRLB) at small shadowing variances [3]. The maximum likelihood estimator of the emitter location requires the minimization of a non-convex cost function. Since this cost function exhibits numerous local minima, its global minimiza- tion is usually realized by means of numerical approaches. One approach is to employ grid search where the algorithm scans all possible grid points in the localization space. The grid point that maximizes the likelihood is selected as the location of the emitter. In a grid-search algorithm, the size of the grid elements must be chosen small to obtain more accurate location estimates. However, smaller grid size increases the computational complexity. The need for reduced complexity grid search tech- niques arises in several fields. For example, a variable-mesh, derivative-free optimization algorithm, namely contracting- grid search method, is used to derive interaction locations in compact gamma cameras in [5]. In [6], the location of a sound source in a distributed sensor network is estimated using a grid- based multi-resolution search to reduce the complexity of an exhaustive maximum likelihood estimator and a smarter multi- resolution search is proposed based on searching around the highest energy reading sensor. [7] proposes a low-complexity positioning procedure that simply searches for the global mini- mum around the sensor exhibiting the smallest local maximum of the cost function and it is shown that it outperforms the naive approach that searches for the global minimum around the sensor reporting the largest signal strength. In [8], a tree search algorithm (TSA) is used to reduce the computational complexity of grid search algorithm in sensor networks assum- ing that the power of the transmitter to be located is known and it is shown that the performance of the TSA algorithm closely achieves the performance of least squares estimator with significantly reduced computational complexity. In this paper, we propose a reduced complexity itera- tive grid-search algorithm for locating primary emitters with unknown power in cognitive radio networks. The proposed technique is based on refining search space based on the