Joint 2D-DOA and Carrier Frequency Estimation Technique Using Nonlinear Kalman Filters for Cognitive Radio

The problem of jointly estimating carrier frequencies and their corresponding two-dimension direction of arrivals (DOA) of band-limited source signals is considered in this paper for cognitive radio. The main problem of estimating carrier frequencies spread over a wideband spectrum is the requirement of high sampling rates. Thus, the Kalman filters are applied in the spatial domain instead of the temporal domain in the proposed algorithm to relax hardware complexity. The proposed algorithm exploits both the azimuth and elevation angles instead of a single DOA to increase the spatial capacity. Two approaches are proposed using two different types of nonlinear Kalman filter: extended Kalman filter (EKF) and unscented Kalman filter (UKF). Using simulations, the factors that affect the performance of both the filters are discussed. Scaling the estimated parameters to the same range and the proper tuning and initialization of the filters are crucial factors to prevent the filter divergence. Although UKF is supposed to have a better performance than EKF, reducing the inter-element spacing of the employed arrays and the proper filter initialization can make EKF approach the performance of UKF. On the other hand, UKF suffers from high processing time. Overall, both filters are able to converge to the true values of the unknown parameters using a number of relaxed analog-to-digital converters equal to the number of the array elements in the employed arrays. However, the approaches can detect a number of source signals higher than one-third of the total number of the array elements.