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The existing Cramer-Rao bound (CRB) expressions in the literature are not applicable to the problem of localization of mixed near-field (NF) and far-field (FF) sources, including noncoherent and coherent signals, using two-dimensional arrays. Given the unique properties of circular arrays, in this article, the mathematical model of received signals in multipath environments, including a mixture of noncoherent and coherent NF/FF signals, is introduced. Then, the stochastic CRBs associated with the above problem are derived. The compact closed-form expression of CRB extracted in this article can be used for the algorithms under the above scenario as a benchmark to evaluate the estimation accuracy of azimuth DOA, elevation DOA, and range parameters as well as fading coefficient parameter. The simulation results show that the CRBs of the azimuth DOAs, elevation DOAs, ranges, and FCs decrease, on average, at a rate of approximately O(M −1.9 ), O(M −1.9 ), O(M −1.2 ), and O(M −1.8 ) as M (number of sensors) goes to infinity, respectively, where O is the notation of the asymptotic growth rate.

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In this paper, we propose a new channel estimation algorithm for orthogonal frequency division multiplexing (OFDM) systems. For fast fading environment, we introduce a new method which is extended to the Alamouti Coded OFDM case. At the first stage of this algorithm, the channel response is estimated for pilot sub-carriers and then, the channel response for data sub-carriers are interpolated by Gaussian Radial Basis function as it is an efficient nonlinear interpolator. The postprocessing and filtering on the estimated channel taps energy are proposed to improve the estimation performance and reduce the noise effects of primary estimation, which is caused by LS estimation at pilot data. The accuracy of our channel estimation algorithm is improved by using iterative decision feedback. The decision feedback method is used to update channel parameters in each OFDM symbol. The effectiveness of new techniques is demonstrated through the simulation of an Alamouti coded OFDM system with two-transmit and two-receive antennas. Finally, the results are analyzed and compared with previous algorithms which show performance enhancement.

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