This paper proposes two accurate source-number estimation methods for array antennas and multi-input multi-output radar. Direction of arrival (DOA) estimation is important in high-speed wireless communication and radar imaging. Most representative DOA estimation methods require the source-number information in advance and often fail to estimate DOAs in severe environments such as those having low signal-to-noise ratio or large transmission-power difference. Received signals are often bandlimited or narrowband signals, so the proposed methods first involves denoising preprocessing by removing undesired components then comparing the original and denoised signal information. The performances of the proposed methods were evaluated through computer simulations.

We address a problem of sampling and reconstructing periodic piecewise polynomials based on the theory for signals with a finite rate of innovation (FRI signals) from samples acquired by a sinc kernel. This problem was discussed in a previous paper. There was, however, an error in a condition about the sinc kernel. Further, even though the signal is represented by parameters, these explicit values are not obtained. Hence, in this paper, we provide a correct condition for the sinc kernel and show the procedure. The point is that, though a periodic piecewise polynomial of degree R is defined as a signal mapped to a periodic stream of differentiated Diracs by R + 1 time differentiation, the mapping is not one-to-one. Therefore, to recover the stream is not sufficient to reconstruct the original signal. To solve this problem, we use the average of the target signal, which is available because of the sinc sampling. Simulation results show the correctness of our reconstruction procedure. We also show a sampling theorem for FRI signals with derivatives of a generic known function.