Irreducible form for AP algorithm for detecting the number of coherent signals based on the MDL principle

This paper presents an improvement of the alternating projection (AP) algorithm for detecting the number of coherent signals based on the minimum description length (MDL) principle using a uniform linear array of sensors. The criterion of the AP algorithm for the detection becomes indefinite, when estimated bearings more than one approach to the identical value. This paper derives an irreducible form of the AP criterion for the detection, which never get indefinite. The irreducible form is represented as a rational function and real-valued version of the FFT can be exploited efficiently. The proposed algorithm reduces the order of the amount of arithmetic operations. Finally, simulation results are shown to demonstrate the validity of the proposed algorithm.