Modeling of Number of Sources Detection Under Nonideal Conditions Based on Fuzzy Information Granulation

In this article, we exploit a granular-based modeling scheme to realize the number of sources detection under nonideal conditions (in low signal-to-noise ratio levels and small snapshots scenarios), in which the idea of information granules and granular computing is integrated with the fuzzy set theory. In the developed scheme, a collection of eigenvalues, which is calculated by the array output correlation matrix, is constructed as a time series. Then, the principle of justifiable granularity criterion is introduced to split the time series into two regions so as to establish a set of upper and lower bounds of prototypes for the signal and noise subspaces. Subsequently, the fuzzy C-means-based encoding and decoding mechanism is employed to optimize the prototypes. During this process, the encoding mechanism is used to produce a pair of information granules, and the decoding mechanism is used to evaluate the quality of information granules. After several rounds of iteration, an optimized prototype vector and a partition matrix are generated. Finally, the structure of the time series is exposed (encoded into) by an optimized prototype vector and a partition matrix, and the number of sources can be determined conveniently through the partition matrix. Simulation results show that the proposed method outperforms the commonly used methods under nonideal conditions.