Spatial spectrum estimation based on compressive sensing

The most prominent subspace decomposition methods for spatial spectrum estimation include multiple signal classification algorithm (MUSIC) as well as estimation signal parameter via rotational invariance technique (ESPRIT). However, the drawbacks of MUSIC is that estimating the number of source signals are constraint by the following two aspects: array aperture and a large number of sampling data. After carefully investigating the theory of compressive sensing (CS), this paper constructs the model for spatial spectrum estimation on the basis of the sparsity of source signals in the angle spectrum. According to the principle of CS, spatial signals can be sampled with much less sensors, which leads to small sampling data. Furthermore, the source signals can be reconstructed accurately by some recovery algorithms. The approaches are compared with MUSIC and three numerical simulation experiments are programmed with MATLAB. The reconstruction results are found to be approximately to the original signals. The most attractive merits of our proposed method not only reduces the number of elements which are needed for sampling as well as decreases the amount of sampling data, but also the source signals can be reconstructed in terms of their amplitude and bearing simultaneously.