Spatial And Frequency Spectrum Estimation Based On Compressive Sensing

As an important research topic in array signal processing, spatial spectrum estimation is widely used in both military and civil fields, such as radar, communications, sonar and seismic exploration. The traditional spatial spectrum estimation requires collecting a lot of data, and after Nyquist sampled, there is a huge amount of data is to be dealed with, in which a lot of redundancy is existed. In the whole system, a lot of power and cost is wasted. AS a development of traditional Nyquist sampling, the proposed theory compressive sensing(CS) has become a novel research direction. It samples data based on the compressibility of signal. Because the number of sensors required in compressive sensing is greatly reduced and the data collected after the acquisition has a much smaller redundancy, this method attracted a lot of attention since it is proposed. Our work in this thesis is focused on the space spectral estimation of narrowband signal and space-frequency spectrum estimation of wideband based on compressive sensing. The main works are as follows:1. The classic spatial spectrum estimation of narrowband and broadband signal is introduced, and three key research contents of compressed sensing theory is described, especially the orthogonal matching algorithm(OMP).2. A reconstruction algorithm based on sparse spatial smoothing covariance matrix is proposed. First, we got the final matrix through averaging the forward and backward smoothed covariance matrix, and then, the final matrix is vectored. According to the sparsity of the space angle we rewritten the covariance matrix, then constructed the over complete dictionary. Then obtain spatial spectrum estimation by solving optimization equation. The experiment results showed that the proposed algorithm in this thesis has higher resolution than others even in the case of low signal-noise ratio. Based on the traditional model of array sampling, we proposed a space-time compressive sampling(STCS) model. Based on compressed sensing technology and use the sparsity of angle and frequency in space we can achieve the angular and frequency of the incoming signal. In practical application this model not only can greatly reduce the sensor the number, but also can reduce the power of the back-end processing and the cost of hardware modules. According to the proposed STCS model, we compressed the received data of array elements in both time domain and frequency domain to realize space-time compression sampling. Finally we achieved the angular and spectral estimation by iterative. 3. With the traditional wideband signal processing method and based on compressed sensing theory, we proposed two algorithms. The first one is by using the reference array element receiving delay data to construction the dictionary and use the sparsity of signal source in space domain algorithm to reconstruction the spatial spectrum estimation by OMP algorithm and FOCUSS algorithm. By this method we can eliminate the operators need for traditional in wideband signal process which need to calculate the covariance matrix of the array. The second algorithm is by using tensor form to processes joint array covariance matrix data with compressed sensing. The received data is rewritten as a linear combination of the array manifold form then use the sparse of angles to construct an over-complete dictionary, finally obtain the space angle estimation by use MMS-OMP algorithm to solve its sparse coefficient vector.