The Application Of Signal Sparse Reconstruction Technique In Frequency Estimation

Parameter estimation, especially the frequency estimation, has found wide applications in practice, for example, radar, communications, speech, image, to name a few. And even more, the signal sparsity has sparked numerous interests in the signal reconstruction recently. The main work of this thesis is to develop frequency estimation approaches in the case of the impulsive noise.Due to the link failure and other unknown reasons, data missing is a normal phenomenon in practice. To recover the data missing pattern, an unknown sparse vector is utilized to represent the missing pattern. Moreover, due to the difference from Gaussian noise, the impulsive noise is particularly troublesome since its second moment does not exit, which is the basis of many Gaussian assumption based approaches. To suppress the impulsive noise, the traditional approaches are often based on the Lp-norm because it is finite. However, this passive noise suppression technique exhibits limited noise tolerance capability. Fortunately, an interesting finding about the noise is that it is a nearly sparse signal in time domain since it contains few big spikes and lots of small values. With this property, noise suppression problem becomes an estimation one. Now with the impulsive noise and data missing, a joint estimation approach is designed to estimate the frequency. Simulation results show that the proposed joint approach demonstrates considerable improvements over the Lp-norm based approach.Off-grid problem is present when a discrete dictionary is utilized to explore the signal sparsity. It means that the true values of signal do not lie exactly on the grid, which creates a mismatch between the true values and the dictionary created. To overcome this issue, off-grid is represented by an offset matrix that is a sparse matrix. With the sparse matrix compensation, the frequency estimation performance is enhanced in the case of using the discrete dictionary.Finally, the sparse property is utilized in the development of the joint estimation method in the above algorithm. During the real data processing, another interesting property about the noise is noted, which is that the noise usually lasts certain period of time and is not just a single pulse. This property is referred to as group sparse. With the assistance of group sparse, another joint estimation approach is developed to simultaneously estimate the frequency and the noise. It is demonstrated by the simulations that the utilizing the group sparse property does enhance the estimation performance.