A Study Of Signal Detection And Parameter Estimation Methods Based On Compressive Sensing

Signal sampling is a necessary way that the real physical world leads to the digital signal world, and most of the currently signal processing methods are still based on the Nyquist sampling theorem. In order to not happen the phenomenon of aliasing in the frequency domain, the sampling rate must be more than twice as much as the signal bandwidth. Increasingly, however, the wide instantaneous signal bandwidth makes either the signal detection or subsequent parameter estimation that requires more storage space and processing time, which are faced with tremendous pressure. The theory of Compressed Sensing(CS) appeared for data acquisition and signal processing provides a new way.CS indicates that for sparse or compressive signal one can acquire it at a sampling rate much lower than Nyquist rate and ensure that the necessary information is already preserved in these samples of the original signal, and thus may be weight directly on the samples for signal detection and parameter estimation on the basis of inaccurate reconstructive the original.This thesis studies the application of CS in signal detection and parameter estimation, both of which are based on partial recovery method. Firstly introduces the basic principles, processing progress and in-depth study of the three core issues in CS. Signal detection algorithm and parameters estimation algorithm in the lower part of the reconstruction based on CS are studied as well. CS signal detection algorithm based on orthogonal matching pursuit,which use the Maximum projection coefficients of original signal in the transform domain as a judgment basis, is one of the detection algorithms that based on part of the signal reconstruction, which reduces the fluctuation of the characteristic quantity based on matching pursuit algorithm and improves the performance. CS signal detection algorithm based on the position information of sparse coefficients, which adopts the sparse coefficients position information of to-be-detected signal instead of the Maximum projection coefficients of original signal in the transform domain, it can reduce the time of threshold selection process and as a result the detection efficiency is improved. CS signal detection method base on numerical characteristics of sampling value, which according to the different characteristics of the expectation of sampling values under different hypothesis, detection is accomplished by using the deviation of the actual sampling values from the expectations under corresponding hypothesis as criterion. The algorithm in low SNR can still apply. CS parameter estimation algorithm is based on three assumptions of morphological component analysis(MCA), because different signals have different sparse matrices and the only unique representation of the signal. On the basis of the mixed signal sparse representation, using a variety of dictionaries, separates the uncorrelated signal, only leavingthe interest signal, and then finding out the maximum position of the sparse coefficient, of which the position of the atomic frequency parameters for signal in the library is the frequency of the signal.