Research On Compressive Sampling And Fast Reconstruction Of Frequency-hopping Signal Under Interference Background

When dealing with wideband frequency-hopping signal, a large number of sampling points will be created by traditional sampling method. So, traditional sampling requires large storage space, and it's very hard for hardware implementation. The proposing of Compressed Sampling (CS) opens up a new way to solve such problems. However, when transmitting ultra wideband frequency-hopping signal, a lot of interference signals will be inevitably mixed, which will make the sparse of the signal very high, and the number of information sampling points which is needed to reconstruct the original signal is large according to the theory of CS. The frequency-hopping signal only appears one certain frequency in a certain moment (the sparse of which is 1), and the frequency set only contain a certain number of frequencies. Therefore, the length of frequency hopping sparse vector is far shorter than that of original signal sparse vector. And the CS information points which are needed to represent the frequency-hopping signal are far less than that to represent the original signal.This dissertation studies three kinds of CS schemes to suppress the frequency-fixed interference, including annihilation filtering method, posteriori compressed sampling method and minimum mean square error method, and detailed analysis and comparison of the performance is made. Simultaneously, a new frequency-hopping compressed sampling method is presented, which is based on frequency selective measurement matrix. By choosing certain measurement matrix, this method can be applied to null suppress all kinds of interference signals which are outside the frequency table in the ideal situation.Measurement matrix is the key to compressed sampling, and the performance of the measurement matrix can be measured in several different aspects, like reconfigurable maximum compression ratio, signal to noise ratio loss of CS, and whether the background noise of CS information still maintain the features of white noise, all of which play important roles for the subsequent processing. As CS information is applied whether for signal detection or parameter estimation, the signal to noise ratio is required as large as possible. This dissertation analyzes the measurement matrix of compressed sampling in detail, proves the Equiangular Tight Frames (ETF) has the best performance in the above sense.In the practical process of frequency-hopping signal reconstruction, the frequency switching and symbol reversing may happen in any time in a CS frame. For the influence of frequency offset and instantaneous frequency extension which is caused by signal saltation, sparsity adaptive matching pursuit algorithm is appropriately modified and makes it more suitable for the practical application of frequency-hopping signal. At last, an efficient and rapid reconstruction method based on ETF is presented in order to adapt to the situation of real time signal reconstruction, and the reconstruction is very simple and fast for the low sparse signal.This dissertation mainly contains following four parts:first, introduces the principle and characteristics of frequency-hopping communication and the compressibility of frequency-hopping signal. The basic theory of compressed sampling is presented from the perspective of discrete signal, three typical implementation structures of analog information converter are introduced and the performance is numerically simulated. Second, studies the features of measurement matrix, analyzes several aspects to describe the performance. Then, in the view of frequency-hopping compressed sampling with combinational interference, a new frequency selective CS method is proposed which is based on the studies of several frequency-fixed suppression technologies. Finally, for the aspect of signal reconstruction, enumerates several existing algorithm, and proposes an efficient and rapid reconstruction algorithm for low sparse signal on the basis of ETF.