Research On Technologies For Wide-Band Signal Adaptive Compressive Sensing

Compressive sensing is a popular topic which develops rapidly in recent years. It is based on the sparsity of samples, and uses compressed measurements to represent the samples, then utilizes effective recovery methods to reconstruct the original samples perfectly. In the field of signal processing, if signal expects to be reconstructed completely, the sampling rate must strictly satisfy the Nyquist sampling theorem, that is the rate is no less than twice of the signal bandwidth. But the processing power of communication equipment is limited, that makes it difficult to process wideband signals, fortunately, the compressed sensing theory provide a method which can be applied to handle the problem. In the field of signal processing, compressed sensing theory develops a new technology called compressive sampling, which makes it possible that on the premise of ensuring the complete reconstruction of the signal, the actual sampling rate is far less than the Nyquist sampling rate.In reality, the wideband sparse signal is time-varying, but usually it changes relatively little. If the sliding window is used to observe the signals, it can be found that there is a strong correlation between the signals in adjacent Windows. Under the hypothesis of short-term stationarity of wideband sparse signal, this paper will study adaptive recovery technique according to the different focuses. In this paper, the main contributions list as follows:1) Put forward an adaptive compressive sampling method used to adjust the number of measurements. In order to reduce the uncertainty of recovery performance brought by the randomness of the measurement matrix, the existing compressive sensing recovery algorithm will choose the measurement number as big as possible. This paper focuses on the wideband sparse signal, and provides a method which is used for adjusting the number of measurement adaptively and reducing it to a proper value quickly, at the same time the method ensures the precision of the recovered signal is within an acceptable range. The method does not simply add or subtract the value when it adjusts the number, but treats the problem as a numerical positioning problem, and the bisection method is used for rapid convergence.2) Put forward an adaptive kalman filtering recovery algorithm without a priori information. When we use the sliding window to observe the signals, there is a strong correlation between the wideband sparse signals in adjacent windows, and the signal can be recovered nicely by using ordinary kalman filtering algorithm. But the ordinary algorithm needs noise variance as a priori information, actually it is difficult to satisfy the conditions. In this paper, an adaptive algorithm is proposed, which does not need to know the noise variance in advance, on the contrary, it adopts a strategy which is convergent in the sense of probability, and update the variance dynamically in the process of recovery. And when the algorithm implements convergence, we compare the precision of recovered signal, there is little difference between the adaptive algorithm and the ordinary algorithm.