Adaptive Measurements Model For Compressed Sensing-based Wideband Spectrum Detection

As we all know, the spectrum is the quite valuable resource in wireless communication system. Some research shows that there exit plenty of spectrum holes among the whole frequency band. To relieve the shortage of spectrum, cognitive radio is proposed to utilize the spectrum more efficiently, which has attracted much attention these days. The first part of cognitive radio system is sampling the analog signal. However, according to Nyquist sampling theorem, it will be a challenge for hardware to sample the wideband signal. Since compressed sensing(CS) theorem has special advantages to process the sparse signal, it is widely used in spectrum sensing for wideband signal.According to CS theorem, if signal s is sparse, we could use an operator matrix to multiply the sparse signal. Meanwhile, it is possible to recover the initial signal using the observations. First, this paper introduces the CS theorem through three aspects: sparse representation, compressive measurement and signal reconstruction. And then two signal reconstruction algorithms are analyzed, followed by the simulations for one-dimension and two-dimension signals. The model for wideband signal sensing is proposed, in which the signal from primary user, the channel condition and the signal received by sensing user are designed. In order to sample the signal using CS theorem, two methods are discussed. After that, a sparsity evaluation algorithm is proposed and analyzed theoretically. Using the sparsity evaluation result, we can adjust the sampling rate. In order to detect the spectrum when the sparsity of signal is unknown, the spectrum detection algorithm for blind sparsity signal is proposed. Specifically, the iteration contribution is defined as the difference between residuals of two adjacent iterations. If the iteration contribution is under the threshold, the iteration is terminated. Compared with the traditional terminated condition, the proposed method is more accurate.According to CS, the reducing data of compressed sensing is at the expense of decreasing in SNR. This paper analyzes the input SNR and output SNR of compressed sampling system, and discusses the source of noise for the system. It is concluded that three parts(original SNR, the sparsity of signal and number of measurements) will influence the output SNR. Based on the analysis about SNR, we propose the method to adjust the number of measurements adaptively. Specifically, the standard is to ensure the same output SNR when other conditions change, which will guarantee the accuracy of spectrum detection. The simulations show that the proposed method can change the number of measurements for different input SNR and different sparsity of signal.