Design And Optimization Of The Measurement Matrix For Non-reconstruction Spectrum Sensing

Cognitive radio can improve the utilization of the spectrum and ease the scarcity of it. Spectrum sensing is the basis of cognitive radio. When we want to sample a broadband signal at Nyquist sampling rate, the existing analog-digital converter may not achieve the desired sampling rate. We can sample the signal using the compressed sensing(CS) theory at a low sampling rate and the CS sampled data still retain all the information of the original signal. The CS sampled data can recover the original signal through the reconstruction algorithm which has a high computation complexity.The non-reconstruction detection method can detect the spectrum directly from the CS sampled data so that the computation complexity is decreased. The measurement matrix is the basis of compressed sampling and it will affect the detection probability of the non-reconstruction detection method. In this paper, the measurement matrixes used for energy based non-reconstruction detection method and sparse decomposition based non-reconstruction detection method were designed. In addition, this paper studied the non-reconstruction detection method based on multi-antenna system and the advantage of the multi-antenna system can reduce the scale of the measurement matrix and improve the spectrum detection probability.For the energy based non-reconstruction detection method, this paper analyzed the distribution of energy of the signal and noise after compression and a principle that the Gram matrix of the measurement matrix should be as close as possible to unit matrix was proposed to design the measurement matrix. According to the proposed principle, this paper applied the iterative training method and the gradient method to optimize the Gaussian random matrix and the result was that the detection probability was improved. This paper also proposed the sparse decomposition based non-reconstruction detection method using the sparsity of the signal. A measurement matrix used for the proposed method was also designed and the simulation results showed that the method could achieve a good result when the signal was sparse. Besides, this paper extended the non-reconstruction detection method to multi-antenna system and designed the measurement matrixes for each antenna by “segment” the measurement matrix used for signal antenna. The scale of the measurement matrixes of each antenna was decreased so that the sampling rate of each antenna was decreased. The non-reconstruction detection method based on multi-antenna system can also improve the detection probability compared to the signal antenna system under Rayleigh channel.