Optimization of the Measurement Matrix Used for CS-based Non-reconstruction Detection Method in Cognitive Radio

Some scholars have been searching for the simplest and most efficient way of spectrum sensing. They have combined the compressed sensing (CS) based non-reconstruction technology with the conventional energy detection (ED) method and proposed a non-reconstruction detection method to detect the spectrum directly from the CS sampled data, these methods can decrease the sampling rate and computation complexity. But these methods assume that the measurement matrix is a Gaussian random matrix, it is hard to generate in a practical application and its detection performance has a big loss compared with the conventional energy detection method. In this paper we propose an iterative method to optimize the measurement matrix aiming at improving the detection performance. The Gram matrix of the optimized matrix will be closer to the identity matrix through iterative method. The simulation result shows that the optimized measurement matrix can improve the detection performance of the non-reconstruction detection method for about 2 dB compared with the Gaussian random matrix.