Ultra wide-band channel estimation and signal detection through compressed sensing

A novel algorithm(CS algorithm) for channel estimation and signal detection is proposed to resolve the problem of excessively high sampling rate of the ultra-wideband signals. The algorithm is based on the compressed sensing(CS) theory. The modulated signal is transmitted after random-filtering, and the received signal is sub-sampled. The mathematical model of CS is developed by cyclic convolution of the modulated signals, the random filter and the channel, so the basic pursuit algorithm can be utilized to perform the task of channel estimation and signal detection. Simulation results show that the number of the sampling data required by the proposed algorithm is only one-third or less of the number of the sampling data needed by the least squares algorithm, while the estimation performance is improved by 4.5 dB under the moderate signal-to-noise ratio(15~25 dB) condition, and that the original transmitted signals are correctly detected.