Toeplitz Matrix for Compressed Multipath Channel Sensing

Reliable wireless communication often requires accurate knowledge of the underlying channel, so the channel estimation is needed. Many real-world channels tend to exhibit sparse multipath channels characterized by a relatively small number of nonzero channel coefficients. For sparse multipath channel estimation, conventional methods, such as the least squares, do not use the inherent low-dimension characteristics of these sparse channels, and the required length of the training sequence is comparatively long, so their estimation cost is comparatively large. The channel estimation method based on compressed sensing is able to take full advantage of the prior information of sparsity to obtain a better estimate with greatly reduced length of the training sequence. Combining the characteristics of the compressed sensing measurement matrix, it proves that when the length of the training sequence is not longer than the length of the channel impulse response and the number of rows is smaller than the number of columns in the Toeplitz measurement matrix, the measurement matrix still satisfies the restricted isometry property; and it proposes specific requirements of the matrix structure for the measurement matrix used in sparse multipath channel estimation. Simulation results verify the feasibility and practicality of the optimized measurement matrix.