Optimal Selection of Fourier Coefficients for Compressed Sensing-Based UWB Channel Estimation

In this letter, we propose a compressed sensing-based approach for channel estimation in wireless ultra-wideband (UWB) communication systems. The channel is estimated from a minimum number of received signal Fourier coefficients, using a measurement matrix dependent on the transmitted waveform. The optimal subset of coefficient locations, which lowers the coherence of this matrix and maximizes the reconstruction performance, is derived. Furthermore, additional constraints are considered on the subset, to allow the corresponding coefficients to be recovered with a low-complexity sub-Nyquist sampling scheme, as well as to enhance the reconstruction stability to noise. The performance improvement of the UWB channel estimation is demonstrated and the proposed approach is validated using both simulated and measured signals from an experimental setup.