Impulse response UWB time-delay estimation with low speed ADC using compressive sensing

Time-delay estimation of ultra-wide-band (UWB) signals arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel. Previous methods for time delay recovery either operate on the analog received signal, or require sampling at the Nyquist rate of the transmitted pulse. In this paper, we propose a system with low speed ADC and formulate time delay estimation as a compressive sensing problem. The framework we develop here leads to recovery of the multipath delays from samples of the channel output at the lowest possible rate. The sampling rate depends only on the number of multipath components and the transmission rate, but not on the bandwidth of the probing signal.