Channel Estimation and Synchronization with Sub-Nyquist Sampling and Application to Ultra-Wideband Systems

We consider the problem of low-complexity channel estimation and timing in digital ultra-wideband receivers. We extend some of our recent results on sampling of certain classes of parametric non-bandlimited signals and develop a frequency domain framework that yields high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. In particular, we show that the minimum required sampling rate in an UWB receiver is determined by the so-called {\em innovation rate}, which corresponds to the number of degrees of freedom of the received UWB signal. Our framework allows for faster acquisition compared to current digital solutions and potentially reduces power consumption and complexity of digital UWB receivers significantly. It is particularly suitable in applications such as ranging or positioning and can also be used for identification of more realistic UWB channel models, where different propagation paths undergo different frequency-selective mitigation.