Low-Sampling-Rate Ultra-Wideband Channel Estimation Using Equivalent-Time Sampling

In this paper, a low-sampling-rate scheme for ultra-wideband channel estimation is proposed. The scheme exploits multiple observations generated by transmitting multiple pulses. In the proposed scheme,
$P$
pulses are transmitted to produce channel impulse response estimates at a desired sampling rate, while the ADC samples at a rate that is
$P$
times slower. To avoid loss of fidelity, the number of sampling periods (based on the desired rate) in the inter-pulse interval is restricted to be co-prime with
$P$
. This condition is affected when clock drift is present and the transmitted pulse locations change. To handle this case, and to achieve an overall good channel estimation performance, without using prior information, we derive an improved estimator based on the bounded data uncertainty (BDU) model. It is shown that this estimator is related to the Bayesian linear minimum mean squared error (LMMSE) estimator. Channel estimation performance of the proposed sub-sampling scheme combined with the new estimator is assessed in simulation. The results show that high reduction in sampling rate can be achieved. The proposed estimator outperforms the least squares estimator in almost all cases, while in the high SNR regime it also outperforms the LMMSE estimator. In addition to channel estimation, a synchronization method is also proposed that utilizes the same pulse sequence used for channel estimation.