Bounds on performance of UWB TOA estimation using finite resolution quantization

Impulse radio ultra-wideband (IR-UWB) technology offers an accurate ranging ability by exploiting the time of arrival (TOA) information of the narrow pulse. However, capturing this sub-nanosecond (ns) width pulse in dense multipath environment requires expensive and power-hungry high performance analog-to-digital converters (ADCs) and complex digital signal processing. To reduce the complexity, a finite resolution (FR) receiver that limits quantization to only a few bits has been proposed recently. In this paper, we develop the Cramer-Rao lower bound (CRLB), as a guidance to evaluate the FR quantization influence on IR-UWB TOA estimation. Firstly we define the quantization efficiency and prove that a 2-bit (4-level) quantization is good enough for TOA estimation because it can reach 88% efficiency as a full resolution method. Subsequently, overlapping coefficient is defined to quantify the performance degradation caused by overlapping between the first path and the following multipaths. Finally, we introduce a sub-optimum but more practical FR quantization scheme whose performance asymptotically converges to optimum as the signal to noise ratio (SNR) decreases. FR quantization scheme is demonstrated to achieve a much higher feasibility while holding an acceptable accuracy loss.