In ultra-wideband (UWB) communications, monobit receivers offer a low complexity implementation but at the same time exhibit a great performance loss. In this paper, a novel detection scheme, denoted as x-law detection (XLD), is proposed to diminish the performance loss caused by employing monobit analog-to-digital converters in transmitted-reference (TR) UWB receivers. Simulation results show that if the optimal value is employed for x, the XLD-based monobit weighted TR (MWTR) receiver can achieve 14.2~15.5 dB and 8~9.2 dB performance gain over the conventional MWTR receiver in LOS and NLOS scenarios, respectively. Moreover, the XLD-based MWTR receiver performance with the optimal value of x is only 1.6~3 dB away from the optimum MWTR receiver performance in intra-vehicle UWB channels. Additionally, the XLD-based MWTR receiver is not sensitive to the summation interval. This feature decreases the receiver complexity and guarantees a robust performance over different multipath channels. The significant performance improvement of the XLD scheme comes at a limited complexity increase. Thus, the XLD approach is a good candidate for TR-based and other training-based monobit receivers requiring low complexity, high performance, and low power consumption.