Optimizing tracking loops for UWB monocycles

This paper explores a correlation timing detector for tracking of Ultra-Wide-Band (UWB) monocycle signals. We seek to examine the optimal relationship between the received and reference UWB monocycle waveforms considering timing jitter and the ability to acquire lock. We modeled the received UWB monocycle waveform as the n^th order derivative of the Gaussian function. We are able to obtain a good fit using the UWB model with n=4 to both UWB impulses measured in an anechoic chamber and UWB impulses obtained in an indoor office environment. The UWB monocycle model, though an idealized representation, allows us to derive a closed form expression for the slope of the characteristic function of the TLL when both the received and reference monocycle are of arbitrary and different orders n and m. Using this compact formula, we can analyze the timing jitter of the error-tracking TLL in an additive white Gaussian noise (AWGN) channel. Computer simulation is also used to examine the dynamics of the tracking process when the loop is second order. Notably the phase plane plot is examined that gives us an indication of the ability of the TLL to acquire lock. The analysis allows us to make informed choices of the order of the monocycle waveform considering trades-off between timing error variance due to AWGN in the channel and the ability of the TLL to acquire lock. We conclude this paper by discussing a possible automatic gain control (AGC) scheme, whose main purpose is to remove the dependence of the TLL on variations in input signal amplitude.