Appendix10.A.Range Analysis of UWB Signals Using Time of Arrival

Appendix 10.A. Range Analysis of UWB Signals Using Time of Arrival

Nathaniel J. August

UWB can determine location by measuring the Time of Arrival (TOA) of signals [4]. Note that there are many other methods for determining range, such as time difference of arrival (TDOA), angle of arrival (AOA), and their combined radiolocation methods. The Cramer-Rao Lower Bound (CRLB) indicates the low bound on a TOA estimate as [6]

Equation 10.A.1

where is the variance (or error) of the TOA estimates, b_f is the bandwidth of the received signal, and SNR is the energy per bit divided by the noise power (E_b/N₀). The CRLB for the ranging distance can be obtained as the product , where c is the speed of light (= 3 x 10⁸ m/sec). The equation indicates that the impact of the SNR to CRLB is linear, while the impact of the bandwidth is quadratic, thus making UWB a good candidate for accurate ranging.

Figure 10.A.1 shows CRLBs on the ranging error in terms of SNR for four different UWB bandwidths: 0.5 GHz, 0.75 GHz, 1 GHz, and 3.3 GHz. The figure indicates that precise location information can be obtained even for UWB signals near a minimum bandwidth of 500 MHz and at moderate-to-low SNR values.

Figure 10.A.1. Lower Bound of Ranging Errors.

SOURCE: W. C. Chung and D. S. Ha, "An accurate ultra wideband (UWB) ranging for precision asset location," Proc. 2003 IEEE Conference on Ultra Wideband Systems and Technologies [4]). © IEEE, 2003. Used by permission.

The basic process for ranging is as follows. First, the nodes synchronize to a reference clock. The reference clock may be a fixed universal reference like MSSI's PAL650 system [46], or the nodes may negotiate a local reference like Aether Wire's Localizers [50]. After synchronization, a TOA estimate for a received signal is obtained by detecting the peak of either (a) the original received signal or (b) the signal correlated with a template. A simple method of distance estimation is to multiply the time difference between two devices by the speed of light. However, due to noise and timing jitter, a single pulse may not provide an accurate estimation of distance. To overcome this error, one may estimate the average TOA of a train of pulses instead of a single pulse [4]. The time average of the received pulses reduces AWGN to enhance the accuracy. The use of multiple pulses increases the processing time, but the overall time required may still be a fraction of second.