Low complexity ultra-wideband ranging in indoor multipath environments

Modeling Distance and Bandwidth Dependency of TOA‐Based UWB Ranging Error for Positioning

“…m(B, d) becomes larger for smaller B, since in this case, the number of nonresolvable multipath components that follow the direct path increases, resulting in more bias. At the same time, the bandwidth dependency becomes more evident with larger d. In fact in LOS, for increasing d, the direct path tends to have less weight with respect to the total signal, since the path loss exponent corresponding to the first path power is close to 2 [8], while that corresponding to the total power is usually between 1 and 2 [8], thus smaller; this means that multipath is more deteriorating for the resolvability of the direct path for larger d. Moreover, by increasing d, the distance difference between the direct path and the reflected ones tends to decrease, making the nonresolvable multipath more dense. For NLOS, the distance and bandwidth dependency of m(B, d) can be explained with similar arguments; its significantly larger values compared to LOS, even for larger B, are due to the additional delay introduced by the propagation through dielectric materials.…”

Performance Evaluation of a Low-Complexity Receiver Concept for TOA-Based Ultrawideband Ranging

“…However, due to the large number of multipath components, this variation is very small and therefore can be neglected in the analysis. Realistic values of S TP for different bandwidths can be found in [27]. Under this hypothesis, the energy in s 1 and s 2 are given in (21) and (22), shown at the bottom of the page, respectively.…”

“…Unfortunately, the IEEE models [28] do not provide an accurate statistical characterization for S FP . For this reason, results in [27] are used to evaluate (11), where a characterization of S FP for typical indoor office environments is provided. It is shown that it can be modeled as a zero-mean log-normal RV with standard deviation σ S FP , which depends on the bandwidth.…”

“…From simulations, E n MAX can be approximated as a Gaussian RV. 5 The last step to evaluate (27) is to determine the pdf of E MAX1 = max{E s 1 , E n MAX } and of E MAX2 = max{E s 2 , E n MAX }. Based on [30], E MAX1 and E MAX2 can be approximated as Gaussian RVs; considering, for example E MAX2 , the exact expressions for its mean μ MAX2 and variance σ 2 MAX2 are, respectively, as follows:…”

“…The received noise power in a 3-GHz bandwidth is P N = −174 dBm/Hz + 10 log 10 (3 · 10 9 ) ≈ −79.2 dBm. The link margin can now be calculated considering P MAX T ≈ 26.4 dBm and a minimum FPNR MIN = 10 dB, and observing that the first-peak path loss exponent n FP is approximately 2 in LOS propagation [27]. From the relation L FP = −10 log 10 ((c/ (4πf 0 d)) n FP ) ≤ P MAX T − P N − F P NR MIN , results in d MAX ≈ 300 m. It is worth noting that while the fine TOA estimation is based on the first peak, which propagates with path loss exponent n FP , the coarse acquisition step is based on the total signal, which propagates with path loss exponent n TP .…”