Ziv-Zakai Lower Bound for Impulse Radio Ultra-WideBand Ranging Error Based on Geometry of Indoor Environments

We consider the Ziv-Zakai lower bound for Impulse Radio (IR) Ultra-WideBand (UWB) ranging error under dense multipath environments and additive Gaussian noise. In contrast to previous work (for example and), our derived bound has following novel points: (1) Our derived bound depends on the geometry of the indoor environments of interest. The uniform distribution is a special case in our bound. (2) We do not introduce any approximation for our log-likelihood function during our derivation process. Therefore, we obtain a more accurate Ziv-Zakai lower bound for the IR-UWB ranging error with IEEE 802.15.4a channel models. (3) Based on the geometry of the indoor environments, we can find the "best" position of the base station which provides the lowest Ziv-Zakai lower bound of the IR-UWB ranging error. (4) Our derived bound can also be used in real environments with the channel measurements from real environments.