Precise Timing for Multiband OFDM in a UWB System

Precise positioning is one attractive application of ultra wideband (UWB) systems. Its enormous bandwidth has generated high expectation on the spatial resolution that it could achieve. However, synchronization in the presence of dense multipath is challenging, since the first arrival is not necessarily the strongest one due to channel fading. It is unclear how high a spatial resolution can be realized in practical implementation, and how reliable it will be. We in this paper address practical synchronization algorithms for multiband OFDM UWB transmission, and analyze the performance of a maximum likelihood (ML) joint timing/channel estimation algorithm. We show that the probability of mis-timing in single band OFDM has only diversity order one. Most timing errors lie closely around the right timing, as we show that the probability of timing error equal to or greater than Delta having diversity order of min(Delta, L), where L the number of channel taps. We reveal the benefit of frequency hopping across multiple subbands that enables an N_B-fold diversity increase in timing performance, where N_B is the number of subbands used