Best permutation search strategy for ultra-wideband signal acquisition

Recently, it was shown that equal gain combining (EGC) is a practical way of exploiting dense multipath in the ultra-wide band channel (UWB) to get better acquisition performance. By taking system performance subsequent to acquisition into account, it was shown that there are multiple phases (called the hit set) where a receiver lock can be considered as successful acquisition. In this case, the serial search may no longer be the optimal choice for the sequential search strategy in the acquisition system. We consider the set of all search strategies which are permutations of the search space and show that, in the low signal-to-noise ratio (SNR) regime, there exists an optimal permutation search strategy which minimizes the mean detection time. Furthermore, we show that this optimal strategy has a simple jump-by-H structure.