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The problem of initial acquisition of ultrawideband (UWB) signals in the dense multipath channel is addressed. We demonstrate the advantages of designing the acquisition system so that the size of the uncertainty region is a Fibonacci number and propose a simple search strategy for coarse synchronization that uses no channel knowledge, extending a previous work where we proposed a method based on the golden section, which practically achieved the minimum mean acquisition time (MAT) under a simplistic model. We derive the MAT of the new strategy for this model and compare it with simulation results for a realistic propagation scenario with a high signal-to-noise ratio (SNR). There is an agreement between the theoretical and simulated MATs, which is limited by the differences between the two models. Simulations from moderate to high SNRs confirm that the proposed strategy provides a simple way to achieve the performance of the best strategies for acquisition of wide-bandwidth signals. In particular, it is similar in terms of complexity and performance to the popular bit reversal search, thus providing alternatives in the choice of design parameters wherever the bit reversal search is advisable.