Correlation Function Algorithm of Time-Hopping Sequences for TH-UWB

Time-hopping (TH) sequences play an important role in time-hopping ultra wideband (TH-UWB) communication systems. The proper measure for the performance of TH sequences is time-hopping correlation function (TH-CF). For TH sequences with a long period, the total number of computations to implement directly TH-CF will be huge, and it will increase very rapidly as the period increases. Hence, it is of practical interest to develop more efficient algorithm for computing TH-CF. In this paper, by transforming the decimal TH-CF into a binary one, a fast TH-CF algorithm is proposed on the basis of the well-known fast Fourier transform (FFT). The presented algorithm can obviously decrease the number of computations of TH-CF, which will result in significant improvement in the computer-based evaluation of TH correlation properties