Sub-band divided ray tracing (SDRT) is one technique that has been extensively used to obtain the channel characteristics for ultra-wideband (UWB) radio wave propagation in realistic indoor environments. However, the computational complexity of SDRT scales directly with the number of sub-bands. Although we have proposed a low-complexity SDRT algorithm for one terminal position , the computational complexity i s still extremely high when involving multiple mobile terminal positions. Moreover, some indoor positioning techniques require for high positioning accuracy data from measurements/simulations with a very fine spatial resolution. To cope with this, we propose an algorithm to reduce the computational complexity of SDRT for multiple mobile terminal positions. The algorithm uses a projection of all propagation paths on a subspace spanned by two-dimensional discrete prolate spheroidal (DPS) sequences at each sub-band. It is important to note that, since the geometrical information of the propagation paths is the same in all sub-bands, the subspace dimension and basis coefficients in frequency dimension do not need to be recalculated at different sub-bands. We justify the simplifications of the proposed method by numerical simulations. Furthermore, we evaluate the effect of antenna characteristics on the proposed algorithm. Our proposed algorithm reduces the computational complexity by more than one order of magnitude for indoor scenarios.
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