Energy conservation is a critical problem in recently-emerging wireless sensor networks (WSNs). Pulse position modulation (PPM), as an exploring-worthy modulation format for energy efficiency, is tailored for WSNs into two schemes, mono-mode PPM and multi-mode PPM, in this paper. Resorting to an idealized system model and a practical system model, which combine the power consumptions in transmission and reception modules of nodes with the idealized and realistic battery characteristics, the battery energy efficiencies of mono-mode PPM and multi-mode PPM are evaluated and compared. To minimize the battery energy consumption (BEC), these schemes are further optimized in terms of constellation size M for a link in path-loss channels. Our analytical and numerical results show that considerable energy can be saved by multi-mode PPM; and the optimization performances of these schemes are noticeable at various communication distances though their optimization properties are different.wireless sensor networks (WSNs), mono-mode PPM, multi-mode PPM, battery energy consumption (BEC), parameter optimization

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Abstract:We give the equivalence between perfect nonlinear functions and appropriate splitting semi-regular relative difference sets, construct a class of splitting relative difference sets by using Galois rings and bent functions, and prove that there exists a 4-phase perfect nonlinear function if and only if the number of input variables is at least twice the number of output variables. # 2005 Wiley Periodicals, Inc. J Combin Designs 13: [349][350][351][352][353][354][355][356][357][358][359][360][361][362] 2005

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Abstract. With the help of some p-adic formal series over p-adic number fields and the estimates of character sums over Galois rings,

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