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A time domain (TD) hybrid solution based on uniform theory of diffraction-physical optics (UTD-PO) is presented to analyze the multiple diffraction under nonline-of-sight (NLOS) environment where an obstacle causes shadowing of the transmitter from the receiver in wireless sensor networks (WSNs). The channel impulse response of the model is derived, which utilizes a recursion relation and does not need to incorporate the slope diffraction in the transition zone. The received signals can be predicted through a simple operation of convolution, which provides a faster and easier final solution for UWB radio propagation and significantly reduces the computational time. The TD result can be applied to analyze the UWB pulse distortion by multiple diffraction under NLOS environment in WSNs. Emerging of application of ultra-wide band (UWB) are foreseen for WSNs that combine low to medium rate communications over distances of 100m(1). When sensors are placed in different areas, a nonline-of-sight propagation is encountered very often, sometimes in military communications(2). During propagation in urban areas, UWB signals usually undergo double or multiple diffraction before they are received. The recent interest in the use of UWB technique has motivated the propagation analysis of UWB channel characteristics due to the fact that the propagation characteristics play a fundamental role in the design and implementation of the UWB systems(3). In the case of the UWB propagation, using the impulse response of a scattering object in the TD is more convenient than applying numerical inverse Fourier transform algorithms to convert frequency domain (FD) solutions into the TD, since the bandwidth of UWB signals is so large that the distortion of an UWB pulse is frequency dependent. Karousos and Tzaras(4) have presented a TD-UTD solution which successfully analyzes multiple diffraction through the incorporation of the slope diffraction. Nevertheless, it is difficult to apply their solution in multiple diffraction where the number of obstacles is large since their solution has to incorporate the slope diffraction(5) in the transition zone, which increases both the mathematical complexity and the computational efficiency of the solution. Han and Long(6) have presented a hybrid UTD-PO solution to derive the impulse response of Bertoni's urban propagation configuration where the transmitting antenna is located at a certain distance from the array of buildings with rectangular cross sections. In this paper, the work(6) is extended to another model, in which an array of knife edges are surrounded by an obstacle modeled as a knife edge, considering spherical-wave incidence. The impulse response of the channel is obtained and it is convolved with the transmitted pulse to produce the received signal for analysis the TD characteristics for the abovementioned model. Based on UTD-PO for multiple diffraction, the received signal may be seen as the average of possible signals from different knife edges, which avoids the incorporation of the slope diffraction. The predicted signal is compared with the numerical inverse fast Fourier transforms of the FD solution. The results show a very good agreement between the two solutions with our solution offering much shorter computation times due to a recursive relation in which only single diffractions are involved in the calculations.

Study on the multiple diffraction for UWB signals under NLOS environment in WSNs