Abstract
In wireless communication, the travelling electromagnetic (EM) wave nature of the signal is not reported comprehensively in the literature. To date, the majority of reported work analyzed the nature of the signal propagating through the channel in time and frequency domains only, whereas the travelling EM wave which is actually propagating through the channel, has both time and spatial dependencies. Very little work has been reported in which this aspect of EM wave is being analyzed, but the time dependency of frequency and spatial dependency of propagation constant associated with the EM wave have not been included, which will affect the performance of the channel in practical conditions. In this paper, all these aspects of EM wave and channel are considered to define a new method (DDT-FRFT) to analyze the travelling EM wave for wireless communication.
Highlights
The fractional Fourier transform FRFT is an integral transform defined in time-frequency plane, that is, it can be considered as a generalization to the Fourier transform FT with an order or power parameter a
A new dual-domain transform based on fractional Fourier transform DDTFRFT has been proposed
Simulation results shown above are in the conformity of this statement, because at angle parameter “α” associated with FRFT having value of “π/2”, that is, the case of Fourier transform, the transformed quantity does not have a clear peak Figure 1, while for α 0.2, a clear peak is observable in the magnitude response of DDT-FRFT of travelling wave Figure 2
Summary
The fractional Fourier transform FRFT is an integral transform defined in time-frequency plane, that is, it can be considered as a generalization to the Fourier transform FT with an order or power parameter a. The travelling wave has been analyzed with the help of dual-domain transform DDT-FT 13 , by transforming the travelling wave expression twice, first from time domain to frequency domain and second in spatial coordinate domain to propagation constant domain, by considering transform method as Fourier transform in both cases. The results of this transform are applied to estimate the transfer function of a wireless communication channel with multiple phase shifts, and, has been established that the channel acts as a band pass filter in both the frequency domain and the propagation constant domain.
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