Introduction Theoretical work Numerical results Propagation of signals from indoor small cells at ultra-high frequencies. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath March 26, 2018 Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Figure: Photograph by 1 1Rama. Wikimedia Commons Cc-by-sa-2.0-fr https://commons.wikimedia.org/wiki/File:Apple_II_IMG_4212.jpg . 2010. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results New technology Smaller cells. Higher frequency. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results The Problem The Aims Create an accurate and efficient model to simulate indoor-to-indoor ultra-high frequency wave propagation in a domestic environment. (2.4GHz upto 30 GHz and higher) This model should give an idea of the coverage in an environment where not all parameters are known. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Mathematical motivation Propagation model equation 1 The Helmholtz 1 models wave propagation, � 1 − |∇ S ( x ) | 2 � k 2 ∇ 2 u ( x )+ u ( x ) = 0 ∇ 2 φ ( x ) + k 2 φ ( x ) = 0 . (1) Then for k → ∞ , this gives the Eikonal equation 2 . Using a WKB approximation, |∇ S ( x ) | 2 = 1 . φ ( x ) = u ( x ) e ikS ( x ) (3) (2) 1Michel Cessenat. Mathematical Methods in Electromagnetism: Linear theory and applications . Vol. 41. World scientific, 1996 2Zhengqing Yun and Magdy F Iskander. “Ray tracing for radio propagation modeling: principles and applications”. In: IEEE Access 3 (2015), pp. 1089–1100 Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Mathematical motivation Propagation model equation 1 The Helmholtz 1 models wave propagation, � 1 − |∇ S ( x ) | 2 � k 2 ∇ 2 u ( x )+ u ( x ) = 0 ∇ 2 φ ( x ) + k 2 φ ( x ) = 0 . (1) Then for k → ∞ , this gives the Eikonal equation 2 . Using a WKB approximation, |∇ S ( x ) | 2 = 1 . φ ( x ) = u ( x ) e ikS ( x ) (3) (2) 1Michel Cessenat. Mathematical Methods in Electromagnetism: Linear theory and applications . Vol. 41. World scientific, 1996 2Zhengqing Yun and Magdy F Iskander. “Ray tracing for radio propagation modeling: principles and applications”. In: IEEE Access 3 (2015), pp. 1089–1100 Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Mathematical motivation Propagation model equation 1 The Helmholtz 1 models wave propagation, � 1 − |∇ S ( x ) | 2 � k 2 ∇ 2 u ( x )+ u ( x ) = 0 ∇ 2 φ ( x ) + k 2 φ ( x ) = 0 . (1) Then for k → ∞ , this gives the Eikonal equation 2 . Using a WKB approximation, |∇ S ( x ) | 2 = 1 . φ ( x ) = u ( x ) e ikS ( x ) (3) (2) 1Michel Cessenat. Mathematical Methods in Electromagnetism: Linear theory and applications . Vol. 41. World scientific, 1996 2Zhengqing Yun and Magdy F Iskander. “Ray tracing for radio propagation modeling: principles and applications”. In: IEEE Access 3 (2015), pp. 1089–1100 Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Ray-tracing theory Field strength loss Friis transmission equation 1 : Loss at reflection: - r the distance from the source - The Fresnel reflection coefficient 1 , is a function of the to receiver, - λ the wavelength , permittivity and permeability of the mediums, � λ � � � | u r | = | u ∗ 0 | G a G b . � 4 π r u ref u in � �� � = R ���� ���� � . � Gain’s ���� ���� ���� Field Field of the strength strength Field strength Fresnel Field strength antennas at emitted reflection after reflection into reflection receiver at source coefficient 1Alejandro Aragon-Zavala and Simon R. Saunders. Antennas and propagation for wireless communication systems . John Wiley & Sons, 2008 Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Ray-tracing theory Phase change Destruction from phase change occurs but needs detailed environmental knowledge to calculate deterministically. Using a random model is just as good an approximation as a deterministic model given the environment changes. It is also quicker to compute. Phase change occurs at reflection and summation of rays. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Ray-tracing theory Phase change Destruction from phase change occurs but needs detailed environmental knowledge to calculate deterministically. Using a random model is just as good an approximation as a deterministic model given the environment changes. It is also quicker to compute. Phase change occurs at reflection and summation of rays. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Ray-tracing theory Phase change Destruction from phase change occurs but needs detailed environmental knowledge to calculate deterministically. Using a random model is just as good an approximation as a deterministic model given the environment changes. It is also quicker to compute. Phase change occurs at reflection and summation of rays. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Ray-tracing theory Phase change Destruction from phase change occurs but needs detailed environmental knowledge to calculate deterministically. Using a random model is just as good an approximation as a deterministic model given the environment changes. It is also quicker to compute. Phase change occurs at reflection and summation of rays. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Ray-tracing implementation Figure: The room layout before ray tracing Figure: The rays propagating from two different sources. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Field strength Figure: The field strength over the environment unbounded Figure: The field strength over the environment bounded Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
Introduction Theoretical work Numerical results Field strength with phase change (a) Unbounded (a) Unbounded (a) Unbounded (b) Bounded (b) Bounded (b) Bounded Figure: No phase change Figure: Phase change on reflection Figure: Phase change on reflection and summation. Hayley Wragg Supervisors: Prof. C. J. Budd, Dr. R. Watson Industrial supervisors: Dr. K. Briggs, Dr. M. Fitch University of Bath Propagation of signals from indoor small cells at ultra-high frequencies.
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