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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 by1

• 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 The Helmholtz equation1 models wave propagation, ∇2φ(x) + k2φ(x) = 0. (1) Using a WKB approximation, φ(x) = u(x)eikS(x) (2) 1 k2 ∇2u(x)+u(x)

• 1 − |∇S(x)|2

= 0 Then for k → ∞, this gives the Eikonal equation2. |∇S(x)|2 = 1. (3)

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 The Helmholtz equation1 models wave propagation, ∇2φ(x) + k2φ(x) = 0. (1) Using a WKB approximation, φ(x) = u(x)eikS(x) (2) 1 k2 ∇2u(x)+u(x)

• 1 − |∇S(x)|2

= 0 Then for k → ∞, this gives the Eikonal equation2. |∇S(x)|2 = 1. (3)

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 The Helmholtz equation1 models wave propagation, ∇2φ(x) + k2φ(x) = 0. (1) Using a WKB approximation, φ(x) = u(x)eikS(x) (2) 1 k2 ∇2u(x)+u(x)

• 1 − |∇S(x)|2

= 0 Then for k → ∞, this gives the Eikonal equation2. |∇S(x)|2 = 1. (3)

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:

• r the distance from the source

to receiver,

• λ the wavelength,

|ur|

• Field

strength at receiver

= |u∗

0|

• Field

strength emitted at source

• GaGb

Gain’s

• f the

antennas

λ 4πr

• .

Loss at reflection:

• The Fresnel reflection

coefficient1, is a function of the permittivity and permeability of the mediums, uref

• Field strength

after reflection

= R

• Fresnel

reflection coefficient

uin

• Field strength

into reflection

.

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 (b) Bounded Figure: No phase change (a) Unbounded (b) Bounded Figure: Phase change on reflection (a) Unbounded (b) Bounded 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.

Introduction Theoretical work Numerical results

Comparing results

(a) No phase change vs phase change. (b) Phase change at reflection vs phase change at summation. Figure: Residuals for the unbounded results. (a) No phase change vs phase change. (b) Phase change at reflection vs phase change at summation. Figure: Residuals for the bounded 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

Distributions of the results

(a) Unbounded (b) Bounded Figure: Phase change on reflection and summation. (a) Unbounded (b) Bounded Figure: Histograms 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

Distributions of the results with phase change

(a) Unbounded (b) Bounded Figure: Phase change on reflection and summation. (a) Unbounded (b) Bounded Figure: Histograms (a) Values unbounded (b) Values bounded Figure: Cumulative distribution 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

Advantages of ray-tracing

Fast implementation ≈ 8 seconds. The results are not specific to just one environment.

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

Future work

Random reflection coefficient. Distribution research. Location of obstacles to also be random. 3D improve upon the layered result. Consider the contribution from diffracted and refracted rays. Analyse results. Compare an easy domain to HE for validation. Eventually look at using the model to optimise cell location.

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

Questions Any questions?

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.