1. RESTORATION OF THE RET PHASE FUNCTION USING DECONVOLUTION Huajian Cui

2. Outline Why Deconvolution and ill-posed problems Methods and results Methods of measurements Brief introduction to the RET theory

3. Background of the research It is important to accurately predict excess loss when radio waves propagating through vegetation for Radiowave channel planner such as Ofcom Following a 15-month project to develop a generic model of 1-60 GHz narrowband radio signal attenuation in vegetation, Oct. 2002 A contract between the UK Radiocommunications Agency (RA) an a QinetiQ-led consortium comprised of QinetiQ, the Rutherford Appleton Laboratory (RAL), and the Universities of Portsmouth and Glamorgan

4. Convolution Distortion The received signal can be obtained by summing the arriving scattered radio waves from all directions with appropriate weighting Where P RX is the received directional spectrum, G RX is the radiation pattern of the receiver

5. Deconvolution Deconvolution is the inverse operation of the convolution Convolution theorem y(t) = x(t) * h(t) (1) Y(w) = X(w)H(w) (2) H(w)=Y(w)/X(w) (3) In practical applications, the deconvolution problem is mathematically classified as an ill-posed problem. The cause of the “ill-posed problems” occurring is that the information represented by the data (sequences) or the equations (continuous functions) are incomplete

6. Cause of the ill-posed problems Inaccuracy of sampling or digitisation and data acquisition process Natural variability of the signal Always present random noise

7. Deconvolution Methodology The optimum compensation iterative deconvolution The automated regularisation iterative deconvolution

8. Deconvolution Results

13. The RET Modelling The Radiative Energy Transfer Theory is an theoretical model utilised to predict the excess attenuation and directional spectra while radio waves propagating through vegetation. It can be expressed as follow:

14. Directional Spectra The theoretical directional spectra can be 3-D demonstrated as following based on mathematical calculations

15. The Phase Function The Phase Function is assumed to be Gauss-like, and expressed by: Graphical depiction its characteristics depending on various parameters

16. Other methods considered Maximum likelihood estimation Maximum/minimum entropy Monte Carlo method Finite element method Project onto convex sets Neural method