Polarization Model for 60 GHz

1. Polarization Model for 60 GHz Date: 2009-04-02 Authors: Alexander Maltsev, Intel Corporation

2. Abstract This contribution presents a polarization model proposal for 60 GHz WLAN Systems Alexander Maltsev, Intel Corporation

3. Polarization Model • Polarization impact for 60 GHz is significant because even NLOS (reflected) signals remain strongly polarized (i.e. coupling between orthogonal polarization modes is low) and cross-polarization discrimination (XPD) is high even for NLOS signals. • The polarization of signals is changed by reflections and different types of antenna polarizations provide different received power for various signal clusters (e.g., LOS, first-order reflection, second-order reflection). • Therefore, support of polarization characteristics in 60 GHz WLAN channel models is very important. Alexander Maltsev, Intel Corporation

4. Polarization Impact Modeling • Polarization is a property of EM waves describing the orientation of electric field E and magnetic intensity H orientation in space and time.The vector H due to properties of EM waves can always be unambiguously found if E orientation and the direction of propagation is known. So the polarization properties are usually described for E vector only. • In order to support polarization impact in the channel model, polarization characteristics of antennas and polarization characteristics of the propagation channel should be introduced. Alexander Maltsev, Intel Corporation

5. Antenna Polarization Properties • In the far field zone, the electric vector E is a function of the radiation direction (defined by the azimuth angle  and elevation angle  in the reference coordinate system) and decreases as r-1 with increase of the distance r. • Vector E is perpendicular to the propagation direction r and can be decomposed into two orthogonal components: E and Eφ that belong to the planes of constant φ and constant  angles, respectively. • Knowledge of E and Eφ of the radiated signal (which may be functions of φ and ) fully describes polarization characteristics of the antenna in the far field zone. Alexander Maltsev, Intel Corporation

6. Polarization Description Using Jones Vector • Wave polarization can be described using Jones calculus introduced in optics to describe polarized light. In general case Jones vector is composed from two components of electric filed of EM wave. • The Jones vector e is defined as the normalized two-dimensional electrical field vector E. The first element of the Jones vector is reduced to the real number. The second element of this vector defines phase difference between orthogonal components of the E field. • For example, for antenna polarization model the orthogonal components of Jones vector are defined for Eand Eφ components respectively. Alexander Maltsev, Intel Corporation

7. Examples of Antennas Polarization Description Using Jones Vector Alexander Maltsev, Intel Corporation

8. Polarization Characteristics of Propagation Channel • With the selected E field bases (Eand Eφ components) for TX and RX antennas, the propagation characteristics of each ray of the propagation channel may be described by channel polarization matrix H. • In this case, transmission equation for one ray channel may be written as: • Where x and y are transmitted and received signals, eTX and eRX are polarization (Jones) vectors for TX and RX antennas, respectively. • Components of polarization matrix H will define gain coefficients between Eand Eφ components at the TX and RX antennas. • Matrix H includes the attenuation of the signal due to reflection. To separate the reflection attenuation (reflection coefficient) impact, matrix H may be normalized by its largest singular value. Alexander Maltsev, Intel Corporation

9. Polarization Characteristics of Propagation Channel (Cont’d) • For LOS signal path matrix HLOSis the identity matrix. • For NLOS (reflected) paths, H has more complex structure. • The model for NLOS channel polarization matrix is defined based on the following considerations: • It is known that reflection coefficients are different for E field components belonging (parallel) to the plane of incidence and for perpendicular to the plane of incidence. Also these coefficients depend on the incident angle. The theoretical coupling between parallel and perpendicular components is zero for plane interfaces but due to non-idealities (roughness) some coupling always exists. • Therefore, the polarization matrix for the given first-order reflected signal path may be found as a product of a matrix that rotates E vector components from the coordinate system associated with TX antennas to the coordinate system associated with incident plane. Next, a matrix with reflection coefficients (and cross-polarization coupling coefficients) is applied followed by a rotation of the coordinate system associated with RX antenna. Alexander Maltsev, Intel Corporation

10. Polarization Channel Matrix for First Order Reflections • The figure shows an example of the first order reflected signal path. • Equation shows a structure of the channel propagation matrix for the case of the first order reflected signals. • The reflection matrix R includes reflection coefficients R and R|| for perpendicular and parallel components of the electric field E and E || respectively. • Elements 1 and 2 in matrix Rare cross-polarization coupling coefficients Alexander Maltsev, Intel Corporation

11. Polarization Channel Matrix for Second Order Reflections • To obtain polarization channel matrix for the second order reflections, additional rotation and reflection matrices are added. Alexander Maltsev, Intel Corporation

12. Polarization Impact Model Development Methodology • To develop polarization model the following methodology is proposed: • Define elements of reflection matrix R. It may be found from experiments [1] or theory (Fresnel formulas) • Perform ray-tracing of interesting environments (conference room, cubicle environment, and living room) with taking into account geometry and polarization characteristics of the propagation channel • Define channel polarization matrices H for different types of clusters and make statistical models approximating empirical distributions of matrices elements [1] K. Sato et al, “Measurements of Reflection and Transmission Characteristics of Interior Structures of Office Building in the 60 GHz Band”,IEEE Trans. Antennas Propag., vol. 45, no. 12., pp.1783-1792, Dec. 1997. Alexander Maltsev, Intel Corporation

13. Example of Polarization Characteristics for Conference Room Channel Model • To demonstrate the proposed approach, reference results were generated for the conference room channel model. • The R and R|| elements of the reflection matrix R were obtained using Fresnel formulas. The cross-coupling elements 1 and 2 of matrix R were taken equal to zero. • 3D ray tracer with polarization support was used to generate multiple realizations of channel polarization matrices H for different types of clusters (with taking into account the information about the reflection incident angles and rotation angles needed to perform all geometrical transformations). Alexander Maltsev, Intel Corporation

14. Reflection Coefficients Dependence on Incident Angle • The figure shows graphs of reflection coefficients vs. incident angle for parallel and perpendicular polarizations for the interface between regions with the refraction indices n1 = 1 and n2 = 2. • Reflection coefficients are calculated using Fresnel formulas: where inc is an incident angle Alexander Maltsev, Intel Corporation

15. Channel Polarization Matrix Coefficients Distribution for the First Order Wall Reflections • For the first order reflected signals from walls the plane of incidence is horizontal. • Since zero cross-polarization coupling coefficients were used in the ray-tracing model, there is no coupling between horizontal and vertical polarized signals. • The reflection coefficients may be both positive and negative to correctly model circular polarization. • The obtained results may be used to generate final statistical models (by approximating the graphs and taking into account major statistical dependences). Alexander Maltsev, Intel Corporation

16. Channel Polarization Matrix Coefficients Distribution for the First Order Ceiling Reflections • For the first order reflected signals from ceiling the plane of incidence is vertical. • Also there is no coupling between Eand Eφ components. • The signs of reflection coefficients (diagonal elements) has changed relatively to the case of the first order reflections from walls. • If circularly polarized antennas are used then TX and RX antennas with different handedness will have approximately matched polarization characteristics. (The same applies to the first order wall reflections). Alexander Maltsev, Intel Corporation

17. Channel Polarization Matrix Coefficients Distribution for the Second Order Walls Reflections • For the second order reflected signals from walls the plane of incidence is horizontal. • Also there is no coupling between different polarizations. • Both reflection coefficients (diagonal elements) have approximately same distributions. Alexander Maltsev, Intel Corporation

18. Channel Polarization Matrix Coefficients Distribution for the Second Order Wall-Ceiling Reflections • The second order reflections from wall-ceiling go through two reflections from wall and ceiling or from ceiling and wall. • As a result, there is a non-zero “geometrical” coupling in matrix H (coupling between components Eand Eφ of the TX and RX antennas) even though cross-polarization coupling coefficients or matrix R are taken to be equal to zero. Alexander Maltsev, Intel Corporation

19. Conclusion for Polarization Model • The concept to introduce polarization characteristics into the channel model is proposed. • The proposed approach based on calculation of channel polarization matrix H for each cluster in the channel model with taking into account reflection properties of the surfaces (reflection matrix R) and ray tracing geometry • As an example, the polarization model for the conference room is considered. Alexander Maltsev, Intel Corporation