Converting antenna and UE positions to spherical coordinates for gain calculation

Aliakber2k10 · Apr 10, 2015

Hi this is my first post here.
Sorry for this naive question xD

I want to calculate antenna gain for which I need the horizontal Φ and vertical θ angle of an antenna beam.
The formula for gain is.

$Three equations for antenna gain: horizontal pattern A_H(φ) = -min[12(φ/φ_3dB)^2, SLL] dB; vertical pattern A_V(θ) = -min[12((θ-90)/θ_3dB)^2, SLL] dB; and gain G = G_MAX - min{-[A_H(φ) + A_V(θ)], SLL}.$

is it ok to convert the rectangular coordinates of antenna into spherical coordinates and compute Φ & θ using standard equations (Cartesian to Spherical)

Equations giving Cartesian to spherical conversion: rho = sqrt(x^2 + y^2 + z^2); phi = arctan(y/x) = arccos(x/sqrt(x^2 + y^2)) = arcsin(y/sqrt(x^2 + y^2)); theta = arctan(sqrt(x^2 + y^2)/z) = arccos(z/sqrt(x^2 + y^2 + z^2)).

Similarly if there is a user in the cell can I calculate Φ & θ of user position, and then compute the relative difference and utilize it in the gain equation. i.e.

$Equations defining angle differences: Δφ_p = |φ_{b_i} − φ_p| and Δθ_p = |θ_{b_i} − θ_p|, where φ and θ are the horizontal and vertical angles of the base station and the user p.$

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Moreover is it also possible that i consider them in-terms of vectors and use inner product to compute the angles Φ & θ? e.g:

3D coordinate diagram in two panels, (a) Beam Vectors and (b) Position Vectors, showing base station and beam or user vectors with angles theta and phi relative to a z-axis and reference vector.

and their inner product which can be,

Handwritten-style typeset formulas: inner product a · b = |a| × |b| × cos(θ), then φ_bi = cos⁻¹(V_B'i · V_R / (|V_B'i| |V_R|)) and θ_bi = cos⁻¹(V_Bi · V_BS / (|V_Bi| |V_BS|)).

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I would appreciate any kind of help.

Thank you in advance. :)

marcusl · Apr 11, 2015

Hi and welcome to PF. I'm afraid it's not at all clear to me what situation you are analyzing, what you are trying to find, and how you are approaching the problem. Please explain your problem as though you are talking to someone (everyone here at PF in fact) who doesn't yet know what it is. And where did you get the first two equations? These do not look like general gain equations to me.

Converting antenna and UE positions to spherical coordinates for gain calculation

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