Signal Level Simulation Modeling for Antenna Array of Aperture Synthesis Radiometer Based on the Equivalent Complex Baseband Representations

Abstract

This paper presents a signal-level simulation model for simulating the process that antenna array of Aperture Synthesis Radiometer (ASR) collecting thermal radiation and transforming thermal radiation signal into radio frequency (RF) signal. By using the equivalent complex baseband signals to represent the practical thermal radiation and RF signals, simulation efficiency is improved significantly. The statistic characteristics of simulation results are found to match the corresponding theoretical analysis well. Results of an imaging simulation experiment show that this model can be employed in ASR system-level simulator design.

Appendix

This appendix is devoted to modeling the process that individual antenna element collecting spatial thermal radiation. It is a power transformation corresponding to the signal transformation of Part-2.

Assuming that the apparent brightness temperature distribution T _AP (θ, ϕ) which arrived antenna aperture is consisted of atmosphere element T _DN (θ, ϕ) and point source element T _p (θ, ϕ), the output brightness temperature of antenna is [1]:

$$T_A = \frac{1}{{\Omega _e }}\iint\limits_{4\pi } {T_{AP} }\left( {\theta ,\varphi } \right)F_n \left( {\theta ,\varphi } \right)d\Omega = \frac{1}{{\Omega _e }}\iint\limits_{4\pi } {T_{DN} }\left( {\theta ,\varphi } \right)F_n \left( {\theta ,\varphi } \right)d\Omega + \frac{1}{{\Omega _e }}\iint\limits_{\Omega _t } {T_p }\left( {\theta ,\varphi } \right)F_n \left( {\theta ,\varphi } \right)d\Omega $$

(16)

Where Ω _e is the pattern solid angle of antenna element, Ω _p is the solid angle of point source relative to antenna, F _n (θ, ϕ) is the normalized power pattern of antenna element.

In order to solve equation (16) numerically, antenna pattern is discretized. As it is shown in Fig. 4, θ and ϕ are divided into N and M equal divisions respectively. So the whole space is divided into N×M divisions with the solid angle of each division is:

$$\Delta \Omega _{ij} = \sin \theta _i \Delta \theta \Delta \varphi $$

(17)

Fig. 4

Antenna beam discreteness.

Where $\theta _i = i \cdot \Delta \theta$, i = 0, 1......N-1, $N \times \Delta \theta = \pi$

If N and M are large enough, the atmosphere brightness temperature distribution and normalized power pattern of antenna element are assumed to be constant T _DN (θ _i , ϕ _j ) and F _n (θ _i , ϕ _j ) respectively, in each ΔΩ _ij ; If the point source is far enough, Ω _p is less than ΔΩ _ij , so the brightness temperature of point source is assumed to be a constant T _p (θ _p , ϕ _p ) in Ω _p , where (θ _p , ϕ _p ) is the direction of point source. Under these assumptions, (16) is given by

$$T_A = \frac{1}{{\Omega _e }}\sum\limits_{i = 0}^{N - 1} {\sum\limits_{j = 0}^{M - 1} {T_{DN} \left( {\theta _i ,\varphi _j } \right)F_n \left( {\theta _i ,\varphi _j } \right)} } \Delta \Omega _{ij} + \frac{1}{{\Omega _e }}T_p \left( {\theta _p ,\varphi _p } \right)F_n \left( {\theta _p ,\varphi _p } \right)\Omega _p $$

(18)

Where $\varphi _j = \left( {j + \frac{1}{2}} \right) \cdot \Delta \varphi$, j = 0, 1......M-1, $M \times \Delta \varphi = 2\pi$

T _DN (θ _i , ϕ _i ) and T _p (θ _p , ϕ _p ) are derived from fabricated scene.

To discretely simulating the process that antenna collecting the spatial thermal radiation and making latter reconstruction process convenient, two point sources, whose radiation brightness temperature are T _DN (θ _i , ϕ _j )ΔΩ _ij and T _p (θ _p , ϕ _p )Ω _p respectively, are used to represent atmosphere radiation in ΔΩ _ij and point source radiation in Ω _p , respectively.