This paper presents a theoretical analysis for the accuracy requirements of the planar polarimetric phased array radar (PPPAR) in meteorological applications. Among many factors that contribute to the polarimetric biases, four factors are considered and analyzed in this study, namely, the polarization distortion due to the intrinsic limitation of a dual-polarized antenna element, the antenna pattern measurement error, the entire array patterns, and the imperfect horizontal and vertical channels. Two operation modes, the alternately transmitting and simultaneously receiving (ATSR) mode and the simultaneously transmitting and simultaneously receiving (STSR) mode, are discussed. For each mode, the polarimetric biases are formulated. As the STSR mode with orthogonal waveforms is similar to the ATSR mode, the analysis is mainly focused on the ATSR mode and the impacts of the bias sources on the measurement of polarimetric variables are investigated through Monte Carlo simulations. Some insights of the accuracy requirements are obtained and summarized.
Recently, the weather radar community has paid much attention to the polarimetric phased array radar (PPAR) due to its agile electronic beam steering capability, which has the potential to significantly advance weather observations [
As shown in [
Although the weather radar polarimetry has matured for years, there are some challenges for the planar polarimetric phased array radar (PPPAR) [
The array configuration and spherical coordinate system used for radiated electric fields.
Usually, there are two operation modes chosen for weather observations, the alternately transmitting and simultaneously receiving (ATSR) mode and the simultaneously transmitting and simultaneously receiving (STSR) mode. Each mode has its advantages and disadvantages. With a “perfect” antenna, the STSR mode is vastly superior to the ATSR mode in the worst-case polarimetric/spectral situations. Thus, the STSR mode is the preferred mode from a meteorological standpoint. However, both the theoretical analysis and measurement experiments have shown that the STSR mode has higher accuracy requirements than the ATSR mode. This paper is mainly focused on the ATSR mode as it is simple for the analysis.
The remainder of this paper is organized as follows. Section
The coordinate system and array configuration are shown in Figure
We consider the array has a
The element pattern in a dual-polarized phased array can be written as
For a practical dual-polarized antenna element, the cross-polarization components
Figure
Dual-polarized
Channel imbalance and channel coupling.
For each element, we use a
Similarly, the channel isolation CIS can be defined as
The array transmission pattern
The mutual coupling between array elements is complicated so that a thorough analysis of the mutual coupling usually includes the full-wave electromagnetic computation and measurement experiments, which is beyond the scope of this paper. Moreover, for a large array, most of the elements are far from an edge. Therefore, except for the phase center displacement, all of the central element patterns are nearly the same. So it is reasonable to use the array average element pattern to replace the single element pattern. Hence,
For a point target with the polarization scattering matrix (PSM)
The received voltage matrix for distributed precipitations can be expressed as an integral. Consider
Assuming
the intrinsic differential reflectivity
According to (
An array with perfect
For the transmission pattern, the radiation power is principal. Thus, a uniform illumination is applied. For the reception pattern, a beam with low sidelobes is desired. Here, we choose the Taylor weighting. So
According to Appendix, we know that the upper bound of
First, we analyze a simple case to get some insights towards
The relation between
Using the same procedure, the average ICPR is derived in (
The relation between
From Figures
As revealed in [
Array parameters.
Array size |
|
Elements separation |
|
Sidelobe level of |
|
Specify the polarization distortion calibration error
Generate
Calculate
Calculate
Calculate
The simulation parameters are listed in Table
Simulation parameters.
|
0 dB |
|
|
|
0.01 |
|
|
|
|
Arg |
|
Arg |
|
Arg |
|
The ranges of
The model parameters of a pair of crossed dipoles in the beam direction (60°, 45°).
|
|
|
| |
---|---|---|---|---|
|
0.0000 |
|
|
0.99 |
|
0 | 0 | 0 | None |
|
1.1526 |
|
0.0007 | 0.99 |
|
0.5769 | 0.0000 |
|
0.99 |
The model parameters of a pair of crossed dipoles with the length of
|
|
|
| |
---|---|---|---|---|
|
|
|
0.0076 | 0.99 |
|
0 | 0 | 0 | None |
|
|
|
0.0003 | 0.99 |
|
2.3362 | 0.0000 |
|
0.99 |
Figures
We then set
With imperfect
First, we analyze the case with a single spherical scatterer in the beam direction
Figure
In order to evaluate the bias under different conditions, we use the Monte Carlo simulation method again, which is shown below.
Specify
Generate
Generate
Calculate
Calculate
Figures
We then set
The impact of the channel coupling on
The impact of the channel coupling on
In the STSR mode, the received voltages for distributed precipitations are expressed as
The orthogonal waveforms are usually employed to improve the polarimetric performance [
In practice,
Once the waveforms
In this paper, we analyze the accuracy requirements of a PPPAR in the ATSR and STSR modes. Among many factors, we focus on the polarization distortion due to the intrinsic limitation of a dual-polarized antenna element, the antenna pattern measurement error, the entire array patterns, and the imperfect
The polarization distortion calibration error
The finite beamwidth considerably affects the measurement of
In the STSR mode, if orthogonal waveforms are applied, the analysis is the same as that in the ATSR mode. Otherwise, the measurement performance may be worse than that in the ATSR mode. In the future research, those ignored factors could be taken into account to have a better understanding about the accuracy requirements of a PPPAR.
The measured element pattern
The calibrated element pattern
For a well-designed antenna element, the copolar patterns are larger than the cross-polar patterns. In addition, since
Since the relative error is more essential to represent the measurement accuracy than the absolute error, we define the relative error upper bound
For a well-designed antenna element, (
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grant nos. 61201330, 61490690, and 61490694. The authors sincerely express their gratitude to the anonymous reviewers.