Fast prediction of a high directivity antenna characterization for future wireless communication based on terahertz photonics

Fast prediction of high-directivity antenna characterization has been presented. The Cassegrain antenna working at J band frequency has been evaluated using a terahertz (THz) photonic system based on near-field measurement. The generation and detection of THz signal are based on a non-polarimetric electrooptic (EO) frequency down-conversion technique combined with a self-heterodyne system. The synthesis method is introduced to estimate far-field E and H-plane antenna characteristics. The antenna result is calculated using amplitude and phase-synthesized data based on the measured data. A near-field (NF) to far-field (FF) transformation is employed in the antenna radiation pattern. The effect of blocking objects on the antenna (supporting rods and sub-reflector) is discussed. The antenna characteristics of the measured and synthesized data are compared to the ITU F.699 recommendation. The synthesized result agrees with the measured one on the main lobe angle.


Introduction
Millimeter wave and terahertz (THz) frequencies are envisioned as future 5G and beyond wireless technology [1][2][3].The drawback of using a higher frequency band is excessive loss compared to the existing lower band.One of the solutions is the utilization of a high-gain and high-directivity antenna, which can be achieved by a parabolic antenna, such as for backhaul link applications [4].However, the characterization of the antenna is not a trivial measurement due to the lack of a suitable far-field anechoic chamber.The near-field measurement is the main solution to that problem [5][6][7].
Several near-field measurements for a high-directivity parabolic antenna have been reported.The near-field system has been popular for antenna characterization because it does not need the conventional anechoic chamber.It does not require a large measurement room, which is difficult to prepare.The near-field to far-field transformation is used to obtain the antenna characteristic.A highgain antenna in the 300 GHz band for fixed wireless communication systems has been constructed [8].The two high-gain antennas, i.e., the offset parabolic and Cassegrain antennas, have been measured using a standard anechoic chamber.The near-field system is used to characterize the J-band antenna based on a self-heterodyne technique and a non-polarimetric frequency down-conversion technique [9].Previously, near-field measurement was also employed to investigate a high-gain Cassegrain antenna at a 300 GHz band based on photonics technology [10].This measurement has a disadvantage due to the long measurement time needed to achieve high-resolution.The resolution is dependent on how many samples will be collected to get a good result using the mechanical XY scanner.
Here, we propose a fast prediction of the high-gain parabolic antenna characterization based on the synthesis method.The amplitude and phase distribution of the measurement at 300 GHz have been synthesized using our algorithm, which mimics the two-dimensional near-field amplitude and phase distributions.The Gaussian wave is assumed to be the waveform-measured amplitude distribution.Then, the synthesized data on amplitude and phase distribution is applied to the near-field to far-field transformation to obtain the far-field antenna characteristic.This method is not only a fast method to obtain the antenna under test characteristics but can also be used to apply the various scenarios to the two-dimensional synthesized amplitude and phase distribution to obtain the result without doing the real measurement.The scenario used in the report is to analyze the effect of sub-reflector supporting rods.In the analysis, the far-field antenna results of the proposed method were compared to the measurement result and the ITU recommendation F.699 as a benchmark.
Previously, we investigated high-directivity antenna characterization based on near-field measurements [10,11].The generation of the THz signal using a self-heterodyne technique and a nonpolarimetric frequency down-conversion technique is depicted in Figure 1 [12,13,14].The two free running 1.55 μm laser diodes (LDs) are used to generate an optical beat signal.The frequencies of the laser diodes are set to be  1 and  2 ( 2 >  1 ).One of the two LDs (LD 1) is frequency-fixed at λ = 1550.04nm.The LD 2 is a frequency-tunable laser source.Therefore, the frequency of the beat signal (  ),   =  2 −  1 can be tuned.The frequency of LD 1 is shifted by an EO frequency shifter   = 100 kHz to realize self-heterodyne detection.A UTC-PD connected to a Cassegrain antenna was used as an optical-to-electrical (O/E) converter.A THz signal of 300 GHz was radiated into space through the antenna.
In the receiver, the detection of the electric field has been performed using a DAST (4′-Dimethylamino-N-Methyl-4-Stilbazolium Tosylate) EO crystal as the sensor with a dimension of 1 mm × 1 mm × 1 mm, mounted on a polarization-maintaining optical fiber (PMF).The sensor was placed 5 mm in front of the center antenna.The optical signal ( 1 and  2 components) reflected by a high reflection mirror placed at the surface of the DAST crystal was filtered by an optical bandpass filter (OF) and detected by a photodiode (PD).The frequency-converted signal was detected by a lockin amplifier with a time constant of 10 ms.We scanned the fiber-mounted EO sensor in the X-Y plane to measure amplitude and phase distribution in the near-field region in the area of 160 mm by 160 mm to capture a planar wavefront antenna.The Cassegrain antenna has been used in this investigation, as depicted in Figure 2. The antenna's main reflector has a diameter of 152 mm and four supporting rods to hold the sub-reflector.The subreflectors to reflect the signal have been placed in the center of the antenna.The horn antenna has been used as the feed antenna.The far-field antenna radiation pattern has been calculated based on nearfield measurement using a near-field to far-field transformation.The near-filed measurement is one of the solutions to overcome the difficulties of the conventional far-filed measurement of the antenna in term of the environment requirements.The requirement for far-field distance, 2 2 /, will span up to 46.2 m for the antenna, which is difficult to fulfill in a general measurement condition.

Antenna Characterization
The near-field to far-field transformation is one technique to obtain a far-field antenna radiation pattern.The amplitude and phase distributions in the radiating near field region are sampled by a scanning field probe, and then the measured distributions are transformed to the far field employing the Fourier transform.The Fourier transform algorithm was implemented using MATLAB based on 2D measured amplitude and phase distribution on flat-plane scanning.
However, such near a measurement also has several drawbacks.To obtain enough sampling resolution, according to the Nyquist sampling criterion,   ≥ 2  , the sampling has been determined by λ/4.This result is 640 x 640 sample points for λ = 1 mm in the 160 mm x 160 mm scanning areas.The measurement needs a long scanning time.It takes 12 hours to complete one measurement.The measurement complexity needs to be considered.The proof-of-concept in the laboratory has been successfully conducted.However, the requirements to obtain the portable system and outdoor usage encounter difficulties such as the availability of the required environment, the difficulty of setup measurement, and several bulky measurement tools involved.On the other hand, a numerical solution based on simulation software can be used to obtain the antenna characterization.However, the higher frequency and the larger antenna dimension require a lot of resources as well.The computation time also needs to be taken into account.The measurement system is based on a self-heterodyne electro-optic detection system.In the system, phase stability gained attention.The previous phase drift measurement for a short measurement (10 minutes) had results there was no phase drift in the system [14].This means that the measured phased distribution is introduced by the device under test only.This is a long measurement that takes about 12 hours to complete.There is a possibility of phase drift due to this long measurement, such as phase drift due to temperature change during the test as appeared on the phase measurement result or due to an internal noise system as appear in the measured phase distribution (the red color).

Fast prediction based on synthesis method.
As shown in Figure 3, the amplitude and phase distribution have been successfully measured.The effect of the sub-reflector and supporting rods has been seen in the result, which gives a special pattern on both amplitude and phase distribution.The far-field antenna characterization was calculated using a near-field to far-field transformation based on the amplitude and phase distribution data.Based on this calculation, the synthesis method can be performed to obtain a fast prediction of the far-field antenna performance using a near-field to far-field transformation.The proposed synthesis method is to replicate the amplitude and phase distribution intensity using software and then apply the same nearfield to far-field transformation to obtain the far-field antenna pattern.Here, the profiling amplitude and phase distribution are required.Both antenna patterns based on measured and synthesized methods were then compared.In addition, the proposed method can be used to evaluate the accessories of the antenna, such as the effect of supporting rods and sub-reflector.Not only the position of these objects but also the structure and dimension as well.

Profiling the amplitude and phase distribution
Profiling both amplitude and phase distribution intensity can be estimated using the center values of sample points.First, profiling the amplitude distribution employed the center value of the measured amplitude and phase sample point both horizontally and vertically.We assume that the measured amplitude distribution in a homogeneous circle is affected by the shadow profile from the supporting rods and subreflector reflector as a blocking object in front of the antenna.Taking one line of horizontal and vertical data, a two-dimensional (2D) Gaussian wave equation can be applied to estimate the 2D amplitude distribution of the measured data.Then, we can determine the amplitude distribution of the measured ones analytically using the synthesis method.The two-dimensional Gaussian wave equation is described by: where A and C were estimated from the measured amplitude distribution data.We calculated that the two-dimensional Gaussian wave equation for amplitude distribution is approached by Using equation 2, we can synthesize the amplitude distribution.
The profiling phase distribution is similar to the amplitude distribution.However, based on the measured phase distribution, the variation in the phase distribution is generally small.Intuitively, the phase distribution should be homogenous.The variation in the phase distribution of the measured data came from the noise of the system.So, we assume that the phase distribution is constant and homogeneous in the measured area.Figure 4 shows the synthesized amplitude and phase distribution using an analytical method based on equation ( 3).Here we compared the one-line center value of the synthesized data booth amplitude and phase distribution with the measured one.The result was a good agreement.

The effect of supporting rods and sub reflector
The synthesizing method can not only be used to replicate the amplitude and phase distribution but can also be applied to investigate the effects of other objects, such as supporting rods and sub-reflectors.We employ these advantages to investigate rods and sub-reflectors in the antenna.In a Cassegrain antenna, the sub reflector is placed in the center front of the antenna, which is supported by several supporting rods.There are four supporting rods used to hold the sub-reflector.The dimension of the sub reflector is 25.26 mm.The diameter of each supporting rod is 5 mm.The sub-reflector is placed 44 mm in the center front of the antenna.However, this distance does not affect the synthesized methods because this method does not consider the object distance to the antenna but rather captures the objects on the front of the antenna.The replica of both amplitude and phase distribution using the analytical method, shadowed with a blocking object, is depicted in Figure 5.The particular shadowed pattern of four supporting rods can be seen on each side.The generated patterns have been linearly assumed from the center to the outer edge of the antenna.However, this model is slightly different compared to the measured pattern, where from the center to the outer of the antenna the pattern goes slightly larger.To reduce the complexity of the analytical method, we simplified the models.On the other hand, the sub-reflector introduces a hollow pattern in the center of the antenna.The center of the antenna has low intensity and is almost like noise.In the synthesized model, we simplify by assuming that the center of the antenna is completely blocked by the sub-reflector no signal can be detected there.This leads to the hollow profile in the center of the antenna of the synthesized model.
We show that the synthesized model can be easily extended to various parameters on the blocking object, such as the number of supporting rods used in the antenna, the dimension of the sub-reflector and supporting rods, and the location of the blocking objects that can be modeled.

Far-field antenna radiation pattern
Figure 6 shows the comparison of the E plane and H plane far-field antenna characteristics among the measured and synthesized data compared to the ITU R F.699.The scenario of the synthesized data without any object blocking is the finest result.However, this scenario is not realistic.The second scenario uses synthesized data introduced by object blocking (supporting rods and sub-reflector).The side lobes do not vary much compared to the measured ones.As expected, we do not consider the noise signal in our model.However, the main lobe of the proposed method agreed with the measured data on narrow angles.Between two scenarios of the synthesized data (with and without the blocking object), there is a degree of discrepancy.The consideration of the dimension of the object affects the far-field result.On one side, this is a drawback of this methods, however, this method can be useful to investigate the effect of blocking objects in front of an antenna.The variation measured in the signal needs to be properly evaluated in the synthesized data to match the result.A well-known noise profile, such as Additive White Gaussian Noise (AWGN) can be applied to the synthesized data.

Conclusion
A fast prediction of a high directivity antenna characterization based on the synthesis method has been described.The investigation of a far-field Cassegrain antenna at 300 GHz has been studied using nearfield measurement.The synthesis method replicates the measured amplitude and phase distribution to calculate the far-field antenna characteristic.In addition, the effect of blocking objects in the front of the antenna, such as sub-reflector and supporting rods, can also be modelled using this method.The far-field results of several scenarios have been presented compared to the measured data and the ITU recommendation.The result has a high degree of match in the main lobe antenna for narrow-angle measurement.For the sidelobe, there are slight discrepancies from the measured one due to the simplification of the models.

Figure 3
displays the measurement result of the near field scanning, showing the amplitude and phase distribution.

Figure 3 .
Figure 3.The amplitude (a) and phase (b) distribution ant its properties at horizontal dan vertical center values.

Figure 4 .
Figure 4.The synthesized amplitude (a) and phase (b) distribution without blocking objects.

Figure 5 .
Figure 5.The synthesized amplitude (a) and phase (b) distribution with blocking objects.Diameter of supporting rods 5 mm and the diameter of sub reflector is 25.26 mm.

Figure 6 .
Figure 6.Far-field antenna pattern E Plane (a) and H Plane (b).