Near-Field Calibration Methods for Integrated Analog Beamforming Arrays and Focal Plane Array Feeds

Active millimeter-wave beamforming arrays and focal plane array antennas require extensive calibration to compensate for impairments, such as phase and gain variations between elements, as well as unintended coupling between changes in gain and phase. When far-field calibration methods are used for calibrating focal plane array antennas, the required size of the anechoic chamber is exceedingly large. For this reason, a near-field calibration method for millimeter-wave analog beamforming array antennas and focal plane array antennas is proposed. Nonidealities of the beamformer integrated circuits with vector modulators are taken into consideration, and a way to reduce the measurement set for vector modulators with high resolution is proposed. This method is both practical and achieves a good calibration as evidenced by measurements of the radiation patterns, and it is suitable for use in an automated factory calibration setup. The important trade-off between the radiated power and side-lobe level is highlighted.


I. INTRODUCTION
I N FUTURE 5th generation (5G) and 6th generation (6G) wireless networks, a primary goals is to increase the data rates that can be achieved for mobile devices. One of the important innovations to achieve this, is moving towards millimeter wave (mmWave) frequencies. For example, the frequency range of interest for mmWave 5G is FR2, denoting the range from 24.25 GHz to 52.60 GHz. In this frequency range several GHz of spectrum is available that can be used to increase the channel bandwidths.
In order to overcome the additional path loss and increased attenuation at these frequencies, it is a requirement that the base-stations utilize arrays of antennas that can steer beams towards the user equipment. The main technology that is currently being developed, is planar antenna arrays based on patch antenna elements, where each element is connected directly to phase shifters and variable gain amplifiers, or to vector modulators (VM's). This way the phase and gain for each element can be individually controlled. In the simplest form, which is currently the solution furthest in its development, a power divider distributes the single RF input to each VM. Sometimes the array contains multiple power dividers, one per orthogonal polarization for example. Because the beamforming is performed by changing the phases and gains using the VM's instead of digitally altering the baseband inputs themselves, this is called analog beamforming. More advanced designs include hybrid beamforming or digital beamforming, which offer increased spectral efficiency at the cost of complexity and/or power use [1].
To overcome the increased path loss and attenuation by objects and rain at mmWave, planar antenna arrays require hundreds or even thousands elements, depending on the frequency range. The focal plane array antenna (FPA) is a proposed technology that can overcome this challenge [2], [3], [4]. The FPA is an antenna system consisting of a beamforming antenna array such as the one used in this paper, and a reflector or lens system. For analog beamforming arrays and focal plane array feeds, it is required to characterize the array in order to find the optimum gain and phase settings of the VM's to achieve the desired beam shapes. We refer to this as calibration of the array. For analog beamforming arrays, several characterization and calibration methods based on far-field measurements have already been reported. In this paper we discuss these present methods and their limitations, and propose to calibrate antenna arrays in a planar near-field setup instead. In addition, we propose a method that can reduce the total measurement time significantly for arrays with high resolution VM's. The planar near-field setup leads to reduced mechanical complexity, where only the probe antenna is moving and not the device under test. This allows for automated calibration of phased array antennas, analog beamforming array antennas and FPA antenna feeds, such as in a production line environment. For the FPA antenna feeds this is especially useful since the feeds can be calibrated separately in a small anechoic environment, rather than in large antenna range, where the system including the reflector would be calibrated as a whole. Currently, there are no practical factory calibration methods reported in literature for FPA systems based on analog beamforming array feeds.
Obtaining the calibration data set is not the entire story. It is also important to investigate how the calibration data should be used to calibrate the system. An important question, for example, is what strategy should be chosen when there is a large amplitude variation over the array elements due to imperfections in the electronics. If one element radiates more than average, we may reduce its power, but the other way around is not possible. When the entire array is scaled to the lowest performing element for example, the most rigorous calibration is achieved, but the total radiated power is reduced. If this is not desired, one could also choose to only calibrate the phases of the elements and not the amplitudes. Doing so may result in an increased side-lobe level (SLL). To shed light on these trade-offs, we investigate several such methods and compare them in terms of SLL and radiated power in this paper.
The calibration methods proposed in this paper are experimentally verified using a dual polarized 8-by-8 beamforming array, with a frequency range of 24.25 GHz to 27.5 GHz and a wide-scan parabolic toroid reflector with a width of 0.6 m [5]. The array is shown in Fig. 1(a), and the complete FPA system is shown in Fig. 1(b). The array utilizes (MMW9014K [6]) 8-channel beamforming chips, 4 channels per polarization. The two power dividing networks (one per polarization) are shared by the Tx and Rx chain. We use the array with the obtained calibration data to show the applicability of the procedure for calibrating FPA's for the first time.
The paper is structured as follows. In Section II a review of existing literature on beamforming array calibration is done. In Section III the near-field measurement setup is described and a characterization of the array is performed. A strategy is described and tested that can be used to decrease the measurement time. In Section IV the calibration strategies used in the paper are discussed. The measurement results with the array are shown in Section V. With the obtained calibration values, the array is used as an FPA antenna feed and the full system is characterized in the near-field test range. The measurement results are shown in Section VI. A discussion and subjects for future work are given in Section VII and the work is concluded in Section VIII.

II. LITERATURE REVIEW
In this section we expand on the literature concerning beamforming array characterization and calibration techniques.
For analog beamforming arrays, several characterization and calibration methods based on far-field measurements or coupling between elements have already been reported [7], [8], [9], [10], [11], [12], [13], [14]. Most methods result in a limited set of data, being a single complex coefficient that describes the offset in gain and phase of one element relative to the other elements in the array. However, an important limitation to these concepts that it does not take into account that the actual gain and phase do not always change predictably when changing the gain or phase settings. For example, changing the gain setting can lead to a difference in phase (gain-phase coupling) and vice-versa (phase-gain coupling). This effect must be accounted for when these coupling mechanisms become significant. This means that a complex coefficient should be obtained for each gain or phase setting that is available, for each element in the array. This can be cumbersome for arrays with for example 8-bit VM's (256 gain and 256 phase steps).
In addition, the measurement methods discussed in [7], [8], [9], [10] all rely on far-field methods. For large planar arrays and for FPA systems, issues arise with these measurement methods. As the array becomes larger, the required spacing between the probe and the array increases, since the Fraunhofer distance is increased. This means that the room must become larger, which can be costly. As the spacing is increased, the path loss becomes restrictive, impacting the signal to noise ratio (SNR) negatively. This reduces the accuracy of the measurement, especially for the lower gain settings of the VM. Lastly, taking a full two-dimensional radiation pattern measurement in the far-field, which is useful for verifying the calibration is working as intended, can be difficult with planar arrays and FPA's, since most anechoic measurement chambers rely on rotating the antenna around at least one of it's axes. When there are many connections to the array (one or multiple RF, DC, control, water cooling tubes) this can be too restrictive. Instead, we propose a measurement strategy which can be entirely performed in a near-field setup. This reduces the chamber size, increases the SNR and simplifies the setup because the antenna system does not need to rotate around any of its axes.
As a first step, it is worthwhile to investigate if it would be possible to completely omit calibration. In [15] it is claimed that it is possible to build arrays that do not require calibration to achieve good performance. Here a peak gain difference between elements of the array of ±2 dB and a peak phase difference between elements of the array of ±20 • is reported, which is not out of the ordinary. In the paper it is claimed that these errors have a negligible effect on the performance, based on a simulation with random errors in the aperture. Despite this claim, we expect that if the array were calibrated, a non-negligible performance improvement would occur, in part because some errors in the array are not random but structural. For this reason we compare the effect of performing no calibration at all, to various calibration strategies in terms of the effect on SLL and radiated power in Section V.
Methods to self-calibrate the array using the mutual coupling are presented in, among others, [11], [12], [13], [14]. Here measurements are taken by having one element sweeping through its gain and phase settings, while having a neighbouring element observing the changes in gain and phase. This method can be used in the field to continuously calibrate the array. These methods have been experimentally verified using vector network analyzers (VNA's) for taking S-parameter measurements. For calibration in the field this would require hardware to be present in the antenna system to accurately measure the gain and phase. More limiting facts are that the self-calibration technique requires that it must be possible to transmit and receive simultaneously with neighbouring elements or tiles. This would imply that the Rx and Tx paths have separate beamforming networks [11], which is not the case for arrays such as the one used in this paper. This limitation can be circumvented by using the orthogonal polarizations of the array as in [12], [13]. Here elements of one polarization can be used to characterize the elements of the other polarization. However, it must still be possible to transmit on one polarisation while receiving on the other [11], which is also not possible with this array. In addition, the methods presented in these papers rely on symmetries in the array [12], because the mutual coupling between the two ports of the two neighboring elements must be the same, which is not always the case for dual (H/V) polarized antenna arrays based such as the array that is used here.
A method that has attracted much attention is the rotating element electric field vector method [10], or REV in short. To summarize, this method works by placing the array in the far-field, and turning on all the elements. Then, by changing the amplitude and phase of a single element, the change in the measured total electric vector is used to find the contribution of that individual element. The benefit is that the array is being used in a setting where all elements are active, which is the most realistic scenario. To an extent, the mutual coupling and temperature effects are taken into consideration. However, the effect of the coupling depends on the beam steering angle, so this method only works well if it is performed at multiple angles, necessitating rotating the array around its axis in a far-field measurement setup.
For the reasons mentioned above, a calibration strategy in the near-field is most desirable for analog beamforming arrays and FPA feeds.

III. VECTOR MODULATOR MEASUREMENTS
In this section the measurement procedure for measuring the gain and phase responses of the antenna elements is described. Results are shown that highlight impairments of the array which are typical for arrays in this frequency range.

A. THE MEASUREMENT PROCEDURE
Measurements of the VM's are performed in the near-field setup shown in Fig. 1(a). For each measurement, the probe is aligned with the antenna element under test at a distance of 5 wavelengths and an S-parameter measurement is performed for several VM settings. This process is fully automated and can be run for all elements, in Tx and Rx, without action from the operator. The only action that must be taken is to switch the input cable between H-pol and V-pol inputs, but with a 4-port VNA or by using a mechanical switch both ports can be connected at the same time, removing the need for switching any cables during the measurement. The motors of the near-field system allow for aligning and rotating the probe automatically.

B. MEASUREMENT RESULTS
An example of a result for a single element at 24.0, 26.0 and 27.5 GHz is shown in Fig. 2. Here the measured constellations in transmit mode (Tx) and receive mode (Rx) are shown, along with a unit circle as a reference. From the figures a couple things become clear.
• The measured responses are 'egg-shaped'; a sweep across the phase at the highest gain setting does not appear circular. By sweeping the phase, the gain also changes, showing phase-gain coupling is present. This effect is more noticeable in Tx mode. • The gain sweeps are not straight lines. By sweeping the gain, the phase is also changes, showing gain-phase coupling is present. This effect is more noticeable in Rx mode. • The amount of gain-phase coupling is dependent on the frequency, especially in Rx mode. Therefore it is necessary to carry out this calibration at multiple frequency points when a calibration across a wide band is desired.  In addition to these effects, the measured gain is dependent on the frequency. This is shown in Fig. 3. Here the power transfer is shown, normalized at 24.0 GHz, for both Tx and Rx mode. It becomes clear that the power transfers are frequency dependent, which is another indication that the calibration should be carried out at multiple frequency points when a calibration across a wide band is needed.
Finally, the power transmitted is different for each element. Under the highest excitation, some elements can radiate several dB more power than others. This can have several reasons, such as inequalities in the split network, errors due to manufacturing tolerances, and to an extent, errors in the measurement itself. The distribution of the radiated powers at 26.0 GHz is shown in Fig. 4. Here the mean power transfer is normalized to 0 dB. From this figure it can be seen that 4 Tx mode elements radiate 2.0 dB less power than average, while 1 element radiates 2.5 dB more than average. To achieve a low SLL it is necessary to calibrate the array such that each element radiates close to the same amount of power. The only way to accomplish this is to attenuate the strongest elements by reducing the gain setting, reducing the effective isotropic radiated power (EIRP) in the process. The same reasoning holds for the Rx case, where reducing the gain settings reduces the overall Rx gain of the array.

C. MEASUREMENT INTERPOLATION AND INTERPOLATION ERROR
The array being used in this paper has 8-bit VM's, meaning it has 256 possible gain settings and 256 possible phase settings for each of the 64 elements. Each element is dual polarized and given the Tx and Rx responses are different, this would require 256 2 · 2 · 2 · 64 = 16.8 million measurements per frequency point to perform the calibration. This is not feasible and instead we opt to measure a smaller number of gain and phase settings, and interpolate the measured responses so that the full resolution can be used.
The question then becomes how many samples are required for the interpolation, and how much error is caused by it. In order to quantify this, one element was measured in both Tx and Rx mode with all available steps. This serves as a reference (S ref ). This response is taken and samples are left out to resemble a reduced measurement size. Then it is interpolated back to the full grid (S interp ) and compared to the reference in terms of the root-mean-square (RMS) error. The RMS error E RMS can be expressed in terms of an error vector as in where M is the number of points in the constellation. This is done for multiple choices of the number of measurement point, running from only 12 total measurements to 576 total measurements. The best results were achieved using cubic interpolation across the gain sweeps, and spline interpolation across the phase sweeps. The results for a single element and at one frequency point for both Tx and Rx can be seen in Fig. 5. Here we see that more measurements are required to reconstruct the constellation in Rx than in Tx. In Rx more gain measurements are required, which is due to the gain-phase coupling, which can be seen in Fig. 2. In the remainder of the paper we used 16 phase and 5 gain measurements for each element, which is a good trade-off between low error (around 1.2 % for both Tx and Rx) and measurement time.

IV. ANTENNA ARRAY CALIBRATION TECHNIQUES
In this section the used calibration techniques are discussed. To show how tapering influences the SLL and the EIRP, it is shown how tapering can be applied on top of calibration.

1) NO CALIBRATION
Fist, no calibration is performed. The excitations of the array are set according to rounded to integers. Here the w vector represents the complex excitation weights, with the length of the vector equal to the number of elements in the array. In this case we expect poor SLL but a high radiated power because none of the elements are scaled back. All elements are set to the maximum gain setting of 255 and a phase setting of 0.

2) PHASE-ONLY CALIBRATION
With phase calibration, the gain setting is still in accordance with (2), but the phase settings are chosen such that the expected phase response is as close as possible to the wanted phase response. This is done by looking up the optimum setting from the interpolated VM measurement results. With respect to the no-calibration method, the SLL is improved and the power is improved as well since the array is now radiating in-phase. Since none of the elements are scaled back this is expected to be the highest EIRP scenario. An additional benefit is that VM's only need to be characterized at the maximum gain setting, significantly decreasing the measurement time.

3) PER-ANTENNA GAIN AND PHASE CALIBRATION
With this method both the gain and phase are calibrated. The gain and phase settings are chosen such that the expected complex weight most closely matches the wanted complex weight. Furthermore, the weights are scaled according to where the R min |gain = 255 vector, having a length equal to the number of elements in the array, represents the lowest measured gain response of each element in the full phase sweep, under the condition that the gain setting is maximum, 255 in this case. The • symbol denotes an element-wise multiplication. This scaling results in a reduction of power if the VM responses appear egg-shaped as in Fig. 2, but the benefit is that the coupling between sweeping in gain and phase is removed. This strategy is expected to further improve SLL but the EIRP is decreased. The gain and phase settings associated with w corrected can be found using gain settings = round(|w corrected | · 255) phase settings = round ∠w corrected 2π · 255 .

4) FULL CALIBRATION
The full calibration is the most aggressive one in the list.
Here the array is completely calibrated such that the amplitudes per element are equal across the entire array. As such we have to scale the weights such that w corrected,n = w max|w| · min(R min |gain = 255) where min(R min |gain = 255) is a single value which represents the lowest measured response gain of all elements in the array, in the full phase sweep, under the condition that the gain settings are set to 255. In essence this means the array is scaled to the least performing channel. As such, a significant reduction in EIRP is expected if one of the channels performs poorly. On the other hand, the SLL is expected to be optimized since the amplitude distribution across the array is now flat. The associated gain and phase settings can be found using (5) and (6).

5) POWER SCALING CALIBRATION
Since the full calibration is expected to reduce the EIRP significantly, we take an intermediate approach, where the amplitudes of the responses are calibrated in such a way that at most 1 dB, 2 dB or 3 dB of transmitted power is lost. The transmitted power can be estimated using P Tx, estimate = N n=1 |w n | 2 (8) with N the number of elements in the array. The initial weights are found using (7) and the power estimate is computed using (8). As a reference, the highest possible relative power that can be transmitted with an optimal array that requires no calibration, is when w n = 1 for all N, resulting in P Tx, reference = N. From this point, we can iteratively decrease the excitation weights until the power estimate is reduced by the wanted amount. This calibration scheme leads to an improvement in SLL with a limited loss in power and represents a trade-off between calibration and power.

B. TAPERING IN COMBINATION WITH CALIBRATION
In order to decrease the SLL further than what can be achieved by calibration alone, a taper can be applied. A popular taper to use is the Taylor taper [16]. The taper choice is free from the calibration choice. In this case we show the situation where a full calibration is applied, with a successive −20 dB Taylor taper. The taper imposes an additional power reduction of approximately 4 dB. The intention of full calibration is to achieve a flat amplitude distribution across the array, by scaling back the most powerful elements. In the case of the Taylor taper, this is not necessary. Instead, the power should be scaled such that the amplitude distribution follows the taper. This is beneficial if the weaker elements reside on the edges of the array. This method we refer to as joint taper and calibration.

V. PATTERN MEASUREMENTS, SLL AND RADIATED POWER RESULTS
For each of the proposed calibration strategies, the weights and settings are calculated in order to shape a beam in the (0 • , 0 • ) direction. A planar near-field scan is performed with a subsequent transformation to the far-field in order to calculate the radiation pattern. For details about the implementation of the near-field to far-field transformation, as well potential sources of error for both the planar near-field measurement and traditional far-field measurements, the reader is referred to [17] and [18]. The resulting gain settings for each method are shown in Fig. 6. In Fig. 6(a), 6(b) the phases are shown instead, since the gain settings are all 255. It is clear that the gain settings depend significantly on the calibration strategy. Most notably, when moving from no amplitude calibration or per-antenna calibration to a full array calibration, the gain is significantly reduced. In addition, the Taylor taper further reduces the gain by 4dB. The joint taper and (full) calibration gives a small benefit in this regard. The radiation patterns for each method are shown in Fig. 7. Here it becomes clear that the calibration does have an effect on both the peak and the average SLL. The full calibration method has the lowest SLL. When a Taylor taper VOLUME 4, 2023 865 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. is applied, the SLL is further reduced. The joint taper and calibration gives almost the same SLL. The directivities are annotated for each case. It is interesting to note that the directivity slightly increases as the calibrations become more strict. For example, the phase calibration case has a directivity of 22.6 dBi where a full calibration case has an improved directivity of 22.9 dBi. By finding the magnitude of far-field pattern in the (0 • , 0 • ) direction we obtain an indication of the difference in EIRP between the cases. The results are summarized in Fig. 8. Here the measured power (y-axis) is normalized to the phase-only calibration case. The x-axis shows the calculated power sum as in (8). A linear fit shows that the calculated power sum and measured power are directly related as the slope of the fitted line is 1.09. Several things stand out from the figure.
• Calibrating only the phases of each element increases the gain of the array by more than 2 dB without drawback in power, showing that not calibrating the array is not a good option if high performance is desired. • The full calibration strategy reduces the power by 5 dB, which is very restrictive. • The joint Taylor taper and full calibration outperforms the separate calibration and taper by approximately 1.8 dB.
The mean SLLs across the highest 4 side-lobes are compared in Fig. 9, with the measured power on the x-axis. Here we see a clear relation between the power in the far-field pattern and the SLL. A couple things stand out from this figure.
• Calibrating the phase leads to a significant reduction in SLL and in addition increases the power, compared to performing no calibration at all. • The full calibration approaches the theoretical value of −13 dB for the SLL. However it is not reached indicating that there are further impairments in the panel that are not accounted for. The cost in terms of power is comparatively high. • The joint and taper calibration method increases the power without a significant SLL reduction.
In general these observations show that changing the excitation weights in order to achieve a lower SLL comes with an unavoidable reduction in EIRP. The only exception is the calibration procedure where only the phases are calibrated while leaving the gain settings as high as possible.

VI. FOCAL PLANE ARRAY CALIBRATION AND MEASUREMENTS
In this section, the antenna array is characterized using the suggested near-field approach, in the same measurement setup as in Fig. 1(a). It is then utilized as a feed for an FPA antenna, as shown in Fig. 1(b). The reflector is a parabolic toroid reflector with a scan range of ±30 • in azimuth. As a reference, the array is excited such that it produces a Gaussian beam which excites the reflector. The excitation beam has a −10 dB taper at θ = ±14 • with respect to its boresight. This corresponds to the design criterion of the reflector [5]. The casing of the array is removed because it is too large to fit below the reflector.

A. MEASUREMENT RESULTS
For each of the proposed calibration strategies, the weights and settings are found to shape a beam in the (0 • , 0 • ) direction using the Gaussian excitation. A near-field scan is performed with a subsequent transformation to the far-field in order to calculate the radiation pattern. The resulting gain settings for each method are shown in Fig. 10. The phase settings are omitted here for brevity. The resulting radiation patterns for each method are shown in Fig. 11. For the FPA measurements the directivity is almost the same for all calibration cases, with a 0.1dB improvement over the no calibration case. The notated directivity is compensated by a 0.4 dB spillover loss, which was estimated through simulation in [4].
For each of the strategies the radiated power relative to the phase calibration only case is calculated using (8). These results are shown in Fig. 12. What stands out from this result is that the calculated power according to (8) and the measured peak magnitude of the far-field are on a line with a slope of 0.99, similar to the phased array measurements in Section V. This shows that (8) can also be used to estimate changes in EIRP of the FPA system, depending on the excitation weights. In addition, the difference between calibrating only the phase and not calibrating at all is only 0.3 dB. In this case, calibrating the phase even leads to a decrease in measured power instead of an increase. This is in stark contrast with the result from Section V where a 2 dB power increase is observed in the phased array case.
To expand on the effect of the calibration, the SLL is shown with respect to the calculated power sum in Fig. 13. From this figure it becomes clear that calibrating the phases of the elements of the FPA system can reduce the SLL by 2.7 dB, but further calibration does not lead to a significant improvement anymore. This can also be observed from the patterns in Fig. 11, as the patterns are very similar in shape except from the un-calibrated case.  In general, for the FPA case, the calibration of the gain of the elements is not necessary for achieving a good SLL. In addition, if the SLL is not important, then the FPA system does not necessarily require any calibration since it does not lead to an increase in EIRP. Thus, calibration of an FPA feed is less critical than for a planar array.

VII. DISCUSSION AND FUTURE WORK
A detailed description of calibration strategies in the nearfield for analog beamforming arrays and FPA's are given and the results are used to compare them in terms of power and SLL. As evidenced by these measurements, it is possible to make a trade-off between the two. However, the best SLL that can be achieved by these methods is limited by the performance of the array itself. For example, in Fig. 7, the SLL is not the same for the primary four side-lobes, which would be expected if the calibration can indeed produce a flat aperture distribution. What is not taken into account is that the embedded element patterns can be different for each element, and that the casing of the array can contribute to the radiation patterns in an unexpected way. To show this, we back-transformed the measured near-field of the full-calibration case to the aperture using the holography method [17]. The result is shown in Fig. 14. The physical aperture size is shown by the blue square. The aperture distribution inside the box is quite flat, but there are still some low areas which highlights that further improvement may be possible. Interestingly, outside of the box, there are also some regions with high power, which are likely caused by reflections or refractions from the environment or from the casing. These unexpected contributions will increase the SLL. In order to reduce this effect, the case can either be designed to reduce this effect, or the calibration should take (measurements of) the embedded elements into account. This however significantly increases the measurement time.

VIII. CONCLUSION
A measurement procedure for calibrating beamforming array antennas and FPA antenna systems was proposed. The full characterization can be completed in a planar near-field setup, rather than in a more conventional far-field setup. This has several benefits, as no rotation of the antenna under test is required, and the test range is small. This makes it suitable for automated testing and for factory calibration.
In the proposed procedure, nonidealities of the beamformer integrated circuits with VM's are taken into consideration by addressing differences in gain and phase between elements. Gain-to-phase and phase-to-gain coupling is addressed as well. Based on interpolation of the measured near-field data, the measurement set can be significantly reduced for high-resolution VM's. A mmWave 5G array was effectively calibrated with an error of only 1.2% by measuring only 16 phase steps and 5 gain steps, out of the 256 possible gain steps and 256 possible phase steps, and interpolating this result.
Using the acquired measurement data, the array is calibrated according to several strategies, showing that there is an important trade-off in improving the SLL and lowering the EIRP. Calibrating only the phases of the array leads to an improvement in radiated power of 2dB and a reduction in SLL of 2.7dB. This shows that calibrating the phase is highly desirable, omitting calibration completely leaves valuable performance on the table. Further SLL improvements can be obtained by calibrating the array such that the amplitudes of the elements become equal, but this leads to a decrease in EIRP.
The described measurement procedure is suitable for calibration of FPA antenna systems. Instead of a calibration of the system as a whole, including the reflector, the feed can be characterized and calibrated separately. This keeps the near-field antenna test range small and automated testing or factory calibration remains a possibility. The effect of calibration of an FPA antenna is different compared to the planar array case. Calibrating only the phases changes the power by approximately 0.3dB, while the SLL improves by 2.7dB. calibration of the gain reduces the power significantly, without worthwhile improvement of the SLL. We can conclude here that calibration of the phases is required to achieve a good SLL with an FPA antenna, but calibrating the gains is not required. If the only concern is radiated power, then calibration of an FPA system is not necessary at all.
In general, the proposed measurement and calibration method is both practical and effective, and is suitable for use as a factory calibration procedure in an automated testing environment, for planar beamforming array antennas and FPA antennas.