Highly Efficient Calibration of Antenna Arrays by Active Targets in the Near-Field

To enhance the capabilities of high-resolution imaging or beamforming, the trend goes towards arrays with high-channel count and large aperture sizes. The operation at increasing mm-wave frequencies exacerbates the consequences of manufacturing tolerances on the array performance, further necessitating the development of high-quality calibrations. Thereby, a large number of array response vectors, addressed in the following as data points, is stored. Typically, one data point is measured at a time for each angle. To reduce the calibration effort, hereby defined as the number of required measurements, a calibration setup employing active calibration targets (ACT) is proposed. This setup allows the storage of a multitude of data points within a single measurement. In addition, this measurement setup is placed in the near-field of the array to relax the requirements on the size of the anechoic chamber. Employing multiple targets makes it challenging to compensate the near-field effects. Therefore, methods are discussed to ensure a consistent quality of the calibration considering the near-field influences from the ACTs. Exemplary measurements deploying an antenna array operating at 78.5 GHz demonstrate that this calibration measurement setup employing three ACTs placed in the near-field of the array reduces the calibration effort by a factor of 3 compared to state-of-the-art setups. The average deviation of the antenna phase relations amounts to 4.1 degree, proving that the presented setup achieves the same calibration quality as state-of-the-art setups.


I. INTRODUCTION
P HASED arrays and millimeter-wave imaging radars have many applications in civil and military domains [1], [2], [3], [4], [5], [6]. These systems are employed for measurements of the direction-of-arrival (DoA) estimation of incoming waves or beamforming at the transmitter. Latest works focus on the DoA estimation in azimuth and elevation to achieve 4D imaging [7], [8], [9]. As these operations require a precise array model, calibration of the antenna array is crucial. Effects like manufacturing tolerances, varying feed line lengths, and mutual antenna coupling lead to deviations of the ideal array response. These effects become even more significant in the upper mm-wave frequency range [10]. Therefore, a measurement of the array response vector has to be performed [11], [12], [13] to adjust the array model. This adjustment can be performed either by means of calibration parameters, namely the antenna positions (antenna phase centers) and phase offsets [10] or alternatively nonparametrically applying a calibration matrix, which contains the obtained angle-dependent reference measurements [14]. Thus, systematic errors during the subsequently performed DoA estimation can be avoided [15].
Particularly for large-aperture sizes, the calibration effort increases drastically [14]. Therefore, enhancements in calibration techniques are needed to obtain accurate antenna array models with low measurement effort during the calibration procedure [16], [17]. A typical calibration setup is sketched in Fig. 1. The array under test (AuT) is mounted on a rotatable positioning system. At each angular step, a measurement with a stationary calibration target is performed, and the array response vector for this data point is captured. Common calibration targets are corner reflectors, as they ensure a high SNR. Typically, a single calibration target is used. For a total of N i data points, the same amount of rotation steps is needed. For large-aperture arrays, this leads to a significant duration of the calibration measurement.
Highly efficient calibration methods have been developed that require a low number of data points [17], [18] but at the cost of a high computational effort. To decrease the calibration effort, the recording of a multitude of data points within a single measurement snapshot by applying active calibration targets (ACT) placed at different angles is proposed. This procedure can also be combined with efficient calibration methods like [17]. When applying N T ACTs, the calibration effort can be reduced by a factor of N T , as N T data points are recorded within a single snapshot. In this article, an advanced calibration setup with N T = 3 as in Fig. 1(b) is aimed for. To further relax requirements on the anechoic chamber, the calibration measurement is performed in the near-field region of the AUT, leading to the dashed anechoic chamber size. The positioning of ACTs in the nearfield region, where a plane wave can no longer be assumed, leads to effects that must be compensated for [19]. Common calibration techniques in the near-field of the AuT consider one passive target [19], [20]. The compensation of multiple active targets increase the complexity and necessitate new methods.
This article is organized as follows: In Section II, the calibration using an ACT is described mathematically and investigated by simulations and measurements. The fusion of data sets recorded with several ACTs is conducted in Section III, the derived theory is proven by measurements and a procedure for efficient calibration of the measurement setup is described. In Section IV, the calibration measurement is performed with an ultra-compact setup using three ACTs. For the compensation of near-fields effects by a path model, the determination of the required parameters from calibration measurements is described. Further, the influence of target alignment inaccuracies is investigated. Finally, the near-field effects are compensated, and the calibration parameters are compared to the calibration parameters obtained from a reference setup with a single corner reflector positioned in the far-field of the AUT.

II. ARRAY CALIBRATION WITH AN ACTIVE CALIBRATION TARGET
The calibration setup employing ACTs requires adjustments of the calibration procedure. These adjustments are explained in this section. First of all, the general array calibration and DOA estimation is explained. Afterwards, the target detection for ACTs is described, followed by investigations of the bistatic target influence and the compensation of it.

A. GENERAL ARRAY CALIBRATION AND DOA ESTIMATION
For the calibration procedure, the array response vector a(φ) is measured versus the desired DoA range [14]. For an incident plane wave impinging at an azimuth angle φ, the array response vector is [11] where I is the total number of angular sampling points, A k (φ) the angle-dependent amplitude information for each receive antenna of index k, and N RX the total number of RX antennas. The calibration parameters consist of the antenna position x k and ψ h as phase offset. Usually, the amplitude terms can be neglected if antennas with a wide beamwidth are used. Since this condition is met in the majority of imaging systems, the amplitude term is omitted in this article. A straightforward way to perform the DoA estimation is the deterministic maximum likelihood approach [21], where the measured array response vector at the virtual receive antennas (VX) is compared with a reference calibration matrix C. For multiple-input multiple-output (MIMO) radars, the measured signal phase corresponds to the sum of the phases at the TX and RX antennas. Usually, the definition of an equivalent VX antenna is used to describe this behaviour. The array response vector of the virtual array is thereby calculated as the Kronecker product of the transmit and the receive array response vectors [22]. Thus, the calibration matrix has the dimensions I × N VX and stores the array response vectors of all reference samples at different angles in the azimuth plane. The comparison between the received array response vector a and C is mathematically calculated as the cross-correlation with the symbol (·) H denoting the complex conjugate (Hermitian) matrix and || · || denoting the Euclidean norm. The DoA of the measured array response vector φ est is determined by finding the direction that maximizes the cross-correlation Instead of measuring the complete calibration matrix, it can be modelled using the calibration parameters. This modelling is based on (1) and is restricted to scenarios with sufficiently large SNR. The calibration parameters can be obtained by the standard method as described, e.g., in [14]. Hereby, the antenna positions are determined from the slope of the phase progression versus the measured angle. The second calibration parameter is the phase offset, which is the phase relation of one antenna to the reference antenna while facing a target at boresight (φ = 0 • ) direction. The phase offsets are obtained after linearisation to achieve a higher robustness against noise. All calibration methods have in common that they require a specific amount of measurement points to ensure a certain quality of the determined calibration parameters [14], [17], [23], [24].

B. CALIBRATION CONCEPT WITH AN ACTIVE CALIBRATION TARGET
Calibration with several targets in parallel is only possible if these targets can be separated. Depending on the system, the targets can be separated by different methods. In case of an array employed for communication purposes, the separation takes place in the frequency-domain. A small frequency offset is added by modulating the received signal at the ACT. Thereby, small modulation frequencies are deployed to ensure approximately equal antenna characteristics. For radar operations, the separation can be conducted in the r-v-(range, velocity) domain. In the following, an FMCW radar is used as exemplary demonstrator. In case of passive calibration targets, these targets need to be placed in different range cells. This placement leads to several effects such as different near-field effects and range-angle coupling that have to be compensated for [19]. With the usage of ACTs, this requirement may be overcome. ACTs are used widely in radar target simulators [25], [26] to evaluate radar systems and to simulate not only different distances but also different velocities of targets [27]. Unlike passive targets, this allows target detection for ACTs through preset velocities. This possibility of target separation is used to build up an innovative measurement setup for calibrations using a variety of calibration targets in the same range of the AUT. The separation of the targets takes thus place in the v-domain.
The operation principle of an ACT is depicted in Fig. 2. The RX antenna receives the incoming signal that is amplified by a variable gain amplifier (VGA). In order to implement the desired shift in v, the signal is modulated [28]. This modulation is deployed by a mixing operation performed by an IQ-mixer with the modulation frequency f mod . A second VGA is employed to compensate for conversion losses of the mixer and to amplify the TX signal, which is then radiated by the TX antenna.
With the choice of the antenna types and the amplification of the signal by the VGA, the ACT provides more degrees of freedom as the corner reflector, which can only be adjusted with respect to its RCS value when scaled.
While the corner reflector acts as a point target, the ACTs have separated points of interaction for receive and transmit operation. Thus, the ACT represents a bistatic target and requires additional compensation depending on the measurement setup. Furthermore, when using ACTs, a free choice of r-v bins is made possible by signal modulation.

C. TARGET DETECTION FOR ACTIVE CALIBRATION TARGETS
At first, the corner reflector as commonly used calibration target is investigated. For the corner reflector, the point target assumption can be met representing a single target. The phase of the receive signal after down conversion is [29] with the center frequency f c , the bandwidth B of the signal, the ramp duration T, and the path delay τ = 2R/c 0 resulting from the target distance R and the speed of light c 0 . In reality, phase noise influences are present, which are neglected here.
Eq. (4) shows that a separation of targets is only possible if they are located in different range cells. The separation of ACT targets at radar operation is not limited to FMCW operations, as shown here [30] for orthogonal frequencydivision multiplexing (OFDM) operation.
Assuming that the path length for the wave propagating from the AUT's TX to the ACT's RX antenna R TX,RX equals the path length from the ACT's TX antenna to the array's RX antenna R RX,TX and neglecting the time duration caused by line lengths inside the ACT, the target phase at the receiver for the stationary ACT leads to a shift in range of [28] R and a velocity shift of with T r as chirp repetition interval and f mod as modulation frequency, introduced by the ACT's IQ-mixer. Even if positioned at the same distance to the antenna array, by supplying different modulation frequencies for the ACTs, they can be separated due to different measured velocities. Moreover, an undesired range shift is caused by the modulation frequency, that has to be compensated during the calibration procedure as this range shift falsifies the range measured. Since this range shift can be accurately predicted, it can be compensated with ease. In the simulation model, a wrong target distance can alter the near-field effects. In theory, this range shift can be used to separate the targets, in practice, this is more prone to errors as there are more distortions in the r-than in the v-domain. This can lead to a lower SNR of the receive signal or even that a wrong target is evaluated.

D. INFLUENCE OF THE BISTATIC TARGET
As the ACT possesses separated antennas for receiving and transceiving, the assumption of a point target in (4) is not valid anymore. If not compensated, this assumption can lead to systematic errors in the calibration procedure.

1) MATHEMATICAL MODEL
The geometry of the measurement setup for the simulation based on optical paths is depicted in Fig. 3. The signal emitted from the transceiver is received by the ACT, which in turn transmits it back to the AUT. At the u-th RX antenna of the AUT, the phase is defined as with the wave number k, the phase offset added by the ACT ϕ Target , the phase offsets of the u-th virtual antenna ϕ u , and the path lengths from the AUT's TX to the ACT and ACT to the AUT's RX antenna d TX/RX . As the calibration method is only based on phase relations, the phase change φ Target introduced by propagation through the ACT does not affect the relative phase at the u-th receive antenna referred to the w-th receive antenna: In the following, all channels are referred to channel 1, which is closest to the rotation centre of the positioning system. Since some systematic errors exert almost the same influences on all channels, such as the inaccuracy of the positioning unit, these influences are reduced by referencing.

2) HARDWARE DEMONSTRATOR
To analyse this effect, a uniform linear array (ULA) is operated in a single-input multiple-output (SIMO) mode. A photograph of the antenna array is shown in Fig. 4(a). The antenna positions of the physical and virtual array are sketched in Fig. 4(b). As only the bistatic influence of an active target is investigated here, the mixer is not accounted for. For analysis, the setup in Fig. 4(c) is employed, which consists of two horn antennas, a waveguide amplifier with a gain of 17.5 dB, and waveguide transmission lines as connectors. By adding waveguide transmission lines, the size of the target d Target , associated with the distance between RX and TX antenna phase center, can be adjusted. The radar parameters applied with the SIMO operation are listed in Tab. 1.

3) VERIFICATION BASED ON MEASUREMENTS
To verify the mathematical model developed in the previous paragraph, three different measurement setups are deployed. As a reference, a calibration measurement with a conventional corner reflector with σ = 14.4 dBsm is conducted at a target distance of 4.7 m, which fulfills the far-field condition of the array. For analyzing the bistatic effects on the calibration procedure, the active target shown in Fig

4) ACCURACY OF DETERMINED CALIBRATION PARAMETERS
To evaluate the quality of the calibration based on ACTs, the calibration parameters x i and ϕ i according to (1) are analyzed. The deviation of these parameters compared with those obtained from a conventional calibration measurement with a corner reflector as passive target are depicted in Fig. 6. The phase offsets in Fig. 6(a) are determined after compensating the bistatic influence of the target by means of the simulation model (9). The mean deviation is 1.1 • for d Target = 92 mm and 1.0 • for d Target = 192 mm. In Fig. 6(b), the deviations of the VX-antenna positions are plotted, where the mean deviation is 0.012 λ 0 for d Target = 92 mm and 0.014 λ 0 for d Target = 192 mm. As the calibration parameters obtained by bistatic targets agree well with the results of the conventional calibration, the feasibility of ACTs in calibration measurements is demonstrated.

III. DATA FUSION OF ACTIVE CALIBRATION TARGETS
In this section, the fusion of multiple data sets, obtained by different ACTs simultaneously, is derived and evaluated. This reduces the calibration effort, as a smaller number of measurements has to be conducted. First, the separability of targets by shifts in the velocity-domain is demonstrated by measurement. Afterwards, a calibration of the measurement setup is described. Finally, the fusion of data sets, recorded with multiple ACTs simultaneously, is conducted.    Fig. 7(d) shows the hardware setup for the following measurements. To analyse the effects occurring during the calibration process, especially when the far-field condition is violated, a tailored antenna array is employed. A photograph of the array is shown in Fig. 7. The antennas are fed by a FMCW radar system as described in [31], which is operated as listed in Tab. 2. Fig. 7(b) shows the antenna positions of the array. The resulting 1-D virtual array can be subdivided into 2 sub-arrays. Sub-array 1 has a lower far-field distance r FF and sub-array 2 has a higher r FF . Channels close to the rotation axis have the lowest r FF as they can be assigned to a sub-array with reduced dimensions. By that, the near-field effects on calibration measurements violating the far-field condition can be directly compared to those measured in the far-field region. Fig. 7(c) shows an exemplary ACT of which three specimens are employed for the following experiments. To enable separation in the r-v domain, the ACTs operate at different modulation frequencies, listed in Tab. 3. In Fig. 8, the corresponding r-v plot of a radar measurement is depicted. All targets are ideally located at the same distance towards the rotation center of the positioning system.

B. SIGNAL SEPARATION IN CASE OF MULTIPLE ACTS
For the determination of the phases of the ACTs, 2f mod is additionally employed at each ACT [30]. It can be seen that in addition to the actual intended target responses, undesired targets appear from harmonics and intermodulation products.  Since the velocity cells in which the target appears can be set with high precision, the unwanted targets can be positioned in non-critical cells. This allows for undisturbed target extraction. By that, the extraction of the targets is quite convenient and windowing in the v domain can be used. In Fig. 8, the carriers are visible at v = 0 m/s.

C. COMPENSATION OF THE ACTIVE TARGET PHASE
As the phases of the active targets are not synchronized with the AUT, the phase relations between the channels are distorted, especially if time-domain multiplexing (TDM) is used. In the case of MIMO operation, these phase errors are not cancelled out by referring to a reference channel, as the ACT leads to different phase shifts on the array transceivers for each data point. This effect can be seen in Fig. 9 for the ACT placed at boresight direction. Since the time interval between active transmit periods is always the same, this leads to regular phase progressions along the transmitters. The compensation of this effect is described in detail in [30]. After the compensation, the phase shifts between the transceivers vanish.

D. CALIBRATION OF THE MEASUREMENT SETUP
In case of a passive calibration target, it is helpful to consider two Cartesian coordinate systems as depicted in Fig. 10. The origin of the first coordinate system (AUT) is located at the rotation center, whereas the origin of the second system (Target) is located at the calibration target, which is considered as a point target. Ideally, the coordinate system origins only differ by a shift of the desired target distance. In practice, due to limited alignment accuracy, a misplacement along the x-axis, designated as d Mis , is probable. This in turn results in an angular misalignment φ Mis , and a rotation of the target's coordinate system as the y-axis of the target is defined to intersect with the arrays coordinate system's origin.
In the presence of N ACT ACTs, N ACT + 1 coordinate systems are needed to describe the measurement setup. To reduce this number of required systems to one, the ACTs are being related to one reference ACT. Thereby, all ACTs are combined into one coordinate system. In this work, this kind of alignment is understood as calibration of the measurement setup. In the following, a measurement setup of three ACTs, depicted in Fig. 11, is used.

1) DETERMINATION OF ACT PLACEMENTS
For the calibration of the measurement setup, φ Mis has to be determined for N ACT − 1 targets. Equally to the calibration with a passive calibration target, one active target and its corresponding coordinate system are employed as reference. The other targets are arranged in this reference coordinate system. The accuracy with which this reference target was positioned is decisive for the calibration quality. The procedure for arranging the targets in the reference coordinate system is referred to in this article as setup calibration. Fig. 12 visualizes the calibration measurement scenarios for φ Array = φ Target,n with n ∈ {1, 2, 3} as target identifier. If ideally positioned, the array response vector is the same for all depicted scenarios, as all targets appear in bore sight direction. The scanning angle is chosen to cover all angles φ Array , where the targets are potentially placed, with some additional safety margin. As the measurement points recorded by Target 2 overlap with those of the other targets, it is deployed as reference target. The outermost target position is at |φ Array | = 20 • . Thus, the maximum scanning For the alignment process of the targets, the array response vector a 2 at φ Array = φ Target,2 = 0 • is obtained by the reference target (2). To determine the angular position of the first target, the calibration matrix C 1 is obtained from the measured array response vectors over φ of Target 1. If Targets 1 and 2 are positioned ideally, the angle estimation performed with this calibration matrix C 1 and array response vector a 2 has its maximum at φ Array = φ Target,1 as both result in the same array response vector, which can be seen in Figs. 12(a) and 12(b). To determine the angular position of the third target, an analogous procedure is performed with corresponding Figs. 12(b) and 12(c). The results of this DoA estimations for the angular position determinations are depicted in Fig. 13(a). The highest correlations appear at 20 • and −20 • , which are the desired target angles of Targets 1 and 3. Both targets were therefore positioned at the correct angles, relative to the reference Target 2. For possible misalignments, a correction value β n can be obtained for the n-th ACT to take the offset into account.
For this procedure, near-field effects have no impact as the calibration matrix and the array phase responses are obtained in the same range cell. Furthermore, an uncalibrated array can be employed as the required calibration matrix is recorded from the non-reference targets during the calibration measurement of the setup. For the setup calibration shown here, the same array is deployed for the calibration of the measurement setup and later on as AUT. Alternatively, an array with greater aperture and higher angular resolution capabilities can be employed for the calibration of the measurement setup to enhance the accuracy. Overlapping regions reduce the efficiency of the multiple calibration target setup. They are only necessary during the setup calibration due to limited positioning accuracy of the ACTs. Afterwards, this overlap has to be avoided in order to obtain the greatest benefit from the calibration measurement setup. As general proof of concept, the mean phase deviations from the overlapping phase response vectors are depicted in Fig. 13(b), showing that the measurement results of different ACTs achieve approximately the same results. Therefore, the datasets obtained from the different targets can be combined with negligible phase deviations between the measurements.

2) DATA FUSION
After the alignment of calibration targets, the datasets C n are combined for further processing to The associated collection of related target angles is determined by . . .
with β n as correction value of the angular misplacement of the n-th ACT, determined during the calibration of the measurement setup. With the second ACT chosen as reference, β 2 = 0 follows. As the targets are placed with finite accuracy, and the calibration of the measurement setup only includes an angular alignment, there may still be a range shift between targets. Fig. 14 shows the angle-dependent phase of two exemplary channels after fusion of the datasets. For those two channels, phase steps occur at φ Array = 10 • . This is due to the existence of range deviations between the calibration targets. This range deviation is equal for all channels. Due to this fact, the steps can be eliminated by referencing the phase resulting in relative phases. During the calibration procedure, relative phases are calculated for further processing. In Fig. 14, based on the phase of channel 16 relative to channel 1, it can be seen that the steps have been compensated for. To summarize, range deviations lead to phase steps that cancel out when relative phase relations are calculated. Therefore, the calibration procedure employed here shows high robustness against small range deviations in the ACT placement.

IV. CALIBRATION WITH ACTIVE CALIBRATION TARGETS IN A NEAR-FIELD SETUP
To get the greatest benefit from the usage of N T ACTs, they have to be placed with an angular spacing of By that, the overlapping of scanning regions covered by different ACTs is minimized. For a calibration measurement setup using N T ACTs, this condition can lead to sizes of the anechoic chamber that are undesirable. To reduce the requirements on the sizes of the chamber, the calibration employing multiple ACTs is performed in the near-field region of the antenna array.

A. MODELLING NEAR-FIELD EFFECTS
For the compensation of near-field effects, the path lengths have to be precisely known. In the following, a method based on distance measurements employing the AUT is shown. The compensation of a calibration setup deploying a passive calibration target is described in detail in [19]. Thereby, the assumed antenna positions obtained from manufacturing data in combination with the target position are employed to model the spherical waves in order to compensate them.
In comparison to the calibration measurement setup with a passive calibration target, this setup with N T = 3 increases the complexity. A propagation model of the setup is depicted in Fig. 15 for one ACT. The propagation path length measured of one exemplary channel adds up to with R Frontend representing the paths along the transmission lines on the frontend consisting of the paths from the MMIC (monolithic microwave integrated circuit) to the TX antennas R TX, Line and the paths from the MMIC to the RX antennas R RX, Line . R FS models the paths propagated in free space and R ACT considering the range shifts caused by the ACT. To model and to compensate the influence of spherical waves, R FS has to be extracted from the measured distance R. Therefore, the other range shifts have to be determined and subtracted. According to (5), the modulation of the signal causes a shift in the measured range described by R mod . Therefore, the actual path length used to describe the propagation of the spherical wave is limited to R FS and calculated with = R measured − R TX, Line + R RX, Line + R ACT, Line + 2 R mod . (16) As the propagation speed through dielectric material differs from free space, the permittivity must be considered.
Inserting (5) leads to [32] R FS = R measured − d TX, Line + d RX, Line √ ε r,Array with √ ε r,Array and √ ε r,ACT describing the dielectric constants of the antenna array and the ACT, respectively. The physical lengths of the propagations paths on the AUT are defined as d TX, Line , d RX, Line and d ACT, Line √ ε r,ACT for the ACT. To obtain the physical lengths of the AUT, manufacturing data is used. Simulations are deployed to gather the offsets R mod,i caused by the modulation frequency f mod for each ACT individually. Determining the distance propagated in free space enables the calculation of the correction steering vector a RX,corr , which is employed for the compensation of the near-field influence [19]. Thereby, the target distance and roughly known positions from the antennas of the AUT are deployed to calculate the influences caused by spherical waves in order to compensate them from the data samples.
For the first channel as example, the evaluation of the calibration measurement shows a target distance of 1.52 m. The offset introduced by line lengths on the array is R TX, Line = 62 mm and R RX, Line = 79 mm leading to a total length of R Frontend = 141 mm. The range shift caused by the exemplary modulation frequency of 75.5 kHz can be read out from Tab. 3 as R mod = 104 mm. The offset introduced by line lengths on the ACT is R ACT, Line = 120 mm, which was obtained from scattering parameter measurement. The combination of all offsets is leading to a target distance of R Target = 1.52 m − R R Array + R mod + R Target, Line = 1.52 m − 0.365 m = 1.155 m.
This is the target distance needed for the compensation of near-field effects.
By means of simulation the phase changes introduced by the near-field are calculated to subtract them from the measured phase responses [19]. After this compensation, the spherical wave influences are compensated for.

B. MEASUREMENT RESULTS
The results with and without the near-field compensation are compared in Fig. 16. As reference within the antenna array, the channels of sub-array 1 (see Fig. 7(b)) are included in the first two subfigures and due to their lower far-field condition here referenced as FF channels. For evaluation, a reference calibration is performed in the far-field of the antenna array with a corner reflector as calibration target. Figs. 16(a) and 16(b) show the deviation of the determined calibration parameters from the near-field with and without the compensation compared to the calibration parameters determined by the reference calibration. Fig. 16(a) shows the effect on the determined VX positions. The compensation causes a higher deviation for 3 of 48 channels with a strong violation of the far-field condition. The mean deviation of the NF channels decreases from 0.056 λ 0 to 0.022 λ 0 when the compensation is applied. In Fig. 16(b), the effect of the compensation on the phase offsets is shown. If uncompensated, the phase offsets differ considerably. The near-field compensation decreases the mean deviation of NF channels from 164.2 • to 5.2 • , thus showing a significant impact. The mean deviation over all channels amounts to 4.1 • for the phase offsets and 0.014 λ 0 for the VX positions. In case of an erroneous target distance on the spherical wave model, the compensation quality suffers. If the distance is too large, the spherical wave influences are insufficiently compensated. In the case of an underestimated target distance, larger nearfield influences are modeled, overcompensating the actual ones. This dependency on the correct target distance is depicted in Fig. 16(c). If the measured target distance is chosen without taking the different offsets into account, the mean deviation of the VX positions increases for the NF channels from 0.022 λ 0 to 0.031 λ 0 and the phase offsets from 5.2 • to 42.3 • . In case of the phase offsets the mean deviation of NF channels increases by 715 %. It should be noted that the lowest mean phase offsets deviation is reached for a compensation distance of 1.141 m leading to 4.3 • . The difference of 14 mm can be caused by tolerances of the permittivities used for range offset calculation, line lengths, inaccuracies during the positioning of the measurement set up or noise influences on the phase responses. Although the compensation distance of the lowest mean is not hit, the result is close to the optimum.

V. CONCLUSION
In this article, a measurement setup for phased array calibration, based on the application of ACTs, is proposed. With this setup, it is possible to reduce the calibration measurement effort significantly without a reduction of data points recorded, ensuring high quality array calibrations. This is done by recording multiple data points in parallel. It is shown that systematic errors from the active target architecture can be compensated by a simulation model and an initial calibration of the measurement setup. To reduce the requirements on the anechoic chamber sizes, the calibration with three ACTs was performed in the near-field region of the AUT. Furthermore, the calibration features high robustness against small range offsets of the ACTs. Moreover, ACTs make the calibration measurement much more flexible, as the choice of the ACT antennas influences the angular beamwidth and the coverage of the calibration target. The selection of amplifiers leads to an easily adaptable signal strength. By taking all the relevant effects into account, the quality of a calibration measurement performed in the farfield region of the AUT can be restored. Subsequently, the proposed setup enables a significant acceleration of angular array calibrations with relaxed requirements with respect to the measurement area without degrading the calibration quality.