Using multiple-receiver arrays, the techniques of spaced antennas and spatial domain interferometry have been widely utilized in mesosphere-stratosphere-troposphere (MST) VHF and meteor radars. As these techniques are applied, the phase imbalance between the receiving channels will cause a biased result if it is not considered in the use of phase angles of the radar returns received in different receiving channels. In view of this, many methods have been employed for the phase calibration of receiving channels. In this paper, we propose one more method/procedure for the calibration, in which the commercial airplane flying routinely is used as a radar target. We measure the zenith and azimuth angles of the airplane with a video camera and estimate the range and height of the airplane from observation using the frequency domain interferometry (FDI) technique. Consequently, the track of the airplane in the vicinity of the radar site can be determined. The phase difference between the two radar echoes received by a pair of receiving channels is then predicted in accordance with the track of the airplane. Comparing the predicted phase difference with that observed, the phase imbalance between a pair of receiving channels could be obtained. Tens of cases show consistent results and so verify the reliability of the method. Also shown is the drift of system phase imbalance from season to season, which might be caused by the temperature dependence of antenna system components.
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 Using multiple-receiver arrays, the techniques of spaced antennas (SA) and spatial domain interferometry (SDI) have been applied with mesosphere-stratosphere-troposphere (MST) VHF and meteor radars for tens of years [e.g., Robertson et al., 1953; Woodman, 1971]. Applying these techniques to the atmosphere allows many measurements of atmospheric parameters, such as wind field, aspect sensitivity, gravity waves, and so forth. Recently, the so-called coherent radar imaging (CRI), a general and improved version of the SDI technique with the capability of high-angular resolution, was further developed in MST radar society. For more details of the above techniques and their applications, the reader can refer to some papers published recently, for example, Woodman , Palmer et al. , Chau , Yu et al. , and Chau and Woodman .
 When one applies the multiple-receiver interferometry technique, the phase information of the radar echoes is needed. For example, SDI/CRI method estimates the phase difference (SDI phase hereafter) between the radar returns received by spaced receiving channels and then derives the angle of arrival of the scattering center. It is known that the received radar return also contains a phase term due to the radar system itself (system phase hereafter). In case the system phases of the spaced receiving channels are different (system phase imbalance hereafter), the derived angle of arrival would not be accurate and can lead to incorrect estimations of atmospheric parameters, for example, of vertical wind [Röttger and Ierkic, 1985]. The system phase is susceptible to environmental conditions and the performance of the radar system, including temperature, aging of components, cable length and quality, and so forth. In order to obtain a correct measurement using the SDI technique, proper compensation of the system phase imbalance is required, and so several calibration methods have been employed. For example, having an airplane with known height fly over the receiver arrays several times and measuring its angular position with an optical instrument, the average system phase imbalance of a meteor radar system can be obtained according to the difference between the two positions determined with SDI and optical instruments, respectively [Robertson et al., 1953]. Calibration of the meteor system was also done in terms of the beacon signal transmitted by a satellite [e.g., Clark, 1978] or the signals transmitted from a set of remote sources located on the ground [Glanz, 1971; Dorny and Meagher, 1980; Valentic et al., 1997]. In addition, for the radar receiver with a large antenna array the methods using stellar sources [Woodman, 1971; Palmer et al., 1996] and magnetic field-aligned ionospheric irregularities [Wang and Chu, 2001] were employed. No matter which of the above methods is used, the location of the target is known a priori. Another method of calibration is to feed a common signal to the receiving lines and measure the phase difference of the outputs [Vandepeer and Reid, 1995; Chau and Balsley, 1998]. On the other hand, Röttger et al. [1990b] assumed that the SDI phase of atmospheric echoes should have zero mean in statistical sense; thus the long-term-averaged SDI phase angle could represent the system phase imbalance. This method was also employed by Thorsen et al. .
 In this paper, one more method is applied for the phase calibration of spaced receivers, which is proved workable by using the Chung-Li VHF radar. Inspired by the previous work utilizing an airplane [Robertson et al., 1953], we found that the commercial airplanes flying routinely in the vicinity of the Chung-Li radar site are good objects for the calibration task. For atmospheric observation, the radar echo reflected from the airplane is some kind of interference because it is usually much larger than that reflected/scattered from the atmospheric irregularities. Because of this, however, it is easy to detect the airplane. To develop a pertinent calibration procedure using the commercial airplane, one of the basic requirements is to determine the track of the airplane, which is totally unknown for the observer at the radar site. It is thus the first step of the task to obtain the range and angular location of the airplane. In our method the angular location of the airplane was recorded by a video camera placed very close to the radar receiving antennas. The range of the airplane, which cannot be measured accurately due to the finite range resolution of pulsed radar, was obtained by means of the technique of frequency domain interferometry (FDI) [Kudeki and Stitt, 1987]. With the range and angular location of the airplane, the track of the airplane in the vicinity of the radar site can thus be determined. Once the track of the airplane is obtained, the “theoretical” SDI phase is easy to estimate/predict. Comparing the theoretical SDI phase with that observed, we can obtain the system phase imbalance. Although the target employed in this study is the same as that used by Robertson et al. , our approach is quite different from that of Robertson et al. . For example, there is no need to know the height of the airplane in advance because of the use of the FDI technique.
 It should be mentioned that the purpose of this study is to provide an additional option for the task of phase calibration, not to demonstrate the superiority of our method over the existing ones. This article is arranged as follows. A description of the Chung-Li VHF radar and experimental setup is given in section 2. In section 3, we briefly describe the SDI and FDI techniques as well as the details of the calibration methods. Experimental results along with a discussion are given in section 4. Section 5 is the conclusion.
2. Chung-Li VHF Radar and Experimental Setup
2.1. Chung-Li VHF Radar
Figure 1 shows the configuration of antenna array of the Chung-Li VHF radar. There are two main antenna arrays: One is operated mainly for the studies of troposphere and lower stratosphere (ST array), while the other one is used for ionospheric observation (IONO array). Both arrays consist of three subarrays formed by 8 × 8 (ST) and 4 × 8 (IONO) 4-elememt linear Yagi antennas, respectively, which are connected to three identical, independent, and phase locked radar modules. ST and IONO arrays cannot be used simultaneously because they use the same radar transmitting/receiving modules. A switch is used for selection. The separations between the central positions of the subarrays A and B, B and C, and C and A of the ST array are 44.72, 40, and 44.72 m, respectively, while they are 41.22, 19.6, and 44.34 m in the IONO array. Besides, a small array consisting of three 4-element linear Yagi antennas (Yagi array) with 5-m separation between the antennas was constructed next to the ST array for receiving the radar returns from meteor trails and lightning channels. The three antennas of the Yagi array are connected to the three parallel receiving channels that are also used with ST and IONO arrays. When the Yagi array is employed for reception, either the ST or the IONO array can be used for transmission. An electronic control is set up for automatically switching the reception and transmission channels during observation. In principle, the three antenna arrays mentioned above have the capability of spatial domain interferometry, except that the ST and IONO arrays may suffer the more serious problem of 2π phase alias due to the large separations between the centers of subarrays [Chu and Wang, 1999]. Other detailed characteristics of the Chung-Li VHF radar are given by Röttger et al. [1990a]. In this study, the central location of subarray antenna B and the position of Yagi B are chosen to be the origins of the coordinate systems for the calibration of the ST and Yagi arrays, respectively.
2.2. Experimental Setup
Figure 2 depicts the collocation of experimental setup. An 8-mm video camera was placed close to the antenna arrays to measure the angular position of the airplane. This measurement was achieved by means of an angular scale in front of the lens of the camera (1° resolution). For the calibration of the ST/IONO array, the ST/IONO array was used for transmission and reception. For the calibration of the Yagi array, however, the ST array was selected for transmission while the Yagi array is for reception. Three phase locked receiving channels were employed. Furthermore, two frequencies, 51.75 and 52.25 MHz, were used for FDI operation. The interpulse period (IPP), pulse length, and sampling interval used in the experiment were 2400 μs, 2 μs, and 2 μs, respectively. With these radar parameters, an FDI phase difference of 2π in a range bin of 300 m was obtained. In light of the fast movement and strong radar echo of the airplane, no coherent integration for the radar returns was made. However, the sampling time of radar data was 4800 μs because the radar pulses with different carrier frequencies were transmitted alternately in FDI operation. Either of the data sets collected in FDI operation can be used for SDI analysis. In this analysis, we employed the data set observed with the frequency of 51.75 MHz.
3. Techniques and Approaches
3.1. SDI and FDI Techniques
3.1.1. SDI Technique
 The details of the SDI theory can be found in plenty of studies, such as those mentioned in the introduction and their references. We describe the simplest version here for a single target because the airplane is such a case for the radar observation. That is, the radar echoes of the airplane received by two separated receivers can be simply expressed as
where j indicates complex form, A1 and A2 are the amplitudes of the two radar returns, respectively, k is the wave number corresponding to the transmitted frequency, rt is the distance from the transmitter to the target, r1 and r2 are the distances between the target and receiving antennas 1 and 2, respectively, and φ1 and φ2 are the system phases of the two receiving channels. SDI phase is calculated from the cross-correlation analysis of (1), namely,〈S1S2*〉, where the asterisk denotes complex conjugation, and so can be obtained as k(r2 − r1) − (φ2 − φ1). The phase term, φ2 − φ1, is the system phase imbalance that is the object in the calibration. As mentioned, the obtained angle of arrival of the target would not be accurate if the system phase imbalance is not considered in the estimation using SDI phase.
 It is worth mentioning that May  and Chau and Balsley  revealed two geometric effects on SDI phase that should be included in (1). However, one of the two effects can be ignored because the radar echo from the airplane is the case of specular reflection. In addition, either the separation between the receiving antennas of the Yagi array is small (5 m) or the distance of the airplane employed for the ST array is quite large (>10 km, see section 4.2), the other effect is really little. Therefore the two geometric effects can be discarded in this study.
3.1.2. FDI Technique
 The method using adjacent frequencies has been employed in the field of astronomy [e.g., Hagfors, 1961, 1963]. As this method was introduced to the investigations of the atmosphere using MST radars [Kudeki and Stitt, 1987], plenty of works improved its content (for more information of this technique, see Chen and Chu  and the references in their paper). Recently, the multiple-frequency FDI technique was successfully developed and applied to the investigations of multiple layers in the radar volume [Palmer et al., 1999, 2001; Luce et al., 2001; Chilson et al., 2001]. Basically, the application of FDI technique with two or more frequencies is based on the cross-correlation function of two radar returns with slightly different carrier frequencies. For a reflecting target such as an airplane, the theoretical expression of the cross-correlation function is much simpler than that for a diffusive target. Assuming that the airplane is located at the range of r from the receiver, and two different carrier frequencies are transmitted simultaneously, the received radar echoes can then be written as
where j, A, and k have the same meaning as in (1), and φ is, again, a system phase term. In the study using the airplane, only the phase of the cross-correlation function of (2) is employed, which can be written as 2r(k2 − k1) − (φ2 − φ1). It should be noted that the phase term, φ2 − φ1, might not be zero even if the same receiver is used for reception. This is because different carrier frequencies are employed for transmission and so we cannot discard some unknown effects from the radar system on the signal phases. However, since the same receiver is used, the effect of different receivers on the term of φ2 − φ1 does not exist anymore; likewise the factors of the aging of radar system and environmental condition can be ignored because the FDI cross-correlation analysis with the two radar echoes received by same receiver erases the variation of φ that arises from these factors. Accordingly, other factors are responsible for the existence of φ2 − φ1. It should be mentioned here that because the two radar pulses with different carrier frequencies were transmitted alternately with a time delay of IPP (2400 μs in this study), such a time difference indeed results in a shift of FDI phase due to the movement of the airplane. This shift, however, is small and can be ignored.
 In reality, the FDI phase angle observed has extent 0–2π and so only indicates the location of the target in the range gate, not the real range of the target from the receiver. Therefore the parameter r in (2) should be written as Ro + Δr, where Ro is the range of bottom edge of the gate and Δr is the radial position with respect to the bottom edge of the gate. As a result, the phase of the cross-correlation function in (2) can be rewritten as [2Ro(k2 − k1) − (φ2 − φ1)] + 2Δr (k2 − k1), in which Ro can be estimated from the sampling delay time. In the case that the sampling delay time is not precise (for example, considering the signal time delay in the radar system) or the phase term of φ2 − φ1 indeed exists, Δr cannot be derived properly from the observed FDI phase, so that the real range of the target from the receiver cannot be determined accurately. Nevertheless, such an inaccuracy is possible to depress if further calibration for the FDI observation is carried out. Before this further calibration, a proper uncertainty of range was considered in this study to show the reliability of the result.
3.2. Track of the Airplane
 The coordinate of the track of the airplane with respect to the video camera can be estimated as
where r′ is the range of the airplane with respect to the video camera and θ and ψ are zenith and azimuth angles of the airplane measured by the video camera, respectively. In this study, the height and flight direction of the airplane are assumed to remain unchanged during the period (usually shorter than 1 minute) when the airplane appears in the regions viewed by radar and video camera. This assumption should be valid for most airplanes. Considering the short separation between the video camera and the receiving antennas (20–30 m for the Yagi array and 40–80 m for the ST array) as well as the long distance from the airplane to the receiving antennas, r′ can be approximated by the range r determined from FDI observation. Since the position of the video camera is known a priori, it is not difficult to transform (x′, y′, z′) into the coordinate system of radar SDI analysis. As the coordinate of the airplane is known, the “predicted” SDI phase between two receiving channels can be computed. Consequently, the system phase imbalance can be obtained after comparing the observed and predicted SDI phases.
 Before comparing the observed and predicted SDI phases, synchronization of timing for the observations of radar and video camera is indispensable considering the fast movement of the airplane. In this study, the timing of radar observation is used to determine the location-time variation of the airplane that can reach to an accuracy of 0.0048 s (sampling time of radar data). The approach is as follows. The radial velocity of the airplane measured by radar is known to vary with the line-of-sight of the airplane. When the line-of-sight of the airplane is perpendicular to the track of the airplane, the radial velocity of the airplane is zero, as indicated by the location of Po in Figure 2. At the location of Po, the airplane is closest to the radar-receiving antenna. Therefore, with the help of the temporal variation of velocity of the airplane, the time at the location of Po can be determined (termed as reference time thereafter). Once the reference time is determined and the speed of the airplane is also known, the location of the airplane aloft for any time can be obtained from the video-recorded angular position and FDI-estimated range.
3.4. Speed of the Airplane
 As depicted in Figure 2, V and VD are the horizontal and radial velocities of the airplane, respectively, r is the range of the airplane estimated from FDI observation and ro is the shortest range between the airplane and radar-receiving antenna. When the airplane is located at P, the mathematical relationships between the parameters of V, VD, ro, r, and Φ (see Figure 2) are
If the airplane flies horizontally with a constant speed, the value of V estimated from (5) at any location on the track of the airplane should be the same, provided that the measurements of VD, ro, and r are accurate.
4. Calibration Results
 In this section, the calibration results of the ST and Yagi arrays of the Chung-Li VHF radar are presented. The examination of the IONO array is not available at this moment due to damage of some antennas in the array during the experimental period. Because it is much easier to conduct the calibration with the Yagi array, we show the results of the Yagi array first and then those of the ST array.
4.1. A Typical Case
4.1.1. FDI Observation
Figure 3 shows the range-time-intensity plot of radar echoes for one of the examples observed with the Yagi array, in which two airplanes with strong echoes are clearly seen. In the following, the one with lower range is examined. Apparently, the range-time variation of echo intensity depicts that the airplane approached the receiving antenna first and then flew away. Figure 4 shows the range-time variation of FDI phases for the echoes between 2.7 and 4.5 km, in which the results of three receiving channels are displayed and the phase range for each gate is from 0 to 2π. As shown, first, the FDI results of the three receiving channels are in good agreement for the airplane. In view of this, the FDI results of the receiving channel B are used to estimate the range of the airplane in the following studies. Second, a primary phase trace for the airplane is seen, which varies almost continuously throughout the range gates and indicates that the shortest range between the airplane and radar receiver is around 3.15 km. The continuous change of FDI phase is consistent with the movement of the airplane. Nevertheless, two features are noteworthy in Figure 4: (1) Duplicated phase traces occurred intermittently in upper and/or lower range gates of the primary phase trace, and (2) there is discontinuity of the primary phase trace between two adjacent gates. The first one is attributed to the receiver filtering effect. Namely, the filter response causes an overlap between the ranges of gates, so that the target in one gate can also be seen in its adjacent gates. The second feature might be associated with the system phase or other factors. If a phase compensation of −70° is given to the observed FDI phase, the second feature can be depressed well. Inspecting other observations of airplanes in this study, such a kind of phase discontinuity always exists, and the compensative phase angles are between −50° and −90°. A detailed investigation of this discontinuous behavior is underway. In view of such phase bias in the present FDI observations and for the consideration of uncertainty, an error of ±150 m in the FDI-determined range is taken into account in the calibration analysis. Such an error, however, can be depressed or removed after further calibration of FDI observations is achieved. The continuous variation of FDI phase within and between range gates, which indicates the change of range of the airplane, can provide more accurate estimation of parameters such as airplane speed and predicted SDI phase.
4.1.2. Track of the Airplane
 The upper panel of Figure 5 displays the track of the airplane in zenith and azimuth angles recorded by video camera (solid-arrowed straight line), which indicates northeast flight. Also shown in the plot are the locations of the three Yagi antennas (A, B, C) with respect to the video camera (see rectangular coordinate). The dashed lines passing through the Yagi antennas are perpendicular to the track of the airplane and indicate the locations where the airplane is closest to the receiving antennas. When the airplane is closest to the receiving antennas, its radial velocity measured by radar is zero, and the reference time can thus be determined. According to the sequence of the dashed lines and the flight direction of the airplane, the reference time for receiver B leads the other two.
 To determine the real track aloft, the height of the airplane must be known. As indicated in Figure 2, the height of the airplane, zo, can be calculated from the parameters of ro and θo at the location of Po. ro is determined by FDI observation, which is about 3.15 km, as shown in Figure 4. θo can be obtained from the record of video camera. Therefore zo = rocos(θo). The lower panel of Figure 5 shows the projection of real track of the airplane on the ground, in which the origin is Yagi antenna B.
4.1.3. Reference Time
 As mentioned in the previous section, the reference time is the moment when the radial velocity of the airplane is zero. In practice, we first calculate the radial velocity for the airplane at its lowest range gate (3.0–3.3 km, see Figure 4) by using a 256-point FFT algorithm (corresponding to a time duration of 1.2288 s) to find the approximate time of zero radial velocity, then a sliding window with 512 data points was applied to the data set within a shorter period containing the moment of zero radial velocity to compute again the radial velocity. As a result, we obtain a time series of radial velocity with time resolution of 4800 μs (namely, the sampling time of data point). As shown in Figure 6, the radial velocities change very smoothly with time and from negative to positive values, which is consistent with the flight of airplane; that is, the airplane approaches the receiving antenna and then recedes. It is calculated in Figure 6 that the times of zero radial velocity are 43.4112, 43.3920, and 43.4112 s for the receivers A, B, and C, respectively. Referring to the upper panel of Figure 5, it is reasonable that the reference time for receiver B leads that of the other two, which are almost identical to each other.
4.1.4. Horizontal Speed of the Airplane
Figure 7 presents the temporal variation of horizontal speed of the airplane estimated from (5). To obtain this result, the radial velocity of the airplane in (5) was computed first by using 256-point FFT algorithm and then V was estimated. The three curves with different thickness in Figure 7 represent the results of the three receiving channels, respectively. The three curves are basically the same, indicating that the results are reliable. The speed of the airplane is nearly constant except for the time period of 32–53 s, when the airplane is in the vicinity of the location closest to the receiving antenna. This is because the term of denominator in (5) is close to zero when r approaches ro, uncertainties of r and ro will ause large variation of V. Ignoring the unrealistic values of speed during the time period of 32–53 s, on average we find that the horizontal speed of the airplane is about 130 m/s.
4.2. Results and Discussions
4.2.1. Yagi Array
 Once the track, reference time, and horizontal speed of the airplane are known, the SDI phase of the airplane at any time can be predicted. Nevertheless, in addition to the range, uncertainties also exist in the measured/estimated parameters of speed, azimuth and zenith angles. According to the experimental setup and observation in this study, the uncertainties of the above parameters are supposed to be about 150 m (range), 10 m/s (speed), and 1° (azimuth and zenith angles), respectively. Taking these uncertainties into account, we obtain the SDI phases of the airplane predicted for each receiver pair, as shown in the left panels of Figure 8, where upper, middle, and lower panels display the results of receiver pairs AB, BC, and CA, respectively. In the left panels of Figure 8, the solid lines are the results using the originally estimated/measured parameters of airplane, while the dashed lines indicate the maximum error of the predicted SDI phase if the uncertainties of the parameters mentioned above are considered. The thick curves with small and rapid perturbation in Figure 8 are the SDI phases of the airplane observed by radar, and the zero value in the abscissa represents the reference time. As shown, the predicted SDI phases are quite reliable in view of the small range of error. In addition, the slopes of the curves for the predicted and observed SDI phases are in good agreement, indicating that the horizontal speed of the airplane estimated is close to the real one. According to these features, the nearly constant differences between the curves of observed and predicted SDI phases are meaningful. After calculation, the histograms of the differences between the observed and predicted SDI phases are shown in the right three panels of Figure 8, where each phase bin in the histogram is 1°. To improve the accuracy of SDI result, however, only the data within the period of 2 s centered on the reference time are adopted in these histograms. As indicated in the plots, the means of SDI phase differences for the three receiver pairs are about 55.86°, −25.81°, and −29.76°, respectively, and the corresponding standard deviations are about 3.90°, 3.94°, and 5.40°, respectively. The sum of the three mean values is close to zero, which is expected in accurate SDI measurement. Furthermore, the standard deviations are small, implying that the estimated mean values are reliable. According to these results, the mean values of SDI phase differences can be regarded as the system phase imbalance between the receiving channels.
 The same experiments were carried out for many times from 13 July 2000 to 13 March 2001, covering the summer and winter seasons. After applying the same procedures as done above, 54 cases having good data quality are obtained and shown in Figure 9, where upper and lower panels display the mean and standard deviation of SDI phase difference, respectively. As shown, the standard deviations for each pair of receiving channels are small, indicating the reliability of the estimated results. The mean values are basically stable during the summertime, which are about 56° ± 6°, −27° ± 5°, and −30° ± 6° for receiver pairs of AB, BC, and CA, respectively. Nevertheless, remarkable drift of the mean value can be seen after 16 Jan 2001. The average values become 51° ± 5°, −40° ± 6°, and −12° ± 5°, respectively. The reason for this drift might be due to the change in atmospheric conditions such as temperature. According to the measurements of the ground weather station next to the radar site, the environmental temperatures during the experimental days in July and August are around 30°C, while they are about 15°C during the experiments in January and March. In view of this, the change of environmental temperature, which affects the electrical characteristics of the radar components outdoors (e.g., cable line), could be one of the main factors for the drift of mean value of the SDI phase difference.
 If the SDI phase difference shown above indeed resulted from the system phase imbalance, the results shown in Figure 9 prove that such phase imbalance can be measured by using the methods and procedures applied here.
4.2.2. ST Array
 In principle, the system phase imbalances of ST and IONO arrays of the Chung-Li VHF radar can also be examined in the same way. However, some difficulties have to be considered in a practical experiment. First, because the wavelength of radio wave is 5.77 m, the viewing region without phase ambiguity in SDI measurements is much narrower than that of the Yagi array due to the large separation (20 to 45 m) between the central positions of the receiving subarrays. This difficulty can be overcome by measuring the airplane parameters precisely. Second, the synthetical phase of the radar echoes received by the antennas in the subarray may not always equal the phase of the echo received by the antenna at the center of the subarray. That is, the physical separations between the centers of the receiving subarrays may not be always valid for the analysis of SDI data. One-meter variation in the separation of the receiving centers can cause an error of SDI phase as large as tens of degrees, according to our estimations (not shown). To resolve this problem, only the targets far from the receiving antennas can be used. For such targets, the arrival directions of the radar echoes received by the antennas in the receiving subarray can be regarded as parallel so that the location of phase center of the received signals is very close to the center of the receiving subarray. Based on this, the airplane having a range larger than 10 km is possibly available. Unfortunately, the tracks of such airplanes in the video camera are more difficult to follow, and moreover, the corresponding radar returns are weaker. These deficiencies lead to the fact that only a few cases are reliable and can be utilized.
Figure10 presents the result of the ST array, in which only 5 cases having good data quality are shown. It should be mentioned that one-degree error in angular measurement for the airplane flying at very high altitude would cause large deviation in the track of the airplane. Therefore the uncertainty of angular location was ignored in Figure 10. In spite of this deficiency, they are not arbitrary for the mean values of the differences between the observed and predicted SDI phases, which are, on average, 9° ± 4°, −22° ± 6°, and 14° ± 4° for the receiver pairs AB, BC and CA, respectively. This result suggests that the method applied here is capable of measuring the system phase imbalances of large antenna arrays and can be a good method for radars where strong radio stars are not available. To improve the correctness and reliability, however, a delicate angular scale for the measurement of angular location of the airplane is preferable. After this improvement, it is then able to examine the time variation of system phase imbalance for a large antenna array.
 An investigation of phase imbalance between the receiving channels of the Chung-Li VHF radar is made by means of commercial airplanes and the FDI technique. The track of the airplane aloft is determined from the range and height, observed with FDI technique, and the angular position, measured with a well-calibrated video camera. The phase imbalance for a pair of receiving channels is obtained by comparing the observed and predicted SDI phases, in which the predicted SDI phase is calculated according to the location of the airplane. For the experiment of Yagi array in summertime, the results show that the phase imbalances between receiver pairs AB, BC, and CA are 56° ± 6°, −27° ± 5°, and −30° ± 6°, respectively, but they drift to 51° ± 5°, −40° ± 6°, and −12° ± 5°, respectively, in wintertime. Accordingly, the magnitudes of the changes of the mean values are 5°, 13°, and 18°, respectively, for the three receiver pairs. Such drift could be caused by the change of environmental temperature, which affects the path length of the electromagnetic waves in the cable line. On the other hand, the phase imbalances of the ST array are 10° ± 4°, −23° ± 6°, and 14° ± 4°, respectively, for receiver pairs AB, BC, and CA. The change of phase imbalance from season to season for the ST array is not available yet due to the lack of experimental data.
 Because the calibration utilizes commercial airplanes flying routinely and is performed under normal radar operation, it can be carried out routinely and economically. Certainly, some improvements will be helpful for the correctness of calibration. For example, the angular location of the airplane measured by video camera and the range of the airplane observed with FDI technique can be amended. A scale of angle with better resolution is recommended, which is an important promotion for the calibration of a large receiving array using an airplane far from the receiving array. Moreover, the phase bias in FDI observation is worth examining, which will give a more reliable and precise value of system phase imbalance. The latter is a further issue and is being investigated by the authors of this paper.
 This paper was supported by the National Science Council of the Republic of China, under grant NSC90-NSPO(B)-RS3-FA07-02. The authors would like to thank the reviewers for their valuable comments.