EP1804334A1

EP1804334A1 - Phased array antenna apparatus

Info

Publication number: EP1804334A1
Application number: EP05078009A
Authority: EP
Inventors: Henricus Wilhelmus Leon Naus
Original assignee: Nederlandse Organisatie voor Toegepast Natuurwetenschappelijk Onderzoek TNO
Current assignee: Nederlandse Organisatie voor Toegepast Natuurwetenschappelijk Onderzoek TNO
Priority date: 2005-12-27
Filing date: 2005-12-27
Publication date: 2007-07-04
Also published as: EP1969673B1; ATE450903T1; WO2007075083A1; EP1969673A1; DE602006010907D1

Abstract

A phased array antenna is calibrated by obtaining time-dependent signals from respective ones of the antenna outputs and computing Hilbert transforms of the time dependent signals. Products of complex signals formed from the time dependent signals and their Hilbert transforms are computed. Phase correction factors for the antenna outputs are estimated from the products. The estimated phase correction factors are used to set phase corrections applied to signals from the antenna outputs.

Description

The invention relates to a phase array antenna apparatus, and a calibration method for such an apparatus.
Phased array antennas are well known. A simple example of a phased array antenna comprises a plurality of antenna elements located at mutually different positions in a plane. Signals from antenna outputs of respective elements are added to form the output signal of the antenna. With such an antenna a sharp main lobe in a main direction perpendicular to the plane can be realized, because signals from that direction interfere constructively.
In many cases it has been found necessary to calibrate a phased array antenna. Factors such as construction spread can introduce different phase delays into the signals from different antenna elements. It is necessary to correct for these differences before the signals from different antenna elements are added, for example to ensure that the signals from all antenna outputs have the same phase when they are added, if they are the result of incoming radiation from the main direction.
Known calibration methods comprise using a transmitter to transmit calibration radiation in the form of sine wave radiation to the phased array antenna, and comparing the phase of the sine wave signals from each antenna output with the phase of the sine wave signal from a reference antenna output. The resulting phase differences are subsequently used to control respective amounts of compensating phase shift that are introduced between respective antenna outputs and the point where the signals are summed.
This method of calibration has the problem that a special calibration set-up involving transmission of such calibration radiation is needed. This would require permanent transmission of such sine wave radiation if it is desirable to calibrate the phased array antenna "in the field", at arbitrary time points, for example when mechanical operating conditions or temperature variations etc. make testing desirable.
Among others, it is an object of the invention to provide for a method and device for calibrating a phased array antenna wherein no calibration radiation in the form of a sine wave is needed for transmission.
A method and device for calibrating a phased array antenna are set out in the independent claims. Hilbert transforms of signals from the antenna outputs are used to compute complex phase vectors for the different antenna outputs. The phase correction factors between the antenna outputs are estimated from products of these phase vectors. Because a Hilbert transform is used, the calibration method works even if no perfect sine wave radiation is available for calibration. The phased array antenna may be directed for example at any transmitter for which the direction is known, to obtain a calibration even if that transmitter transmits modulated signals over a frequency band of some width.
These and other objects and advantageous aspects will become apparent from a description of exemplary embodiments, using the following figures.

Figure 1 shows a receiver apparatus
Figure 2 shows an alternative receiver apparatus

Figure 1 shows a receiver apparatus comprising a phased array antenna 10 with a plurality of antenna outputs 12, adaptable attenuator circuits 15, adaptable phase correction circuits 18, a combination circuit 19 and a signal processing circuit 20. Each antenna output 12 is coupled to combination circuit 19 via a respective chain containing a series arrangement of an adaptable attenuator circuit 15 and an adaptable phase correction circuit 18. Combination circuit 19 has a result output coupled to data processing circuit 20. Phase correction circuits 18 may be implemented for example as adaptable phase correction circuits, or as digital phase correction circuits.
In an embodiment phase array antenna 10 comprises a plurality of discrete antenna elements (not shown) placed at mutually different spatial positions, each element being coupled to a respective one of the antenna outputs. Antenna elements distributed over a flat plane may be used for example, but alternatively positions that are not limited to a single plane may be used. Also, instead of an array of separate antenna elements an integrated structure may be used, which has different antenna outputs (for example a waveguide structure with different tap points corresponding to different antenna outputs).
In normal operation phased array antenna 10 receives incoming radiation and outputs resulting signals at antenna outputs 12. Signals from different elements outputs 12 are attenuated by adaptable attenuator circuits 15 and their phase is changed by different set amounts by adaptable phase correction circuits 18. The phase correction is realized for example by delaying each signal by a respective set amount of delay. Combination circuit 19 adds the resulting signals, optionally after another, predetermined phase adjustment. The resulting sum signal is fed to signal processing circuit 20.
The apparatus of the figure is shown by way of example only. Various alternative embodiments may be used. For example, in one embodiment adjustable attenuator circuits 15 may be omitted.
Figure 2 shows another embodiment where signal combination takes place at a digital level. In addition to the elements of figure 1 this figure contains a local oscillator 11, mixers 14, analog to digital converters 16. Each chain contains a series arrangement of a mixer 14, an analog to digital converter 16 and an adaptable phase correction circuit 18. Local oscillator 11 is coupled to local oscillator inputs of mixers 14. In the embodiment of figure 2 the antenna signals are mixed down, sampled and converted to digital signals before being phase corrected and combined. In this embodiment combination circuit 19 is a digital signal processing circuit that is configured to add signals obtained from different antenna outputs 12. Adaptable phase correction circuits 18 may be part of the digital processing circuit. Phase correction may be performed for example by combining samples for different time points for different antenna outputs 12, optionally interpolating between sample values. As an alternative, the signals derived from the respective antenna outputs may be multiplied with respective complex factors, whose phases correspond to the respective phase corrections.
As other examples of alternative embodiments analog signal adaptable phase correction circuits 18 may be used, inserted in front of mixers 14, or between mixers 14 and analog to digital converters 16. Furthermore, the addition of signals may be performed at an analog stage after mixing or even before mixing. In such an embodiment the adaptable phase correction circuits 18 are included between the stage where adding is performed and the antenna outputs 12.
Prior to normal operation, or intermittently during normal operation a calibration of the antenna is performed. Calibration involves setting differences between the amounts of phase correction introduced by adaptable phase correction circuits 18.
The differences between the amounts of phase correction are selected by a calibration measurement. During the calibration measurement phased array antenna 10 is directed at a known angle to a reference transmitter and preferably directed at the reference transmitter. Signals from individual antenna outputs are processed separately. In the embodiment of figure 1 for example combination circuit 19 is set to a mode wherein signals from a selected pair of antenna outputs 12 are passed. In the embodiment of figure 2 combination circuit 19 digitally selects a pair of signals. Signal processing circuit 20 receives these signals and digitizes these signals if still necessary, by using sampling and analog to digital conversion.
Form the digital signals S1, S2 from the pair of antenna outputs signal processing circuit (20) computes Hilbert transform signal H(S1), H(S2) of the antenna output signals. The analytic Hilbert transform of a signal S(t') as a function of time t' is known per se and corresponds to the principal value of an integral over time t' of $S (tʹ) / (t - tʹ)$
Herein the principal value of the integral is defined in terms of the value P of the integral of S(t')/(t-t') over t' from minus infinity to t-x plus the integral of S(t')/(t-t') from t+x to infinity. The principle value is the limit value of P when x approaches zero from above.
Methods of determining approximate or exact Hilbert transforms are known per se. Preferably a digital numerical computation is mandatory. In modern signal processing one analyzes discrete time signals. As used herein the term "Hilbert transform" is used for the result of a computation that computes the integral defined above as well as for results of computations that compute approximations of this integral..
Methods for computing the Hilbert transform of a signal s(t) by means of samples s(n) = s(na) (where na, are regularly spaced time points at distance a) are known per se, for example from S.L. Hahn, Hilbert Transforms in Signal Processing, Artech House, Inc., Norwood (1996).
Known numerical integration techniques may be used. In one example, interpolation functions are defined which can be used to find an interpolated value of the signal s for any time point a sum of the products of respective sample values s(na) and respective interpolation functions of the signal. In this case the Hilbert transform of the signal can be expressed in terms of the Hilbert transforms of the interpolation functions times the sample values. For a low frequency band limited signal s(t) for example, which can be interpolated with sync signals, the Hilbert transform of s(t) for a time point t can be computed as $2 \sum_{n = - \infty}^{\infty} s (na) \frac{\sin^{2} \frac{1}{2} π (f_{s} t - n)}{π f_{s} t - nπ}$
Herein fs is a sampling frequency (at least twice the band frequency of s(t)) and a=1/fs. For a signal s(t) of finite duration the sum over n may be limited to values of n for which s(na) is not negligible. A similar expression can be derived for band limited signals whose spectral content is limited in a limited high frequency band. Interpolation functions for this are known per se. Each antenna output signal S1, S2 and its Hilbert transform defines a complex signal vector according to $V 1 = S 1 + i H (S 1) and V 2 = S 2 + i H (S 2)$
Herein i is a square root of-1. Signal processing circuit 20 computes a product M of the vector V1 and the complex conjugate of V2: $M = S 1 * S 2 + H (S 1) * H (S 2) + i (H (S 1) * S 2 - S 1 * H (S 2))$
Signal processing circuit 20 averages M over time t and computes a phase value of the resulting averaged vector. Thus (averaging denoted by "AV") $phase value = arctg ({AV [H (S 1) * S 2 - S 1 * H (S 2)]} / \{AV [S 1 * S 2 + H (S 1) * H (S 2)]\})$
For each pair of antenna elements, labeled i, j, a nominal designed phase difference N(i,j) is defined for the direction in which phase array antenna 10 is directed relative to the reference transmitter (e.g. N(i,j)=0 for certain antenna's and directions) . The measured phase value and the nominal designed value N(1,2) for the pair of antenna elements define a phase deviation D $D = phase value - N (1 2)$
This deviation D is subsequently used to adjust amounts of phase correction provided by at least one of the phase correction circuits 18 for the pair of antenna outputs, so that the difference between the amounts phase correction is changed by a phase change that corresponds to minus the deviation D for the operating frequency of the antenna (or a frequency in an operating band of the antenna, e.g. a central frequency in that band).
In one embodiment deviations D are determined in this way for respective pairs of antenna outputs 12 that each contain the same reference antenna output and a respective one of the other antenna outputs 12. In this case combination circuit 19 is switched successively to pass signals for respective different pairs of antenna outputs 12. In this embodiment the amount of phase correction of each respective one of the other antenna outputs 12 is adjusted according to the deviation D involving that respective one of the other antenna outputs 12. (Obviously, no adaptable phase correction circuit 18 is needed for the reference antenna output 12 in this embodiment).
It should be appreciated that alternative embodiments are possible. For example deviations D(i, j) between more antenna outputs 12 (labeled i, j) may be determined and the amounts of adjustment A(k)for different antenna outputs 12 (labeled k) may be selected to as to minimize a sum of squares of (D(i,j) -A(i)+A(j)).
Although an embodiment has been described were the product of two signals is computed at a time it should be appreciated that alternatively the products of signals from more pairs of antenna outputs 12 may be computed at a time. In another embodiment signals derived from a plurality of antenna outputs 12 simultaneously may be stored for use in computing products of these signals for different pairs of antenna outputs.
Although it is preferred to use time-averages of products M of signals from pairs of antenna outputs 12 it should be appreciated that alternatively not averaged signals may be used. However, this increases dependence on noise and/or modulation of the signals. Preferably an averaging time interval is used that exceeds an inverse of a modulation bandwidth of the signals. More preferably this bandwidth is exceeded by at least a factor of ten. Similarly the integration time is preferably selected at least so long that the signal to noise ratio of the average is at least ten. Because the average is determined for the product of the phase vectors and not for the phase values errors due to the periodic nature of phase values are avoided.
Although it is preferred to use signal from pairs of antenna outputs 12 it should be appreciated that alternatively pairs of signals may be used wherein one or both of the signals are combinations of signals from different antenna outputs 12. In this case required phase adjustments can be estimated for example by minimizing a quality criterion like a sum of squares of (AV[M(i,j)] - R(i,j;-A)), wherein M(i,j) are different products of computed phase vectors and R(i,j;-A) are predicted products for different sets of phase adjustments A. In a simple embodiment a flat phase array antenna is directed at a reference transmitter requires nominal designed phase difference N(i,j) equal to zero. However, alternatively different nominal designed phase difference N(i,j) may be used, for example when the antenna is known to be directed at an angle to the reference transmitter, or if corrections must be made because the reference transmitter is not in the far field with respect to phase array antenna 10, or if the design of the antenna is such that different phase differences are required (e.g. for nulling purposes, or due to the arrangement of antenna elements).
The computations for the calibration are preferably performed by a signal processing circuit 20 in the apparatus, which also sends electronic control signals to adaptable phase correction circuits 18 to adapt the phase corrections according the calibration. In this case signal processing circuit 20 switches from a normal operating mode to a calibration mode to perform calibration. Such a mode switch may be accomplished for example by executing different parts of a program of signal processing circuit 20. Similarly, under control of signal processing circuit 20 combination circuit 19 is switched to a mode wherein respective signals derived from pairs of antenna outputs are passed to signal processing circuit 20. Alternatively calibration may be performed by combination circuit 19. The required processing may be performed by one or more programmable digital signal processors, programmed with a program to perform the required operations.
In an embodiment the phase corrections are also applied using the Hilbert transform. In this embodiment combination circuit 19 stores averaged complex factors F(j) obtained for respective antenna outputs 12 (labeled j=0,1,...) from signals Sj from these outputs in combination with a signal Sr from a reference one of the outputs: $F (j) = AV \{Sj * Sr + H (Sj) * H (Sr) + i (H (Sj) * Sr - Sj * H (Sr))\}$
The average AV is taken over time. Optionally the factor F(j) is normalized by dividing it by its absolute value (for example if the antenna outputs are designed to output different strength-signals, but in this case alternatively a predetermined design-dependent normalization may also be used). In normal operation, combination circuit 19 computes (approximate) Hilbert transforms H(Xj) of normal time-dependent operating signals Xj from respective outputs j and multiplies complex signals time dependent Xj + i H(Xj) that are obtained in this way to obtain corrected signals Yj: $Yj = Fc (j) * \{Xj + iH (Xj)\}$
Herein Fc(j) is the complex conjugate of F(j). The signals Yj are then combined (summed) to form an antenna output signal. In this way no arctangent needs to be computed at all, so that uncertainty about 360 degree phase errors is avoided. Of course said summing may involve using predetermined, designed phase factors and/or weighting factors used to realize a desired antenna pattern. These factors may be integrated in the factor F(j) in order to reduce the amount of computation
Although an embodiment has been described wherein combination circuit 19 isolates signals from pairs of antenna outputs 12, it should be appreciated that alternatively dedicated circuits may be used to obtain signals from respective antenna outputs in isolation. Thus a calibration circuit may be provided that is at least partly distinct from the normal operating circuit. Preferably, such a calibration circuit is part of the apparatus, but alternatively a detachable calibration unit may be used.
Although an embodiment of a receiver apparatus has been described, it should be appreciated that alternatively calibration may be applied to a transmitter. In one embodiment phase correction circuits 18 are used in reverse for transmission. Alternatively, similar phase correction circuits coupled from a transmitter part of the apparatus to antenna outputs 12 may be used, which are set to corresponding amounts of phase correction as in the receiver.

Claims

A method of calibrating a phased array antenna that comprises a plurality of antenna outputs, the method comprising
- obtaining time-dependent signals from respective ones of the antenna outputs;

- computing Hilbert transforms of the time dependent signals;

- computing products of complex signals formed from the time dependent signals and their Hilbert transforms;

- estimating phase correction factors for the antenna outputs from the products;

- using the estimated phase correction factors to set phase corrections applied to signals to or from the antenna outputs.
A method according to claim 1, the method comprising averaging the products over time and estimating the phase correction factors from the time-averaged products.
A method according to claim 1 or claim 2, wherein the products are formed of complex signals formed from the time dependent signals and their Hilbert transforms for respective ones of the antenna outputs with complex signals formed from the time dependent signal and its Hilbert transform for a reference one of the antenna outputs.
A method according to any one of the preceding claims, comprising directing the phased array antenna at a predetermined angle to a transmitter during the step of obtaining the time-dependent signals.
An apparatus comprising
- a phased array antenna that comprises a plurality of antenna outputs;

- a signal combining circuit with a plurality of signal inputs and configured to add signals from the signal inputs;

- adaptable phase correction elements coupled between the antenna outputs and respective ones of the signal inputs;

- a signal processing circuit that is operable in a calibration mode, the signal processing circuit being configured to perform a calibration when in the calibration mode, the calibration comprising

- obtaining time-dependent signals from respective ones of the antenna outputs;

- computing Hilbert transforms of the time dependent signals;

- computing products of complex signals formed from the time dependent signals and their Hilbert transforms;

- estimating phase correction factors for the antenna outputs from the products;

- using the estimated phase correction factors to set phase corrections applied to signals to or from the antenna outputs.
An apparatus according to claim 5, wherein the signal processing circuit is configured to average the products over time and to estimate the phase correction factors from the time-averaged products.
An apparatus according to claim 5 or 6, wherein the adaptable phase correction elements are adaptable signal delay circuits.
An apparatus according to claim 5 or 6, wherein the adaptable phase correction elements comprise one or more computational circuits, configured to perform complex multiplications of complex correction factors derived from the phase correction factors for respective ones of the antenna outputs and complex signals formed from signals from respective ones of the antenna outputs and their respective Hilbert transforms.
A computer program product, comprising a program of instructions for a programmable data processing circuit, which when executed by the data processing circuit, cause the data processing circuit to
- obtain time-dependent signals from respective ones of the antenna outputs;

- compute Hilbert transforms of the time dependent signals;

- compute products of complex signals formed from the time dependent signals and their Hilbert transforms;

- estimate phase correction factors for the antenna outputs from the products;

- use the estimated phase correction factors to set phase corrections applied to signals to or from the antenna outputs.
A computer program product according to claim 9, comprising a program of instructions for a programmable data processing circuit, which when executed by the data processing circuit, cause the data processing circuit to switch between a normal operating mode and a calibration mode, the steps of claim 9 being performed in the calibration mode, the program of instructions causing the data processing circuit to perform the following steps in the normal operating mode
- obtaining time-dependent signals from respective ones of the antenna outputs;

- compute Hilbert transforms of the time dependent signals;

- compute products of complex signals formed from the time dependent signals and their Hilbert transforms with factors derived from the estimated phase correction factors;

- summing said products to form an antenna output signal.