WO2011093805A1

WO2011093805A1 - A system and a method for simultaneous position, mutual coupling and gain/phase calibration of antenna arrays

Info

Publication number: WO2011093805A1
Application number: PCT/TR2010/000015
Authority: WO
Inventors: Engin T. Tuncer
Original assignee: Tuncer Engin T
Priority date: 2010-01-27
Filing date: 2010-01-27
Publication date: 2011-08-04
Also published as: TR201208632T2

Abstract

A system and a method comprised of a laser range and position finder (213), antennas with dielectric reflective and non-reflective coatings (201, 203), multi-channel receivers (407) for signal collection and base band conversion, calibration unit (409) and a calibration processing (111) is presented. The method is used to calibrate antenna positions, gain/phase and mutual coupling simultaneously. Laser range and position finder (213) is used to measure the nominal antenna positions. The antennas have reflective coatings (201) for good laser reflection and coded position identification. Known direction-of-arrivals for a calibrated source (401,403) are used in the calibration processing (111). Calibration processing (111) involves the fine position, antenna mutual coupling and gain/phase calibration.

Description

A SYSTEM AND A METHOD FOR SIMULTANEOUS POSITION, MUTUAL COUPLING AND GAIN/PHASE CALIBRATION OF ANTENNA ARRAYS

Related Field of the Invention:

This invention relates to a system and a method for sensor array calibration in general and more particularly accurate calibration of antenna arrays for measuring the nominal and fine three dimensional positions, mutual coupling and gain/phase mismatches simultaneously.

Background of the Invention (Prior Art):

Three major sources of distortion for the antenna arrays are the antenna position errors, mutual coupling between antennas, and the gain/phase mismatches of antenna channels which involve the antenna and the subsequent devices and cables. Conventional array calibration methods usually consider a subset of the above three sources of error since simultaneous calibration of these is a challenging task. One of the common approaches is to transmit known signals from a calibrated antenna and use the known signal in the received antenna for calibration purpose. This approach has certain limitations since the transfer function between the transmitter and receiver is not known perfectly. In addition, the use of several received samples only helps to improve the signal-to-noise ratio (SNR) and does not contribute to generate equations sufficient to solve for the unknowns. The linearly independent set of equations required to solve for the unknowns can be obtained by using calibration sources transmitting from different known direction-of-arrival (DOA) angles.

Another major limitation of the prior art which attempts to calibrate the sources of error simultaneously is their use of known information at once and iterate using the same information. In those methods, assuming perfect antenna positions, antenna gain/phase matrix is estimated by taking an initial mutual coupling matrix. Then the gain/phase matrix is employed for the estimation of mutual coupling using the same data set or information. This approach does not lead to a satisfactory result since the mutual coupling matrix turns out to be exactly the same as the initial mutual coupling matrix. In this respect, iterative approach should be carried out with great care in order to improve at each step. Antenna mutual coupling and gain/phase mismatch are closely related in the sense that any error in one can be compensated by the other to satisfy the cost function. Therefore known information should be used in parts during the calibration loop. Even though this leads to better results in calibration, it is not sufficient for the best performance. A good cost function and a search in the neighborhood of the nominal parameters are also important. For a single source, the known direction-of-arrival angle for the source should be used appropriately and the solution of the parameter values should be done with care. The prior art for this purpose have problems since the resulting solution may be ill-conditioned.

In practice, different size and types of antennas are used to cover the large bandwidth of operation. Some of these antennas are mounted over a long antenna mast. These antennas are affected by several environmental factors and physical forces. The position of such antennas as well as their orientation should be calibrated periodically for the best operational performance. In this respect, a method and apparatus for measuring their position and orientation from a distance is of practical value.

The following patent documents are cited for the position determination in general with a laser device. Additional documents are cited for the previous methods for finding the mutual coupling and gain/phase terms of antennas.

· US patent 5006721- LIDAR scanning system

• US patent 5361217- Position measuring/plotting apparatus

• US Patent 6034803 - Method and Apparatus for directing energy based range detection sensor

• US patent 6246468 Bl- Integrated system for quickly and accurately imaging and modeling three-dimensional objects

• US Patent 6922234 - Method and apparatus for generating structural data from laser reflectance images

• "Direction finding in the presence of mutual coupling", Benjamin Friedlander, Anthony J. Weiss, IEEE Trans. On Antennas and Propagation, Vol. 39, No.3, March 1991.

· H. Krim, M. Viberg, "Two decades of array signal processing research: the parametric approach", IEEE Signal Processing Magazine, vol. 13, pp.67-94, July 1996.

Brief Description of the Invention:

The present invention discloses a system and a method for the calibration of antenna arrays for nominal and fine three dimensional positions, antenna mutual coupling and antenna gain/phase mismatches simultaneously. Antenna position calibration can be done in two steps. The first step involves the measurement and calibration of the nominal antenna positions (101) by a laser range and position finder (213). This laser device is essentially a laser radar (also called as LIDAR). It measures the target range, azimuth and elevation angles in spherical coordinates. The target spherical coordinates can be converted to Cartesian coordinates. The antenna positions are measured with respect to the laser device. Therefore, the laser device is at the center of the reference coordinate system (0,0,0) (219) in terms of (x,y,z) coordinates. The laser device can also be positioned with respect to a certain reference. Laser position finder can be placed on a platform which can be adjusted manually as well as automatically. This device can include a global positioning unit (GPS) as well as an inertial measurement unit (IMU) for accurate positioning. A wireless as well as wired connection allows the operator to collect the data during the position calibration. This device can be positioned at different places to increase the number of calibration measurements and these measurements are then collectively used to improve the position accuracy. Antennas are coated with reflective and non-reflective coatings (201, 203) in order to improve the laser beam spotting and positioning. These coatings can be used as a code for the laser device to differentiate between the surrounding as well as the antenna center, top and bottom. This allows the laser device to automatically determine the three dimensional positions of the points on the antenna structure during a horizontal (237) and vertical scan (231). The scan data can be transferred to the calibration unit (409) through the input/output and communication unit (411) to determine the antenna positions, orientations as well as the three dimensional image of the antenna array. The nominal antenna positions are recorded and used in the following stages of the calibration procedure.

The second step of the antenna position calibration serves for fine position calibration. This step is performed in the antenna calibration loop (111). The calibration data is collected (103) by placing the transmitter (401) in different places. The direction of arrival (DOA) azimuth and elevation angles (Θ -> azimuth angle, φ -> elevation angle) for the source are recorded as well as the received signal to obtain the covariance matrix of the data.

In order to perform antenna fine position search and estimation (105) together with the antenna coupling matrix search and estimation (107) and antenna gain/phase matrix estimation (109), data should be collected from a single calibration source emitting from different positions successively for the satisfactory performance. The direction of arrival angles for these positions should be known. The source signal should be transmitted separately at different times from these positions. The DOA angle separation is preferred to be larger than ten degrees (10°) for the best performance. If the antenna fine position calibration step is omitted, then only two transmissions from two different positions may be sufficient. In this case, two known DOA angles are required for the mutual coupling and gain/phase calibration. In this innovation, the content of the transmitted signal is not used. More specifically, there is no need to transmit a specific coded signal and know it at the receiver. The received data is used to obtain the covariance matrix for the computation of a cost function. If the array mutual coupling matrix does not have a special form like banded complex symmetric Toeplitz or symmetric circulant form, more calibration DOA angles are required in order to solve for the number of unknowns.

The antenna calibration loop (111) involves three main components. In the antenna fine position search and estimation (105), three dimensional search in a grid in the neighborhood of the nominal antenna positions are done. At each case, antenna positions are updated (609, 619) within a number of loops (603-617) for the positions of the antennas. The mutual coupling and gain/phase parameters are found and a cost function (623) is computed. This value of the cost function is stored for each antenna position in order to select the minimum which in turn gives the position, mutual coupling and gain/phase calibration values.

As the number of the known DOA angles for the transmitting source increases, the accuracy for the estimation of the antenna mutual coupling and gain/phase parameters increases. The initial mutual coupling parameter set (501) can be given as an input. Then a search in a uniform grid in the neighborhood of the initial parameter values is done for the mutual coupling parameters. At each update of a single mutual coupling parameter, gain/phase parameters are found and a cost function is evaluated. This cost function is stored as well as the coupling and gain/phase parameter. Once the search grid for the single mutual coupling parameter is all covered, the coupling parameter value and gain/phase parameters for the minimum cost are selected. The mutual coupling parameter vector is updated and the process is continued until all the mutual coupling parameters are updated accordingly. The final set of mutual coupling parameters and gain/phase parameters are found. The main loop (503) is iterated for a better performance at each iteration.

There are several advantages of the present invention;

• A complete calibration of an antenna array is achieved by considering position, antenna mutual coupling and gain/phase calibrations, • There is no need to know the transmitted signal. Instead, the direction-of-arrival of the signals and the corresponding covariance matrices are used,

• The accuracy of the position, mutual coupling and gain/phase calibrations are high,

• The calibration can be performed when the antenna array is on the operational platform.

Definition of the Figures:

In order to explain the present invention in more detail, the following figures have been prepared and attached to the description. The list and the definition of the figures are given below.

FIGURE 1 is a description of the stages involved in the calibration operation;

FIGURE 2.A illustrates the antenna position measurement by a laser device;

FIGURE 2.B shows the vertical and horizontal scan of the laser beam;

FIGURE 3.A illustrates the antenna top, center and bottom midpoints;

FIGURE 3.B shows the calculation of the distance to the antenna center midpoint;

FIGURE 4 illustrates the calibration setup;

FIGURE 5 is a block flow diagram of the described method for finding the antenna mutual coupling and gain/phase parameters for the given antenna positions;

FIGURE 6 is a block flow diagram of the antenna calibration loop,

FIGURE 7 shows the antenna structure for a horn antenna and the points on the antenna to characterize the three dimensional structure using the antenna coatings.

Definition of the Elements (Features/Components/Parts) on the Figures:

The definition of the features/components/parts which are covered in the figures that are prepared in order to explain the present invention better are separately numbered and given below.

101 - The measurement and calibration of the nominal antenna positions

103 - Transmit signal generation And calibration source adjustment 105 - Antenna fine position search and estimation

107 - Antenna mutual coupling matrix search and estimation

109 - Antenna gain/phase matrix estimation

111 - Antenna calibration processing

201 - Reflective coating

203 - Non-reflective coating

205 - Laser beam spot on the reflective coating

207 - Top coating

209 - Center coating

211 - Bottom coating

213 - Laser range and position finder

215 - Dipole antenna

217 - Tripod

219 - Reference coordinate system

231 - Vertical scan

233 - Laser beam spot

235 - Scan area upper left corner coordinate (χι,ν.,Ζι)

237 - Horizontal scan

239 - Scan area lower right corner coordinate (x₂,V2,z₂) 241 - Scanning path

301 - Antenna center midpoint with spherical coordinate

303 - Triangular relations

305 - Triangular relations

321 - Antenna top midpoint

323 - Antenna center midpoint

325 - Antenna bottom midpoint

401 - Calibration transmitter 403 - Incident plane wave with known DOA angle (φ,θ)

405 - Antenna array

407 - Multi-channel receiver

409 - Calibration unit

411 - Input/Output communication unit with display

501 - Initial mutual coupling parameter setting

503 - Main loop

505 - Loop for antenna mutual coupling parameters

507 - Intermediate parameter setting

509 - Search loop 1

511 - Search loop 2

513 - Coupling parameter update and coupling matrix generation

515 - Computation of the gain/phase matrix

517 - Computation of the cost function for the mutual coupling and pain/phase parameters 519 - Comparison for finding the best values of coupling and gain/phase parameters

corresponding to the minimum cost value.

521 - Setting the local variables

523 -Test for loop 2

525 -Setting the loop variable kb

527 - Test for loop 1

529 -Setting the loop variable 2

531 - Setting the local variable c_ki

533 - Test for the variable of the loop for mutual coupling

535 - Setting the loop variable p for the mutual coupling

537 - Test for the main loop

539 - Setting the variable of the main loop ki

541 - Setting the final result for the mutual coupling and gain/phase parameters 601 - Taking the inputs and setting the initial parameter values

603- Loop for x axis search of the first antenna

605- Loop for y axis search of the first antenna

607- Loop for z axis search of the first antenna

609- First antenna position update

611- Remaining loops for the other antennas

613- Loop for x axis search of the Mth antenna

615- Loop for y axis search of the Mth antenna

617- Loop for z axis search of the Mth antenna

619- Mth antenna position update

621- The algorithm for mutual coupling and gain/phase estimation (107,109)

623- Computation of the cost function

625- Test for the cost function to find the minimum value

627- Setting the local variables after the test operation

629- Test for the z axis loop parameter of the Mth antenna

631- Setting the z axis loop parameter for the Mth antenna

633- Test for the y axis loop parameter of the Mth antenna

635- Setting the y axis loop parameter for the Mth antenna

637- Test for the x axis loop parameter of the Mth antenna

639- Setting the x axis loop parameter for the Mth antenna

641- Remaining tests and settings for the other antennas

643- Test for the x axis loop parameter of the first antenna

645- Setting the x axis loop parameter for the first antenna

647- Setting the final values of antenna positions, antenna mutual coupling and gain/phase terms

701- Horn antenna structure

703- Points on the antenna structure for the three dimensional characterization of the antenna

705- Example of the antenna reflective and nonreflective coatings for marking the antenna structure point Detailed Description Of The Invention:

Referring now to drawings, FIGURE 1 illustrates the antenna array calibration process. In FIGURE 1, nominal antenna position measurement and calibration (101) is achieved by using a laser range and position finder device (213) in FIGURE 2. This laser range and position finder (213) can measure the range by emitting laser pulses and measuring the time of flight of the returned pulse. The direction of the laser pulse in azimuth and elevation can also be accurately adjusted. Therefore the position of the object which caused the laser pulse return can be found as (d,9,†) in spherical coordinates as shown in FIGURE 3.B. This laser range and position finder (213) is a laser radar (also called as LIDAR). Laser range and position finder (213) can scan the scene in horizontal (237) and vertical (231) directions. It can have wireless and wired connection where both commands and data can be exchanged between the laser range and position finder (213) and the calibration unit (409). It can be operated manually as well as automatically. Remote control of the laser range and position finder (213) can be done through the wireless or wired connection. This laser range and position finder (213) can scan a predetermined region automatically as shown in FIGURE 2B and by the corner coordinates (235), (239). The scan region coordinates can be uploaded to the laser range and position finder (213) to start the scanning operation. The scan data is composed of the three dimensional coordinates of the objects in the scene as well as the intensity value of the reflections. This three dimensional data can be transferred to the calibration unit (409) and used for the nominal position measurement of the antenna elements (101) as well as their orientations. Laser range and position finder (213) can be mounted on different platforms including a tripod (217). The laser range and position finder (213) can include a GPS (Global Positioning System) unit and IMU (Inertial Measurement Unit) for accurate positioning of the laser range and position finder (213). It can also adjust its position relative to a reference point. A reference coordinate system (219) can be created by considering the position of the laser range and position finder (213) and its three dimensional position is chosen as the origin of this reference coordinate system (219), namely the (0,0,0) coordinates of the x,y,z coordinate system. The reference coordinate system (219) can then be mapped to the global coordinate system. The three dimensional positions of the antennas in the antenna array (405) can be determined with respect to the reference coordinate system. These coordinates can be mapped to the global coordinate system. A dipole antenna (215) is chosen as an exemplary while different types of antenna can be used. This innovation can be applied to more general types of antennas and array structures. An example of a different type of antenna where the innovation can be used is the horn antenna (701) in FIGURE 7. The antennas in the antenna array (405) are coated with a dielectric reflective (201) and non-reflective (203) coatings in order to have a good laser pulse reflection and good positioning. These coatings are accurately done with respect to the antenna center midpoint (323) and they are used as codes to identify the three dimensional position of the antennas. The coatings can also be used to identify the identity of the individual antennas, and the relative positions with respect to each other within the antenna array (405). The size of the coating layers (207) (209) (211) (dci,dc2,d_c3,dc4,dc5,dc6) depends on the laser resolution. The larger the coating size, d_c_, the less accurate is the laser beam spot (233) positioning but the more probable is to find the coded place during the laser scan. The spatial information coded by these coatings can be changed by changing the features such as size, texture, reflection coefficient of the coatings and the number of reflective and non- reflective coating strips (201), (203) on the antenna. The spatial information in its simple form is coded by using consecutive reflective and non-reflective coatings (201), (203) on the antenna. The intensity of the laser beam reflection from the antenna coating is coded by a binary number. The reflection intensity above a given threshold is coded by a binary number '1' and below the threshold is coded by a binary number ^λ0'. The laser beam reflections from the antenna top, center and bottom generate a binary code for each antenna. The size d_ci of these coatings also carry the information. If there are two consecutive reflective and non-reflective coatings (201), (203) with sizes d_ci and

respectively, and the size of d_ci corresponds to one unit of the vertical (231),-(233) resolution of the laser range and position finder (213), the code the coating represents would be a binary number 100 (reflective=l, non-reflective=0) in a vertical (231) laser scan. An alternative type of coding can be the treatment of the transitions from the reflective coating (201) to a non-reflective coating (203). The spatial information coded by these coatings can be used to identify the orientation of the antennas with respect to the vertical axis. The top and bottom as well as the antenna center have these coatings but the coated layer structures are different. The antenna center coating (209) is symmetric whereas the top (207) and bottom (211) coatings are not symmetric. This type of coded coatings generates different laser pulse return sequence at the bottom, center and at the top of the antenna during a scene scan. This in turn is used to identify the position of the antenna center midpoint (301) and antenna center midpoint with spherical coordinates (323) where the distance from the laser range and position finder (213) is measured.

The scanning process takes the scanning area coordinates, the antenna coating codes, the threshold for the laser beam intensity and the antenna dimensions as the input. Optionally antenna relative coordinates with respect to each other and the number of antennas can be taken as the input as well. The laser range and position finder (213) starts the scan from the upper left corner (235) of the predetermined scanning area coordinates and follows a scanning path (241) as shown in FIGURE 2B. Once the vertical path is traversed, laser spot is moved to the next point horizontally and vertical scan is continued upwards indicated by the scanning path (241) as shown in FIGURE 2B. Scan process continues until the lower right scan coordinate (239) is reached.

During the scan process performed on the scanning path (241), the laser reflections are evaluated and compared with the input for the intensity threshold. The intensity of the reflections above the threshold is taken as binary one "1" and the intensity below the threshold is taken as binary zero "0". When the binary codes of the reflections match to the predetermined codes of the antenna, the antenna with the coded information is declared to be found. If the relative positions of the antennas in the antenna array (405) are known, the remaining antennas within the scanning area are searched more effectively. In this case, when the positions of the two antennas are determined, the laser range and position finder (213) is pointed to the scan area where the remaining antennas are located in order to save time for the scanning process. The laser beam spot (233) in the scan process as shown in FIGURE 2B at the central reflective coating (da) (209) which returns the maximum reflection is selected as the point to measure the antenna center midpoint (323). Laser range and position finder (213) can also position its laser beam spot (233) more accurately to the desired antenna center position by considering the antenna dimensions and the reflections from the antenna top (207) and bottom coatings (211). Laser range and position finder (213) measures the distance to the antenna center, d, as well as the azimuth and elevation angles as in FIGURE 3.B. The antenna radius, r, is taken into account to find the distance to the antenna center midpoint with spherical coordinate, p, (301). The antenna center midpoint coordinates in spherical coordinates (ρ,θ,φ-ψ) (301) is obtained by using the triangular relations (303), (305). This type of measurement allows accurate position measurement of the antenna elements in the antenna array (405). The process to find the coordinates of the antenna center midpoint (323) can also be used to find the coordinates of the antenna top (321) and bottom midpoints (325). Once the antenna center midpoint is found, the antenna dimensions can be used together with the scanning results in order to aid the identification of the antenna top (321) and bottom midpoints (325). However antenna top and bottom midpoints (321, 325) can be found independently as well. The laser beam spots which return the maximum reflection are selected as the points to measure the antenna top and bottom midpoints. These laser beam spots are selected in accordance with the antenna dimensions and therefore the distance between the antenna center midpoint and the top and bottom midpoints are considered. The coordinates for the antenna top and bottom midpoints are found similar to the antenna center midpoint as shown in Figure 3B. The determination of the antenna top and bottom midpoints allows the identification of the inclination of the antenna with respect to the reference coordinate system as well as the complete positioning of the antennas with respect to the reference coordinate system (219). Additional points on the three dimensional antenna structure can be determined from the antenna coatings and the known antenna dimensions as described before for the antenna top, center and bottom midpoints. An example is given in Figure 7 where a horn antenna (701) is shown. The three dimensional coordinates for the points (703) on the antenna structure are used to characterize the antenna structure more accurately in three dimensions. The antenna reflective and nonreflective coatings (705) mark these points on the antenna structure.

The antenna position is measured by considering the coordinate system which takes the laser range and position finder (213) as the center of the x,y,z, reference coordinate system (219) namely the (0,0,0) point. It is possible to represent the reference coordinate system (219) either in (x,y,z) parameters as in rectangular coordinate system or in (d,6,†) parameters as in spherical coordinate system and it is always possible to convert from one coordinate system to the other. Laser range and position finder (213) has GPS and IMU units and therefore its position in global coordinates is known accurately. The measured local position of the antennas can be converted to the global coordinates. The accuracy of the measured antenna positions may not be sufficient for accurate characterization of the antenna array (405) especially for high frequencies where the wavelength is small. For example when the operation frequency for the antenna array (405) is lGHz, any antenna position error on the order of centimeters generates a large error during the operation of the antenna array (405). In this respect, the measurements done by the laser range and position finder (213) for the determination of the antenna positions are considered as the nominal antenna positions. The nominal antenna positions may be known beforehand. In this case, the step for measurement and calibration the nominal positions (101) can be skipped. The fine antenna positions can be found during the antenna calibration processing (111). In some cases, three dimensional antenna positions are known accurately. In this case, antenna calibration processing (111) takes the known positions and skips the step for finding the fine antenna positions (105).

Antenna calibration processing (111) takes the number of antennas, the antenna nominal positions, the number of grid points in x, y and z directions, i.e., Pi,P₂, 3, the number of significant mutual coupling coefficients, L, initial mutual coupling vector, Ci, the number of iterations in mutual coupling and gain/phase parameter estimation, Ki, mutual coupling search grid size, , and the antenna position search grid size in x,y,z coordinates Δ_χ, Δ_ν, and Δ_ζ as the inputs.

Calibration for fine antenna positioning (105), antenna mutual coupling (107) and gain/phase parameters (109) requires data collection (103) when a calibration transmitter (401) transmits from different locations. There is no need to know the data transmitted but the transmitter direction-of-arrival should be known. The calibration transmitter (401) in FIGURE 4 is positioned in different locations with respect to the reference coordinates so that different DOA angles (403) are generated with respect to the reference coordinates (219). The DOA angle separation is preferably greater than ten degrees. The method works even when the separation is less than this value. The calibration transmitter (401) is preferably moved along a circle whose center is positioned with respect to the antenna array center. If the antenna gain/phase terms change for large separations of the direction-of- arrival angle, the data collection for the transmitting source can be done for small DOA angle separations. While there is some change in mutual coupling (107) and gain/phase terms (109) as the DOA angle changes, this change is small and these parameters are usually assumed to be independent of DOA angle in general. When the change in mutual coupling (107) and gain/phase terms (109) are large for large separations of DOA angles, the calibration transmitter (401) can be positioned within a narrow angular sector where the calibration DOA angle separation is small. In this case, calibration accuracy may decrease but the method still works with an accuracy of practical value. The calibration transmitter (401) is assumed to be positioned at a fixed elevation angle, φ, in order to avoid the gain/phase dependency on the elevation angle. However, if the antenna gain/phase dependence is not significant for small changes in elevation angle, data from different elevation angles can also be collected. For significant changes of antenna gain/phase parameters (109) depending on the calibration transmitter (401) elevation angle, different set of data for each elevation angle should be collected in order to find the corresponding parameter sets. If the antenna positions are measured and known accurately, fine position calibration (105) for the antenna elements can be omitted. In this case, only two different DOA angles are sufficient to find the mutual coupling (107) and gain/phase parameters (109) of the antennas assuming that the coupling matrix has a structure like banded symmetric Toeplitz or symmetric circuiant. Additional data collected from more than two DOA angles may improve the performance. Linear and circular antenna arrays (405) have banded symmetric Toeplitz and symmetric circuiant mutual coupling matrices respectively. If the mutual coupling matrix (107) does not have one of these forms, additional data should be collected from different DOA angles. If the fine antenna position calibration (105) is also performed then more data sets corresponding to different DOA angles are needed.

Calibration processing (111) is composed of fine antenna position search and estimation (105), antenna mutual coupling matrix search and estimation (107), antenna gain/phase matrix estimation (109). The operations for (105), (107) and (109) are performed in a nested loop. When the calibration processing (111) is finished, the calibration parameters are saved in order to display and transmit to a remote operator through the inputyoutput communication unit (411). The input/output communication unit (411) is also used for the user input/output. The DOA angle information is used at different stages of the calibration processing (111). (105) and (107) involve a search operation where the parameters are searched in a uniform grid in the neighborhood of nominal parameter values. This search operation is important and allows the method to find the global minimum of a cost function. The cost function used in this innovation is the MUSIC pseudo-spectrum. Alternative cost functions such as deterministic maximum likelihood cost function or stochastic maximum likelihood cost function in H.Krim, M. Viberg, "Two decades of array signal processing research: the parametric approach", IEEE Signal Processing Magazine, Vol.13, pp.67-94, July 1996, can also be used. A combination of these cost functions as well as the use of a completely different cost function is also the other alternatives.

It is assumed that there is a single signal which impinge on the M element antenna array (405) in azimuth, Θ, and elevation angle, φ, (θ,φ). The array geometry can be arbitrary in general but the sensors are assumed to be placed on a plane. The received signal at the antenna (405) outputs for a single snapshot at time t is given as,

where y(t) is a M x 1 vector, a(9,†) is the Mxl array steering or direction vector, s(t) and v(t) are the signal and noise vectors respectively. Noise is assumed to be temporally and spatially uncorrelated. Signal, s(t), is assumed to be composed of complex valued samples uncorrelated with the noise. C is the complex MxM antenna mutual coupling matrix, T = diag[g₁ g₂ .. - g_M ] = diag(g) is a MxM diagonal matrix of antenna gain/phase terms with g, being complex coefficients. N snapshots are assumed to be taken by sampling the data at a common period t=nT. The sampling instants are integer multiples of the sampling period, T, and for notational simplicity the sampling period is ignored leaving t=l,2,..., N. For a given azimuth and elevation angle pair (θι,φι), the elements of the array steering vector α(θ,φ) = [a_l ...a_MJ are given as complex exponential functions, ^a _m = exp J l≤m≤M (2)

where (d_xm,d_ym,d_zm) is the (x,y,z) coordinates of the m"¹ antenna. exp(.) is the exponential function. is the wavelength, c is the speed of the wave, f_c is the center frequency.

Above model is for narrowband signals. However this invention can be applied for the wideband signals as well with some additional processing. The sample covariance matrix for N snapshots is given as,

R = ^∑y( * ( (3 where y^H(t) is the Hermitian transpose of the vector y(t). The singular value decomposition of the covariance matrix can be written as,

R =UAU^H (4)

U = [u_j u₂ ...u^ ] is the matrix of eigenvectors Ui, Λ is the diagonal matrix of eigenvalues in descending order. Assuming that there is only one source signal, the noise space is represented by the Mx(M-l) eigenvector matrix G = [u₂ u₃ ...u_M ].

The cost function used in this innovation is generated by using the MUSIC pseudo- spectrum and this cost function is given as,

J(D,r,C) = aiD^^^^ r^GG^CraCD,^,^) ₍₅₎ D is the matrix of sensor positions in (x,y,z) coordinates, i.e.,

FIGURE 5 shows the steps involved for finding the antenna mutual coupling and gain/phase parameters assuming that the sensor positions are fixed. In this case, it is assumed that Bi DOA angles are known, i.e., (θι,φι), (Θ₂,φ2) up to (Θ_Β_,ΦΒΙ)- The mutual coupling matrix is assumed to have a complex banded symmetric Toepiitz structure. It is possible to consider the case equally well when the mutual coupling matrix has symmetric circulant form. When the mutual coupling matrix does not have a special structure, then additional DOA measurements are needed for identifiability. Assuming that the mutual coupling matrix is fixed and has banded symmetric Toepiitz form, the gain/phase parameters can be found as follows. It is known that,

where g is the vector of gain/phase parameters, Γ = diag(g) , and Qi is a MxM matrix with an be written as,

J_\ = g"Q₁ ^ffC^/iG₁G₁ ⁱⁱCQ₁g ₍₇₎ The minimization of Ji should be done in an indirect manner for a single source to avoid ill- conditioned solution.

T₂ = [t₂ t₃ t_M] where the noise space eigenvector matrix Gi is obtained from Ri as it is described after equation (4). Ri is the sample covariance matrix for the measurement when the source is positioned at the DOA angle (θι,φι). The solution for the gain/phase terms is found as, g_e = -T₂ ⁺t,

f = diag(g) _(g) where T₂ ⁺ is the Moore-Penrose pseudoinverse of the matrix T₂. In (501), an initial estimate for gain/phase matrix, f _f can be found by assuming that C=I where I is the identity matrix. This f is then used to find an initial estimate for the mutual coupling vector, Ci and the corresponding mutual coupling matrix C in (501). The process for finding this initial estimate is as follows. It is known that

Cx = Q₂c ₁₀^ where x = f a(<9₂,^₂) is a Mxl vector, Q₂ is a MxL matrix and c is a L_xl vector of complex coupling coefficients, i.e., c = [l c, c₂ ...c_L_ . and the elements of Q_a and Q_b matrices are obtained as,

The form of the Q₂ matrix for symmetric circulant matrix can be found in "Direction finding in the presence of mutual coupling", Benjamin Friedlander, Anthony J. Weiss, IEEE Trans. On Antennas and Propagation, Vol. 39, No.3, March 1991. The cost function that is to be minimized can be given as follows,

J₂ = a(0₂,<fi₂)^H T^HC^HG₂G₂ ^HCTa{9_{2 2})

= c"Q₂ ^HG₂G₂ ^ffQ₂c (₁₂) The solution for the mutual coupling coefficients are found as,

where the noise space eigenvector matrix G₂ is obtained from R₂ which is the sample covariance matrix for the measurement when the source is positioned at the DOA angle (Θ₂,φ2). tj vectors are the column vectors of T. The banded symmetric Toeplitz mutual coupling matrix can be constructed from c An example is given below for L=4 coefficients.

1 c₃ 0 0

1 0

1 Cl

C =

1

0 c₃ c₂ 1

0 0 ^£3 c₂ 1

In (501), Γ is set as Γ = r_and Ci is set as Ci= c . An alternative setting for Ci, which may result better performance, is obtained by setting the coefficients of Ci to zero except the first two coefficients if the antenna positions are known accurately. Another alternative setting is

and Ci(p)=0, p=2,...,L, when it is known that the antenna positions are not accurate. Ci can also be given as the input to the system.

In (503), there is a loop which is used to iterate the solution for (r,C) Ki times to obtain better results. In (505), there is a loop to update each coupling coefficients starting from Ci(2) in a uniform grid in the neighborhood of the initial values. In (507), a large predetermined limiting value is set to e as e=E and Ci is stored in c_<. E=10⁵ is a possible choice. The uniform grid for the update is generated by the search loops in (509) and (511). The complex coupling coefficient is updated as,

(15) in (513) where is the grid size. The complex gain/phase terms in Γι are found in (515) using the C matrix constructed from c_x, Gi and Qi as in equations (8) and (9). Gi and Qi are found from the data when the DOA angle is (θι,φι). In (517), a cost function is computed. This cost function to find the best values for c_x and Γ is,

where Bi, (Bi < B₂) is the number of DOA angles used in finding the mutual coupling and gain/phase terms when B₂ is the total number of DOA angles available. G_b is the matrix of noise space eigenvectors corresponding to the covariance matrix Rb which is obtained when the calibration source transmits from a DOA angle (θι,,φι - This value of the cost function is stored to er(ka,kb), i.e.,

and it is compared with the previous values of the cost function in (519). If the value of er(ka,kb) is smaller than e, then e=er(ka,kb), c₀=c_x, r_x=n settings are done in (521). Otherwise, the values of ka and l¾ are tested in (523) and (527) and incremented by one in (525) and (529) and the loop computation proceeds. When both k_a and k_b reach their limiting values, the mutual coefficient vector for the k^ iteration is set as

in (531). The iterations continue until all the mutual coupling coefficients are processed and p reaches the limiting value L which is tested in (533). If p is less than L, p is incremented by one in (535). When the main loop (503) parameter ki is tested in (537) and it is less than Ki, ki is incremented by one. If

the main loop is terminated, the final result for the mutual coupling vector is set as, c=c_ki and gain/phase matrix is Γ=Γ_Χ in (541).

In FIGURE 6, fine calibration for sensor positions is illustrated. It is assumed that the nominal sensor positions are known or measured as described in FIGURE 2 and FIGURE 3.B. It is assumed that there are M antennas and each antenna position is searched in three dimensions in a uniform grid in the neighborhood of the nominal sensor positions to obtain an accurate solution. A large predetermined limiting value is set to e_d=E in (601). A possible value for E is E=10⁵. Also the nominal sensor positions are taken as the input. (603), (605) and (607) are used to generate a three dimensional search grid for the first antenna. In (609), the position of the first antenna is updated. The update expression for all the antennas is the same and it is given as,

d.„ = d"

(17)

where (dⁿ _xm, dⁿ _ym, d"_2m) is the nominal position of the m* antenna, Δχ,Δγ, and Δζ are the grid size in x,y and z coordinates respectively. The search grid is also generated for the sensors from m=2 to

corresponds to rounding the number p to the closest integer. (613), (615) and (617) are for the generation of the M* sensor grid. The algorithm in FIGURE 5 is applied (621) to find the mutual coupling and gain/phase parameters (C,r) for the antenna positions. The cost function for the parameter values (D_u, C, Γ) is computed (623) as,

J_B =∑ ^_u A)" T^{H H}G_bG_b ^HCTa{Ti_uA )

»=· (18) where D_u is the updated antenna positions, 6_b is the matrix for the noise space eigenvectors corresponding to the DOA angle (e_b,†_b) as it is described after equation (4). er_d=J_B is set. It is assumed that the data is collected by placing the transmitting source in B₂ positions and therefore B₂ DOA angles are known.

The minimum of the cost function and the corresponding antenna positions, mutual coupling and gain/phase terms are found in (625), and (627). In (629), (633) and (637) the loop parameters for the sensor are tested for their limiting values. In (631), (635) and (639), these parameters are incremented by one. The loops for the generation of the sensor position grids is continued until all the points in the grid are covered. (641) indicates that the loops are closed for each parameter. In (643) and (645), the last parameter test and update is done. After all the antenna positions in the generated grid are covered, the antenna positions, mutual coupling and gain/phase terms corresponding to the minimum cost function J_B in (18) are reported in (647). As it is pointed before, alternative cost functions can be used instead of Ji,J₂, JA and J_B. A combination of cost functions may also be an alternative. In case of deterministic maximum likelihood cost function, the cost functions Ji,J₂, J_A and J_B can be easily updated since the forms of these functions are similar. Let A⁺ and n_A be defined as,

A⁺ = (8* 8^ 3

n_a = AA (19) πί = Ι -Π_β

where I is the identity matrix. The cost function in (18), J_B, can be expressed for the deterministic maximum likelihood case as

1

<¾ is the matrix constructed for the DOA angle (G_b,c|>b) given the sensor positions D_u. Rb is the sample covariance matrix for the same DOA angle as described in (3). traced ) is the operator which gives the trace of a matrix. Ji, J₂ and J_A cost functions can be modified similarly using (19) and (20) if the deterministic maximum likelihood cost function is used.

While the invention is described in detail in the foregoing embodiments for the purpose of illustration, those skilled in art will recognize that the invention can be practiced with variations within the scope and spirit of the following claims.

Claims

1) A system for measuring the nominal three dimensional positions (101) of the antennas in an antenna array (405) with respect to a reference coordinate system (219) comprising of a laser range and position finder (213) that transmits a laser beam with a precision direction in terms of azimuth and elevation angle and measures the reflected beam intensity and the range of the object that caused the reflection, the azimuth and elevation angle by which the laser beam is pointed; the said laser range and position finder (213) also includes a global positioning device and an inertial measurement unit for determining its three dimensional position; the said system is characterized in that : a) An antenna array (405) which is composed of antennas wherein each antenna has a number of reflective and non-reflective coatings (201, 203) with different size, texture and reflection coefficient in order to code the spatial position of antenna top, center and bottom, said antenna coatings (201, 203) are also used to identify the individual antennas and the position of these antennas with respect to each other in the antenna array (405), the intensity of the laser beam reflection from the antenna coatings (201, 203) is coded by a binary number, the reflection intensity above a given threshold is coded by a binary number ^Χ and below the threshold is coded by a binary number ', the laser beam reflections from the antenna top, center and bottom generate a binary code for each antenna;

b) A method for measuring the nominal three dimensional antenna positions (101) with respect to a reference coordinate system (219) and comprising the steps of:

• Taking the scanning area coordinates, the antenna coating codes, the threshold for the laser beam intensity and the antenna dimensions as the input;

• Scanning the site of the antenna array (405) by the laser range and position finder (213) in vertical and horizontal dimensions (231, 237) according to predetermined site coordinates and recording the intensity of the reflected laser beam for each azimuth and elevation angle and the range of the object that caused the reflection;

• Said scanning starts from the upper left corner (235) of the scanning area, continues in vertical direction until the scanning area limit is reached, then moves horizontally to the next scanning spot and continues vertically in upwards direction, the said scanning continues until all the scanning area is scanned; • The laser beam reflections in vertical and horizontal scans (231, 237) are compared with the intensity threshold and the binary code for the reflections is generated; if the binary code of the reflections matches to those coded by the antenna coatings in claim l.a, the antenna is declared to be found, the laser beam spot (233) at the central reflective coating which returns the maximum reflection is selected as the point to find the distance to the antenna center midpoint (323), laser range and position finder (213) measures the distance to the antenna center as well as the azimuth and elevation angles;

• The three dimensional position of the antenna center midpoint (323) with respect to the reference coordinate axis is found by considering the antenna dimensions, the distance from the antenna center, azimuth and elevation angles for the antenna center.

2) A system for measuring the nominal three dimensional positions (101) as claimed in claim 1 characterized in that the reference coordinate system (219) origin in claim 1 can be selected as the coordinates of the laser range and position finder (213) supplied by the global positioning device and inertial measurement unit in claim 1.

3) A system for measuring the nominal three dimensional positions (101) as claimed in claim 1 characterized in that the number of antennas and antenna relative positions within the antenna array (405) can also be given as the input for the scanning method in claim 1 wherein, the laser range and position finder (213) is pointed to the scanning area where the remaining antennas are located once the positions of two antennas are found as in claim 1.

4) A system for measuring the nominal three dimensional positions (101) as claimed in claim 1 characterized in that the antenna center coating (209) in claim 1 is symmetric and the same coded binary sequence is generated during the top-to-down or bottom-to- top laser scan of this coating.

5) A system for measuring the nominal three dimensional positions (101) as claimed in claim 1 characterized in that the antenna top and bottom coatings (207, 211) in claim 1 are not symmetric and a different coded binary sequence is generated during the top-to- bottom or bottom-to-top laser scan of top and bottom coatings (207, 211) alone.

6) A system for measuring the nominal three dimensional positions (101) as claimed in claim 1 characterized in that the laser pulse intensity threshold in claim 1 can be changed dynamically during the laser scan. A system for measuring the nominal three dimensional positions (101) as claimed in claim 1 characterized in that the method in claim l.b is used to find the antenna top and bottom midpoints (321, 325); the antenna dimensions are used together with the laser range and position finder scan results as in claim l.b and the antenna top and bottom midpoint three dimensional positions are found as the complete positioning of the antennas with respect to the reference coordinate system (219).

A system for measuring the nominal three dimensional positions (101) as claimed in claim 1 characterized in that the method in claim l.b and claim 7 is used to find the three dimensional coordinates of the points (703) on the antenna structure marked by the antenna coatings; the antenna dimensions, the laser range and position finder scan results as in claim l.b, are used to find the points on the antenna structure to accurately characterize the antenna structure.

A system and a method for calibrating an antenna array (405) by simultaneously finding the fine three dimensional positions of the antenna midpoints (321, 323, 325), mutual coupling parameters (107) between antennas and gain/phase parameters (109) for the antennas; the system is comprised of an antenna array (405), multi channel receiver (407), a calibration unit with a display (409), input/output and a communication unit (411); the method for simultaneously finding the fine three dimensional positions of the antenna midpoints (321, 323, 325), mutual coupling (107) and gain/phase parameters (109) comprising the steps of:

• Taking the number of antennas, the nominal antenna positions (101), the number of grid points for fine position estimation in x, y and z directions, the number of significant mutual coupling coefficients, initial mutual coupling vector, the number of iterations in mutual coupling and gain/phase parameter estimation, mutual coupling search grid size, and the antenna position search grid size in x, y, z coordinates as the inputs;

• Transmitting a signal with a known frequency from a calibrated antenna placed at different positions with respect to the reference coordinate system (219) where the direction-of-arrival angle with respect to the reference coordinate system (219) is known;

• Receiving each signal from the antennas by a multi channel receiver (407) that performs the reception processing on each of the received signals from the antennas; applying an antenna calibration processing (111) on the received signals using a calibration unit (409) wherein the antenna calibration processing (111) is comprised of fine three dimensional antenna position estimation (105), antenna mutual coupling parameter estimation (107) and antenna gain/phase parameter estimation (109); said calibration processing is comprised of the steps:

i. Obtaining a covariance matrix from the received signals corresponding to each of the known direction of arrival with respect to the antenna array (405) and the reference coordinate system (219);

ii. Generating a three dimensional uniform search grid in the neighborhood of the nominal three dimensional antenna positions;

iii. Considering each antenna position in the search grid, antenna mutual coupling (107) and gain/phase parameters (109) are found; the method for finding the antenna mutual coupling (107) and gain/phase parameters (109) is comprised of the steps:

• Initial values for the mutual coupling parameters (107) are set except the first parameter which is set to one; a uniform search grid in the neighborhood of each mutual coupling parameter (107) except the first one is constructed;

• For each grid point for the selected mutual coupling parameter (107), the corresponding antenna gain/phase parameters (109) are found;

• A cost function is evaluated for the selected mutual coupling parameter (107) on the grid and the corresponding gain/phase parameters (109);

• When all the grid points for the selected mutual coupling parameter (107) are considered with their corresponding cost function values, the mutual coupling parameter (107) and the corresponding gain/phase parameters (109) which return the minimum cost value are selected as the estimates of the mutual coupling parameter (107) and gain/phase parameters (109), the mutual coupling vector is updated by the said mutual coupling parameter (107); the process is repeated for the remaining mutual coupling parameters (107) in the mutual coupling vector one by one, and the mutual coupling vector is updates at each case; the process terminates when all the mutual coupling parameters (107) in the coupling vector are considered A cost function is evaluated for the obtained antenna positions, mutual coupling (107) and gain/phase parameters (109) and the value of the cost function is recorded;

When all the antenna positions in the search grid are considered with their corresponding cost function values, the antenna positions, mutual coupling (107) and gain/phase parameters (109) corresponding to the minimum cost value are selected as the estimates of the true antenna positions, mutual coupling (107) and gain/phase parameters (109).

10) A system and a method for calibrating an antenna array (405) by simultaneously finding the fine three dimensional positions of the antenna midpoints (321, 323, 325), mutual coupling parameters (107) between antennas and gain/phase parameters (109) for the antennas as claimed in claim 9 is characterized in that the nominal antenna positions can be provided by the system in claim 1.

11) A system and a method for calibrating an antenna array (405) by simultaneously finding the fine three dimensional positions of the antenna midpoints (321, 323, 325), mutual coupling parameters (107) between antennas and gain/phase parameters (109) for the antennas as claimed in claim 9 is characterized in that if the antenna positions in the antenna array (405) are known accurately, the nominal antenna positions are fixed as the given antenna positions and the antenna fine position estimation (105) is skipped.

12) A system and a method for calibrating an antenna array (405) by simultaneously finding the fine three dimensional positions of the antenna midpoints (321, 323, 325), mutual coupling parameters (107) between antennas and gain/phase parameters (109) for the antennas as claimed in claim 9 is characterized in that the cost functions are positive valued functions.

13) A system and a method for calibrating an antenna array (405) by simultaneously finding the fine three dimensional positions of the antenna midpoints (321, 323, 325), mutual coupling parameters (107) between antennas and gain/phase parameters (109) for the antennas as claimed in claim 9 is characterized in that the cost functions can be the MUSIC cost function.