This application is the U.S. national phase of international application PCT/SE2003/000833 filed 21 May 2003 which designated the U.S., the entire contents of which is hereby incorporated by reference.
The present invention relates to wide-band antenna arrays, and more particularly to a method and system for unambiguous angle resolution of a sparse wide-band antenna array.
It is complicated or even almost impossible to build classic wide-band array antennas providing good angle resolution. The reason for this is that the separation of the elements is set by the highest frequency, typically half a wavelength at fmax. The physical size of the elements is set by the lowest frequency, typically half a wavelength at fmin. Thus, there is apparently a contradiction between obtaining a wide bandwidth of the antenna and the array density needed to avoid grating lobes at large scan angles.
Another problem is that array antennas having a large number of elements will be undesired complex and expensive. Furthermore rotating antennas are generally undesired as that implies further mechanical complexity. From a strategic point of view there is also a desire to be able to keep peak power as low as possible to minimize the risk of being detected.
Typical solutions of today utilize fully filled arrays and rotating antennas combined with range coded long pulses, for instance using a binary phase code. Signal classification is difficult with present solutions and different hardware solutions have to be used for a respective function category, for instance, a radar function or a jamming function.
Therefore there is a demand for further improvements of wide-band arrays for obtaining also a better angular resolution produced by a less complex solution compared to the state of the art.
A method and a system for unambiguous angle resolution of a sparse wide-band array antenna in a bistatic or monostatic radar configuration utilize an ultra-wide-band signal, which in a typical embodiment may be continuous bandwidth limited white noise or colored noise. The noise signal is generated and radiated for instance by an omnidirectional transmitting antenna covering the entire reception range of a receiving array. An echo signal is received by the receiving array containing n antenna elements. The n antenna elements are generally positioned with separation distances of several wavelengths without creating strong grating lobes. By means of a selected auto-correlation function defining the wide-band noise signal power spectrum, the convolution of the radiated output signal and the received echo input signal will give the target range information, the individual time-delay setting for each antenna element will give an unambiguous angular resolution.
A system according to the present invention is set forth by the independent claim 1, and further embodiments of the invention are set forth by the dependent claims 2 to 9.
Further a method according to the present invention is set forth by the independent claim 10, and further embodiments are defined by the dependent claims 11 to 17.
The invention, together with further objects and advantages thereof, may best be understood by referring to the following detailed description taken together with the accompanying drawings, in which:
In a typical illustrative embodiment a very broad-banded signal, which may be continuous band-limited white or colored noise is generated and transmitted by an antenna, which for instance is isotropic in its horizontal plane. The echo signal in a bistatic or monostatic configuration is received by n receiver antennas. The n antennas are spaced at distances of several wavelengths, e.g. 10 wavelengths at fmin. These antennas being placed at separation distances of several wavelengths do not create dominating grating lobes due to the frequency spread achieved by the large bandwidth. By grating lobes we refer to periodic repetitions of a main lobe.
Each antenna may be a vertical array to increase the gain in the horizontal plane. To minimize leakage between the transmitting antenna and the receiver antennas the transmitting antenna preferably is positioned as far as possible from the receiving antennas and for instance at a different height than the receiving antennas.
The idea of using a continuous ultra broad-band signal like band-limited white noise is, that only the central lobe can be considered additive for all frequencies within the wide band used. Grating lobes resulting from the different frequencies within the broadband signal will not be added in the same way as the grating lobe pattern will for each separate frequency component being a function of the spacing of antenna elements used. This will result in an angle resolution, which may be used, for instance, for radar purposes. This was simulated in a frequency range of 6-18 GHz, which can simply be obtained. The distance to the target is determined by finding the peaks in the convolution between the input and output signal.
Principle for Range Resolution
Assume an array wherein the main lobe of each antenna element points in a radial direction in the circular case and in a direction θ=0 in the linear case. Further assume that the diagrams of the elements have the simple frequency independent form according to Equation (1):
The radiated noise signal is assumed to be et(t). The sum from all n receiver antennas may then for a spot target be written according to Equation (2):
Where R, φ are distance and bearing, respectively, to the target. θ means current antenna search angle. Time corrections τn are calculated according to Equation (3):
Convolution between the radiated and the received signal can, according to Equation (4), be written:
Where denotes the Fourier transform. We have assumed that et(t) is white bandwidth limited noise from ω1 to ω2.
Principle for Angle Resolution
The principle for resolution in angular direction is that grating lobes of respective frequency will land in different directions. The level of other lobes than the main lobe seen over the entire bandwidth will be expected to be low as grating lobes over the wide bandwidth generally will counteract each other. The radiated noise signal is assumed to be e(t). Ree(τ) is the auto-correlation function of e(t). If we presume that e(t) is white bandwidth limited noise from ω1 to ω2 it is easy to prove that the auto-correlation function can be written according to Equation (5) below:
Here σ denotes the noise standard deviation and the mean power of the noise signal is σ2.
Linear Array
For a basic first emrbodiment of the present invention assume a linear array with a length L where the main lobe of each antenna element points in the direction θ=0 and has the simple frequency independent shape according to Equation (6):
The sum of all n receiver antennas then can be written according to Equation (7):
Where R, φ are distance and bearing to the target, respectively. θ is the current antenna search angle. Time corrections τn are calculated according to Equation (8):
Expected value of the antenna diagram AP(θ, φ) is calculated according to Equation 9:
AP(θ,φ)=10·log {E[EΣ2(θ,φ)]} (9)
We will now be able to perform the following calculation:
Circular Array
For a second embodiment of the present invention assume a circular array having the main lobe of each antenna element pointing in a radial direction and according to Equation (10) has the simple frequency independent shape:
The sum, from all n receiving antennas then can be written according to Equation (11):
R, φ are distance and bearing to the target, respectively, and θ is the current antenna search angle. Time corrections τn are calculated according to Equation (12):
Expected value of the antenna diagram AP(θ, φ) is calculated according to Equation (13):
AP(θ,φ)=10·log {E[EΣ2(θ,φ)]} (13)
Then, we can perform the following calculation:
Conformal Array
In yet a third embodiment the antenna array may well be formed as a conformal array and calculated in a similar way corresponding to the above examples of the linear and circular array.
Simulations
For the simulations 100% bandwidth and a center frequency of 12 GHz was chosen. In other words the frequency range of the radar was 6-18 GHz. The distance to the target is determined by finding the peaks of the convolution between input and output signal.
The principle for the angular resolution utilized is that grating lobes integrated over the large frequency range become rather low, while signals of a main lobe generally will be summed, which of course clearly comes out from the auto-correlation.
As is also seen in
It will be understood by those skilled in the art that various modifications and changes could be made to the present invention without departure from the spirit and scope thereof, which is defined by the appended claims.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/SE03/00833 | 5/21/2003 | WO | 00 | 11/18/2005 |
Publishing Document | Publishing Date | Country | Kind |
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WO2004/104628 | 12/2/2004 | WO | A |
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