US20060273948A1 - Selectable range lobes using wide-band array - Google Patents

Abstract

The present inventive concept for bistatic or monostatic radar utilization discloses a method and a system for unambiguous range resolution utilizing an ultra wide-band signal, generally a wide-band noise signal which may be continuous bandwidth limited white or colored noise. The noise signal is typically generated and radiated by a transmitting antenna covering the entire reception range of a receiving sparse antenna. An echo signal is received by the receiving antenna. 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.

Description

TECHNICAL FIELD
• The present invention relates to a method and system for unambiguous range resolution of a radar system.
BACKGROUND
• In radar systems there is a desire to keep peak power as low as possible to minimize the risk of detection.
• Typical solutions of today utilize fully 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 large duty cycle (low peak power) good range estimation for wide-band system not necessarily being pulse coded with non-deterministic transmit signals.
SUMMARY OF THE INVENTION
• A method and a system for controlling range resolution of a radar system in a bistatic or monostatic configuration utilize an ultra-wide-band signal, which in a typical embodiment may be continuous bandwidth limited white 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 antenna and an echo signal is received by the receiving antenna. 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 the target range information is obtained.
• 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 18.
SHORT DESCRIPTION OF THE DRAWINGS
• 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:
• FIG. 1 illustrates an illustrative array antenna for use according to the present inventive concept;
• FIG. 2 illustrates a principal embodiment of a wide-band array used in line with the present inventive idea and having the number of receiving antenna elements n=32;
• FIG. 3 illustrates in a number of graphs a) to f) the auto-correlation function for Gaussian noise with bandwidth from 200% and down to 6.25% expressed as percent of center frequency;
• FIG. 4 illustrates in a number of graphs a) to f) the auto-correlation function for white bandwidth limited noise using a bandwidth from 200% and down to 6.25% expressed as percent of center frequency; and
• FIG. 5 illustrates in a graph the convolution of radiated and received signal as a function of signal-to-noise ratio.
DETAILED DESCRIPTION
• In a typical illustrative embodiment a very broad-banded signal is generated. The generated signal may be continuous band-limited white or colored noise and transmitted by an antenna, which for instance is isotropic in its horizontal plane. Echo signals in a bistatic or monostatic configuration are received.
• 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.
• FIG. 1 illustrates a principal shape with n=3, the transmitting antenna is denoted as 1 and the receiver antennas are denoted 3. A structure carrying the transmitter antenna is denoted as reference number 5. A transmitter and n receivers with accompanying signal processing is housed in the electronic unit 7. FIG. 2 illustrates a practical embodiment of a circular array with n=32, the transmitting antenna sitting elevated in the middle and the receiving antenna in a ring below. One transmitter, n receivers with accompanying signal processing being housed in the base of the array.
• The range to the target is determined by finding the peaks in the convolution between the input and output signal.
• Basic Theory
• Suppose that the radar station is not moving and transmits the ergodic waveform s(t) having a zero average value. For a non-moving target having an extension L and a target area profile ρ(τ) the received signal r(t) may be written according to: $\begin{array}{cc}r\left(t\right)={\int }_{\frac{2·\left(R-L/2\right)}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="US20060273948A1-20061207-D00008.png"\; state="\{\{state\}\}">c</figure-callout>}}_0}}^{\frac{2·\left(R+L/2\right)}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="US20060273948A1-20061207-D00008.png"\; state="\{\{state\}\}">c</figure-callout>}}_0}}\rho \left(\zeta \right)·s\left(t-\zeta \right)·d\zeta +n\left(t\right)& \left(1\right)\end{array}$
  where R is the target range, ζ the time integration variable and c₀ the velocity of light. n(t) represents additive noise and possible disturbances.
• According to the theory for ergotic processes also r(t) becomes stationary and ergotic. Therefore the time correlation may be used for approximating the cross-correlation between a delayed copy of the conjugate of the transmit signal s*(t−ç) and the received signal r(t) according to: $\begin{array}{cc}{g}_T\left(t,\tau \right)={\int }_{-T/2}^{T/2}{\int }_{\frac{2·\left(R-L/2\right)}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="US20060273948A1-20061207-D00008.png"\; state="\{\{state\}\}">c</figure-callout>}}_0}}^{\frac{2·\left(R+L/2\right)}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="US20060273948A1-20061207-D00008.png"\; state="\{\{state\}\}">c</figure-callout>}}_0}}\rho \left(\zeta \right)·s\left(t-\zeta \right)·s^{*}\left(t-\tau \right)·d\zeta ·dt+{\int }_{-T/2}^{T/2}n\left(t\right)·s^{*}\left(t-\tau \right)·dt& \left(2\right)\end{array}$
  where T represents the correlation integration interval. For large T:s the second term of equation (2) will go towards zero as n(t) is not correlated with the transmit signal s(t). This gives: $\begin{array}{cc}g\left(\tau \right)=\underset{T->\infty }{\lim }{g}_T\left(t\right)={\int }_{\frac{2·\left(R-L/2\right)}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="US20060273948A1-20061207-D00008.png"\; state="\{\{state\}\}">c</figure-callout>}}_0}}^{\frac{2·\left(R+L/2\right)}{{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="US20060273948A1-20061207-D00008.png"\; state="\{\{state\}\}">c</figure-callout>}}_0}}\rho \left(\zeta \right)·p\left(\tau -\zeta \right)·d\zeta =\rho \left(\tau \right)\otimes p\left(\tau \right)& \left(3\right)\end{array}$
  {circle around (×)} symbolizes convolution. Besides it is valid that: $\begin{array}{cc}p\left(\tau \right)=\underset{T->\infty }{\lim }{\int }_{-T/2}^{T/2}s\left(t\right)·s^{*}\left(t-\tau \right)·dt& \left(4\right)\end{array}$
  where ρ(τ) is the auto-correlation function of the transmitted noise signal s(t).
• It comes out of equation (3) that the received signal is the convolution of the target area profile and the auto-correlation function of the transmitted signal. Thus the range resolution of the auto-correlation function τ(τ) of the transmit signal depends on the bandwidth of the transmit signal and the form of its power spectrum P(ω). It is easy to prove that there is a simple relation between the auto-correlation function ρ(τ) of the signal and it power spectrum P(ω). These constitute namely a pair of Fourier transforms: $\begin{array}{cc}\begin{array}{c}P\left(\omega \right)={\int }_{-\infty }^{\infty }p\left(t\right)·e^{-j·\omega ·\tau }·d\tau \\ p\left(\tau \right)=\frac{1}{2·\pi }·{\int }_{-\infty }^{\infty }P\left(\omega \right)·e^{j·\omega ·\tau }·d\omega \end{array}\}& \left(5\right)\end{array}$
• Thus, it is possible to select range resolution ρ(τ) and calculate power spectrum P(Ω).
• Examples of Auto-Correlation Functions
• In FIGS. 2 and 3 the auto-correlation function is demonstrated as a function of time t. But time is directly proportional to the range R according to equation (6) $\begin{array}{cc}t=\frac{2·R}{c_0}& \left(6\right)\end{array}$
  for Gaussian noise the auto-function may be written as: $\begin{array}{cc}p\left(\tau \right)={\sigma }^2·\cos \left[\left({\omega }_2+{\omega }_1\right)·\frac{\tau }{2}\right]·e^{-\left({\omega }_2-{\omega }_1\right)·\frac{\tau }{2}}& \left(7\right)\end{array}$
• For white bandwidth limited noise the auto-correlation function may be written as: $\begin{array}{cc}p\left(\tau \right)={\sigma }^2·\cos \left[\left({\omega }_2+{\omega }_1\right)·\frac{\tau }{2}\right]·\frac{\sin \left[\left({\omega }_2-{\omega }_1\right)·\frac{\tau }{2}\right]}{\left({\omega }_2-{\omega }_1\right)·\frac{\tau }{2}}& \left(8\right)\end{array}$
  where like in Equation (7) σ denotes the noise standard deviation and the mean power of the noise signal is σ² and ω₁ and ω₂ are the lower and upper limits of the angular velocity.
  Simulations
• FIG. 4 demonstrates the auto-correlation function for white bandwidth limited noise according to equation (1). As can be seen a bandwidth of 100% is needed to get the sidelobes down to a reasonable level.
• 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.
• FIG. 5 illustrates a simulation result when signal-to-noise was varied. In this case the target is an object, 1 meter long, standing still at a distance of 750 meters. The target area as function of distance is an equally distributed random number per distance sample. The sampling rate in this case was 50 GHz. From the response of the convolution the signature of the target can be interpreted in the form of the derivative of target area as function of distance. This may then be used to classify and identify the target by comparison with suitable library data.
• Interesting is that the auto-correlation function as a matter of fact can be chosen such that desired characteristics are obtained. The Fourier transform of the selected auto-correlation function gives necessary power spectrum of the radiated signal.
• 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.

Claims (14)

1. A system for controlled range side-lobes in a bistatic or monostatic radar system, characterized in that

an ultra wide-band band microwave signal is generated and radiated via a transmitter antenna, echo signals are received via receiver antennas;

whereby a transmitted power spectrum of a transmitted signal and its auto-correlation function form a Fourier transform pair, such that for a given range sidelobe characteristic the power spectrum of a corresponding output signal is calculated as an inverse Fourier transform of given range sidelobe characteristic.

2. The system according to claim 1, characterized in that the ultra wide-band microwave signal is generated as band-limited white noise, the convolution result being read out as a signature of the target for 100% bandwidth approximately in form of the derivative of the target area as function of range.

3. The system according to claim 1, characterized in that the ultra wide-band microwave signal is generated as band-limited colored noise, by using a selected auto-correlation function for the generated noise.

4. The system according to claim 1, characterized in that the ultra wide-band microwave signal comprises a frequency range of the same order as the center frequency.

5. The system according to claim 1, characterized in that the antenna used are vertical linear arrays.

6. The system according to claim 1, characterized in that the receiver antennas form a circular array.

7. The system according to claim 1, characterized in that in an monostatic configuration an omnidirectional transmitting antenna is generally positioned at another height than receiving antennas to minimize leakage between transmit and receive antennas.

8. A method for obtaining controlled range side-lobes in a bistatic or monostatic radar operation, characterized by the steps of

generating an ultra wide-band band microwave signal being radiated via a transmitter antenna;

arranging receiving microwave antennas;

forming a Fourier transform pair with a transmitted power spectrum of transmitted signal and its auto-correlation function;

calculating for a given range sidelobe characteristic the power spectrum of the corresponding output signal as the inverse Fourier transform of the given range sidelobe characteristic.

9. The method according to claim 8, characterized by the further steps of generating the ultra wide-band microwave signal as band-limited white noise, and reading out the convolution result as a signature of the target for 100% bandwidth approximately in form of the derivative of the target area as function of range.

10. The method according to claim 8, characterized by the further step of generating the ultra wide-band microwave signal as band-limited colored noise by using a selected auto-correlation function for the generated noise.

11. The method according to claim 8, characterized by the further step of generating the ultra wide-band microwave signal in a frequency range having an order about equal to the value of the center frequency.

12. The method according to claim 8, characterized by the further step of using vertical linear arrays as antennas.

13. The method according to claim 8, characterized by the further step of using circular arrays as receiving antenna.

14. The method according to claim 8, characterized by the further step of in a monostatic configuration generally positioning an omnidirectional transmitting antenna at a different height compared to the receiving antennas to minimize leakage between transmit and receive antennas.

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