Cost-effective method for determining a pulse response of a high-resolution, band-limited radar channel

• US 5,805,107 A
• Filed: 04/18/1997
• Issued: 09/08/1998
• Est. Priority Date: 04/18/1996
• Status: Expired due to Term

• Current Assignee: Deutsche Forschungsanstalt Fur Luftund Raumfahrt E.V.
• Original Assignee: Deutsche Telekom AG
• Inventors: Schroth, Arno, Baier, Walter, Felhauer, Tobias
• Primary Examiner(s): Sotomayor, John B.
• Application Number:
  US08/837,602
• Time in Patent Office: 508 Days
• Field of Search: 342/189, 342/29, 342/33, 342/36, 342/39, 342/59, 342/93, 342/148, 342/159, 342/162, 342/194, 342/195, 342/203, 342/196, 342/205, 342/201, 342/202
• US Class Current: 342/189
• CPC Class Codes: G01S 13/003 Bistatic radar systems; Multistatic radar systems
• CPC Class Codes: G01S 13/284 using coded pulses
• CPC Class Codes: G01S 13/87 Combinations of radar systems, e.g. primary radar and secondary radar
• CPC Class Codes: G01S 13/934 on airport surfaces, e.g. while taxiing
• CPC Class Codes: G01S 7/40 Means for monitoring or calibrating
• CPC Class Codes: G01S 7/41 using analysis of echo signal for target characterisation; Target signature; Target cross-section

Abstract

For less expensive estimation the impulse response x_MOS of a high-resolution, band-limited radar channel in a radar station operating with an expanded transmitted pulse a(t), from a received signal e, over which a correlated or uncorrelated additive interference signal n can be superimposed, with the use of knowledge about the spread code c and the use of a channel estimator with which a so-called linear, optimum unbiased estimation of the radar channel impulse response x_MOS is performed in a time range covering M range gates of interest, the linear, optimum estimation in the unbiased channel estimator is modified in such a way that the pulse response x_MOS of the band-limited radar channel is determined according to the basic principle of a multiplication of the sampled received signal e and an inverse estimation matrix A_E^-1. The matrix A_E is formed by the extension of the rectangular matrix represented by the components c_i of the spread code c to form a quadratic matrix that circulates to the right, that is, the modified, optimum unbiased estimation:

x.sub.MOS =A.sub.E.sup.-1 e

applies for a radar channel.

Claims

1. A method for determining a complex impulse response of a high-resolution, band-limited radar channel in a radar station transmitting a binary phase-coded expanded transmitted pulse a(t), the method including

receiving a complex vector signal e,

expanding the transmitted pulse a(t) with respect to bandwidth using a binary complex vector spread code c of length N and a chip duration T_c, from the received signal e;

superimposing a complex vector additive interference signal n;

performing in a time range covering M range gates of interest according to the spread code c; and

modifying the linear optimum estimation by determining a linear optimum unbiased estimation pulse response x_MOS of the band-limited radar channel according to

space="preserve" listing-type="equation">x.sub.MOS =A.sub.E.sup.-1 e,

where the step of determining further comprises

forming a complex matrix A_E by widening of the rectangular matrix represented by the complex scalar components c_i of the spread code c to form a quadratic matrix that circulates to the right,

forming an inverse estimation matrix A_E^-1 of the matrix A_E, and

multiplying the inverse estimation matrix by the sampled received signal e and to modify the linear, optimum estimation in the channel estimator.

2. The method according to claim 1, wherein the step of determining the modified, optimum unbiased channel estimate x_MOS includes:

providing a cyclical, digital correlator in a first line of the inverse estimation matrix A_E^-1 comprising means for cyclical correlation of the received signal e having elements W₁.i, with i=1 . . . M+N-1, with the (M+N-1) filter coefficients t_i =W₁.i, wherein the cyclical, digital correlator is a function of both the expanded transmitted pulse spread code c and the number M of range gates of interest, whereby a priori knowledge about the number M of range gates of interest and therefore the maximum range of the radar system to be considered is used in addition to the knowledge about the spread code c.

3. The method according to claim 1, wherein the step of determining the modified, optimum unbiased estimation pulse response x_MOS further comprises three steps:

first, calculation of the discrete Fourier spectrum of the received signal e;

second, division of the discrete spectral values of the received signal e by discrete spectral values of the effective transmitted signal obtained through a calibration measurement; and

third, determination of the modified unbiased estimation x_MOS by means of an inverse discrete Fourier transformation of the estimation value obtained from the division performed in the second step.

4. The method according to claim 3, wherein:

the first step is performed through the formation of the discrete Fourier transformation T_DFT e of the received signal e;

the second step is performed through an actual channel estimation, in which the optimum unbiased estimation

space="preserve" listing-type="equation">Λ

.sup.-1 T.sub.DFT e=T.sub.DFT x.sub.E +Λ

.sup.-1 T.sub.DFT n

of the discrete Fourier-transformation T_DFT x_E of the extended channel pulse response ##EQU21## is determined with the received signal e and the diagonal matrix Λ

in that the ith component of the vector T_DFT e is divided by the ith component λ

_i of the discrete Fourier-transformation

space="preserve" listing-type="equation">λ

=T.sub.DFT (c.sub.1, c.sub.2 . . . c.sub.N, 0 . . .

     0).sup.T =T.sub.DFT c.sub.E

of the extended, expanded transmitted pulse c_E, where

space="preserve" listing-type="equation">Λ

=diag(λ

.sub.1,λ

.sub.2 . . . λ

.sub.M+N-1)=diag(λ

.sub.i), i=1, 2 . . . M+N-1;

and

the third step is performed through the inverse discrete Fourier transformation T_DFT of the estimation

space="preserve" listing-type="equation">Λ

.sup.-1 T.sub.DFT e=T.sub.DFT x.sub.E +Λ

.sup.-1 T.sub.DFT n,

such that the modified, optimum unbiased estimation x_MOS of the extended channel pulse response x_E is in the form of

space="preserve" listing-type="equation">x.sub.MOS =A.sub.E.sup.-1 e=T.sub.DFT.sup.-1 Λ

.sup.-1 T.sub.DFT e.

5. The method according to claim 1, including application of Sensitivity Time Control (STC) by providing an amplifier unit including means for changing amplification over time through a control voltage provided in a receiver such that the control voltage, stored with respect to its course over time, is selected such that an influence of radio-field damping is compensated, and the analog received signal e(t) is amplified to a compensated analog received signal e_k (t) as a function of the stored control voltage.

6. The method according to claim 5, wherein, after being digitized, analog received signals e_k (t) subjected to STC amplification regulation are supplied as digital received signals e_k to a compensation device (29) in which the influence of the previous STC amplification is compensated again.

7. The method according to claim 1, including use of a binary code for the spread code and, consequently, of a corresponding binary-coded, phase-shift keying modulation of the transmitted pulses.

8. The method according to claim 7, including a step of selecting the spread code c to achieve a virtually constant course of the magnitude |A(f)| of the spectrum according to an equation ##EQU22## such that degradation of the signal-to-noise ratio is as low as possible.

9. The method according to claim 1, wherein the vector signal e is an analog received signal e(t) and time signal quadrature components e_I (t) and e_Q (t) of the analog received signal e(t) are formed in a receiver, are sampled at a sampling frequency f_c =1/T_c of the spread code, and samples e_i are subsequently subjected to a quantization

10. The method according to claim 1, comprising

providing a microprocessor or a digital signal processor (DSP) whose internal word lengths are significantly greater than a word length m_e or m_M,

where m_e /bit is a quantization word length of the samples of the received signal e, and m_M /bit is a finite word length of the elements of the estimation matrix, and

using the microprocessor or digital signal processor as a digital computing unit for channel estimation.

11. The method according to claim 1, including

establishing an optimum value of a process gain that can be attained through coherent integration by the product f_dmax ·

T_r where f_dmax is a maximum Doppler shift and T_r is a pulse repetition frequency.

12. The method according to claim 1, wherein the radar station is a modular short-range radar (NR) network.

13. The method according to claim 12, including application of Sensitivity Time Control (STC) by providing an amplifier unit including means for changing amplification over time through a control voltage provided in a receiver such that the control voltage, stored with respect to its course over time, is selected such that an influence of radio-field damping is compensated, and the analog received signal e(t) is amplified to a compensated analog received signal e_k (t) as a function of the stored control voltage.

14. The method according to claim 13, wherein, after being digitized, analog received signals e_k (t) subjected to STC amplification regulation are supplied as digital received signals e_k to a compensation device (29) in which the influence of the previous STC amplification is compensated again.

15. The method according to claim 12, including use of a binary code for the spread code and, consequently, of a corresponding binary-coded, phase-shift keying modulation of the transmitted pulses.

16. The method according to claim 15, including a step of selecting the spread code c to achieve a virtually constant course of the magnitude |A(f)| of the spectrum according to an equation ##EQU23## such that degradation of the signal-to-noise ratio is as low as possible.

17. The method according to claim 12, wherein the vector signal e is an analog received signal e(t) and time signal quadrature components e_I (t) and e_Q (t) of the analog received signal e(t) are formed in a receiver, are sampled at a sampling frequency f_c =1/T_c of the spread code, and samples e_i are subsequently subjected to a quantization

18. The method according to claim 12, comprising

providing a microprocessor or a digital signal processor (DSP) whose internal word lengths are significantly greater than a word length m_e or m_M,

where m_e /bit is a quantization word length of the samples of the received signal e, and m_M /bit is a finite word length of the elements of the estimation matrix, and

using the microprocessor or digital signal processor as a digital computing unit for channel estimation.

19. The method according to claim 12, including

establishing an optimum value of a process gain that can be attained through coherent integration by the product f_dmax ·

T_r where f_dmax is a maximum Doppler shift and T_r is a pulse repetition period.