Pulse or digital communications – Receivers – Particular pulse demodulator or detector
Reexamination Certificate
2000-06-02
2003-11-04
Le, Amanda T. (Department: 2634)
Pulse or digital communications
Receivers
Particular pulse demodulator or detector
C342S189000, C342S378000, C708S422000
Reexamination Certificate
active
06643337
ABSTRACT:
STATEMENT OF GOVERNMENT INTEREST
The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.
BACKGROUND OF THE INVENTION
The present invention relates to methods and apparatuses for correlating or establishing a statistical correlation of plural random variables, more particularly to methods and apparatuses for doing same in relation to physical phenomena such as impulsive signals or noise.
The alpha-stable distribution is an important area for investigation. One reason for the importance of the alpha-stable distribution is that it models impulsive noise. Another reason is that this statistical distribution is expected from superposition in natural processes. The parameter alpha, &agr;, is the characteristic exponent that varies over 0<&agr;≦2. The alpha-stable distribution includes the Gaussian when &agr;=2. For &agr; less than two, the distribution becomes more impulsive, more non-Gaussian in nature, and the tails of the distribution become thicker. This makes the alpha-stable distribution an attractive choice for modeling signals and noise having an impulsive nature. Also, from the generalized central limit theorem, the stable distribution is the only limiting distribution for sums of independent and identically distributed (IID) random variables (stability propert). If the individual distributions have finite variance, then the limiting distribution is Gaussian. For a less than two, the individual distributions have infinite variance. For detailed information, see the following two books, each of which is hereby incorporated herein by reference: C. L. Nikias and M. Shao, Signal Processing with Alpha-Stable Distributions and Applications, John Wiley and Sons, New York, N.Y., 1995; G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman and Hall, New York, N.Y., 1994.
Sources that could follow or be modeled by the alpha-stable distribution are abundant and include lightning in the atmosphere, switching transients in power lines, static in telephone lines, seismic activity, climatology and weather, ocean wave variability, surface texture, the slamming of a ship hull in a seaway, acoustic emissions from cracks growing in engineering materials under stress, magnetic avalanche or Barkhausen noise, transition boundary layer flow, etc. Many sources can exist in the area of target and background signatures that affect detection and classification. In underwater acoustics, examples of these sources could include interference to target detection such as ice cracking, biologics, bottom and sea clutter in active sonar, ocean waves near the surface and in the surf zone. They could also include target characteristics such as target strength in active sonar and cavitation. Similar sources in radar and infrared can include: ocean waves in the form of sea clutter and radar cross section (RCS); see R. D. Pierce, “RCS Characterization using the alpha-stable distribution,” Proc. 1996 IEEE National Radar Conference, Ann Arbor, Mich., May, 13-16, 1996, pp 154-159, hereby incorporated herein by reference. A 10 second long example of spiky, horizontally polarized (H-pol), radar sea clutter is shown herein in FIG.
1
.
Two known and limitedly successful methodologies of establishing a statistical correlation, based on the alpha-stable distribution, are classical second-order correlation and covariation correlation. Neither second-order correlators nor covariation correlators have proven capable of obtaining consistent estimates of the relationship between two channels of noise characterized by impulsiveness. Furthermore, second-order correlators operate in a realm wherein alpha is equal to two. Covariation correlators operate in a realm wherein alpha is greater than or equal to one and less than or equal to two. Hence, when alpha is less than one (as would generally be the case, for instance, when the noise is extremely spikey, even more than the noise illustrated in FIG.
1
), neither second-order correlators nor covariation correlators work to provide consistent results.
Of interest and incorporated herein by reference are the following United States patents: Nishimori U.S. Pat. No. 5,982,810 issued Nov. 9, 1999; Honkisz U.S. Pat. No. 5,787,128 issued Jul. 28, 1998; Kazecki U.S. Pat. No. 5,365,549 issued Nov. 15, 1994; Baron U.S. Pat. No. 4,860,239 issued Aug. 22, 1989; Horner U.S. Pat. No. 4,826,285 issued May 2, 1989; Zeidler et al. U.S. Pat. No. 4,355,368 issued Oct. 19, 1982Kaelin al. U.S. Pat. No. 4,234,883 issued Nov. 18, 1980; Baario U.S. Pat. No. 4,117,480 issued Sep. 26, 1978; Fletcher et al. U.S. Pat. No. 4,112,497 issued Sep. 05, 1978; Heng et al. U.S. Pat. No. 4,070,652 issued Jan. 24, 1978.
SUMMARY OF THE INVENTION
In view of the foregoing, it is an object of the present invention to provide an alpha-stable distribution based correlator which can reliably estimate the relationship between two channels of impulsive noise.
It is a further object of the present invention to provide an alpha-stable distribution-based correlator which can operate in a realm wherein alpha is less than one.
The present invention provides a methodology for correlating at least two remotely and/or locally generated signals, e.g., quantifying a relationship therebetween. An inventive method is provided for producing an output signal which is indicative of a correlation of at least two input signals. The inventive method comprises calculating (i.e., estimating) the codifference correlation with respect to at least two input signals, and producing an output signal commensurate with the codifference correlation. The estimating includes considering the sum and difference of codifference estimates wherein each codifference estimate is equated with a corresponding dispersion estimate. According to typical inventive practice, the calculating includes treating each signal as a complex signal representative of real and imaginary terms characterized by values and defined by real and imaginary axes.
Further provided according to this invention is a correlator for correlating a reference signal and a sampler signal. The inventive correlator admits of implementation in a communication system of the type including antenna means for receiving electromagnetic waves, down converter means for down converting a modulated signal received from the antenna, means, sampler means for sampling a down converted. signal received from the down converted means, and memory means for storing a reference signal. The inventive correlator correlates the reference signal (received from the memory means) and the sampler signal (received from the sampling means). The inventive correlator comprises algorithmic means for calculating (i.e., estimating) the codifference correlation based on the sum and difference of codifference estimates, wherein each codifference estimate is equated with a corresponding dispersion estimate.
This invention further provides a correlation detection system for use in association with a modulated signal such as produced by an antenna receiving electromagnetic waves such as radio frequency waves. The inventive correlation detection system comprises a down converter, a sampler, a memory and a correlator. The down converter is adaptable to down converting the modulated signal and producing a down converted signal. The sampler is adaptable to sampling the down converted signal and producing a sampled signal. The memory is adaptable to storing a reference signal. The correlator is adaptable to correlating the reference signal and the sampled signal. The correlator includes processor means and is capable of calculating (i.e., estimating) the, codifference correlation between the reference signal and the sampled signal, based on the sum and difference of codifference estimates. Each codifference estimate is taken from equation with a corresponding dispersion estimate.
In accordance with the present invention,
Kaiser Howard
Le Amanda T.
The United States of America as represented by the Secretary of
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