




CFAR timefrequency processor for signal detection and extraction in noise 
H1726 
CFAR timefrequency processor for signal detection and extraction in noise


Patent Drawings: 
(3 images) 

Inventor: 
Chen 
Date Issued: 
May 5, 1998 
Application: 
08/829,262 
Filed: 
March 31, 1997 
Inventors: 
Chen; Victor C. (Vienna, VA)

Assignee: 

Primary Examiner: 
Pihulic; Daniel T. 
Assistant Examiner: 

Attorney Or Agent: 

U.S. Class: 
342/93 
Field Of Search: 

International Class: 
G01S 7/292 
U.S Patent Documents: 

Foreign Patent Documents: 

Other References: 


Abstract: 
Detection and extraction of unknown signal in noise may be important in radar When an unknown signal of a transient nature is received, representation in terms of basis functions, localized in both time and frequency, such as Gabor representation, may be very useful for signal detection. By using timefrequency decomposition, noise energy tends to spread across entire timefrequency domain, while signal energy often concentrates within a small region with a limited time interval and frequency band. Signal recognition in the timefrequency domain becomes easier than that in either time or frequency domain. By setting a CFAR threshold for and examining timefrequency Gabor coefficients which exceed the threshold, presence of a signal may be determined. CFAR timefrequency processing for detection and extraction of signals in noise improves detection and extraction performance for low Signaltonoiseratio (SNR) signals. Due to low SNR, it may be very difficult to identify signals from within either the time or the frequency domain alone. However, in the timefrequency domain, the signal can be easily recognized and its time location and instantaneous frequency can be measured. By performing CFAR thresholding and taking inverse Gabor transform, an unknown signal embedded in noise may be detected and reconstructed with enhanced quality. 
Claim: 
I claim:
1. In a radar receiver, an improved method for detection and extraction of an unknown information signal and noise comprising:
processing said unknown information signal and said noise received in said receiving step into meaningful information using a series of processing steps comprising:
generating and outputting timefrequency information from said unknown information signal and said noise,
processing said timefrequency information using statistical distribution information of said noise and generating noise filtered information,
receiving said noise filtered information and said timefrequency information and normalizing said noise filtered information and said time frequency information and outputting normalized information,
receiving said normalized information and false alarm rate information and thresholding said normalized information and generating thresholded timefrequency information, and
detecting and extracting a noiseless information signal from said threshold timefrequency information.
2. The method of claim 1, wherein said step of generating and outputting timefrequency information further comprises generating actual timefrequency coefficients and outputting said actual timefrequency coefficients.
3. The method of claim 1, wherein said step of receiving and processing said timefrequency information further comprises:
receiving said timefrequency information representative of said unknown information signal and said noise,
comparing said timefrequency information with a statistical distribution representative of said noise distribution, and calculating a mean value for said noise.
4. The method of claim 3, wherein said statistical distribution information further comprises a Rayleigh distribution.
5. The method of claim 1, wherein said step of receiving said normalized information and false alarm rate information and thresholding said normalized information further comprises Constant False Alarm Rate thresholding.
6. The method of claim 1, wherein said step of detecting and extracting a noiseless information signal from said thresholded timefrequency information further comprises:
receiving said thresholded timefrequency information,
estimating a desired signal corresponding to said thresholded timefrequency information,
generating modified timefrequency information corresponding to said desired signal estimated in said estimating step and outputting said modified timefrequency information, and
processing said modified timefrequency information and outputting said noiseless target information signal.
7. The method of claim 6, wherein said step of estimating a desired signal corresponding to said thresholded timefrequency information further comprises:
estimating an anticipated signal using a Least Squares approximation,
generating approximate timefrequency coefficients for said anticipated signal,
comparing said approximate timefrequency coefficients with said actual timefrequency coefficients,
optimizing said anticipated signal with respect to said desired signal using results from said comparing step and outputting an optimal anticipated signal, and
outputting said desired signal using said optimal anticipated signal derived in said optimizing step.
8. The method of claim 1, wherein said step of generating and outputting timefrequency information from said unknown information and said noise further comprises:
applying a timefrequency transform individually to a plurality of signal inputs having a plurality of scales and outputting a plurality of timefrequency signal outputs,
interpolating said plurality of timefrequency signal outputs and outputting a plurality of interpolated signal outputs, and
summing said plurality of interpolated signal outputs and outputting an improved timefrequency signal output.
9. A filter comprising:
means for providing a signal of interest in the time domain;
means for producing a transformed signal by transforming said signal of interest into the timefrequency domain, said timefrequency domain having a plurality of timefrequency bins; and
means for discarding the portion of said signal in each one of said timefrequency bins in which said portion is less than a preselected threshold. 
Description: 
FIELD OF THE INVENTION
The present invention relates to detection and extraction of unknown signals in noise and enhancing signal to noise characteristics for detected and extracted signals. In particular, the present invention relates to detecting radar signalswithin an environment containing high background noise levels.
BACKGROUND OF THE INVENTION
Constant False Alarm Rate (CFAR) processing is an optimal way to set up a threshold for detecting signals in a noise laden environment. For signals corrupted by strong background noise, it is often difficult to perform signal detection andparameter estimation in either the time domain or the frequency domain. Signals often concentrate their energies within a limited time interval and a limited frequency band, while background noise often has its energy spread widely into the entire timedomain or frequency domain.
A common way to reduce noise in a detected signal is thresholding: after a signal of interest is detected it is transformed into the frequency domain, and "filtered" by discarding all of the frequency bins whose magnitude is below a setthreshold. Because noise has a wider bandwidth than any likely signal of interest, doing this typically improves overall signal to noise. One difficulty with thresholding is that in so doing, one inevitably discards some weaker frequency components ofthe signal, and retains larger components which are predominantly noise. In systems which detect signals in order to determine the presence or absence of a condition, e.g. a military communications system which listens for signals characteristic of anenemy, these thresholding errors cause false alarms, or cause the system to miss legitimate signals. Increasing the filtering threshold will increase misses, but reduce false alarms; decreasing the threshold does the opposite. The algebraicrelationship between threshold level and false alarm rate is known, and current practice is to determine the error rate which is tolerable, and then set the threshold accordingly.
Another difficulty with thresholding is that some signals of interest contain frequencies which are not continuously present and indeed may be present only briefly, n.b. frequencyhopping communications signals. Thus the power at suchfrequencies may be large for a brief time, but total energy at these frequencies may be relatively small compared to noise, which, being continuously present, accumulates continuously throughout signal detection. Therefore, thresholding in the frequencydomain may remove the signal in the noise.
In view of these and other limitations of existing methods, it would be desirable for a radar system which would receive statistically nonstationary signals and noise and generate a stable false alarm rate in proportion to the level of noise inthe signal background and extract signals in noise. It would be further desirable for a system which would accommodate timeinvariance in the received signal.
SUMMARY AND OBJECTS OF THE INVENTION
Accordingly, an object of the invention is to improve the signal to noise ratio of a detected signal.
Another object is to do so in a manner which increases signal to noise of frequency components of the detected signal which are time variant, especially those which are highly localized in time.
In accordance with these and other objects made apparent hereinafter, the invention concerns processing a detected signal by transforming it into the timefrequency domain prior to filtering, rather than just into the frequency domain (e.g. by aFast Fourier Transform), as is currently the common practice. Noise in the transformed signal is spread over both time and frequency, and thus signal frequencies which existed only briefly during signal detection will stand out more prominently, thuspermitting more accurate threshold filtering.
In doing this, one can use any of a number of linear timefrequency transforms thus permitting accurate signal reconstruction in the time domain by use of the inverse Gabor transform. The Gabor transform is preferred because it linear, and hashighest joint timefrequency resolution.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is graph illustrating a Rayleigh distribution.
FIG. 2a is a timefrequency plot of the coefficients of a detected signal.
FIG. 2b is a timefrequency plot of a timefrequency mask, (i.e. contour in the timefrequency domain circumscribing a portion of the domain).
FIG. 3 is a block diagram illustrating a portion of the present invention.
DETAILED DESCRIPTION OF THE DRAWINGS
Linear timefrequency transforms such as the Gabor transform may be used to decompose a signal into its coefficients in the joint timefrequency domain. If we can distinguish those coefficients which belong to a signal from the coefficientswhich belong to noise, the signal's coefficients may be utilized to reconstruct a signal by simply taking the inverse transform.
To establish a relationship between time and frequency, a signal should be compared with those basis functions which are concentrated in both the time and the frequency domain. Such comparisons are possible using Gabor functions as described in"Theory of communication", D. Gabor, J.IEE (London), 93(III) (1946) pp. 429457, incorporated herein by reference. Timefrequency Gabor transforms represent a signal as a linear combination of timeand frequencyshifted Gaussian basis functionsh{m,n}(t).
where m is an integer representing a discrete step along the time axis in the timefrequency domain, and n is a discrete step along the frequency axis in the timefrequency domain.
where T and .OMEGA. are the respective widths in time and frequency of the timefrequency domain (i.e. each nth time step is T time units long; each nth frequency step is .OMEGA. frequency units long, and the choice of T and .OMEGA. determineshow coarse or fine the transformed data will be). A Gabor transform restricts the sampling cell to T.OMEGA.=2.pi., or
From the foregoing, one can see that a Gabor transform is Gaussian. Theoretically, the resolution possible for any Gaussian transform is limited according to the relationship:
where .DELTA..sub.t and .DELTA..sub.107 are the respective resolutions possible on each axis of the transform domain (e.g., here, resolution in time and frequency, respectively.) Thus it is preferred to choose T and .DELTA. to optimizeresolution, i.e. .DELTA..sub.t .DELTA..sub.107 =1/2.
A primary challenge using Gabor transforms may be computing Gabor coefficients. Gabor coefficients may be defined as described in "Discrete Gabor transform", S. Qian and D. Chen, IEEE Trans. on Signal Processing, 41(7), (1993), pp. 24292439incorporated herein by reference, and "Optimal biorthogonal analysis window function for discrete Gabor transform", S. Qian and D. Chen, IEEE Trans. on Signal Processing, 42(3), (1994) pp. 69414 687 incorporated herein by reference.
where * indicates complex conjugate, and
and may be a biorthogonal function of h.sub.m,n (t):
where .delta.(t) is the impulse function of t. Thus one can show that:
and
One advantage of representing signal samples with Gabor basis functions h.sub.m,n (t), which are localized in both time and frequency domain, is that noise energy is spread across the entire timefrequency domain while useful signal energy oftenmay be concentrated within a region with a limited time interval and a limited frequency band. Therefore, the signaltonoise ratio can be enhanced.
In the timefrequency domain, noise has a Rayleigh distribution. For a Rayleigh distribution, it is known that for a given false alarm rate P.sub.fa, the corresponding threshold rate T.sub.fa is:
An appropriate threshold T is one which produces an acceptable false alarm rate for noise, i.e. an acceptably low number of false alarms due to noise, and an acceptable small number of missing rate when signal is present. FIG. 1 illustrates aRayleigh distribution 100. Leftside area A.sub. left 101 of the mean is equal to the rightside area, A.sub. right 102. If C.sub.m,n is a Gabor transformed signal of interest, then a conventional criterion for applying threshold is that:
where .mu. is the mean of the Rayleigh distributed noise, and C.sub.m,n is the transformed signal strength in the m,nth timefreqency bin. To apply this algorithm, one first calculates T.sub.fa. Then one estimates .mu. (in a manner discussedbelow). One then filters the signal by discarding all timefrequency bins whose signal C.sub.m,n does not meet the above threshold criterion.
A preferred way to estimate .mu. is best understood in conjunction with FIGS. 2(a) and (b). Both figures are greyshading diagrams, which represent a signal transformed into the timefrequency domain, with the timefrequency plane being in theplane of the drawing paper, and intensity of grey indicating signal strength. Very dark areas 301 and 302 correspond to a signal, and the lighter areas correspond to noise. One "masks" the region of the timefrequency domain which plainly containssignal, e.g. using an overly low threshold, identifying all bins which have a larger signal, then surrounding all those bins by an expanded contour or contours (303, 304 in FIG. 2(b)) to ensure containment of the signal, locating a portion 306 of thetimefrequency domain sufficiently distant from contours 303, 304 to ensure that signal therein is virtually all noise, adding up the total signal within contour 306, and using this and the mathematics of the Rayleigh distribution to calculate .mu.. This is often called the "four corner" method because contour 306 is chosen as a rectangle (for calculational simplicity), first by selecting tow points 307, 308 distant from contour 303, 304 and then completing the rectangle by choosing two more points309, 310 even more distant from contours 303, 304. This way to calculate noise is exemplary. In general, any conventional means of noise estimation could be used.
FIG. 3 is a block diagram illustrating the overall process. Noise corrupted timedomain signal r(t) is transformed to the timefrequency domain by processor 400. The transformed signal C.sub.m,n is used by processor 401 to determine .mu., andalso preferably masks an appropriate portion of the timefrequency domain, as above described. Processor 402 normalizes C.sub.m,n to .mu., and processor 403 determines the threshold T per the above described algorithm therefor, and a preselected falsealarm rates P.sub.fa. The timefrequency bins which survive the thresholding by processor 403 have their respective amplitudes output to member 405 for annunciation or further processing. The signal magnitude in each surviving timefrequency binrepresents a Gabor coefficient C.sub.m,n, from which one can, e.g., reconstruct a filtered signal in the timedomain.
Of especial importance is that this approach is adaptive: because .mu. is reestimated with each detected signal and the transformed signal normalized to .mu., the false alarm rate is kept relatively constant.
The invention has been described in what is considered to be the most practical and preferred embodiments. It is recognized, however, that obvious modifications to these embodiments may occur to those with skill in this art. Accordingly, thescope of the invention is to be discerned from reference to the appended claims, wherein:
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