Data processing: measuring – calibrating – or testing – Measurement system – Measured signal processing
Reexamination Certificate
2003-02-10
2004-03-23
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Measured signal processing
C324S309000
Reexamination Certificate
active
06711528
ABSTRACT:
BACKGROUND
The present invention is generally related to separating individual source signals from a mixture of source signals, and more specifically related to blind source separation.
A classic problem in signal processing, often referred to as blind source separation (BSS), involves recovering individual source signals from a composite signal comprising a mixture of those individual signals. An example is the familiar “cocktail party” effect, wherein a person at a party is able to separate a single voice from the combination of all voices in the room. The separation is referred to as “blind” because it is often performed with limited information about the signals and the sources of the signals.
Blind source separation (BSS) is particularly applicable to cellular and personal wireless communications technologies, wherein many frequency bands have become cluttered with numerous electromagnetic emitters, often co-existing in the same spectrum. The problem of co-channel emitters is expected to only worsen in years to come with the development of low power, unlicensed wireless technologies such as Bluetooth® and other personal area networks. These developments have resulted in the use of multiple sensors and array signal processing techniques to perform spectral monitoring. Such techniques enable the exploitation of spatial information to separate co-channel emitters for detection, classification, and identification. Additionally, many signals designed for a low probability of detection (LPD) or low probability of intercept (LPI) may use ambient background electromagnetic radiation and known co-channel emitters as a means of concealment. Constructing single sensor receiver systems with the required sensitivity to such emitters is generally prohibitive. Thus, many applications utilize BSS and sensor arrays.
Several techniques have been proposed to solve the BSS problem. These can be classified into two main groups. The first being based on second-order statistics, and the second being based on higher-order statistics, such as those based on independent components analysis (ICA) and other higher-order spectral estimation and spatial filtering techniques.
One second-order blind source separation technique is a spectral estimation method that exploits the rotational invariance of the signal subspace to estimate the direction of arrival. This technique known as Estimation of Signal Parameters via Rotational Invariance (ESPRIT) employs pairs of calibrated elements and uses a matrix-pencil formed by the spatial correlation and cross-correlation matrices. See, for example, R. Roy, A. Paulraj, T. Kailath, “Direction-of-Arrival Estimation by Subspace Rotation Methods,”
Proc. ICASSP
86, pp. 2495-2498 and R. Roy and T. Kailath, “ESPRIT—Estimation of Signal Parameters via Rotational Invariance Techniques,”
IEEE Trans. on ASSP
, Vol. 37, No. 7, July 1989, pp. 984-995, which are each incorporated by reference in their entirety as if presented herein. However, a disadvantage of ESPRIT is that at very low signal-to-noise ratios the signal plus noise subspace and the noise subspace are indistinguishable thus making the conversion of the noise subspace of the spatial correlation matrix impractical. This is due in part to ESPRIT requiring an estimation of the noise variance to convert the noise subspace into a null subspace of the spatial correlation matrix, and assuming that the noise is spatially white.
Another second order blind source separation technique is known as the Constant Modulus Algorithm (CMA), also referred to as Goddard's algorithm. The CMA is an adaptive spatial filtering technique, which is used to perform source separation by determining a set of spatial filter tap weights that forces the output signal to have a modulus as close to unity as possible. Typically, the CMA is performed sequentially to separate all source signals. The CMA has been suggested for use as a blind equalization technique to reduce inter-symbol interference of constant modulus signals, such as FSK, PSK, and FM modulated signals, on telephone channels (See, for example, D. N. Godard, “Self-recovering Equalization and Carrier Tracking in Two-dimensional Data Communication Systems,”
IEEE Trans. Commun
., Vol. COMM-28, November 1980, pp. 1867-1875, which is incorporated by reference in its entirety as if presented herein.), and to perform blind equalization to combat multi-path fading and to suppress co-channel interfering signals (See, for example, B. G. Agee, “The Property Restoral Approach to Blind Adaptive Signal Extraction,” Ph.D. Dissertation, Dept. Elect. Eng. Comput. Science, Univ. of Calif., Davis, 1989, which is incorporated by reference in its entirety as if presented herein). However, the CMA technique works only for signals with a constant modulus and is not practicable for most applications. In practice, because signals are filtered to limit their spectral occupancy at the transmitter and to limit the noise bandwidth at the receiver, true constant modulus signals rarely exist. Furthermore, at very low signal-to-noise ratios, noise dominates the input signal thus distorting the spatial filter's output signal's modulus and causing large fluctuation in the error signal used in adaptation.
Yet another second order blind source separation technique is a spatial filtering technique using second-order cyclostationary statistics with the assumption that the source signals are cyclostationary. This technique was developed as a blind single-input single-output (SISO) channel identification technique for use in blind equalization (See, for example, L. Tong, G. Xu, and T. Kailath, “Blind Identification and Equalization Based on Second-Order Statistics: A Time-Domain Approach,”
IEEE Trans. Information Theory
, Vol. 40, No. 2, March 1994, pp. 340-349, which is incorporated by reference in its entirety as if presented herein), and was later adapted to perform the blind separation of cyclostationary signals (See, for example, L. Castedo and A. R. Figueiras-Vidal, “An Adaptive Beamforming Technique Based on Cyclostationary Signal Properties,”
IEEE Trans. Signal Processing
, Vol. 43, No. 7, July 1995, pp. 1637-1650, which is incorporated by reference in its entirety as if presented herein). One disadvantage of this cyclostationary approach is that it requires different symbol rates and/or different carrier frequencies for separating multiple superimposed signals. Another disadvantage is that residual carrier offsets with a random initial phase can cause the signals to become stationary, causing the cyclostationary assumption to become invalid. Other disadvantages include the fact that this approach precludes separating sources that may use non-linear or non-digital modulations, and this approach assusmes the noise vector is temporally and spatially white.
Still another blind source separation technique based on second-order statistics is referred to as Second-Order Blind Identification (SOBI). See, for example, A. Belouchrani, K. Abed-Meraim, J. F. Cardoso, and E. Moulines, “Blind Source Separation Using Second-Order Statistics,”
IEEE Trans. Signal Processing
, Vol. 45, No. 2, February 1997, pp. 434-444, for a description of this technique, which is incorporated by reference in its entirety as if presented herein. This technique exploits the time coherence of the source signals and relies on the joint diagonalization of a set of covariance matrices. A disadvantage of this technique is that it requires additive noise to be temporally white and uses the eigenvalues of the zero lag matrix to estimate the noise variance and to spatially whiten the sensor output vector. Another disadvantage is that at low signal to noise rations, the estimation of the noise variance is difficult at best and impossible in most cases. Yet another disadvantage is that the number of sources must be known or estimated. Still, another disadvantage is that the SOBI technique is valid for spatially correlated noise. The estimation of the noise covariance is extremely difficult even at high signal-to-noise ratios, thus makin
Beadle Edward R.
Dishman John F.
Martin G. Patrick
Charioui Mohamed
Duane Morris LLP
Harris Corporation
Hoff Marc S.
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