Telecommunications – Transmitter and receiver at separate stations – Plural transmitters or receivers
Reexamination Certificate
1997-12-15
2001-05-22
Trost, William G. (Department: 2683)
Telecommunications
Transmitter and receiver at separate stations
Plural transmitters or receivers
C455S561000, C455S506000, C370S342000
Reexamination Certificate
active
06236862
ABSTRACT:
BACKGROUND OF THE INVENTION.
1. Field of the Invention
The invention pertains to systems for recovering original signal information or content by processing multiple measurements of a set of mixed signals, and more specifically, the invention pertains to adaptive systems for recovering original signals from among several received measurements of their mixtures.
2. Description of the Related Art
The recovery and separation of independent sources is a classic but difficult problem in signal processing. The problem is complicated by the fact that in many practical situations, many relevant characteristics of both the signal sources and the mixing media are unknown.
Two main categories of methods exist in prior art:
1. Conventional discrete signal processing (Please see U.S. Pat. Nos. 5,208,786 and 5,539,832), and 2. Neurally inspired adaptive algorithms (Please see U.S. Pat. Nos. 5,383,164 and 5,315,532).
Conventional signal processing approaches to signal separation originate in the discrete domain in the spirit of traditional digital signal processing methods that use statistical properties of signals. Such signal separation methods employ discrete signal transforms and filter/transform function inversion. Statistical properties of the signals in the form of a set of cumulants are used and these cumulants are mathematically forced to approach zero. This constitutes the crux of the family of algorithms that search for the parameters of transfer functions that recover and separate the signals from one another. Calculating all possible cumulants, on the other hand, would be impractical and too time consuming for real time implementation. Neurally inspired adaptive algorithms follow an algebraic method originally proposed by J. Herault and C. Jutten, now called the Herault-Jutten (or HJ) algorithm. The suitability of this set of methods for CMOS integration have been recognized. However, the HJ algorithm is at best heuristic with suggested adaptation laws that have been shown to work mainly in special circumstances. The theory and analysis of prior work pertaining to the HJ algorithm are still not sufficient to support or guarantee the success encountered in experimental simulations. Both Herault and Jutten recognize these analytical deficiencies and they describe additional problems to be solved. Their proposed algebraic algorithm assumes a linear static filtering with no delays. Specifically, the original signals are assumed to be transferred by the medium via a matrix of unknown but constant coefficients. To summarize, the Herault-Jutten method (i) is restricted to the full rank and linear static mixing environments, (ii) requires matrix inversion operations, and (iii) does not take into account the presence of signal delays. In many practical applications, however, delays do occur and and in many occasions the medium mixing exhibits nonlinear phenomena. Accordingly, previous work fails to successfully separate signals in many practical situations and real world applications.
OBJECTS OF THE INVENTION
It is an object of the invention to recover and separate mixed signals transmitted through a common medium or channel wherein the separation of signals is of such high quality as to substantially increase (i) the signal carrying capacity of the medium or channel, (ii) the quality of the received signal, or (iii) both. The media or channels may consist of a combination of wires, cables, fiber optics, wireless radio or light based frequencies or bands, as well as a combination of solid, liquid, gas particles, or vacuum.
Another object of the invention is to separate mixed signals through a common media or channel wherein a high quality of signal separation is achieved by hardware presently produceable by state of the art techniques.
SUMMARY OF THE INVENTION
Separation of statically mixed signals is of limited use because of additional factors involved in the superposition of signals in real mixing environments. Some examples of additional factors to be considered include (1) the propagation time delays between sources and receivers or sensors, (2) the nonlinear nature of the mixing functions introduced by the mixing medium as well as the signal sensors or receivers, and (3) unknown number of source signals that are to be separated. The system of this invention adds a generalized framework to the described preexisting approaches for coping with a range of dynamic superposition circumstances unaddressed to date. The most practically pertinent of these failures is failure to model the medium of signal mixing, noise generation and interference adequately, in particular assumption of a linear static medium and no delays. The invented method addresses this shortfall by extending the formulation of the problem to include a dynamic modeling of the signal mixing/interference medium.
To best understand the problem solved by the invention, and the approach of the prior art to solve this problem, the following problem statement is helpful:
With reference to
FIG. 1
of the attached drawings, consider several independent signals as s
1
(t), . . . , and S
N
(t). These signals may represent any of, or a combination of, independent speakers or speeches, sounds, music, radio-based or light-based wireless transmissions, electronic or optic communication signals, still images, videos, etc. These signals may be delayed and superimposed with one another. We assume a linear time-invariant medium or environment. One desires a “network” that, upon receiving the delayed and superimposed signals, works to successfully separate the independent signals.
The problem is illustrated in
FIG. 1
, from prior art. In addition, two distinct practical situations that summarize the problem are shown pictorially in FIG.
2
and FIG.
3
. In
FIG. 2
, two signals are illustrated that originate from two different sources and are received by one receiver tuned to both sources. These two mixtures are used to recover both original signals. In
FIG. 3
, two signals are illustrated that originate from two different sources and are received by two sensors separated by a distance D. The sources are mixed in the propagation medium and their wave fronts hit the sensors at different angles and at different phases. As the distance between the two receivers decreases, this situation approaches a static problem since the source signals arrive with less delay with respect to one another. The situations described in
FIGS. 2 and 3
can be schematically equated to a symbolic diagram shown in
FIG. 4
wherein the schematic illustration represents two signals originating from two different sources that are mixed dynamically. The sources are mixed in the propagation medium and the mixing involves relative delays in addition to gains determined by the entries ij of the mixing matrix.
A simple practical mixing problem of two signals and their delayed versions could be formulated as
[
E
1
(
t
)
E
2
(
t
)
]
=
[
a
11
0
0
a
22
]
[
s
1
(
t
)
s
2
(
t
)
]
+
[
0
a
12
a
21
0
]
[
s
1
(
t
-
δ
1
)
s
2
(
t
-
δ
2
)
]
where &dgr;
1
and 62 are the time delays for s
1
and s
2
, respectively. If &dgr;
1
=&dgr;
2
=0, this would reduce to linear static signal mixing as the situation described in the Herault-Jutten problem.
First, let us note that the problem involving delays (i.e., &dgr;
2
≠0 or &dgr;
1
≠0 as in
FIG. 2
) is significantly more difficult to solve.
FIG. 5
shows two sine wave signals of different frequencies which are dynamically mixed as discussed below. In the example discussed here, source 1, s
1
(t), is a sine wave of frequency 2 kHz, source 2, s
2
(t), is a sine wave of 5 kHz. Each signal is delayed 100 microseconds (i.e., &dgr;
1
=&dgr;
2
=0.0001 sec). The mixing coefficients are a
11
=a
22
=1 and a
12
=a
21
=0.7.
The Herault-Jutten approach to signal separation assumes that the “statistically independent” signal vector
S(t)=[s
1
(t), . . . , and s
N
(t)]
7
is statically mixed via a constant ma
Erten Gamze
Salam Faihi M.
Intersignal LLC
Smith Sheila
Trost William G.
Young & Basile P.C.
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