System employing dissipative pseudorandom dynamics for communications and measurement
First Claim
1. A communication or measurement system including:
- A. a transmitter for transmitting a modulated signal, the transmitter including a first feedback shift register that produces a pseudo-random noise signal that is used to modulate a message signal;
B. a receiver for receiving the modulated message signal, the receiver including a second feedback shift register for reproducing the pseudo-random noise signal from the received modulated signal and using the noise signal to recover the message signal from the received signal, the second feedback shift register being characterized by a non-chaotic expression that is associated with the expression that governs the first feedback shift register and has stable fixed points at integer values and unstable fixed points at 1/2 integer values.
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Accused Products
Abstract
A communication and/or measurement system includes a transmitter that modulates a pseudo-random noise signal with a message signal to produce a wideband signal for transmission. A receiver, which demodulates the wideband signal to recover the message signal, includes an "analog" feedback shift register that reproduces the noise signal based on samples of the received signal. The analog feedback shift register ("AFSR") is a generalization of a linear feedback shift register ("LFSR"). The AFSR is characterized by a function that agrees with the function that characterizes the LFSR, at the points at which that function is defined. Further, the AFSR characterizing function has stable fixed points at these values, i.e., it has a slope of less than one in these regions. Specifically, the AFSR'"'"'s function has stable fixed points at integer values and unstable fixed points at half-integer values and, the stable fixed points act as attractors. The AFSR thus produces a sequence that relaxes to the nearest integer-valued sequence. One example of such a function is: ##EQU1## where the αi '"'"'s are the coefficients of the maximum length polynomial used to produce the wide-band noise signal and yn-1 is the state of the (n-i)th stage of the register. As long as the samples of received signal that are fed to the AFSR fall within the basins of attraction that surround the stable values, the AFSR can accurately determine the expected next state of the shift register. While this can be done explicitly, the AFSR merges the symbol parsing, acquisition, tracking and update rules into a simple governing equation. The AFSR will thus entrain and produce a binary-valued pseudo-random noise signal. In one embodiment the signal yn is coupled to the register by a coupling circuit that sums (1-ε)yn and εSn, to produce the update signal y'"'"'n where ε is a coupling factor selected between 0 and 1, and Sn is a sample of the received signal.
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Citations
9 Claims
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1. A communication or measurement system including:
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A. a transmitter for transmitting a modulated signal, the transmitter including a first feedback shift register that produces a pseudo-random noise signal that is used to modulate a message signal; B. a receiver for receiving the modulated message signal, the receiver including a second feedback shift register for reproducing the pseudo-random noise signal from the received modulated signal and using the noise signal to recover the message signal from the received signal, the second feedback shift register being characterized by a non-chaotic expression that is associated with the expression that governs the first feedback shift register and has stable fixed points at integer values and unstable fixed points at 1/2 integer values. - View Dependent Claims (2, 3, 4, 5, 6, 8)
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7. An analog feedback shift register for use in a communication or measurement system, the shift register including:
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A. a plurality of stages connected together such that the contents of one stage are used to update a next stage; and B. means for producing a feedback signal by combining the contents of the stages in accordance with the following expression;
##EQU10## where the α
i '"'"'s are the coefficients of the maximum length polynomial and yn-1 is the state of the (n-i)th stage of the register, andC. coupling means for coupling an update signal to a first stage of the register, the coupling circuit adding (1-ε
)yn and ε
Sn to produce the update signal y'"'"'n =(1-ε
)yn +ε
Sn, where ε
is a coupling factor selected between 0 and 1 and Sn is a sample of a received signal.
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9. An analog feedback shift register for use in a communication system, the shift register including:
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A. a plurality of stages connected together such that the contents of one stage are used to update a next stage; and B. means for producing a feedback signal by combining the contents of the stages in accordance with the following;
##EQU11## where the α
i '"'"'s are the coefficients of the maximum length polynomial and yn-1 is the state of the (n-i)th stage of the register, andC. coupling means for coupling an update signal y'"'"'n to a first stage of the register, the coupling circuit using as an update y'"'"'n =(1-ε
)yn +ε
sgnSn, where ε
is a coupling factor selected between 0 and 1 and sgnSn is the sign of a sample of a received signal.
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Specification