Duffing equation-based weak complex signal detection method

A complex signal and equation technology, applied in the field of weak complex signal detection based on complex Duffing equation

Inactive Publication Date: 2012-06-27
BEIJING INSTITUTE OF TECHNOLOGYGY
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Problems solved by technology

[0004] The technical problem to be solved in the present invention is to provide a weak complex signal detectio...

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  • Duffing equation-based weak complex signal detection method
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  • Duffing equation-based weak complex signal detection method

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Embodiment Construction

[0024] The technical solution of the present invention will be further explained below in conjunction with the accompanying drawings and a specific embodiment.

[0025] Assuming that the signal used is a complex single-frequency signal A·exp(jt), that is, ω=1rad / s, it is subject to a mean value of 0 and a variance of σ 2 The pollution of the additive complex white Gaussian noise n(t), that is, the signal to be detected cs(t)=A·exp(jt)+n(t), and the signal-to-noise ratio of the signal to be detected is defined as The following are the specific implementation steps of using the proposed complex chaotic oscillator detection system to detect the above signals:

[0026] Step S00, parameter assignment, set parameters k=0.5, p=1, ω=1, γ c = 0.72.

[0027] In general, k=0.5, p=1, under this condition γ c =0.72, at this time the complex chaotic equation is in the critical chaotic state. The value of ω is best taken as the angular frequency of the useful signal to be detected. If i...

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Abstract

The invention discloses a Duffing equation-based weak complex signal detection method, which utilizes the parameter sensibility and the noise immunity of the Duffing equation solution to detect the useful signal which is annihilated in the noise. At first, the complex Duffing detection equitation is built, and is then utilized to detect the complex signal, the method comprises the steps that: all the parameters in the equation are determined; the noise variance of the complex signal is estimated, the estimated value is utilized to calculate the gain, wherein e is the expected noise variance of the complex signal to be detected after the gain, the unit is watt, then the complex signal to be detected is multiplied by the gain, so the complex signal to be detected after the gain is obtained; the complex signal g multiplied by cs(t) to be detected after the gain is substituted in the complex Duffing detection equation which is adjusted to the critical state, the solution to the equation is solved, and is utilized to calculate the maximum Lyapunov exponent of the equation; and the output is judged to be detected with useful signal or not according to whether the maximum Lyapunov exponent of the stabilized equation is smaller than 0 or not.

Description

technical field [0001] The invention relates to the technical field of weak complex signal detection, in particular to a weak complex signal detection method based on a complex Duffing equation. Background technique [0002] Chaos theory is one of the most important achievements of nonlinear science. At present, chaos theory has been widely used in control, synchronization, prediction, communication, detection and other fields. In the field of signal detection, the use of real-domain chaotic oscillators to detect weak real signals in real noise has achieved some excellent application results, which can detect small signals with extremely low signal-to-noise ratios. However, complex signals are often used in many scientific and engineering digital signal processing processes, such as digital communication systems, radar systems, antenna beamforming, coherent pulse measurement systems, etc., so it is very meaningful to study the chaos detection of complex signals in noise . ...

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Application Information

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IPC IPC(8): G01D1/00
Inventor 邓小英曾涛刘海波龙腾
Owner BEIJING INSTITUTE OF TECHNOLOGYGY
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