2012 7th International ICST Conference on Communications and Networking in China (CHINACOM)

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1 22 7th International ICST Conference on Communications and Networking in China (CHINACOM) A High-resolution Weak Signal Detection Method Based on Stochastic Resonance and Superhet Technology 2 Shuo Shi, 2 Wanyi Yin, 2 Mingchuan Yang, 3 Mingjie He National Key Laboratory of Communication System and Information Control Technology 2 Harbin Institute of Technology 3 University of Science and Technology of China Abstract-A detection method based on the strong low-frequency weak-signal detection ability of stochastic resonance is proposed, aimed at the detection of the unknown weak signal. By mixing the unknown signal with a continuous linear changing local oscillator signal, a difference frequency signal will be generated, which will be sent to the stochastic resonance system. Thus, an obviously changed output can be obtained. Because the stochastic resonance system is extremely sensitive to low frequency, the system will have a maximum output when the local oscillator and frequency of the unknown signal are closest. The frequency of the unknown signal will be measured precisely from the local oscillator frequency and the difference frequency. It can be inferred from the theoretical analysis and numerical simulation that this method has a large detection range, high resolution, and good prospect. Key works: weak signals, stochastic resonance, superhet technology Ⅰ. INTRODUCTION Compared with noise, the amplitude of a signal is weak; the signal is completely submerged in the noise. On signal detection, the detection of the particular frequency is the most important. In the past, the weak signal detection in general focused on the methods of reducing noise to improve the signal to noise ratio (SNR), but often damaging the actual signal in the process of suppressing noise. Stochastic resonance (SR) in this bistable system can take advantage of the noise energy to improve the signal detection capability. But stochastic resonance can only be used for the low frequency signals, thus, its utility has limited application[-2]. In this paper, the frequency range of detection of stochastic resonance system is discussed and recommendations are made for a high-frequency weak signal detection method. Ⅱ. THE PRINCIPLE OF STOCHASTIC RESONANCE The concept of stochastic resonance was put forward by the Italian physicist Roberto Benzi, American physicist Alfonso Sutera and Italian physicist Angelo Vulpoiani in the study of ancient meteorological glaciers in 98 []. Stochastic resonance describes the phenomenon of back and forth transition between noise and the periodic signal, in non-linear bistable system under overdamped Brownian particle motion[4]. The potential curve of the non-linear bistable system and the transitions curve of particlse between the two potential wells is shown in Fig.. x(t) is the position of the output particles at any time, and this introduces the equation describing the particle motion-langevin equation[5-6]. dx = ax dt bx3 + Acos(ω t) + ε(t) () In equation (), a,b are a real numbers representing the shape parameters of the potential well (In figure, a =, b = ). s t = Acos 2πf t, ε(t) is the Gaussian white noise. Among them. A is amplitude of signals, ω is modulation frequency. The potential function of a bistable system is shown as follows. U x = 2 ax2 + 4 bx4 x(acos ωt + ε(t)) (2) /2/$3. 22 IEEE

2 U(x) Fig. The potential curve of non-linear bistable system and the transitions of particle between the two potential wells When there is no signal and noise input, the equation represents a system of two symmetric potential wells, the central barrier height U = a2, two stable statesx = ± a, and the output state of the system should b be determined by the initial state. The signal and noise that are gradually increased or adjusted; the shape parameters cause the potential well to form, and this makes the particles go back and forth between the two potential wells. Since the potential difference between the potential wells of the bistable systems is much larger than the amplitude of the signal input, it makes the amplitude of the output signal far larger than the input. So the input signal is amplified effectively. Meanwhile, effectively suppressing the noise in the system output, transferring less energy of noise into signal, and enhances the SNR[4]. U x = ax 2 /2 + bx 4 / x Ⅲ. LIMITATIONS OF STOCHASTIC RESONANCE FREQUENCY DETECTION U = a2 4b 4b the adiabatic approximation theory and linear response theory, the various effect of noise generated in the non-linear conditions are revealed[7-8]. The power spectrum of non-linear bistable system consists of two parts, one is caused by sinusoidal signal which has the same frequency of the input signal; the other one is caused by noise, and it has the form of Lorentz distribution. The power spectrum of Lorentz distribution present its noise characteristics of spectral energy concentrated to the low frequency region, therefore, the band of stochastic resonance spectrum peak will be limited in low frequency. When f >, it will deviate from the adiabatic approximation theory, and the increase of frequency leads to a lag in the system response. Because of this much larger range of signal-driven is needed to generate the stochastic resonance, therefore, stochastic resonance system is only suitable for low frequency (f ) signal detection[9]. Ⅳ. INTEGRAL COMPENSATION SLIGHTLY IMPROVE THE DETECTION RANGE A. Modeling of Detection The stochastic resonance system has very strict frequency requirements on the input signals. For the bistable nonlinear system represented by the Langevin equation, the condition of stochastic resonance isf. In order to make a signal whose characteristic are f > to produce stochastic resonance, an integral compensation can be added and the compensation coefficient must be no less than 2πf[]. When the input frequency f, it can be compensated by damping with an integral compensator. With this stochastic resonance can occur. But with the improvement of input signal frequency, it happens that Fig.2 The simulinjk model of stochastic resonance Fig.2 The simulink model of stochastic resonance In the weak signal(a )condition, according to the greater the frequency of input signal is, the more 33

3 Mag 2 /(rad/sec) Mag 2 /(rad/sec) obvious the hysteresis will be. So, this concludes that the frequency of detection is not infinite by using integral compensation. We need to discuss the maximum available frequency of the system which has added the integral compensation. The model of stochastic resonance with integral compensation is shown in Fig.2. dx = ax dt bx3 + Acos ω t + ε t G (3) B. For Each Magnitude Frequency Simulation a. Bandwidth: Hz-Hz, f=4hz, a=2 b=, G=8π SNR=-dB; history (secs) x -4 Power Spectral Density Frequency (rads/sec) Fig.3 a=2, b=, f=4hz, G=8π Stochastic Resonance output b. Bandwidth:.KHz-KH, f=.5khz, a=2 b=, G=π SNR=-dB; history (secs) Ⅴ. STOCHASTIC RESONANCE HETERODYNE DETECTION A. Principle of Mixing METHOD Mixing is a kind of frequency conversion process which changes the modulate signal whose central frequency is f (carrier frequency) to the frequency f i without distortion. In high-frequency signal detection, it can move the high frequency into the range of detection frequency of stochastic resonance system and then go through the stochastic resonance. We define input signal as s(t), noise as n(t), local oscillator signal v c t = cos(2πf c t) (4) the result of mixing is as follows, v m +n t = s t + n t v c t = Acos 2πf t + n t cos 2πf c t = Acos 2πf t cos 2πf c t + n(t) cos 2πf c t (5) n(t) is white Gaussian noise, then, v m t = Acos 2πf t cos 2πf c t = 2 Acos[2 π f f c t] + 2 Acos[2π f + f c t] (6) The input signal and the carrier signal produce two different frequency signals through the mixer, they are f f c and f + f c. With a proper frequencyf c, the difference frequency (f f c ) will meet the input frequency range of the stochastic resonance system. The sum frequency that does not meet the adiabatic approximation condition cannot produce stochastic resonance. B. Principle of Superhet The block diagram of the principle of superhet is shown in Fig.5. x Power Spectral Density Input signal Acos 2πf t Carrier signal generator Frequency (rads/sec) Mixer Fig.4 a=2, b=, f=.5 KHz, G=π Stochastic Resonance output Power Spectral Density(phase) Following the simulation, when input signal frequency f >.5KHz, we cannot see the obvious power spectrum peak in the output, continually increasing input signal frequency, stochastic resonance cannot occur. Noise n(t) Non-linear bistable system Output x(t) Fig.5 Block diagram of superhet Stochastic resonance frequency detection 33

4 Amp For an unknown input signal f, when continuously adjusted the carrier frequencyf c, the difference frequency f f c will also continuous change, so as the peak of stochastic resonance spectrum is []. Each f c has its C. Stochastic Resonance Superhet Detection Method Simulation Sample frequency f s = Hz; range of frequency-scan is KHz-5KHz; real signal frequency 2 Superhet Local oscillotar frequency (Hz) x 4 Fig.7 The result of stochastic resonance heterodyne detection method simulation maximum output amplitude and we use this maximum f=5 KHz; A=.5; Gaussian white noise D=.2; statistic to determine whether the signal ranges parameters of the potential wells a=, b=; in( f c + 5Hz, f c 5Hz). The output signal of Bistable system will change from small to large and suddenly disappear with the change off c. When resonance peak appears, frequency f can be captured by f c and the step size of f c. At that time, f has a high resolution about frequency-scan interval is 5Hz (resolution =Hz). The result of simulation is the statistics of stochastic resonance output strength after mixing with each local oscillator. Among them, the frequency of the highest point is close to the real signal frequency. The result of Hz ( f c + 5Hz, f c 5Hz). The principle of simulation is shown in Fig. 7. frequency-scan is shown in Fig.6. Ⅵ. CONCLUSION Frequency Frequency of input signal Mixer output frequency Output of stochastic resonance Local oscillator frequency A stochastic resonance detection method with large range of frequency-scan is presented. The theoretical analysis and numerical simulation indicate that this method has accurately achieved the detection of signal and improved the practicality of stochastic resonance. By mixing the input signal with a changing local oscillator frequency, the input frequency is shifted. This solves the problem of high-frequency detection and takes the advantage of the characteristic that the minimum difference frequency corresponds to the maximum output. Even though, there is no theoretical limit to the frequency range of the detection signal. However, due to the limitations of CPU, it takes long time searching for larger frequency range. This concludes that the searching speed is something that has to be further investigated. REFERENCE Fig.6 Frequency-scan principle [] Gang Hu. Stochastic Forces and Nonlinear Systems[M]. Shanghai 332

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