Stochastic-Resonance-Networks-Enhanced Wireless Channel Parameter Estimation Approach
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The estimation accuracy of conventional parameter estimation methods, including the maximum likelihood (ML) estimator and subspace-based estimation methods, diverges from the Cramer-Rao lower bound (CRLB) under low signal-to-noise (SNR) ratio conditions. Conventional stochastic resonance (SR) technique has shown appealing weak signal improvement advantages under low SNR, but it still needs a priori information such as the probability density functions (pdfs) of weak signal and channel noise. In this study, to address the channel parameter estimation for weak signal conditions, a novel channel parameter estimation algorithm based on dynamic stochastic resonance networks (SRN) is introduced. Since the signal statistical properties are altered by the SRN processing, the CRLB of the wireless channel parameter estimation employing the SRN-enhanced signal is derived, and then the corresponding ML estimator is presented. Theoretical analyses show that the CRLB is lower than those from the original signal and stochastic-resonance-enhanced signal. Computer simulations are performed to verify the effectiveness of the theoretical CRLB expressions. Both simulation and real experimental results indicate that the proposed SRN processing approach outperforms the conventional SR processing through achieving the CRLB improvement, the ML estimation performance enhancement under low SNR conditions, and the hardware complexity reduction.Keywords:
Cramér–Rao bound
Stochastic Resonance
On the basis of mixed‐signal simulations, we demonstrate that signal‐to‐noise ratio (SNR) gains much greater than unity can be obtained in the double‐well potential through stochastic resonance (SR) with a symmetric periodic pulse train as deterministic and Gaussian white noise as random excitation. We also show that significant SNR improvement is possible in this system even for a sub‐threshold sinusoid input if, instead of the commonly used narrow‐band SNR, we apply an equally simple but much more realistic wide‐band SNR definition. Using the latter result as an argument, we draw attention to the fact that the choice of the measure to reflect signal quality is critical with regard to the extent of signal improvement observed, and urge reconsideration of the practice prevalent in SR studies that most often the narrow‐band SNR is used to characterise SR. Finally, we pose some questions concerning the possibilities of applying SNR improvement in practical set‐ups.
Stochastic Resonance
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Stochastic Resonance (SR) is a nonlinear phenomenon that the input signal's signal-to-noise ratio (SNR) could be enhanced under special conditions. This paper proposes a novel parameter estimation algorithm for PSK signals based on SR. By introducing a nonlinear system into traditional estimation algorithms to enhance the signal's SNR, this proposed algorithm can achieve higher accuracy with respect to the traditional algorithm at the same SNR condition. Computer simulation shows the efficiency of this new algorithm.
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The Cramer-Rao lower bound (CRLB) provides a useful tool for evaluating the performance of parameter estimation techniques. Several techniques for the computation of the CRLB for ARMA and AR-plus-noise models are presented. It is shown that the CRLB can be expressed as an explicit function of the model parameters.
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Maximum-likelihood (ML), also given its connection to least squares (LS), is widely adopted in parameter estimation of physiological system models, i.e., assigning numerical values to the unknown model parameters from the experimental data. A more sophisticated but less used approach is maximum a posteriori (MAP) estimation. Conceptually, while ML adopts a Fisherian approach, i.e., only experimental measurements are supplied to the estimator, MAP estimation is a Bayesian approach, i.e., a priori available statistical information on the unknown parameters is also exploited for their estimation. Here, after a brief review of the theory behind ML and MAP estimators, the authors compare their performance in the solution of a case study concerning the determination of the parameters of a sum of exponential model which describes the impulse response of C-peptide (CP), a key substance for reconstructing insulin secretion. The results show that MAP estimation always leads to parameter estimates with a precision (sometimes significantly) higher than that obtained through ML, at the cost of only a slightly worse fit. Thus, a 3 exponential model can be adopted to describe the CP impulse response model in place of the two exponential model usually identified in the literature by the ML/LS approach. Simulated case studies are also reported to evidence the importance of taking into account a priori information in a data poor situation, e.g., when a few or too noisy measurements are available. In conclusion, the authors' results show that, when a priori information on the unknown model parameters is available, Bayes estimation can be of relevant interest, since it can significantly improve the precision of parameter estimates with respect to Fisher estimation. This may also allow the adoption of more complex models than those determinable by a Fisherian approach.
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An optimal stochastic resonance approach is proposed in this paper to overcome the defects of traditional stochastic resonance system in real applications. By introducing the stochastic resonance noise with optimal variance when the driving parameter is selected within the region which ensures the maximal output signal-to-noise ratio (SNR), the improvement of SNR gain can be guaranteed. Simulation results show that the SNR gain can reach 7~8.5dB even when the SNR of the original signal is lower than 0dB.
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The Cramer-Rao lower bound (CRLB) provides a useful tool for evaluating the performance of parameter estimation techniques. Several techniques for the computation of the asymptotic form of the CRLB for ARMA models are presented. It is shown that the asymptotic CRLB can be expressed as an explicit function of the model parameters.
Cramér–Rao bound
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The estimation accuracy of conventional parameter estimation methods, including the maximum likelihood (ML) estimator and subspace-based estimation methods, diverges from the Cramer-Rao lower bound (CRLB) under low signal-to-noise (SNR) ratio conditions. Conventional stochastic resonance (SR) technique has shown appealing weak signal improvement advantages under low SNR, but it still needs a priori information such as the probability density functions (pdfs) of weak signal and channel noise. In this study, to address the channel parameter estimation for weak signal conditions, a novel channel parameter estimation algorithm based on dynamic stochastic resonance networks (SRN) is introduced. Since the signal statistical properties are altered by the SRN processing, the CRLB of the wireless channel parameter estimation employing the SRN-enhanced signal is derived, and then the corresponding ML estimator is presented. Theoretical analyses show that the CRLB is lower than those from the original signal and stochastic-resonance-enhanced signal. Computer simulations are performed to verify the effectiveness of the theoretical CRLB expressions. Both simulation and real experimental results indicate that the proposed SRN processing approach outperforms the conventional SR processing through achieving the CRLB improvement, the ML estimation performance enhancement under low SNR conditions, and the hardware complexity reduction.
Cramér–Rao bound
Stochastic Resonance
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The problem of Cramer-Rao bound for parameter estimation in norrowband bistatic Multiple-Input Multiple-Output (MIMO) radar system is considered. In this paper, we propose a new narrowband signal model to accurately estimate parameter from a moving target. The Cramer-Rao bound for target parameter estimation is derived and computed in closed form which shows that the optimal performance is achieved. Target location and parameter estimation performances are evaluated and studied theoretically and via simulations.
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Abstract In this paper, the mean square error performance of the maximum a posteriori (MAP) probability direction finding by sensor array in terms of its Cramer‐Rao lower bound (CRLB) is analyzed. Based on the principle of Bayesian estimator, a log posteriori probability function is formed when the a priori knowledge of location is given. The Fisher information matrix (FIM) is found accordingly. It shows that the CRLB of the MAP estimator is much lower than that of maximum likelihood technique, especially when the element SNR is low and/or the number of snapshots is small. In addition, the CRLB remains at a relatively low level in terms of the variance of DOA of sources. It also shows that the location variance dominates the behavior of the MAP direction finder when locations of sources are Gaussian distributed.
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We report that the signal-to-noise ratio (SNR) can be improved by the stochastic resonance (SR) in an unconventional bistable system. The system is driven by Gaussian white noise and a sinusoidal signal, and studied by using the second-order Runge-Kutta method. We find that the SNR and the SNR gain exhibit the stochastic resonance behavior, and the SNR gain greatly exceeds unity on some occasions. This result is the latest development of the unconventional bistable stochastic resonance, and has potential applications in the signal detection, processing and communications.
Stochastic Resonance
Bistability
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Gaussian Noise
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