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The existing Duffing oscillator weak signal detection method will lead to the degradation of detection performance when the noise is strong. In order to reduce detection signal-to-noise ratio and improve the detection performance, a weak signal detection method based on Duffing oscillator phase transition rate is proposed. This method uses the phase transition rate of Duffing oscillator to judge, which can effectively reduce the detection error caused by pure noise, and further improve the performance of weak signal detection. Compared with the existing methods, the lower limit of detection signal-to-noise ratio is reduced by 2dB.

In order to obtain the spatiotemporal situation of the evaporation duct accurately from a small amount of measurement data which is mixed into the noise during the transmission process affecting the high-precision reconstruction, this paper proposes an approximate message passing method (AMP) based on variable parameter threshold to realize the denoising reconstruction of noisy signals. By improving the threshold function in AMP, it is more suitable for the sparse characteristics of the evaporation duct parameters and converging more quickly. Theoretical analysis and experiments show that the overall performance of the denoising reconstruction method proposed in this paper is better than the control group.

A channel estimation method based on the spacetime tensor coding scheme is proposed for the one-way three-hop MIMO relay system. The method utilizes tensor coding at the source node and the two relay nodes, constructs the cascaded TUCKER model to reduce the dimension of the higher order received signal according to the cascade characteristic of signal transmission model, and derives the independent matrix decomposition form of unknown matrix. The semi-blind channel estimation is performed by using alternating least squares algorithms at the destination node, and the identifiability conditions and uniqueness of the algorithm are analyzed. Compared with traditional PARATUCK2 and Nested PARAFAC models, the cascaded TUCKER model makes full use of advantage of tensor coding which effectively improves the channel estimation accuracy. The simulation results show that the Normalized Mean Square Error can be decreased by one order of magnitude when $E_{b}/N_{0}$ is 10dB relative to the traditional semi-blind method.

At present, in the one-way two-hop multiple-input and multiple-output relay system, channel estimation algorithms based on tensor model were mainly used by alternating least squares (ALS) and khatri-rao Factorization (KRF) algorithm. ALS algorithm has high computational complexity and slow convergence. KRF algorithm is an algebraic solution based on no-iterative form and has low computational complexity, but its estimation performance is not optimal in the least squares sense. In this paper, a compromise channel iterative optimization algorithm (IOA) is proposed. In the algorithm, cost function is constructed and a regularization method is used to derive an update that minimizes the residual tensor. Initial value of the algorithm uses the estimation result of KRF algorithm, so only a small number of iterations is needed to be convergence. Therefore, compared with ALS algorithm, the proposed algorithm has lower complexity, and the simulation results show that the algorithm has almost the same performance as the ALS algorithm.

Generally, traditional identification algorithm of Duffing oscillator bases on the transitions of phase diagram, which often needs a large number of cumulative inputs to transform the system from chaos to the large-scale periodic state, which limits the applications of Duffing oscillator. A new algorithm based on Kalman gain is proposed in the paper to predict state transitions of the Duffing oscillator before the transitions in the phase diagram. By the establishment of Duffing state equations and setting the control condition of measurement equations, Kalman gain of Extend Kalman Filter (EKF) which are used to estimate the Duffing system can effectively predict the state changes of the Duffing oscillator, experiments of demodulations of communication signals show that the predictive algorithm can not only reduce at least 50% input points to identify the phase transitions of oscillator, but also the demodulation accuracy is obviously improved.

In areas of weak signal detection, considering the algorithm complexity and huge computation in phase transition identification of Duffing oscillator, a novel method based on energy distribution was proposed in this paper. Firstly, chaotic detection theory was analysised, then Teager Energ Operator was associated with nonlinear dynamic theory, which makes symbol identification achievable. Finally, the robustness and real-time property of the algorithm were analyzed. Simulation results show that, compared with the traditional methods, the computation and real-time property of this method has significantly improved to meet the needs of the weak signal detection under the strong noise background.

A new method to suppress speckle noise of SAR images is proposed. The main contributions of the method are to accurately model the autocorrelation function of wavelet coefficient of logarithmically transformed SAR images in steerable pyramid and incorporate the directionalities of subband coefficients into the model. Based on the correlation models of signal and noise, Wiener filter is applied to separate speckle noise from original SAR images. The simulation results on simulated images and real SAR images show that the proposed method has better performance than the previous methods.