Junli Liang

Steady-State Mean-Square Error Analysis for Adaptive Filtering under the Maximum Correntropy Criterion

The steady-state excess mean square error (EMSE) of the adaptive filtering under the maximum correntropy criterion (MCC) has been studied. For Gaussian noise case, we establish a fixed-point equation to solve the exact value of the steady-state EMSE, while for non-Gaussian noise case, we derive an approximate analytical expression for the steady-state EMSE, based on a Taylor expansion approach. Simulation results agree with the theoretical calculations quite well.

Waveform Design With Unit Modulus and Spectral Shape Constraints via Lagrange Programming Neural Network

To maximize the transmitted power available in active sensing, the probing waveform should be of constant modulus. On the other hand, in order to adapt to the increasingly crowed radio frequency spectrum and prevent mutual interferences, there are also requirements in the waveform spectral shape. That is to say, the waveform must fulfill constraints in both time and frequency domains. In this work, designing these waveforms is formulated as a nonlinear constrained optimization problem. By introducing auxiliary variable neurons and Lagrange neurons, we solve it using the Lagrange programming neural network. We also analyze the local stability conditions of the dynamic neuron model. Simulation results show that our proposed algorithm is a competitive alternative for waveform design with unit modulus and arbitrary spectral shapes.

Lagrange Programming Neural Network Approach for Target Localization in Distributed MIMO Radar

In this paper, the problem of source localization in distributed multiple-input multiple-output (MIMO) radar using bistatic range measurements, which correspond to the sum of transmitter-to-target and target-to-receiver distances, is addressed. Our solution is based on the Lagrange programming neural network (LPNN), which is an analog neural computational technique for solving nonlinear constrained optimization problems according to the Lagrange multiplier theory. The local stability of the proposed positioning algorithm is also investigated. Furthermore, we have extended the LPNN based approach to more challenging scenarios, namely, when time synchronization among all antennas cannot be fulfilled, and there are position uncertainties in the MIMO radar transmit and receive elements. The optimality of the developed algorithms is demonstrated by comparing with the Cramér-Rao lower bound via computer simulations.

A Novel Diagonal Loading Method for Robust Adaptive Beamforming

The diagonal loading method is a simple and e-cient method to improve the robustness of beamformers. However, how to determine the ideal diagonal loading level has not been adequately addressed. In this paper, it is observed in the simulation that the peak of the main beam is moved with the diagonal loading level when there exists a Direction of Arrival (DOA) estimation error. Based on the observation, a novel diagonal loading method is proposed, and a tradeofi exists between the robustness and the interference suppression capability by controlling the peak location of the main beam. As long as the DOA estimation error is less than the half of the width of main beam, the proposed beamformer will not suppress the Signal of Interest (SOI) as interference. Numerical experiments prove the efiectiveness of the proposed method.

Robust MIMO radar target localization via nonconvex optimization

This paper addresses the problem of robust target localization in distributed multiple-input multiple-output (MIMO) radar using possibly outlier range measurements. To achieve robustness against outliers, we construct an objective function for MIMO target localization via the maximum correntropy criterion. To deal with such a nonconvex and nonlinear function, we apply a half-quadratic optimization technique to determine the target position and auxiliary variables alternately. Especially, we derive a semidefinite relaxation formulation for the aforementioned position determination step. The robust performance of the developed approach is demonstrated by comparing with several conventional localization methods via computer simulation.

Kernel Least Mean Square with Adaptive Kernel Size

Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample sizes. In previous research, the kernel size was set manually or estimated in advance by Silvermans rule based on the sample distribution. This study aims to develop an online technique for optimizing the kernel size of the kernel least mean square (KLMS) algorithm. A sequential optimization strategy is proposed, and a new algorithm is developed, in which the filter weights and the kernel size are both sequentially updated by stochastic gradient algorithms that minimize the mean square error (MSE). Theoretical results on convergence are also presented. The excellent performance of the new algorithm is confirmed by simulations on static function estimation, short term chaotic time series prediction and real world Internet traffic prediction.

Unimodular Sequence Design Based on Alternating Direction Method of Multipliers

The topic of probing waveform design has received considerable attention due to its numerous applications in active sensing. Apart from having the desirable property of constant magnitude, it is also anticipated that the designed sequence possesses low sidelobe autocorrelation and/or specified spectral shape. In this paper, the alternating direction method of multipliers (ADMM), which is a powerful variant of the augmented Lagrangian scheme for dealing with separable objective functions, is applied for synthesizing the probing sequences. To achieve impulse-like autocorrelation, we formulate the design problem as minimizing a nonlinear least-squares cost function in the frequency domain subject to the constraint that all sequence elements are of unit modulus. Via introducing auxiliary variables, we are able to separate the objective into linear and quadratic functions where the unimodular constraint is only imposed on the former, which results in an ADMM-style iterative procedure. In particular, fast implementation for the most computationally demanding step is investigated and local convergence of the ADMM method is proved. To deal with the spectral shape requirement, we borrow the concept in frequency-selective filter design where passband and stopband magnitudes are bounded to formulate the corresponding optimization problem. In this ADMM algorithm development, unit-step functions are utilized to transform the multivariable optimization into a quadratic polynomial problem with a single variable. The effectiveness of the proposed approach is demonstrated via computer simulations.

On Designing the Transmission and Reception of Multistatic Continuous Active Sonar Systems

Multistatic continuous active sonar (MCAS) systems involve the transmission and reception of multiple continuous probing sequences and can achieve significantly enhanced target detection and parameter estimation performance through exploiting the advantages of continuous illumination and spatial diversity. The main focuses and contributions of this paper are: 1) spectrally-contained continuous sequence sets with low correlation sidelobe levels are designed for the MCAS transmission so that the so-generated sequences meet the spectral containment restrictions and the weak correlations among the received echoes can be exploited to improve the target detection performance; and 2) a decentralized target parameter (position and velocity) determination method is investigated since its conventional centralized counterpart lacks robustness if there is no fusion center (FC) or the FC fails. This paper casts the target position determination problem based on the range measurements and the directions-of-arrival information (RMDI) as a set of decentralized optimization subproblems with consensus constraints imposed on the target position estimates of the receivers. Based on the alternating-direction method of multipliers (ADMM), we introduce the distributed position estimation algorithm to improve the local estimates of each receiver via local computation and information exchange with its neighbors. A similar method is also applied to obtain enhanced target velocity estimation. The effectiveness of the proposed MCAS signal processing techniques is verified using numerical examples.

Smoothed least mean p-power error criterion for adaptive filtering

In this paper, we propose a novel error criterion for adaptive filtering, namely the smoothed least mean p-power (SLMP) error criterion, which aims to minimize the mean p-power of the error plus an independent and scaled smoothing variable. Some important properties of the SLMP criterion are presented. In particular, we show that if the smoothing variable is symmetric and zero-mean, and p is an even number, then the SLMP error criterion will become a weighted sum of the even-order moments of the error, and as the smoothing factor (i.e. the scale factor) is large enough, this new criterion will be approximately equivalent to the well-known mean square error (MSE) criterion. Based on the proposed error criterion, we develop a new adaptive filtering algorithm and its kernelized version, and derive a theoretical value of the steady-state excess mean square error (EMSE). Simulation results suggest that the new algorithms with proper choice of the smoothing factor may perform quite well.

Enhanced multistatic active sonar signal processing

This paper focuses on two signal processing aspects of multistatic active sonar systems, namely enhanced range-Doppler imaging and improved target parameter estimation. The main contributions of this paper are: i) a hybrid dense-sparse method is proposed to generate range-Doppler images with both low sidelobe levels and high accuracy; ii) a generalized K-Means clustering (GKC) method for target association is developed to associate the range measurements from different transmitter-receiver pairs; iii) the extended invariance principle-based weighted least-squares (EXIP-WLS) method is developed for accurate target position and velocity estimation. The effectiveness of the proposed multistatic active sonar system is verified using numerical examples.