Kai Man Tsui

Pattern Synthesis of Narrowband Conformal Arrays Using Iterative Second-Order Cone Programming

A new design method is proposed for the power or shaped beam pattern synthesis problem of narrowband conformal arrays, where only the magnitude response is specified. The proposed method iteratively linearizes the non-convex power pattern function to obtain a convex subproblem in the design variables, which can be solved optimally using second-order cone programming (SOCP). In addition, a wide variety of magnitude constraints such as non-convex lower bound magnitude constraints can be incorporated. An efficient technique for determining a reasonably good initial guess to the problem is also proposed to further improve the reliability of the method. Computer simulations show that the initial guesses so obtained converge to satisfactory solutions while satisfying various prescribed magnitude constraints. Design results show that the performance of the proposed method is comparable to the optimal solution previously obtained for uniform linear arrays with isotropic elements. Moreover, we show by means of examples that the proposed method is also applicable to general non-convex power pattern synthesis problems involving arbitrary array geometries, arbitrary polarization characteristics and mutual coupling effect.

Recursive Steering Vector Estimation and Adaptive Beamforming under Uncertainties

The accurate determination of the steering vector of a sensor array that corresponds to a desired signal is often hindered by uncertainties due to array imperfections, such as the presence of a direction-of-arrival (DOA) estimation error, mutual coupling, array sensor gain/phase uncertainties, and sensor position perturbations. Consequently, the performance of conventional beamforming algorithms that use the nominal steering vector may be significantly degraded. A new method for recursively correcting possible deterministic errors in the estimated steering vector is proposed here. It employs the subspace principle and estimates the desired steering vector by using a convex optimization approach. We show that the solution can be obtained in closed form by using the Lagrange multiplier method. As the proposed method is based on an extended version of the conventional orthonormal PAST (OPAST) algorithm, it has low implementation complexity, and moving sources can be handled. In addition, a robust beamformer with a new error bound that uses the proposed steering vector estimate is derived by optimizing the worst case performance of the array after taking the uncertainties of the array covariance matrix into account. This gives a diagonally loaded Capon beamformer, where the loading level is related to the bound of the uncertainty in the array covariance matrix. Numerical results show that the proposed algorithm performs well, especially at high signal-to-noise ratio (SNR) and in the presence of deterministic sensor uncertainties.

On the design of real and complex FIR filters with flatness and peak error constraints using semidefinite programming

This paper studies the problem of designing digital finite duration impulse response (FIR) filters with prescribed flatness and peak error constraints using semidefinite programming (SDP). SDP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. This property is utilized for the optimal minimax and least squares (LS) design of linear-phase and low-delay FIR filters with prescribed magnitude flatness and peak design error, which are formulated as a set of linear equality and convex quadratic inequality constraints, respectively. A method for structurally imposing these equality constraints in the SDP formulation is also proposed. Using these results, the design approach is further extended to the design of constrained complex coefficient FIR filters and variable digital filters (VDFs). Design examples are given to demonstrate the effectiveness of the approach.

Robust Beamforming With Magnitude Response Constraints Using Iterative Second-Order Cone Programming

The problem of robust beamforming for antenna arrays with arbitrary geometry and magnitude response constraints is one of considerable importance. Due to the presence of the non-convex magnitude response constraints, conventional convex optimization techniques cannot be applied directly. A new approach based on iteratively linearizing the non-convex constraints is then proposed to reformulate the non-convex problem to a series of convex subproblems, each of which can be optimally solved using second-order cone programming (SOCP). Moreover, in order to obtain a more robust beamformer against array imperfections, the proposed method is further extended by optimizing its worst-case performance using again SOCP. Different from some conventional methods which are restricted to linear arrays, the proposed method is applicable to arbitrary array geometries since the weight vector, rather than its autocorrelation sequence, is used as the variable. Simulation results show that the performance of the proposed method is comparable to the optimal solution previously proposed for uniform linear arrays, and it also gives satisfactory results under different array specifications and geometries tested.

Wordlength determination algorithms for hardware implementation of linear time invariant systems with prescribed output accuracy

This paper proposes two novel algorithms for optimizing the hardware resources in finite wordlength implementation of linear time invariant systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first algorithm formulates the design problem as a constrained optimization, from which an analytic closed-form solution of the internal wordlengths subject to a prescribed output accuracy can be determined by the Lagrange multiplier method. The second algorithm is based on a discrete optimization method called the marginal analysis method, and it yields the desired wordlengths in integer values. Both approaches are found to be very effective and they are well-suited to large scale systems such as software radio receivers. Design examples show that the proposed algorithms offer better results and a lower design complexity than conventional methods.

Frequency Invariant Uniform Concentric Circular Arrays with Directional Elements

A new approach for designing frequency invariant (FI) uniform concentric circular arrays (UCCAs) with directional elements is proposed, and their applications to direction-of-arrival (DOA) estimation and adaptive beamforming are studied. By treating the sensors along the radial direction of the UCCA as linear subarrays and using appropriately designed beamformers, each subarray is transformed to a virtual element with appropriate directivity. Consequently, the whole UCCA can be viewed as a virtual uniform circular array (UCA) with desired element directivity for broadband processing. By extending the approach for designing FI-UCAs, the frequency dependency of the phase modes of the virtual UCA is compensated to facilitate broadband DOA and adaptive beamforming. Both the linear array beamformers (LABFs) and compensation filters can be designed separately using second- order cone programming (SOCP). Moreover, a new method to tackle the possible noise amplification problem in such large arrays by imposing additional norm constraints on the design of the compensation filters is proposed. The advantages of this decoupled approach are 1) the complicated design problem of large UCCAs can be decoupled into simpler problems of designing the LABFs and compensation filters, and 2) directional elements, which are frequently encountered, can be treated readily under the proposed framework. Numerical examples are provided to demonstrate the effectiveness and improvement of the proposed methods in DOA estimation, adaptive beamforming, and elevation control over the conventional FI-UCCA design method.

Bayesian Kalman filtering, regularization and compressed sampling

Bayesian Kalman filter (BKF) is an important tool in signal processing, communications, control and statistics. This paper briefly reviews the principle of BKF for Gaussian mixture and proposes a new and efficient method for real-time implementation. Moreover, the close relationship between conventional KF and regularization theory in estimation is reviewed. Using this framework, the problem of sampling, smoothing and interpolation can be treated in a unified framework. New results on under-sampling using non-uniform samples will be presented.

Multiplier-less real-valued FFT-like transformation (ML-RFFT) and related real-valued transformations

This paper proposes a new multiplier-less fast Fourier transform-like (ML-RFFT) transformation for real-valued sequences. Like the ML-FFT, it parameterizes the twiddle factors in the conventional radix-2/sup n/ or split-radix real-valued FFT algorithm as certain rotation-like matrices and approximates the associated parameters inside these matrices by the sum-of-power-of-two (SOPOT) or canonical signed digits (CSD) representations. Because of the symmetry in the algorithm, it only requires about half the number of additions as required by the ML-FFT. Moreover, using the mappings between the DFT and the DCTs and DWTs, new ML-FFT-based transformation called ML-DCTs and ML-DWTs are derived. Design examples of the new transformations are given to demonstrate the proposed approach.

A new visual object tracking algorithm using Bayesian Kalman filter

This paper proposes a new visual object tracking algorithm using a novel Bayesian Kalman filter (BKF) with simplified Gaussian mixture (BKF-SGM). The new BKF-SGM employs a GM representation of the state and noise densities and a novel direct density simplifying algorithm for avoiding the exponential complexity growth of conventional KFs using GM. Together with an improved mean shift (MS) algorithm, a new BKF-SGM with improved MS (BKF-SGM-IMS) algorithm with more robust tracking performance is also proposed. Experimental results show that our method can successfully handle complex scenarios with good performance and low arithmetic complexity.

Minimum Variance Spectral Estimation-Based Time Frequency Analysis for Nonstationary Time-Series

This paper introduces two new time-frequency analysis methods originated from the minimum variance spectral estimation (MVSE) for nonstationary time-series. First, a windowed MVSE (WMVSE) extends the conventional MVSE by windowing the observation data to obtain a time-frequency distribution for the time-series. Moreover, the window lengths are selected adaptively by the intersection of confidence intervals (ICI) rule to improve the time-frequency resolution. Secondly, a new recursive MVSE (RMVSE) is developed to process the input samples recursively at a lower arithmetic complexity for online time-frequency analysis. Simulation results show that the proposed WMVSE with adaptive windows offers better frequency resolutions than the Fourier-transformed-based time-frequency distributions, and the RMVSE has a good performance when tracking sinusoidal signals