Hung Gia Hoang

Low-Dimensional SDP Formulation for Large Antenna Array Synthesis

Bounding the sidelobe and mainlobe levels of an array with complex weights is attractive in that it allows direct control of the radiation pattern. In this paper we propose an efficient beamforming technique for synthesizing the patterns of large arrays with bound constraints on the sidelobe and mainlobe levels. It is shown that the pattern synthesis problem can be posed as a convex semi-infinite program (SIP) which is then turned into a semi-definite program (SDP) via a novel linear matrix inequality (LMI) characterization of semi-infinite trigonometric polynomial constraints. In contrast to existing SDP formulations which require a large number of additional variables, our SDP representation only uses a minimal number of additional variables. This subsequently enables the design of patterns for arrays with several hundred elements to be efficiently achieved on a standard personal computer using existing SDP solvers.

Optimized Analog Filter Designs With Flat Responses by Semidefinite Programming

Analog filters constitute indispensable components of analog circuits. Inspired by recent advances in digital filter design, this paper provides a flexible design for analog filters. All-pole filters have maximally flat passband, so our design minimizes their passband distortion. Analogously, maximally flat filters have maximally flat passband, so our design maximizes their stopband attenuation. Its particular cases provide flexible alternatives to the classical counterparts. Semidefinite program (SDP) formulations for the posed filter design problems are presented, which are efficiently solved by existing optimization software. Several examples and comparisons are provided to validate the viability of our design.

Optimized Analog Flat Filter Design

This paper proposes a systematic approach for the optimized design of analog filters, which includes all well-known classical analog filters as a special case. All specifications including the conventional ones and also filter flatness degrees are explicitly incorporated into design process. Several numerical examples are presented to demonstrate the efficiency and flexibility of the proposed method.

Frequency-Selective KYP Lemma, IIR Filter, and Filter Bank Design

For a transfer function F(ejomega) of order n , Kalman-Yakubovich-Popov (KYP) lemma characterizes a general intractable semi-infinite programming (SIP) condition by a tractable semidefinite programming (SDP) for the entire frequency range. Some recent results generalize this lemma for a certain frequency interval. All these SDP characterizations are given at the expense of the introduced Lyapunov matrix variable of dimension ntimesn. Consequently, formulation and design of high dimensional problem is challenging. Moreover, existing SDP characterizations for frequency-selective SIP (FS-SIP) do not allow to formulate synthesis problems as SDPs. In this paper, we propose a completely new SDP characterization of general FS-SIP involving SDPs of moderate size and free from Lyapunov variables. Furthermore, a systematic IIR filter and filter bank design is developed in a similar vein, with several simulations provided to validate the effectiveness of our SDP formulation.

A Lyapunov Variable-Free KYP Lemma for SISO Continuous Systems

This technical note proposes a novel frequency-selective Kalman-Yakubovich-Popov (FS-KYP) lemma for analysis of single-input single-output (SISO) continuous systems. In contrast to existing approaches, the proposed method only uses a minimal number of variables due to the absence of Lyapunov variables in semidefinite programming (SDP) formulation. The SDP formulation is extended to polytopic uncertain systems also without any additional variable and yields an efficient method for computation of the H infin gain for polytopic systems. The viability of the proposed method are demonstrated through several numerical examples.

Frequency Selective KYP Lemma and its Applications to IIR Filter Bank Design

For a transfer function/filter F(e^jω) of order n, Kalman-Yakubovich-Popov (KYP) lemma characterizes the intractable semi-infinite programming (SIP) condition F(e^-jω)1 Θ [F(e^jω)1]^T ≥ 0 ∀ ω in frequency domain by a tractable semi-definite programming (SDP) in state-space domain. Some recent results generalize this lemma to SDP for SIP of frequency selectivity (FS-SIP). All these SDP characterizations are given at the expense of the introduced Lyapunov matrix variable of dimension n × n, making them impractical for high order problem. Moreover, the existing SDP characterizations for FS-SIP do not allow to formulate synthesis/design problems as SDPs. In this paper, we propose a completely new SDP characterization of general FS-SIP, which is of moderate size and is free from Lyapunov variables. Extensive examples are provided to validate the effectiveness of our result.

Analog flat filter design

This paper proposes a systematic approach for the design of a general class of analog infinite-impulse-response (IIR) filters, which includes all well-known classical analog filters as a special case. All specifications including the conventional ones and also filter flatness degrees are explicitly incorporated into design process. Several numerical examples are presented to demonstrate the efficiency and flexibility of the proposed method.

Mask constrained beam pattern synthesis for large arrays

Antenna array pattern synthesis with mask constraints can be formulated as a convex optimization problem with semiinfinite trigonometric polynomial constraints. The current approach uses a Linear Matrix Inequality (LMI) characterization of the semi-infinite constraints to convert the original problem into a semidefinite programming (SDP) problem. However, an important drawback of this approach is the large number of additional variables incurred in the equivalent SDP representation, which in turn prohibits its use in the design of large antenna arrays that arise in many modern applications. This paper presents an efficient method for the synthesis of large antenna arrays via a novel LMI characterization of semi-infinite constraints that only involves a minimal number of additional variables. Subsequently, the design of patterns for arrays with hundreds of elements can be easily achieved on a standard personal computer using existing SDP solvers.

Beam Pattern Synthesis for Large Symmetric Arrays with Bounds on Sidelobe and Mainlobe Levels

Bounding the sidelobe and mainlobe levels of a symmetric antenna array with complex weights can be posed as semi-infinite trigonometric constraints. Standard optimization techniques can be used to convert the semi-infinite trigonometric constraints into linear matrix inequality (LMI) constraints. However, the drawback of this standard technique is the large number of additional variables incurred in the LMI characterization, which in turn prohibits its use in the design of large antenna arrays that arise in many modern applications. Also, in many cases an additional structure like the symmetric one may destroy the convexity of the optimization reformulation and therefore put the applicability of LMI optimization in doubt. In this paper we propose a technique for synthesizing beam pattern of large symmetric arrays with bound constraints on sidelobe and mainlobe levels. The key lies in a novel LMI characterization of the semi-infinite trigonometric constraints that only involves additional variables of minimal dimensions. Subsequently, the design of patterns for arrays with hundreds of elements can be easily achieved on a standard personal computer using existing SDP solvers

Design of Two-Channel Filter Bank Composed of Linear Phase IIR Filters

This paper proposes a novel method to design two-channel filter banks composed of exactly linear phase IIR filters. Broadly speaking, the design problem is formulated as a semidefinite program (SDP) of minimal order such that the computational complexity is lower than that of existing optimization-based method. Furthermore, it is more flexible than the maximally flat approach as various filter specifications can be easily incorporated. The applicability and efficiency of the proposed method is demonstrated through several numerical examples.