Nonparametric estimation for normalized coprime factors of a MIMO system

This paper extends to multi-input multi-output (MIMO) systems the results on frequency response estimation for normalized coprime factors (NCF) under a stochastic framework from closed-loop frequency domain experimental data. Under the condition that the covariance matrices are available for the external disturbances and measurement errors, an analytic solution has been obtained for the maximum likelihood estimate (MLE), on the basis of a linear fractional transformation (LFT) representation for all the plant possible normalized right coprime factors (NRCF). It is proved that the estimate can be expressed by a linear combination of a normalized random matrix with all its columns having independent complex normal distributions. Some methods are suggested to reduce the estimation bias when high-quality experimental data can be obtained. A numerical example is included that confirms the theoretical results.     

Identification of normalized coprime factors through constrained curve fitting

This paper deals with identifying finite dimensional normalized right coprime factors (NRCFs) under a stochastic framework from a sequence of their frequency response estimates. A two-step procedure is suggested for the estimation in which two cost functions are sequentially minimized. These cost functions are constructed on the basis of weighted curve fitting and the conditions on NRCFs. A numerical procedure is proposed for computing the estimate. Moreover, it is proved that under some conditions, the estimate converges with probability 1 (w.p.1) to its actual value with increasing the data length, and in general the optimal estimate is asymptotically approximately Gaussian. The efficiency of the proposed method in NRCF identification is illustrated by numerical simulations.     

Robust stabilizability of normalized coprime factors: the infinite-dimensional case

The problem of robustly stabilizing a linear system subject to H_∞-bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite-dimensional systems. This class has possible unbounded, finite-rank input and output operators, which include many delay and distributed systems. The optimal stability margin is expressed in terms of the solutions of the control and filter algebraic Riccati equations.     

Riccati equations and normalized coprime factorizations for strongly stabilizable infinite-dimensional systems

The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form Σ(A,B,S^−1/2B^*,D), where A is dissipative and all the other operators are bounded. These systems are not exponentially stabilizable and so the standard theory is not applicable. The second part uses the Riccati equation results to give formulas for normalized coprime factorizations over H_∞ for positive real transfer functions of the form D+S^−1/2B^*(author−A)⁻¹,B.     

An IDFT approach for coprime array direction-of-arrival estimation

In massive multiple-input multiple-output (MIMO) systems, efficiently estimating both the direction-of-arrival (DOA) and the source power with an increased number of degrees-of-freedoms (DOFs) is important but challenging. Aiming at this, we introduce the framework of coprime array signal processing into massive MIMO system and propose an efficient inverse discrete Fourier transform (IDFT)-based DOA estimation algorithm in this paper. By implementing IDFT on the second-order virtual array signals characterized by the equivalent spatial frequency, it is proved that the resulting spatial response enables to effectively estimate both DOA and source power with an increased number of DOFs. Meanwhile, the window method and the zero-padding technique are sequentially considered to alleviate the spectral leakage phenomenon and improve the DOA estimation accuracy. Compared with the existing coprime array DOA estimation algorithms, the implementation of IDFT indicates a remarkably reduced computational complexity as well as the hardware overhead. Simulation results show the effectiveness of the proposed algorithm.     

A connection between normalized coprime factorizations and linear quadratic regulator theory

Given a transfer matrix described by a minimal state-space triple, a method is given for computing state-space realizations for the numerator and denominator of a normalized, stable, right coprime factorization for the transfer matrix. The method involves the solution of an algebraic Riccati equation. It allows the use of existing computational state-space algorithms in finding normalized stable right coprime factorizations, and avoids explicit calculations of spectral factors.     

Guaranteed cost LQG control for uncertain systems with a normalized coprime factor uncertainty structure

The paper extends the robust minimax LQG control design methodology to stochastic uncertain systems with a general uncertainty structure, which includes normalized coprime factor uncertainty, passive uncertainty and sector norm-bounded uncertainty as special cases. The derivation of the result uses a special parameter-dependent Girsanov measure transformation. The efficacy of the proposed methodology is illustrated using the problem of frequency locking of an optical cavity which occurs in the area of experimental quantum optics.     

Remarks on computing coprime factors for distributed parametersystems

Presents an indirect method for computing coprime factors for a class of linear time-invariant distributed parameter systems. The method overcomes the numerical instability of an existing direct decomposition method. It is shown that coprime factorization can be reduced to constructing simultaneously stabilizing finite-dimensional controllers, for which an efficient iterative procedure is developed     

Explicit characterization of decentralized coprime factors

This paper is concerned with parametrization of all decentralized stabilizing controllers. The auxiliary diagonal system, which is defined by the diagonal elements of Bezout factors, plays an important role in the parametrization of decentralized controllers. This paper gives an explicit characterization of the auxiliary system.     

A counterexample on continuous coprime factors

In Georgiou and Smith (1992), the following question was raised: Consider a linear, shift-invariant system on L₂[0, ∞). Let the graph of the system have Fourier transform (MN)H² (i.e., the system has a transfer function P=N/M) where M, N are elements of C_A={f∈H^∞: f is continuous on the compactified right-half plane}. Is it possible to normalize M and N (i.e., to ensure |M|²+|N|²=1) in C_A? The author shows by example that this is not always possible     

Joint direction of arrival estimation and array calibration for coprime MIMO radar

Compared to large-scale MIMO radar, coprime MIMO radar can achieve approximate estimation performance with reduced antenna number. In this paper, joint direction of arrival (DOA) estimation and array calibration for coprime multiple-input multiple-output (MIMO) radar is considered, and an iterative method for the estimations of DOA and array gain-phase errors is proposed. Based on the received data structure of coprime MIMO radar, trilinear decomposition is firstly adopted to obtain the estimations of transmit and receive direction matrices, which are perturbated by the gain-phase errors. Through equation transformation, the un-perturbated direction matrices and gain-phase errors can be iteratively updated based on Least squares (LS). Finally, the unique DOA estimation is determined from the intersection of transmit and receive direction matrices. The proposed algorithm achieves better DOA estimation and array calibration performance than other methods including estimation of signal parameters via rotational invariance techniques (ESPRIT)-like algorithm, multiple signal classification (MUSIC)-like algorithm and joint angle and array gain-phase error estimation (JAAGE) method, and it performs close to the method with ideal arrays. Multiple simulation results verify the algorithmic effectiveness of the proposed method.     

基于互质阵的循环平稳信号低复杂度欠定DOA估计算法

针对现有大多数循环平稳信号DOA估计算法复杂度较高、估计精度低无法实现对有用信号的欠定估计问题,提出了一种基于互质阵的循环平稳信号低复杂度、欠定DOA估计算法.算法的主要思想是利用互质阵良好的稀疏特性,通过矢量化处理构造虚拟阵列模型,扩展阵列孔径,实现阵列自由度的提升.首先,算法构造了互质阵输出的循环自相关矩阵,然后进行矢量化处理得到最大连续虚拟阵元部分,给出其谱峰搜索的表达式.最后,为降低计算复杂度,对算法进行改进,应用多项式求根的方法直接求解DOA估计值.仿真结果表明,所提算法能实现对有用信号的欠定估计,计算复杂度较低,且相比于大多数的循环平稳信号DOA估计算法,所提算法估计自由度和估计精度有了进一步的提升.     

DOA estimation based on the difference and sum coarray for coprime arrays

In this paper, we construct a novel coarray named as the difference and sum (diff–sum) coarray by exploiting an improved Conjugate Augmented MUSIC (CAM) estimator, which utilizes both the temporal information and the spatial information. The diff–sum coarray is the union of the difference coarray and the sum coarray. When taking the coprime array as the array model, we find that the elements of the sum coarray can fill up all the holes in the difference coarray. Besides, the sum coarray contains bonus uniform linear array (ULA) segments which extend the consecutive range of the difference coarray. As a result, the consecutive lags of the diff–sum coarray are much more than those of the difference coarray. For analysis, we derive the hole locations and consecutive ranges of the difference set and the sum set, discuss the complementarity of the two sets, and provide the analytical expression of the diff–sum virtual aperture. Simulations verify the effectivity of the improved method and show the high DOF of the diff–sum coarray.     

Approximation of unstable infinite-dimensional systems using coprime factors

The effectiveness of comprime factor techniques in L₂ and L_∞ model reduction of unstable linear systems is analysed. Asymptotic estimates are given of the achievable error in the stable and unstable parts of the approximate system, measured in a number of different norms, some involving the associated Hankel operators. The chordal metric is introduced as a measure of approximation and is shown to yield the graph topology. Finally it is deduced that asymptotically optimal L₂ and L_∞ convergence rates can be obtained for a large class of unstable systems.     

Frequency response estimation for NCFs of an MIMO plant from closed-loop time-domain experimental data

Frequency response estimation from closed-loop time-domain experimental data is investigated in this paper for normalized coprime factors (NCF) of a multiple-input-multiple-output (MIMO) plant. Based on a linear fractional transformation (LFT) representation for all the NCFs of plants internally stabilizable by a known controller, this estimation problem is converted into the open-loop nonparametric estimation of an inner transfer function matrix (TFM). An estimate is derived through constrained data-matching. It is proved that when the probing signals are periodic and the NCFs of the auxiliary plant are appropriately selected, the estimate is asymptotically unbiased and with a normal/complex normal distribution. It has been made clear that the estimation bias and the estimation variance are always finite. Computationally tractable procedures are suggested for choosing the desirable auxiliary TFMs.     

MC-CDMA系统载波频偏估计

多载波码分多址（MC-CDMA）系统的微小载频偏移将破坏子载波之间的正交性,恶化系统性能,因此需要载频偏移估计和补偿;各个载频偏移的最大似然估计是个多维的全局搜索过程,计算复杂。提出一种MC-CDMA系统上行链路的基于粒子群算法的多用户频偏估计算法,降低了频偏估计方法的计算复杂度。仿真结果表明,基于粒子群算法的MC-CDMA系统多用户频偏估计方法的估计性能好,其均方误差小于基于虚拟子载波的多用户频偏估计的均方误差。     

DOA estimation of mixed coherent and uncorrelated targets exploiting coprime MIMO radar

We propose a new scheme to estimate the directions-of-arrival (DOAs) of mixed coherent and uncorrelated targets exploiting a collocated multiple-input multiple-output (MIMO) radar with transmit/receive coprime arrays. In the proposed scheme, the DOAs of the uncorrelated targets are first estimated using subspace-based methods, whereas those of the coherent targets are resolved using Bayesian compressive sensing. Compared with the previous works, the proposed approach achieves improved DOA estimation accuracy with a flexible coprime array configuration and may resolve more targets than the number of coarray elements. Theoretical analysis and simulation results validate the effectiveness of the proposed technique.