Vandermonde Factorization of Toeplitz Matrices and Applications in Filtering and Warping

Bäckström, Tom

doi:10.1109/tsp.2013.2282271

Cited by 26 publications

(10 citation statements)

References 9 publications

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“…It should be noted that, for Constrained Tyler, the Algorithm 3 in [12] derived for real-valued PSD Toeplitz matrices can not be directly applied. However, the Vandermonde factorization of PSD Toeplitz matrices [44] allows us to use the Algorithm 2 of [12]. In this algorithm, the set of PSD Toeplitz Finally, we compare to the empirical estimate µ obtained by averaging the real and imaginary parts of diagonals of the unstructured ML estimator, which corresponds to the Euclidean projection onto the Toeplitz set.…”

Section: On Implementationsmentioning

confidence: 99%

Robust estimation of structured scatter matrices in (mis)matched models

et al. 2019

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Covariance matrix estimation is a ubiquitous problem in signal processing. In most modern signal processing applications, data are generally modeled by non-Gaussian distributions with covariance matrices exhibiting a particular structure. Taking into account this structure and the non-Gaussian behavior improve drastically the estimation accuracy. In this paper, we consider the estimation of structured scatter matrix for complex elliptically distributed observations, where the assumed model can differ from the actual distribution of the observations. Specifically, we tackle this problem, in a mismatched framework, by proposing a novel estimator, named StructurEd ScAtter Matrix Estimator (SESAME), which is based on a two-step estimation procedure. We conduct theoretical analysis on the unbiasedness and the asymptotic efficiency and Gaussianity of SESAME. In addition, we derive a recursive estimation procedure that iteratively applies the SESAME method, called Recursive-SESAME (R-SESAME), reaching with improved performance at lower sample support the (Mismatched) Cramér-Rao Bound. Furthermore, we show that some special cases of the proposed method allow to retrieve preexisting methods. Finally, numerical results corroborate the theoretical analysis and assess the usefulness of the proposed algorithms.

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Section: On Implementationsmentioning

confidence: 99%

Robust estimation of structured scatter matrices in (mis)matched models

et al. 2019

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“…Hence, the decomposition (36) is unique. This lemma shows that Theorem IV.1 holds if and only if we can construct a dual polynomial which satisfies (38) and (39). Next, our goal is to find one specific dual polynomial satisfying such conditions.…”

Section: A Dual Certificatementioning

confidence: 93%

“…For vectorized ANM, a 2-level Toeplitz decomposition [28] is required which has computational complexity O(P 2 L), where P is the size of 2-level Toeplitz matrix and L is its rank. For our proposed D-ANM method, only two separate 1-level Toeplitz matrix Vandermonde decompositions are required at complexity O(P 2 ) [38].…”

Section: Computational Complexitymentioning

confidence: 99%

Efficient two-dimensional line spectrum estimation based on decoupled atomic norm minimization

2019

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This paper presents an efficient optimization technique for gridless 2-D line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which has been successfully applied in 1-D problems to allow super-resolution frequency estimation for correlated sources even when the number of snapshots is highly limited. The state-of-the-art 2-D ANM approach vectorizes the 2-D measurements to their 1-D equivalence, which incurs huge computational cost and may become too costly for practical applications. We develop a novel decoupled approach of 2-D ANM via semi-definite programming (SDP), which introduces a new matrix-form atom set to naturally decouple the joint observations in both dimensions without loss of optimality. Accordingly, the original large-scale 2-D problem is equivalently reformulated via two decoupled one-level Toeplitz matrices, which can be solved by simple 1-D frequency estimation with pairing. Compared with the conventional vectorized approach, the proposed D-ANM technique reduces the computational complexity by several orders of magnitude with respect to the problem size. It also retains the benefits of ANM in terms of precise signal recovery, small number of required measurements, and robustness to source correlation. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO, radar signal processing and radio astronomy.

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“…and N sym is the size of an OFDM symbol. In (45), T l is a Hermitian Toeplitz matrix [57], and fast algorithms to solve (45) with O(M N tr N sym + M 2 ) multiplications and additions exist [58].…”

Section: Channel Estimationmentioning

confidence: 99%

Iterative Nonlinear Self-Interference Cancellation for In-Band Full-Duplex Wireless Communications Under Mixer Imbalance and Amplifier Nonlinearity

Komatsu

Miyaji

Uehara

2020

IEEE Trans. Wireless Commun.

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This paper presents an iterative estimation and cancellation technique for nonlinear in-band full-duplex transceivers with IQ imbalances and amplifier nonlinearities. The estimation process of the proposed scheme consists of three stages, namely, the channel response estimation, IQ imbalance estimation, and power amplifier and low-noise amplifier (LNA) nonlinearities estimation. For the estimation of the parameters and improvement of the accuracy, distortions are compensated by cancellation or inversion with the latest estimated parameters. On the one hand, the channel response is estimated on the time domain; on the other hand, the IQ imbalance and nonlinearities are estimated on the frequency domain for a more straightforward estimation and superior accuracy. In the cancellation process of the proposed scheme, the received signal is compensated with the estimated parameters of the LNA and receiver IQ imbalance before cancellation because the desired signal is received with a high-power self-interference and is distorted by the radiofrequency receiver impairments. Simulation results show that the proposed technique can achieve higher cancellation performance compared with the Hammerstein canceller when the LNA is saturated by the self-interference. Additionally, the performance of the proposed canceller converges much faster than that of the Hammerstein canceller.

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Vandermonde Factorization of Toeplitz Matrices and Applications in Filtering and Warping

Cited by 26 publications

References 9 publications

Robust estimation of structured scatter matrices in (mis)matched models

Robust estimation of structured scatter matrices in (mis)matched models

Efficient two-dimensional line spectrum estimation based on decoupled atomic norm minimization

Iterative Nonlinear Self-Interference Cancellation for In-Band Full-Duplex Wireless Communications Under Mixer Imbalance and Amplifier Nonlinearity

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