72 research outputs found
The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC
Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case
Non-uniform Array and Frequency Spacing for Regularization-free Gridless DOA
Gridless direction-of-arrival (DOA) estimation with multiple frequencies can
be applied in acoustics source localization problems. We formulate this as an
atomic norm minimization (ANM) problem and derive an equivalent
regularization-free semi-definite program (SDP) thereby avoiding regularization
bias. The DOA is retrieved using a Vandermonde decomposition on the Toeplitz
matrix obtained from the solution of the SDP.
We also propose a fast SDP program to deal with non-uniform array and
frequency spacing. For non-uniform spacings, the Toeplitz structure will not
exist, but the DOA is retrieved via irregular Vandermonde decomposition (IVD),
and we theoretically guarantee the existence of the IVD. We extend ANM to the
multiple measurement vector (MMV) cases and derive its equivalent
regularization-free SDP. Using multiple frequencies and the MMV model, we can
resolve more sources than the number of physical sensors for a uniform linear
array. Numerical results demonstrate that the regularization-free framework is
robust to noise and aliasing, and it overcomes the regularization bias
Wideband DOA Estimation with Frequency Decomposition via a Unified GS-WSpSF Framework
A unified group sparsity based framework for wideband sparse spectrum fitting (GS-WSpSF) is proposed for wideband direction-of-arrival (DOA) estimation, which is capable of handling both uncorrelated and correlated sources. Then, by making four different assumptions on a priori knowledge about the sources, four variants under the proposed framework are formulated as solutions to the underdetermined DOA estimation problem without the need of employing sparse arrays. As verified by simulations, improved estimation performance can be achieved by the wideband methods compared with narrowband ones, and adopting more a priori information leads to better performance in terms of resolution capacity and estimation accuracy
Scaling transform based information geometry method for DOA estimation
By exploiting the relationship between probability density and the differential geometry structure of received data and geodesic distance, the recently proposed information geometry (IG) method can provide higher accuracy and resolution ability for direction of arrival (DOA) estimation than many existing methods. However, its performance is not robust even for high signal to noise ratio (SNR). To have a deep understanding of its unstable performance, a theoretical analysis of the IG method is presented by deriving the relationship between the cost function and the number of array elements, powers and DOAs of source signals, and noise power. Then, to make better use of the nonlinear and super resolution property of the cost function, a Scaling TRansform based INformation Geometry (STRING) method is proposed, which simply scales the array received data or its covariance matrix by a real number. However, the expression for the optimum value of the scalar is complicated and related to the unknown signal DOAs and powers. Hence, a decision criterion and a simple search based procedure are developed, guaranteeing a robust performance. As demonstrated by computer simulations, the proposed STRING method has the best and robust angle resolution performance compared with many existing high resolution methods and even outperforms the classic Cramer-Rao bound (CRB), although at the cost of a bias in the estimation results
Unsupervised Massive MIMO Channel Estimation with Dual-Path Knowledge-Aware Auto-Encoders
In this paper, an unsupervised deep learning framework based on dual-path
model-driven variational auto-encoders (VAE) is proposed for angle-of-arrivals
(AoAs) and channel estimation in massive MIMO systems. Specifically designed
for channel estimation, the proposed VAE differs from the original VAE in two
aspects. First, the encoder is a dual-path neural network, where one path uses
the received signal to estimate the path gains and path angles, and another
uses the correlation matrix of the received signal to estimate AoAs. Second,
the decoder has fixed weights that implement the signal propagation model,
instead of learnable parameters. This knowledge-aware decoder forces the
encoder to output meaningful physical parameters of interests (i.e., path
gains, path angles, and AoAs), which cannot be achieved by original VAE.
Rigorous analysis is carried out to characterize the multiple global optima and
local optima of the estimation problem, which motivates the design of the
dual-path encoder. By alternating between the estimation of path gains, path
angles and the estimation of AoAs, the encoder is proved to converge. To
further improve the convergence performance, a low-complexity procedure is
proposed to find good initial points. Numerical results validate theoretical
analysis and demonstrate the performance improvements of our proposed
framework
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