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

FRIDA: FRI-Based DOA Estimation for Arbitrary Array Layouts

In this paper we present FRIDA---an algorithm for estimating directions of arrival of multiple wideband sound sources. FRIDA combines multi-band information coherently and achieves state-of-the-art resolution at extremely low signal-to-noise ratios. It works for arbitrary array layouts, but unlike the various steered response power and subspace methods, it does not require a grid search. FRIDA leverages recent advances in sampling signals with a finite rate of innovation. It is based on the insight that for any array layout, the entries of the spatial covariance matrix can be linearly transformed into a uniformly sampled sum of sinusoids.Comment: Submitted to ICASSP201

Error Bounds for Uplink and Downlink 3D Localization in 5G mmWave Systems

Location-aware communication systems are expected to play a pivotal part in the next generation of mobile communication networks. Therefore, there is a need to understand the localization limits in these networks, particularly, using millimeter-wave technology (mmWave). Towards that, we address the uplink and downlink localization limits in terms of 3D position and orientation error bounds for mmWave multipath channels. We also carry out a detailed analysis of the dependence of the bounds of different systems parameters. Our key findings indicate that the uplink and downlink behave differently in two distinct ways. First of all, the error bounds have different scaling factors with respect to the number of antennas in the uplink and downlink. Secondly, uplink localization is sensitive to the orientation angle of the user equipment (UE), whereas downlink is not. Moreover, in the considered outdoor scenarios, the non-line-of-sight paths generally improve localization when a line-of-sight path exists. Finally, our numerical results show that mmWave systems are capable of localizing a UE with sub-meter position error, and sub-degree orientation error.Comment: This manuscripts is updated following two rounds of reviews at IEEE Transactions on Wireless Communications. More discussion is included in different parts of the paper. Results are unchanged, and are still vali

Stable super-resolution limit and smallest singular value of restricted Fourier matrices

Super-resolution refers to the process of recovering the locations and amplitudes of a collection of point sources, represented as a discrete measure, given $M+1$ of its noisy low-frequency Fourier coefficients. The recovery process is highly sensitive to noise whenever the distance $\Delta$ between the two closest point sources is less than $1/M$. This paper studies the {\it fundamental difficulty of super-resolution} and the {\it performance guarantees of a subspace method called MUSIC} in the regime that $\Delta<1/M$. The most important quantity in our theory is the minimum singular value of the Vandermonde matrix whose nodes are specified by the source locations. Under the assumption that the nodes are closely spaced within several well-separated clumps, we derive a sharp and non-asymptotic lower bound for this quantity. Our estimate is given as a weighted $\ell^2$ sum, where each term only depends on the configuration of each individual clump. This implies that, as the noise increases, the super-resolution capability of MUSIC degrades according to a power law where the exponent depends on the cardinality of the largest clump. Numerical experiments validate our theoretical bounds for the minimum singular value and the resolution limit of MUSIC. When there are $S$ point sources located on a grid with spacing $1/N$, the fundamental difficulty of super-resolution can be quantitatively characterized by a min-max error, which is the reconstruction error incurred by the best possible algorithm in the worst-case scenario. We show that the min-max error is closely related to the minimum singular value of Vandermonde matrices, and we provide a non-asymptotic and sharp estimate for the min-max error, where the dominant term is $(N/M)^{2S-1}$.Comment: 47 pages, 8 figure