Direction of arrival estimation using sparse ruler array design

2013 Information Theory and Applications Workshop (ITA)

et al. 2013

307

304

Abstract-Next-generation cellular standards may leverage the large bandwidth available at millimeter wave (mmWave) frequencies to provide gigabit-per-second data rates in outdoor wireless systems. A main challenge in realizing mmWave cellular is achieving sufficient operating link margin, which is enabled via directional beamforming with large antenna arrays. Due to the high cost and power consumption of high-bandwidth mixed-signal devices, mmWave beamforming will likely include a combination of analog and digital processing. In this paper, we develop an iterative hybrid beamforming algorithm for the single user mmWave channel. The proposed algorithm accounts for the limitations of analog beamforming circuitry and assumes only partial channel knowledge at both the base and mobile stations. The precoding strategy exploits the sparse nature of the mmWave channel and uses a variant of matching pursuit to provide simple solutions to the hybrid beamforming problem. Simulation results show that the proposed algorithm can approach the rates achieved by unconstrained digital beamforming solutions.

Section: Introductionmentioning

confidence: 99%

Hybrid precoding for millimeter wave cellular systems with partial channel knowledge

Alkhateeb

Ayach

2013 Information Theory and Applications Workshop (ITA)

et al. 2013

307

304

“…No redundancy is required: we are only interested in part of the information, thus allowing a reduction in the number of samples. Designs of this kind include nested arrays [7], coprime sampling [8], minimum-redundancy linear arrays [9] and sparse ruler samplers [10], [11].…”

Section: A Relation To Compressive Samplingmentioning

confidence: 99%

“…On the contrary, the covariance sampling criterion leads to arrays that resolve the maximum number of sources for a given array length 3 . On the other hand, the scheme in [11] actually defines a universal covariance sampler.…”

Section: Relation To Previous Workmentioning

confidence: 99%

Compressive covariance sampling

Romero

2013 Information Theory and Applications Workshop (ITA)

2013

Abstract-Most research efforts in the field of compressed sensing have been pointed towards analyzing sampling and reconstruction techniques for sparse signals, where sampling rates below the Nyquist rate can be reached. When only second-order statistics or, equivalently, covariance information is of interest, perfect signal reconstruction is not required and rate reductions can be achieved even for non-sparse signals. This is what we will refer to as compressive covariance sampling. In this paper, we will study minimum-rate compressive covariance sampling designs within the class of non-uniform samplers. Necessary and sufficient conditions for perfect covariance reconstruction will be provided and connections to the well-known sparse ruler problem will be highlighted. I. PROBLEM STATEMENTConsider the problem of estimating the covariance matrix Σ of a random vector x with components x[n] when it is known that Σ is a linear combination of the matrices in the set S. This problem has a long history and a wide range of applications [1], [2]. Now consider a modification of the same problem where only a subset of the samples x[n] is available, i.e., when the observations are y[m] = x[n m ] for some I = {n 0 , n 1 , . . .} ⊂ Z. Intuitively, if the grid defined by I is dense enough, then this estimation problem, which we label as compressive covariance sampling, can still be solved.More specifically, the above sample selection produces a transformation of the problem: the vector y collecting the compressed observations y[m], has a covariance matrixΣ, which is a linear combination of the matrices inS. The coefficients in the linear combination are in both problems the same so that solving the latter amounts to solving the former. In this paper we address the optimal design of the index set I so that the coefficients can be estimated, i.e., we look for sets of indices with a minimum number of elements guaranteeing that these parameters remain statistically identifiable. A. Relation to Compressive SamplingRecent interest in sampling signals below their Nyquist rate owes to compressive sampling (or compressed sensing) [3], which has motivated a great deal of research efforts in the last few years. In compressive sampling we are interested in reducing the number of samples by focusing on a special family of signals referred to as sparse. These signals are intrinsically redundant, so that this reduction does not entail any information loss if properly done.Non-uniform sampling [4] is a particular case of compressive sampling. Mathematically, this process can be described as first acquiring a continuous-index signal x(t) at rate 1/T , resulting in the sequence x[n] = x(nT ), and then downsampling x[n] to obtain y[m] according to a set of indices I, in a periodic or non-periodic fashion (periodic non-uniform sampling is also known as multi-coset sampling).Either in the context of compressive sampling (the nonuniform sampling version) or in the context of what we call compressive covariance sampling, the design of the set I has ...

“…Most of the current methods are based on subspace techniques or exploit characteristics of the structure present in the covariance matrix [2], [3] [4]. However, none of those methods considers the geometry present in the space of probability distributions parametrized by their covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

Direction of arrival estimation based on information geometry

Coutiño

Pribic

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

2016

Self Cite

In this paper, a new direction of arrival (DOA) estimation approach is devised using concepts from information geometry (IG). The proposed method uses geodesic distances in the statistical manifold of probability distributions parametrized by their covariance matrix to estimate the direction of arrival of several sources. In order to obtain a practical method, the DOA estimation is treated as a single-variable optimization problem, for which the DOA solutions are found by means of a line search. The relation between the proposed method and MVDR beamformer is elucidated. An evaluation of its performance is carried out by means of Monte Carlo simulations and it is shown that the proposed method provides improved resolution capabilities at low SNR with respect to MUSIC and MVDR.