2,435 research outputs found
On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization
The use of multichannel data in line spectral estimation (or frequency
estimation) is common for improving the estimation accuracy in array
processing, structural health monitoring, wireless communications, and more.
Recently proposed atomic norm methods have attracted considerable attention due
to their provable superiority in accuracy, flexibility and robustness compared
with conventional approaches. In this paper, we analyze atomic norm
minimization for multichannel frequency estimation from noiseless compressive
data, showing that the sample size per channel that ensures exact estimation
decreases with the increase of the number of channels under mild conditions. In
particular, given channels, order samples per channel, selected randomly from
equispaced samples, suffice to ensure with high probability exact
estimation of frequencies that are normalized and mutually separated by at
least . Numerical results are provided corroborating our analysis.Comment: 14 pages, double column, to appear in IEEE Trans. Information Theor
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
Multivariate Spectral Estimation based on the concept of Optimal Prediction
In this technical note, we deal with a spectrum approximation problem arising
in THREE-like multivariate spectral estimation approaches. The solution to the
problem minimizes a suitable divergence index with respect to an a priori
spectral density. We derive a new divergence family between multivariate
spectral densities which takes root in the prediction theory. Under mild
assumptions on the a priori spectral density, the approximation problem, based
on this new divergence family, admits a family of solutions. Moreover, an upper
bound on the complexity degree of these solutions is provided
FDD massive MIMO channel spatial covariance conversion using projection methods
Knowledge of second-order statistics of channels (e.g. in the form of
covariance matrices) is crucial for the acquisition of downlink channel state
information (CSI) in massive MIMO systems operating in the frequency division
duplexing (FDD) mode. Current MIMO systems usually obtain downlink covariance
information via feedback of the estimated covariance matrix from the user
equipment (UE), but in the massive MIMO regime this approach is infeasible
because of the unacceptably high training overhead. This paper considers
instead the problem of estimating the downlink channel covariance from uplink
measurements. We propose two variants of an algorithm based on projection
methods in an infinite-dimensional Hilbert space that exploit channel
reciprocity properties in the angular domain. The proposed schemes are
evaluated via Monte Carlo simulations, and they are shown to outperform current
state-of-the art solutions in terms of accuracy and complexity, for typical
array geometries and duplex gaps.Comment: Paper accepted on 29/01/2018 for presentation at ICASSP 201
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