7,772 research outputs found
A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels
In this paper, we establish a general framework on the reduced dimensional
channel state information (CSI) estimation and pre-beamformer design for
frequency-selective massive multiple-input multiple-output MIMO systems
employing single-carrier (SC) modulation in time division duplex (TDD) mode by
exploiting the joint angle-delay domain channel sparsity in millimeter (mm)
wave frequencies. First, based on a generic subspace projection taking the
joint angle-delay power profile and user-grouping into account, the reduced
rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived
for spatially correlated wideband MIMO channels. Second, the statistical
pre-beamformer design is considered for frequency-selective SC massive MIMO
channels. We examine the dimension reduction problem and subspace (beamspace)
construction on which the RR-MMSE estimation can be realized as accurately as
possible. Finally, a spatio-temporal domain correlator type reduced rank
channel estimator, as an approximation of the RR-MMSE estimate, is obtained by
carrying out least square (LS) estimation in a proper reduced dimensional
beamspace. It is observed that the proposed techniques show remarkable
robustness to the pilot interference (or contamination) with a significant
reduction in pilot overhead
Exploring Algorithmic Limits of Matrix Rank Minimization under Affine Constraints
Many applications require recovering a matrix of minimal rank within an
affine constraint set, with matrix completion a notable special case. Because
the problem is NP-hard in general, it is common to replace the matrix rank with
the nuclear norm, which acts as a convenient convex surrogate. While elegant
theoretical conditions elucidate when this replacement is likely to be
successful, they are highly restrictive and convex algorithms fail when the
ambient rank is too high or when the constraint set is poorly structured.
Non-convex alternatives fare somewhat better when carefully tuned; however,
convergence to locally optimal solutions remains a continuing source of
failure. Against this backdrop we derive a deceptively simple and
parameter-free probabilistic PCA-like algorithm that is capable, over a wide
battery of empirical tests, of successful recovery even at the theoretical
limit where the number of measurements equal the degrees of freedom in the
unknown low-rank matrix. Somewhat surprisingly, this is possible even when the
affine constraint set is highly ill-conditioned. While proving general recovery
guarantees remains evasive for non-convex algorithms, Bayesian-inspired or
otherwise, we nonetheless show conditions whereby the underlying cost function
has a unique stationary point located at the global optimum; no existing cost
function we are aware of satisfies this same property. We conclude with a
simple computer vision application involving image rectification and a standard
collaborative filtering benchmark
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