1,129 research outputs found
Maximum Entropy Vector Kernels for MIMO system identification
Recent contributions have framed linear system identification as a
nonparametric regularized inverse problem. Relying on -type
regularization which accounts for the stability and smoothness of the impulse
response to be estimated, these approaches have been shown to be competitive
w.r.t classical parametric methods. In this paper, adopting Maximum Entropy
arguments, we derive a new penalty deriving from a vector-valued
kernel; to do so we exploit the structure of the Hankel matrix, thus
controlling at the same time complexity, measured by the McMillan degree,
stability and smoothness of the identified models. As a special case we recover
the nuclear norm penalty on the squared block Hankel matrix. In contrast with
previous literature on reweighted nuclear norm penalties, our kernel is
described by a small number of hyper-parameters, which are iteratively updated
through marginal likelihood maximization; constraining the structure of the
kernel acts as a (hyper)regularizer which helps controlling the effective
degrees of freedom of our estimator. To optimize the marginal likelihood we
adapt a Scaled Gradient Projection (SGP) algorithm which is proved to be
significantly computationally cheaper than other first and second order
off-the-shelf optimization methods. The paper also contains an extensive
comparison with many state-of-the-art methods on several Monte-Carlo studies,
which confirms the effectiveness of our procedure
Subspace estimation and prediction methods for hidden Markov models
Hidden Markov models (HMMs) are probabilistic functions of finite Markov
chains, or, put in other words, state space models with finite state space. In
this paper, we examine subspace estimation methods for HMMs whose output lies a
finite set as well. In particular, we study the geometric structure arising
from the nonminimality of the linear state space representation of HMMs, and
consistency of a subspace algorithm arising from a certain factorization of the
singular value decomposition of the estimated linear prediction matrix. For
this algorithm, we show that the estimates of the transition and emission
probability matrices are consistent up to a similarity transformation, and that
the -step linear predictor computed from the estimated system matrices is
consistent, i.e., converges to the true optimal linear -step predictor.Comment: Published in at http://dx.doi.org/10.1214/09-AOS711 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Improving Macrocell - Small Cell Coexistence through Adaptive Interference Draining
The deployment of underlay small base stations (SBSs) is expected to
significantly boost the spectrum efficiency and the coverage of next-generation
cellular networks. However, the coexistence of SBSs underlaid to an existing
macro-cellular network faces important challenges, notably in terms of spectrum
sharing and interference management. In this paper, we propose a novel
game-theoretic model that enables the SBSs to optimize their transmission rates
by making decisions on the resource occupation jointly in the frequency and
spatial domains. This procedure, known as interference draining, is performed
among cooperative SBSs and allows to drastically reduce the interference
experienced by both macro- and small cell users. At the macrocell side, we
consider a modified water-filling policy for the power allocation that allows
each macrocell user (MUE) to focus the transmissions on the degrees of freedom
over which the MUE experiences the best channel and interference conditions.
This approach not only represents an effective way to decrease the received
interference at the MUEs but also grants the SBSs tier additional transmission
opportunities and allows for a more agile interference management. Simulation
results show that the proposed approach yields significant gains at both
macrocell and small cell tiers, in terms of average achievable rate per user,
reaching up to 37%, relative to the non-cooperative case, for a network with
150 MUEs and 200 SBSs
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