22 research outputs found
On the Coherence Properties of Random Euclidean Distance Matrices
In the present paper we focus on the coherence properties of general random
Euclidean distance matrices, which are very closely related to the respective
matrix completion problem. This problem is of great interest in several
applications such as node localization in sensor networks with limited
connectivity. Our results can directly provide the sufficient conditions under
which an EDM can be successfully recovered with high probability from a limited
number of measurements.Comment: 5 pages, SPAWC 201
Matrix Completion in Colocated MIMO Radar: Recoverability, Bounds & Theoretical Guarantees
It was recently shown that low rank matrix completion theory can be employed
for designing new sampling schemes in the context of MIMO radars, which can
lead to the reduction of the high volume of data typically required for
accurate target detection and estimation. Employing random samplers at each
reception antenna, a partially observed version of the received data matrix is
formulated at the fusion center, which, under certain conditions, can be
recovered using convex optimization. This paper presents the theoretical
analysis regarding the performance of matrix completion in colocated MIMO radar
systems, exploiting the particular structure of the data matrix. Both Uniform
Linear Arrays (ULAs) and arbitrary 2-dimensional arrays are considered for
transmission and reception. Especially for the ULA case, under some mild
assumptions on the directions of arrival of the targets, it is explicitly shown
that the coherence of the data matrix is both asymptotically and approximately
optimal with respect to the number of antennas of the arrays involved and
further, the data matrix is recoverable using a subset of its entries with
minimal cardinality. Sufficient conditions guaranteeing low matrix coherence
and consequently satisfactory matrix completion performance are also presented,
including the arbitrary 2-dimensional array case.Comment: 19 pages, 7 figures, under review in Transactions on Signal
Processing (2013
Robust and Reliable Stochastic Resource Allocation via Tail Waterfilling
Stochastic allocation of resources in the context of wireless systems
ultimately demands reactive decision making for meaningfully optimizing
network-wide random utilities, while respecting certain resource constraints.
Standard ergodic-optimal policies are however susceptible to the statistical
variability of fading, often leading to systems which are severely unreliable
and spectrally wasteful. On the flip side, minimax/outage-optimal policies are
too pessimistic and often hard to determine. We propose a new risk-aware
formulation of the resource allocation problem for standard multi-user
point-to-point power-constrained communication with no cross-interference, by
employing the Conditional Value-at-Risk (CV@R) as a measure of fading risk. A
remarkable feature of this approach is that it is a convex generalization of
the ergodic setting while inducing robustness and reliability in a fully
tunable way, thus bridging the gap between the (naive) ergodic and
(conservative) minimax approaches. We provide a closed-form expression for the
CV@R-optimal policy given primal/dual variables, extending the classical
stochastic waterfilling policy. We then develop a primal-dual tail-waterfilling
scheme to recursively learn a globally optimal risk-aware policy. The
effectiveness of the approach is verified via detailed simulations.Comment: 5 pages, 7 figure
Risk-Aware Stability of Discrete-Time Systems
We develop a generalized stability framework for stochastic discrete-time
systems, where the generality pertains to the ways in which the distribution of
the state energy can be characterized. We use tools from finance and operations
research called risk functionals (i.e., risk measures) to facilitate diverse
distributional characterizations. In contrast, classical stochastic stability
notions characterize the state energy on average or in probability, which can
obscure the variability of stochastic system behavior. After drawing
connections between various risk-aware stability concepts for nonlinear
systems, we specialize to linear systems and derive sufficient conditions for
the satisfaction of some risk-aware stability properties. These results pertain
to real-valued coherent risk functionals and a mean-conditional-variance
functional. The results reveal novel noise-to-state stability properties, which
assess disturbances in ways that reflect the chosen measure of risk. We
illustrate the theory through examples about robustness, parameter choices, and
state-feedback controllers