18 research outputs found
On the relaxed maximum-likelihood blind MIMO channel estimation for orthogonal space-time block codes
This paper concerns the maximum-likelihood channel estimation for MIMO
systems with orthogonal space-time block codes when the finite alphabet
constraint of the signal constellation is relaxed. We study the channel
coefficients estimation subspace generated by this method. We provide an
algebraic characterisation of this subspace which turns the optimization
problem into a purely algebraic one and more importantly, leads to several
interesting analytical proofs. We prove that with probability one, the
dimension of the estimation subspace for the channel coefficients is
deterministic and it decreases by increasing the number of receive antennas up
to a certain critical number of receive antennas, after which the dimension
remains constant. In fact, we show that beyond this critical number of receive
antennas, the estimation subspace for the channel coefficients is isometric to
a fixed deterministic invariant space which can be easily computed for every
specific OSTB code
When do Trajectories have Bounded Sensitivity to Cumulative Perturbations?
We investigate sensitivity to cumulative perturbations for a few dynamical
system classes of practical interest. A system is said to have bounded
sensitivity to cumulative perturbations (bounded sensitivity, for short) if an
additive disturbance leads to a change in the state trajectory that is bounded
by a constant multiple of the size of the cumulative disturbance. As our main
result, we show that there exist dynamical systems in the form of (negative)
gradient field of a convex function that have unbounded sensitivity. We show
that the result holds even when the convex potential function is piecewise
linear. This resolves a question raised in [1], wherein it was shown that the
(negative) (sub)gradient field of a piecewise linear and convex function has
bounded sensitivity if the number of linear pieces is finite. Our results
establish that the finiteness assumption is indeed necessary.
Among our other results, we provide a necessary and sufficient condition for
a linear dynamical system to have bounded sensitivity to cumulative
perturbations. We also establish that the bounded sensitivity property is
preserved, when a dynamical system with bounded sensitivity undergoes certain
transformations. These transformations include convolution, time
discretization, and spreading of a system (a transformation that captures
approximate solutions of a system)
Sensitivity to Cumulative Perturbations for a Class of Piecewise Constant Hybrid Systems
We consider a class of continuous-Time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which includes the fluid-level dynamics of the Max-Weight scheduling policy as a special case. We study the effect of an external disturbance/perturbation on the state trajectory, and establish that the magnitude of this effect can be bounded by a constant multiple of the integral of the perturbation