680 research outputs found
On Myopic Sensing for Multi-Channel Opportunistic Access: Structure, Optimality, and Performance
We consider a multi-channel opportunistic communication system where the
states of these channels evolve as independent and statistically identical
Markov chains (the Gilbert-Elliot channel model). A user chooses one channel to
sense and access in each slot and collects a reward determined by the state of
the chosen channel. The problem is to design a sensing policy for channel
selection to maximize the average reward, which can be formulated as a
multi-arm restless bandit process. In this paper, we study the structure,
optimality, and performance of the myopic sensing policy. We show that the
myopic sensing policy has a simple robust structure that reduces channel
selection to a round-robin procedure and obviates the need for knowing the
channel transition probabilities. The optimality of this simple policy is
established for the two-channel case and conjectured for the general case based
on numerical results. The performance of the myopic sensing policy is analyzed,
which, based on the optimality of myopic sensing, characterizes the maximum
throughput of a multi-channel opportunistic communication system and its
scaling behavior with respect to the number of channels. These results apply to
cognitive radio networks, opportunistic transmission in fading environments,
and resource-constrained jamming and anti-jamming.Comment: To appear in IEEE Transactions on Wireless Communications. This is a
revised versio
On Optimality of Myopic Sensing Policy with Imperfect Sensing in Multi-channel Opportunistic Access
We consider the channel access problem under imperfect sensing of channel
state in a multi-channel opportunistic communication system, where the state of
each channel evolves as an independent and identically distributed Markov
process. The considered problem can be cast into a restless multi-armed bandit
(RMAB) problem that is of fundamental importance in decision theory. It is
well-known that solving the RMAB problem is PSPACE-hard, with the optimal
policy usually intractable due to the exponential computation complexity. A
natural alternative is to consider the easily implementable myopic policy that
maximizes the immediate reward but ignores the impact of the current strategy
on the future reward. In this paper, we perform an analytical study on the
optimality of the myopic policy under imperfect sensing for the considered RMAB
problem. Specifically, for a family of generic and practically important
utility functions, we establish the closed-form conditions under which the
myopic policy is guaranteed to be optimal even under imperfect sensing. Despite
our focus on the opportunistic channel access, the obtained results are generic
in nature and are widely applicable in a wide range of engineering domains.Comment: 21 pages regular pape
On Optimality of Myopic Policy for Restless Multi-armed Bandit Problem with Non i.i.d. Arms and Imperfect Detection
We consider the channel access problem in a multi-channel opportunistic
communication system with imperfect channel sensing, where the state of each
channel evolves as a non independent and identically distributed Markov
process. This problem can be cast into a restless multi-armed bandit (RMAB)
problem that is intractable for its exponential computation complexity. A
natural alternative is to consider the easily implementable myopic policy that
maximizes the immediate reward but ignores the impact of the current strategy
on the future reward. In particular, we develop three axioms characterizing a
family of generic and practically important functions termed as -regular
functions which includes a wide spectrum of utility functions in engineering.
By pursuing a mathematical analysis based on the axioms, we establish a set of
closed-form structural conditions for the optimality of myopic policy.Comment: Second version, 16 page
The Cognitive Compressive Sensing Problem
In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR)
seeks to optimize the reward obtained by sensing an underlying dimensional
random vector, by collecting at most arbitrary projections of it. The
components of the latent vector represent sub-channels states, that change
dynamically from "busy" to "idle" and vice versa, as a Markov chain that is
biased towards producing sparse vectors. To identify the optimal strategy we
formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem,
generalizing the popular Cognitive Spectrum Sensing model, in which the CR can
sense out of the sub-channels, as well as the typical static setting of
Compressive Sensing, in which the CR observes linear combinations of the
dimensional sparse vector. The CR opportunistic choice of the sensing
matrix should balance the desire of revealing the state of as many dimensions
of the latent vector as possible, while not exceeding the limits beyond which
the vector support is no longer uniquely identifiable.Comment: 8 pages, 2 figure
Joint Design and Separation Principle for Opportunistic Spectrum Access in the Presence of Sensing Errors
We address the design of opportunistic spectrum access (OSA) strategies that
allow secondary users to independently search for and exploit instantaneous
spectrum availability. Integrated in the joint design are three basic
components: a spectrum sensor that identifies spectrum opportunities, a sensing
strategy that determines which channels in the spectrum to sense, and an access
strategy that decides whether to access based on imperfect sensing outcomes.
We formulate the joint PHY-MAC design of OSA as a constrained partially
observable Markov decision process (POMDP). Constrained POMDPs generally
require randomized policies to achieve optimality, which are often intractable.
By exploiting the rich structure of the underlying problem, we establish a
separation principle for the joint design of OSA. This separation principle
reveals the optimality of myopic policies for the design of the spectrum sensor
and the access strategy, leading to closed-form optimal solutions. Furthermore,
decoupling the design of the sensing strategy from that of the spectrum sensor
and the access strategy, the separation principle reduces the constrained POMDP
to an unconstrained one, which admits deterministic optimal policies. Numerical
examples are provided to study the design tradeoffs, the interaction between
the spectrum sensor and the sensing and access strategies, and the robustness
of the ensuing design to model mismatch.Comment: 43 pages, 10 figures, submitted to IEEE Transactions on Information
Theory in Feb. 200
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