Efficient Algorithm Design of Dynamic Spectrum Access by Whittle Index

Abstract

Dynamic spectrum access problem is an important problem that allows a wireless sub-network to use channels temporarily unoccupied by the parent network for minimizing the spectrum waste. Previous work has shown that the sequential channel allocation problem for the sub-network can be formulated within the restless multi-armed bandits (RMAB) framework. The objective is to maximize the expected long-term return over an infinite horizon while minimizing interference to the parent network. Different from the previous work that exploits a binary feedback (e.g., ACK/NAK) to compensate for sensing errors, we leverage the finer and more robust channel quality indicator (CQI) feedback to update the information state (belief vector) of the sub-network. However, the implementation of CQI-based observation model yields significantly more complex belief transition behaviors in an infinite state space and worsens the curse of dimensionality of dynamic programming. To overcome this challenge, we dive into the rich structures of the value functions and obtain tight bounds on their derivatives. These results lead to the proof of optimality of threshold policies on a single-channel problem with subsidy and subsequently a closed-form channel index function using an iterative method to approximate the well-known Whittle index policy, which offers a low-complexity solution for ranking the currently available channels whose states are never directly observable. Through extensive numerical studies, we demonstrate the superior performance and robustness of our proposed algorithm.