  Resource allocation is an important issue in cognitive radio systems. It can
be done by carrying out negotiation among secondary users. However, significant
overhead may be incurred by the negotiation since the negotiation needs to be
done frequently due to the rapid change of primary users' activity. In this
paper, a channel selection scheme without negotiation is considered for
multi-user and multi-channel cognitive radio systems. To avoid collision
incurred by non-coordination, each user secondary learns how to select channels
according to its experience. Multi-agent reinforcement leaning (MARL) is
applied in the framework of Q-learning by considering the opponent secondary
users as a part of the environment. The dynamics of the Q-learning are
illustrated using Metrick-Polak plot. A rigorous proof of the convergence of
Q-learning is provided via the similarity between the Q-learning and
Robinson-Monro algorithm, as well as the analysis of convergence of the
corresponding ordinary differential equation (via Lyapunov function). Examples
are illustrated and the performance of learning is evaluated by numerical
simulations.
