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Public m-health is a new medical service under intensive development, which provides unobtrusive monitoring of people's health conditions from anywhere at any time to enable detection of deteriorating health conditions before severe discomfort or disability occur. A key challenge in practical implementation of public m-health is the use of shared license-free spectrum by body area networks (BANs) to report sampled vital signs continuously and in real time. A cognitive medium access control method called centralized body area network access scheme (CBAS) is proposed in this paper to reduce access delay in a BAN in the presence of coexistent systems. By opportunistic extraction of idle spaces from a pool of orthogonal channels, CBAS dynamically adjusts a BAN's channel access pattern according to the current interference environment, and improves the BAN's visibility among coexistent networks. Performance of a BAN under CBAS is analyzed by modeling the system as a preemptive-resume priority queue. Numerical and simulation results show that the queuing delay and throughput of a BAN employing CBAS outperforms those of a BAN that utilizes a single channel statically, as channel access opportunities suffer less fragmentations and interruptions.