  The Internet of Medical Things (IoMT) facilitates in-home electronic
healthcare, transforming traditional hospital-based medical examination
approaches. This paper proposes a novel transmit scheme for fog
computing-enabled IoMT that leverages uplink and downlink rate splitting (RS).
Fog computing allows offloading partial computation tasks to the edge server
and processing the remainder of the tasks locally. The uplink RS and downlink
RS utilize their flexible interference management capabilities to suppress
offloading and feedback delay. Our overarching goal is to minimize the total
time cost for task offloading, data processing, and result feedback. The
resulting problem requires the joint design of task offloading, computing
resource allocation, uplink beamforming, downlink beamforming, and common rate
allocation. To solve the formulated non-convex problem, we introduce several
auxiliary variables and then construct accurate surrogates to smooth the
achievable rate. Moreover, we derive the optimal computation resource
allocation per user with closed-form expressions. On this basis, we recast the
computing resource allocation and energy consumption at the base station to a
convex constraint set. We finally develop an alternating optimization algorithm
to update the auxiliary variable and inherent variable alternately. Simulation
results show that our transmit scheme and algorithm exhibit considerable
performance enhancements over several benchmarks.
