  In this work, a MIMO broadcast channel under the energy harvesting (EH)
constraint and the peak power constraint is investigated. The transmitter is
equipped with a hybrid energy storage system consisting of a perfect super
capacitor (SC) and an inefficient battery, where both elements have limited
energy storage capacities. In addition, the effect of data processing circuit
power consumption is also addressed. To be specific, two extreme cases are
studied here, where the first assumes ideal/zero circuit power consumption and
the second considers a positive constant circuit power consumption where the
circuit is always operating at its highest power level. The performance of
these two extreme cases hence serve as the upper bound and the lower bound of
the system performance in practice, respectively. In this setting, the offline
scheduling with ideal and maximum circuit power consumptions are investigated.
The associated optimization problems are formulated and solved in terms of
weighted throughput optimization. Further, we extend to a general circuit power
consumption model. To complement this work, some intuitive online policies are
presented for all cases. Interestingly, for the case with maximum circuit power
consumption, a close-to-optimal online policy is presented and its performance
is shown to be comparable to its offline counterpart in the numerical results.
