  In a broadcast channel with random packet arrival and transmission queues,
the stability of the system is achieved by maximizing a weighted sum rate
capacity with suitable weights that depend on the queue size. The weighted sum
rate capacity using Dirty Paper Coding (DPC) and Zero Forcing (ZF) is
asymptotically equivalent to the weighted sum capacity over parallel
single-channels. In this paper, we study the Diversity Multiplexing Tradeoff
(DMT) of the fading broadcast channel under a fixed weighted sum rate capacity
constraint. The DMT of both identical and different parallel weighted MISO
channels is first derived. Finally, we deduce the DMT of a broadcast channel
using DPC and ZF precoders.
