  We consider the well-studied radio network model: a synchronous model with a
graph G=(V,E) with |V|=n where in each round, each node either transmits a
packet, with length B=Omega(log n) bits, or listens. Each node receives a
packet iff it is listening and exactly one of its neighbors is transmitting. We
consider the problem of k-message broadcast, where k messages, each with
Theta(B) bits, are placed in an arbitrary nodes of the graph and the goal is to
deliver all messages to all the nodes. We present a simple proof showing that
there exist a radio network with radius 2 where for any k, broadcasting k
messages requires at least Omega(k log n) rounds. That is, in this network,
regardless of the algorithm, the maximum achievable broadcast throughput is
O(1/log n).
