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Dominating broadcasting is a domination-type structure that models atransmission antenna network. In this paper, we study a limited version of thisstructure, that was proposed as a common framework for both broadcast andclassical domination. In this limited version, the broadcast function is upperbounded by an integer $k$ and the minimum cost of such function is thedominating $k$-broadcast number. Our main result is a unified upper bound onthis parameter for any value of $k$ in general graphs, in terms of both $k$ andthe order of the graph. We also study the computational complexity of theassociated decision problem.

General bounds on limited broadcast domination