Motivated by a satellite communications problem, we consider a generalized coloring problem on unit disk graphs. A coloring is k -improper if no more than k neighbors of every vertex have the same colour as that assigned to the vertex. The k -improper chromatic number χ k (G) is the least number of colors needed in a k -improper coloring of a graph G. The main subject of this work is analyzing the complexity of computing χ k for the class of unit disk graphs and some related classes, e.g., hexagonal graphs and interval graphs. We show NP-completeness in many restricted cases and also provide both positive and negative approximability results. Because of the challenging nature of this topic, many seemingly simple questions remain: for example, it remains open to determine the complexity of computing χ k for unit interval graphs.