In this paper, the problem of input signal design with the property that the estimated model satisfies a given performance level with a prescribed probability is studied. The aforementioned performance level is associated with a particular application. This problem is well-known to fall within the class of chance-constrained optimization problems, which are nonconvex in most cases. Convexification is attempted based on a Markov inequality, leading to semidefinite programming (SDP) relaxation formulations. As applications, we focus on the identification of multiple input multiple output (MIMO) wireless communication channel models for minimum mean square error (MMSE) channel equalization and zero-forcing (ZF) precoding.