In this paper, common pilot signal design for channel estimation of users with different channel strengths simultaneously served by non-orthogonal multiple access (NOMA) is considered. The problem is approached based on two design criteria: minimization of weighted sum mean-square error (MSE) and maximization of weighted sum conditional mutual information (CMI) between the channel and the received signal given the pilot signal. It is shown that the two design problems reduce to semi-definite programming (SDP). Furthermore, in the practical case of two-user clustering, closed-form solutions to the two problems are obtained under some additional assumption on the channel's statistical information. Numerical result shows that the pilot signal design exploiting the multi-group structure of NOMA yields better channel estimation performance than conventional design.