This paper investigates the robust transmission design (RTD) of a multicell device-to-device (D2D) underlaid cellular network with imperfect channel state information (CSI). The bounded model is adopted to characterize the CSI impairment and the aim is to maximize the worst-case sum rate of the system. To protect cellular communications, it is assumed that the interference from all D2D transmitters to each base station (BS) is power-limited. It is first shown that the worst-case signal-to-interference-plus-noise ratio (SINR) of each D2D link can be obtained directly, while that of cellular links cannot be similarly found since the channel estimation error vectors of cellular links are coupled in the SINR expressions. To solve the nonconvex problem, the objective function of the original problem is replaced with its lower bound, and the resulted problem is decomposed into multiple semidefinite programming (SDP) subproblems, which are convex and have computationally efficient solutions. An iterative RTD algorithm is then proposed to obtain a suboptimal solution. Simulation results show that D2D communication can significantly increase the performance of the conventional cellular systems while causing tolerable interference to cellular users. In addition, the proposed RTD algorithm outperforms the conventional nonrobust transmission design greatly in terms of network spectral efficiency
