  This paper investigates the robust transmission design (RTD) of a multi-cell
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
non-robust transmission design greatly in terms of network spectral efficiency.
