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Underlay device-to-device (D2D) communications improve the spectral efficiency by simultaneously allowing direct communication between D2D-users on the same channels as cellular-users (CUs). However, most related works consider perfect channel-state-information (CSI) with single-antenna transmissions and usually assign each channel to one D2D pair. In this work, we formulate an optimization problem for maximizing the aggregate rate of all D2D pairs and CUs in single and multiple antenna configurations under imperfect CSI, by optimizing channel and power resources. Our formulation guarantees probability of outage below a specified threshold and fairness in channel allocation across D2D pairs. The resulting problem is a stochastic-mixed-integer-non-convex problem, we solve it approximately by alternating between power-allocation and channel-assignment sub-problems. The stochastic objective …