The throughput of users with poor channel conditions, such as those at a cell edge, is a bottleneck in wireless systems. A major part of the power budget must be allocated to serve these users in guaranteeing their quality-of-service (QoS) requirement, hampering QoS for other users and thus compromising the system reliability. In nonorthogonal multiple access (NOMA), the message intended for a user with a poor channel condition is decoded by itself and by another user with a better channel condition. The message intended for the latter is then successively decoded by itself after canceling the interference of the former. The overall information throughput is thus improved by this particular successive decoding and interference cancellation.This paper aims to design linear precoders/beamformers for signal superposition at the base stations of NOMA multi-input multi-output multi-cellular systems to maximize the overall sum throughput subject to the users’ QoS requirements,which are imposed independently on the users’ channel condition. This design problem is formulated as the maximization of a highly nonlinear and non smooth function subject to non convex constraints, which is very computationally challenging. Path-following algorithms for its solution, which invoke only a simple convex problem of moderate dimension at each iteration are developed. Generating a sequence of improved points, these algorithms converge at least to a local optimum. Extensive numerical simulations are then provided to demonstrate their merit.