This paper considers a discrete sum rate maximization (DSRM) problem for transmit optimization in multiuser MISO downlink. Unlike many existing sum rate maximization designs, DSRM focuses on a scenario where each user's achievable rate can only be chosen from a given discrete rate set. This discrete rate-based design is motivated by the fact that practical communication systems can support only a finite number of combinations of modulation and coding schemes. We tackle the DSRM problem first by deriving a novel reformulation of DSRM, in which the discrete rate variables are absorbed by the objective function. Then, from this reformulation, an approximation algorithm based on convex optimization and iterative solution refinement is developed. Simulations results are provided to demonstrate the performance of the proposed algorithm compared with some state-of-the-art algorithms.
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