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<p> There are two popular approaches in the communication between multiple receivers and a base station with multiple antennas: dirty paper coding and multiuser diversity. Dirty paper coding can be rather difficult to realize, which motivates people to find some practical schemes. When there are a lot of users, multiuser diversity requires a lot of feedback which decrease the uplink spectrum efficiency.</p> <p> In this paper, we aim to minimize the probability of error subject to the total transmit power constraint and decrease the amount of feedback required by the multiuser diversity instead of trying to achieve the dirty paper coding. There are two main results in this thesis: First, we formulate the minimization of the average probability of error of all the users as a convex optimization problem, subject to the peak or the average power constraints. The proposed transmitter represents a nonlinear one-to-one mapping between the transmitted data vector and the symbol vector. The transmitted data vector going through the base station antennas is obtained as a solution to the proposed convex error probability optimization problem that can be solved using computationally efficient interior point algorithms. Furthermore, we propose a random unitary beamforming technique to reduce the feedback by selecting a threshold for the users. To improve fairness, an equal ratio scheduling algorithm which could serve the users with different rate requirements is developed. We also give an upper and lower bound on the sum rate achievable in our approach. Monte Carlo simulation results is provided to verify the performance of the proposed algorithms.</p> / Thesis / Master of Applied Science (MASc)