Multiuser wireless systems with multiple antennas have the potential for achieving higher capacity while also enhancing quality of service. This thesis investigates the problem of linear processing for the downlink of such systems where a single base station communicates with multiple users. We jointly optimize power allocation and transmit-receive filters of all users for two criteria; (1) minimizing total transmission power given a set of quality of service constraints and (2) minimizing the sum mean squared error over all users given a total power budget. Based on the principle of duality, we propose iterative optimization algorithms for two variations of the linear processing problem; the first one assumes the availability of perfect channel knowledge at the transmitter, while the other is based on channel covariance feedback. Simulation results show that the proposed algorithms offer better performance over existing techniques in terms of reduced complexity and relaxed constraints.