This paper presents an adaptive modulation and power allocation method for uplink multiuser multiple-input multiple-output systems under the assumption that there is perfect channel information at the receiver but not at the transmitter. The receiver jointly optimizes the power level and modulation order for all users under constraints of transmit power and error requirements, and returns these information to each user via a low-rate feedback channel. Power and modulation optimization maximizes the total throughput under a tolerable bit error ratio for each user. The ellipsoid method is used to design efficient algorithms for optimal power and modulation level.