In this paper, we study the fundamental limits on the data rate of multiple antenna systems in a Rayleigh fading environment. WithMtransmit andMreceive antennas, up toMindependent channels can be established in the same bandwidth. We study the distribution of the maximum data rate at a given error rate in the channels between up toMtransmit antennas andMreceive antennas and determine the outage probability for systems that use various signal processing techniques. We analyze the performance of the optimum linear and nonlinear receiver processor and the optimum linear transmitter/receiver processor pair, and the capacity of these channels. Results show that with optimum linear processing at the receiver, up toM/2channels can be established with approximately the same maximum data rate as a single channel. With either nonlinear processing at the receiver or optimum linear transmitter/receiver processing, up toMchannels can be established with approximately the same maximum data rate as a single channel. Results show the potential for large capacity in systems with limited bandwidth.