Performance difference between zero-forcing and maximum likelihood detectors in massive MIMO systems

In massive multiple-input multiple-output (MIMO) systems with hundreds of antennas at the base station (BS) and few users with a single transmitter antenna, linear detectors, such as zero-forcing (ZF), achieve near-optimum performance due to the property of asymptotically orthogonal channel matrix. However, how far away is ZF from the optimum performance. To answer this question, in this Letter, closed-form bit error rate (BER) expressions are derived. These BER expressions are subsequently used to evaluate the performance difference between ZF and the optimum detector, which is a function of the number of antennas at the BS and the number of users. Numerical results verify the tightness of the performance difference.