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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. [ABSTRACT FROM AUTHOR]