  The deployment of massive MIMO systems has revived much of the interest in
the study of the large-system performance of multiuser detection systems. In
this paper, we prove a non-trivial upper bound on the bit-error rate (BER) of
the MAP detector for BPSK signal transmission and equal-power condition. In
particular, our bound is approximately tight at high-SNR. The proof is simple
and relies on Gordon's comparison inequality. Interestingly, we show that under
the assumption that Gordon's inequality is tight, the resulting BER prediction
matches that of the replica method under the replica symmetry (RS) ansatz.
Also, we prove that, when the ratio of receive to transmit antennas exceeds
$0.9251$, the replica prediction matches the matched filter lower bound (MFB)
at high-SNR. We corroborate our results by numerical evidence.
