  In this paper, we study the mean square error (MSE) and the bit error rate
(BER) performance of the box-relaxation decoder in massive
multiple-input-multiple-output (MIMO) systems under the assumptions of
imperfect channel state information (CSI) and receive-side channel correlation.
Our analysis assumes that the number of transmit and receive antennas ($n$,and
$m$) grow simultaneously large while their ratio remains fixed. For simplicity
of the analysis, we consider binary phase shift keying (BPSK) modulated
signals. The asymptotic approximations of the MSE and BER enable us to derive
the optimal power allocation scheme under MSE/BER minimization. Numerical
simulations suggest that the asymptotic approximations are accurate even for
small $n$ and $m$. They also show the important role of the box constraint in
mitigating the so called double descent phenomenon.
