  The maximum-likelihood (ML) decoder for symbol detection in large
multiple-input multiple-output wireless communication systems is typically
computationally prohibitive. In this paper, we study a popular and practical
alternative, namely the Box-relaxation optimization (BRO) decoder, which is a
natural convex relaxation of the ML. For iid real Gaussian channels with
additive Gaussian noise, we obtain exact asymptotic expressions for the symbol
error rate (SER) of the BRO. The formulas are particularly simple, they yield
useful insights, and they allow accurate comparisons to the matched-filter
bound (MFB) and to the zero-forcing decoder. For BPSK signals the SER
performance of the BRO is within 3dB of the MFB for square systems, and it
approaches the MFB as the number of receive antennas grows large compared to
the number of transmit antennas. Our analysis further characterizes the
empirical density function of the solution of the BRO, and shows that error
events for any fixed number of symbols are asymptotically independent. The
fundamental tool behind the analysis is the convex Gaussian min-max theorem.
