Performance Analysis of Closed-Loop MIMO Precoder Based on the Probability of Minimum Distance

Linear closed-loop MIMO precoders are attractive owing to their scalability. They can significantly improve the received signal via optimization of pertinent criterion. The solution of max-d_min precoding is optimal for 4-QAM as it utilizes the channel state information at the transmitter (CSIT) to minimize the system error probability making it very attractive. However, as M increases the solution which is dependent on channel angle gets complex, due to its multi-form precoder search. Motivated by a requirement to provide MIMO system evaluation parameters to upper layer protocol(s) as a function of precoder optimization criterion, we propose deriving a general expression for the probability density function (pdf) of max-d_min. Our approach applies numerical approximations to derive the system bit error rate (BER) and ergodic capacity for any values of M, n_r, and n_t, and with b = 2 data streams. Results show that the performance of our numerical approximation approach is close to the analytical simulation method.