Asymptotic SEP analysis for optimally precoded large MIMO channels with ZF detection

This paper considers the asymptotic analysis of symbol error probability (SEP) for either optimally precoded or uniformly precoded large correlated MIMO fading channels using the zero-forcing (ZF) detector. For such systems, we reveal some very nice structures which naturally lead us to the exploration of two very strong and very useful mathematical tools for the systematic study of asymptotic behaviors on their error performance. The first tool is the Szegö´s theorem on large Hermitian Toeplitz matrices and the second tool is the well known limit: limx→∞(1 + 1/x)^x = e. This new approach enables us to attain a very simple expression for the SEP limit as the number of the transmitter antennas goes to infinity. One of the major advantages for this method is that its convergence rate is very fast. Hence, this expression is very efficient and effective SEP approximation for the large MIMO systems. Due to the constraint on allowable space and limited (sparse) multi-path scattering, fading correlation between neighbouring antenna elements is almost inevitable in a large MIMO architecture. By specifically examining an exponential correlation matrix model, we show that channel fading correlation can lead to significant performance loss. The optimal precoding technique can yield substantial power gain over the uniform power allocation strategy.