On the Impact of Spatial Correlation on the Finite Diversity-Multiplexing Tradeoff

Abstract

We present a tight lower bound on the outage probability of a spatially correlated multielement antenna (MEA) channel. Using this lower bound, an accurate finite-SNR estimate of the diversity-multiplexing tradeoff over a spatially correlated Rayleigh fading channel is derived. This estimate allows gaining insight on the impact of spatial correlation on the diversity-multiplexing tradeoff at finite SNR. As expected, the diversity multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a transmission rate of R = rlog <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (1 + g ldr eta) bps/Hz, where r is the multiplexing gain, g is the array gain and eta is the SNR at each receive antenna, and an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at an SNR of 10 dB in a highly correlated channel, when r ges0.8. Another interesting point is that the maximum diversity gain is not affected by the correlation, provided that the spatial channel correlation matrix is of full rank.