  We study zero-forcing detection (ZF) for multiple-input/multiple-output
(MIMO) spatial multiplexing under transmit-correlated Rician fading for an N_R
X N_T channel matrix with rank-1 line-of-sight (LoS) component. By using matrix
transformations and multivariate statistics, our exact analysis yields the
signal-to-noise ratio moment generating function (m.g.f.) as an infinite series
of gamma distribution m.g.f.'s and analogous series for ZF performance
measures, e.g., outage probability and ergodic capacity. However, their
numerical convergence is inherently problematic with increasing Rician
K-factor, N_R , and N_T. We circumvent this limitation as follows. First, we
derive differential equations satisfied by the performance measures with a
novel automated approach employing a computer-algebra tool which implements
Groebner basis computation and creative telescoping. These differential
equations are then solved with the holonomic gradient method (HGM) from initial
conditions computed with the infinite series. We demonstrate that HGM yields
more reliable performance evaluation than by infinite series alone and more
expeditious than by simulation, for realistic values of K , and even for N_R
and N_T relevant to large MIMO systems. We envision extending the proposed
approaches for exact analysis and reliable evaluation to more general Rician
fading and other transceiver methods.
