Exact ZF Analysis and Computer-Algebra-Aided Evaluation in Rank-1 LoS Rician Fading
Constantin Siriteanu, Akimichi Takemura, Christoph Koutschan,
Satoshi Kuriki, Donald St. P. Richards, Hyundong Shin
AbstractWe study zero-forcing detection (ZF) for multiple-input/multiple-output (MIMO) spatial multiplexing under transmit-correlated Rician fading for an NR×NT 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, NR, and NT. 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 Gröbner 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 NR and NT 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.
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Supplementary electronic material
- Rank1Rice.nb (Mathematica notebook containing the derivation of Pfaffian systems, updated 25.04.2016)
- Rank1Rice.cdf (the notebook in cdf format for the Wolfram CDF Player)
- Rank1Rice.pdf (pdf screenshot of the notebook)
- For executing the commands in the notebook, the additional package HolonomicFunctions is required.