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

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We study zero-forcing (ZF) detection 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 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 that 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.

Original languageEnglish (US)
Article number7456329
Pages (from-to)5245-5259
Number of pages15
JournalIEEE Transactions on Wireless Communications
Issue number8
StatePublished - Aug 2016

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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