MIMO Zero-Forcing Performance Evaluation Using the Holonomic Gradient Method
MIMO Zero-Forcing Performance Evaluation Using the Holonomic Gradient Method
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DOI：
10.1109/twc.2014.2385075
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发表时间：
2014-03
影响因子：
10.4
通讯作者：
C. Siriteanu;A. Takemura;S. Kuriki;Hyundong Shin;C. Koutschan
中科院分区：
文献类型：
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作者：
C. Siriteanu;A. Takemura;S. Kuriki;Hyundong Shin;C. Koutschan
在多输入多输出（MIMO）空间复用传输中，零强制（zero-forcing， ZF）检测因其低复杂度而备受关注。我们最近对与异构网络相关的ririan - rayleigh衰落的MIMO ZF性能进行了分析，得出了ZF中断概率和遍历容量的无穷级数表达式。因为它们是由在0附近展开合流超几何函数1F1（·，·，σ）而产生的，所以它们在数值上并不收敛于实际的高水平k因子值。因此，在这里，我们寻求利用1F1（·，·，σ）满足微分方程的事实，即它是一个完整函数。完整函数可以通过完整梯度法（HGM）计算，即通过数值求解满足的微分方程。因此，我们首先揭示了ZF信噪比（SNR）的矩产生函数（m.g.f.）和概率密度函数（p.d.f.）是完整的。然后，从1F1（·，·，σ）的微分方程推导出信噪比m.g.f.和p.d.f.满足的条件，并证明了HGM有助于在实际相关的k值处精确计算p.d.f.。最后，对HGM产生的信噪比p.d.f.进行数值积分，得到准确的ZF中断概率和遍历容量结果。
For multiple-input-multiple-output (MIMO) spatial-multiplexing transmission, zero-forcing (ZF) detection is appealing because of its low complexity. Our recent MIMO ZF performance analysis for Rician-Rayleigh fading, which is relevant in heterogeneous networks, has yielded for the ZF outage probability and ergodic capacity infinite-series expressions. Because they arose from expanding the confluent hypergeometric function 1F1(·, ·, σ) around 0, they do not converge numerically at realistically high Rician K-factor values. Therefore, herein, we seek to take advantage of the fact that 1F1(·, ·, σ) satisfies a differential equation, i.e., it is a holonomic function. Holonomic functions can be computed by the holonomic gradient method (HGM), i.e., by numerically solving the satisfied differential equation. Thus, we first reveal that the moment generating function (m.g.f.) and probability density function (p.d.f.) of the ZF signal-to-noise ratio (SNR) are holonomic. Then, from the differential equation for 1F1(·, ·, σ), we deduce those satisfied by the SNR m.g.f. and p.d.f. and demonstrate that the HGM helps compute the p.d.f. accurately at practically relevant values of K. Finally, numerical integration of the SNR p.d.f. produced by HGM yields accurate ZF outage probability and ergodic capacity results.