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Linear precoding based on polynomial expansion: reducing complexity in massive MIMO

机译：基于多项式扩展的线性预编码：降低大规模MIMO的复杂度

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Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively “antenna-efficient” regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF.By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
机译：大规模多输入多输出（MIMO）技术有可能为未来的通信系统带来频谱效率的极大提高。与直觉相反，通过扩大系统尺寸，或多或少地自动解决了具有不确定的信道知识，高的传播损耗以及实现最佳的非线性预编码的实际问题。但是，计算预编码的复杂度随系统尺寸而增加。例如，接近最佳和相对“天线效率”的正则归零强制（RZF）预编码在实践中实施起来非常复杂，因为它需要在每个相干周期中快速转换大型矩阵。由于RZF的高性能，我们建议用截断多项式扩展（TPE）代替矩阵求逆和乘法，从而获得新的TPE预编码方案，该方案更适合于实时硬件实现，并显着减少了延迟时间。首次传输的符号。矩阵多项式的阶数可以适应可用的硬件资源，并可以在简单的最大比率传输和更高级的RZF之间进行平滑过渡。 TPE预编码在大规模MIMO系统中实现的信噪比（SINR）。此外，我们为多项式系数提供了一个封闭形式的表达式，该表达式使该SINR最大化。与RZF相比，要保持固定的每用户速率损失，多项式度不必随系统缩放，但应随信道知识的质量和信噪比而增加。

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