毫米波MIMO系统中基于自适应梯度算法的混合预编码

doi:10.11959/j.issn.1000-436x.2021207

摘要/Abstract

摘要：

为了降低毫米波MIMO系统中现有交替最小混合预编码算法和基于动量梯度下降的在线学习混合预编码方案的复杂度，针对单用户通信场景，重新考虑混合预编码器的设计问题，提出一种等效的单隐藏层神经网络架构。在该架构下，数字预编码矩阵和模拟预编码矩阵的每一个组成元素可等效为单隐藏层神经网络的连接权值，其最优解可通过神经网络中的权值训练方法获得。在此基础上，结合反向传播算法，提出一种基于自适应梯度反向传播的混合预编码机制。进一步地，将所提算法扩展到多用户通信场景。仿真结果表明，在单用户场景和多用户场景下，所提算法可实现的频谱效率均接近全数字预编码，同时复杂度低于现有的基于交替最小的混合预编码算法和基于动量梯度下降的在线学习混合预编码方案。

关键词: 毫米波, 混合预编码, 神经网络, 自适应梯度

Abstract:

To reduce the complexity of existing hybrid precoding algorithms based on alternating minimization (AltMin) and online learning via gradient descent with momentum in mmWave MIMO systems, aiming at the single-user scenario, the problem of designing the hybrid precoder was reconsidered and an equivalent single hidden layer neural network was proposed.Under the new architecture, the elements of the digital and analog precoder were equivalent to the connecting weights of a single hidden layer neural network, and their optimal solution could be obtained via the weights training method.Inspired by the back propagation (BP) algorithm in feed forward neural networks, an adaptive gradient (AG)-based BP algorithm for hybrid precoding was proposed.Furthermore, the proposed algorithm was extended to the multi-user scenario.The numerical results show that the proposed algorithm achieves approximately the same spectral efficiency as the fully-digital precoding in both the single-user and multi-user scenarios, while has lower complexity than the existing AltMin-based hybrid precoding algorithms and online learning hybrid precoding based on gradient descent with momentum.

Key words: mmWave, hybrid precoding, neural network, adaptive gradient

中图分类号:

TN92

张煜, 张治, 董晓岱. 毫米波MIMO系统中基于自适应梯度算法的混合预编码[J]. 通信学报, 2021, 42(10): 95-105.

Yu ZHANG, Zhi ZHANG, Xiaodai DONG. Adaptive gradient algorithm for hybrid precoding in mmWave MIMO system[J]. Journal on Communications, 2021, 42(10): 95-105.

图/表 11

图1

表1

算法1每步操作所需复数乘法和除法个数"

操作	复数乘法和除法个数
计算 ${y}_{n = 1}^{N_{d}}$	$N_{d} N_{t} N_{S}$
计算 ${b_{q}^{n}}_{n = 1}^{N_{d}}$	$N_{d} N_{t}^{RF} N_{S}$
计算 ${{\hat{y}}_{p}^{n}}_{n = 1}^{N_{d}}$	$N_{d} N_{t} N_{t}^{RF}$
更新a_p,q	$(4 N_{d} +2) N_{t} N_{t}^{RF}$
重构a_p,q	$2 N_{t} N_{t}^{RF}$
更新d_q,u	$2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF})$

表1

表2

算法1与对比算法的计算开销"

算法	复数乘法和除法个数
算法1	$N_{iter} ((5 N_{d} +4) N_{t} N_{t}^{RF} + N_{d} N_{t} N_{S} + N_{d} N_{t}^{RF} N_{S} +$
	$2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
CG-AltMin	$N_{iter}^{i} (2(N_{t})^{2} N_{t}^{RF} N_{S} + 11 N_{t} N_{t}^{RF} + 1) +$
	$N_{iter}^{o} (2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
BB-AltMin	$N_{iter}^{i} (2(N_{t})^{2} N_{t}^{RF} N_{S} + 8 N_{t} N_{t}^{RF} + 1) +$
	$N_{iter}^{o} (2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
GP-AltMin	$N_{iter}^{i} (2(N_{t})^{2} N_{t}^{RF} N_{S} + 2 N_{t} N_{t}^{RF} + 1) +$
	$N_{iter}^{o} (2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF}))$
GDM	$N_{iter}^{GDM} ((5 N_{d} +4) N_{t} N_{t}^{RF} + N_{d} N_{t} N_{S} + N_{d} N_{t}^{RF} N_{S} +$
	$2 N_{t} {(N_{t}^{RF})}^{2} + N_{t} N_{t}^{RF} N_{S} + f_{inv} (N_{t}^{RF})$

表2

图2

图3

图4

图5

表3

不同算法的平均迭代次数"

N_RF	本文算法		CG			BB			GP		GDM
N_RF	本文算法	$N_{iter}^{o}$		$N_{iter}^{i}$	$N_{iter}^{o}$		$N_{iter}^{i}$	$N_{iter}^{o}$		$N_{iter}^{i}$	$N_{iter}^{GDM}$
2	314.503	3.644		80.213	3.727		102.717	3.846		63.102	2 000
3	453.824	4.016		111.852	3.981		187.170	4.715		126.886	2 000
4	192.281	3.720		104.735	3.755		249.381	3.992		113.690	1 955.35
5	81.701	3.565		94.382	3.604		231.386	3.679		124.113	1 547.26
6	56.548	3.391		86.065	3.427		220.753	3.528		190.989	1 236.19

表3

图6

图7

图8

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