Hybrid beamforming for multi-user mmWave relay networks using deep learning

doi:10.11772/j.issn.1001-9081.2022081231

Abstract

Abstract:

In order to solve the problem of high computational complexity of traditional multi-user mmWave relay system beamforming methods， a Singular Value Decomposition （SVD） method based on Deep Learning （DL） was proposed to design hybrid beamforming for the optimization of the transmitter， relay and receiver. Firstly， DL method was used to design the beamforming matrix of transmitter and relay to maximize the achievable spectral efficiency. Then， the beamforming matrix of relay and receiver was designed to maximize the equivalent channel gain. Finally， a Minimum Mean Square Error （MMSE） filter was designed at the receiver to eliminate the inter-user interference. Theoretical analysis and simulation results show that compared with Alternating Maximization （AltMax） and the traditional SVD method， the hybrid beamforming method based on DL reduces the computational complexity by 12.5% and 23.44% respectively in the case of high dimensional channel matrix and many users， and has the spectral efficiency improved by 2.277% and 21.335% respectively with known Channel State Information （CSI）， and the spectral efficiency improved by 11.452% and 43.375% respectively with imperfect CSI.

Key words: millimeter Wave (mmWave), hybrid beamforming, deep learning, relay network, multi-user, Deep Neural Network (DNN)

摘要：

针对传统多用户毫米波中继系统波束赋形方案计算复杂度高的问题，提出一种基于深度学习（DL）的奇异值分解（SVD）方法来设计混合波束赋形，以优化发送端、中继端和接收端波束赋形器。首先，利用DL方法设计发送端、中继端的波束赋形矩阵最大化可实现的频谱效率；然后，设计中继端、接收端的频带波束赋形矩阵以最大化等效信道增益；最后，在接收端设计最小均方误差（MMSE）滤波器消除用户间干扰。理论分析和仿真结果表明，基于DL的混合波束赋形方法相较于交替最大化（AltMax）与传统SVD 方法在高维信道矩阵和较多的用户情况下，计算复杂度分别降低了12.5%和23.44%；在已知信道状态信息（CSI）的情况下，频谱效率分别提高了2.277%和21.335%，在非完美CSI情况下，频谱效率分别提高了11.452%和43.375%。

关键词: 毫米波, 混合波束赋形, 深度学习, 中继网络, 多用户, 深度神经网络

CLC Number:

TN928

Xiaolin LI, Songjia YANG. Hybrid beamforming for multi-user mmWave relay networks using deep learning[J]. Journal of Computer Applications, 2023, 43(8): 2511-2516.

李校林, 杨松佳. 基于深度学习的多用户毫米波中继网络混合波束赋形[J]. 《计算机应用》唯一官方网站, 2023, 43(8): 2511-2516.

Figures/Tables 6

Fig. 1 Multi-user mmWave AF relay system

Fig.2 Architecture of beamforming based on DL

Tab.1 Computational complexity of proposed method and other beamforming methods

方法	计算复杂度
本文方法	$O (m a x (k 2 N r N t, k 2 N r 2, k 2 N t 2))$
GDM^［2］	$O (N t 2 N r + N t N r 2 + N r 3)$
OMP^［6］	$O (2 N r 3 (N t N r 4 + k N t 2 N r 2 + k 2 N r 2))$
SVD^［10］	$O (N r N t 2, N r 2 N t)$
AltMax^［14］	$O (N t 2 N t, r f + N r 2 N r, r f)$
MMSE^［16］	$O (2 N t N t, r f 4 + N r 2 N r, r f 2)$

Tab.1 Computational complexity of proposed method and other beamforming methods

方法	计算复杂度
本文方法	$O (m a x (k 2 N r N t, k 2 N r 2, k 2 N t 2))$
GDM^［2］	$O (N t 2 N r + N t N r 2 + N r 3)$
OMP^［6］	$O (2 N r 3 (N t N r 4 + k N t 2 N r 2 + k 2 N r 2))$
SVD^［10］	$O (N r N t 2, N r 2 N t)$
AltMax^［14］	$O (N t 2 N t, r f + N r 2 N r, r f)$
MMSE^［16］	$O (2 N t N t, r f 4 + N r 2 N r, r f 2)$

Fig.3 Spectral efficiencies of different methods with perfect CSI when Nt=Nr=32，Nd=8，Nrf=Ns=2

Fig.4 When Nt=Nr=64，Nd=8，Nrf=Ns=2， spectral efficiencies with perfect CSI and imperfect CSI （σe2=0.5）

Fig.5 Spectral efficiencies of different numbers of transmitting and receiving antennas with imperfect CSI and σe2=0.3

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