大规模MU-MIMO系统中关联性到达方向估计算法

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大规模多用户MIMO系统是未来无线通信的关键技术之一，它通过利用大量的天线元素来提升频谱效率和数据传输能力。然而，当系统规模扩大时，传统的到达方向（DOA）估计方法面临着巨大的挑战，因为高维DOA参数空间使得精确估计变得复杂且计算成本高昂。本文的研究论文针对这一问题，提出了一个基于相关性的DOA估计方法。论文的核心思想是利用相邻天线间的天然相关性，这是由于实际阵列尺寸的物理限制导致的。作者注意到，尽管阵列尺寸大，但邻近天线接收到的信号在空间上可能存在一定程度的相关性。因此，他们提出了一种新的DOA估计算法，该算法能够有效捕捉和利用这种关联性，从而提高DOA估计的精度，并显著降低计算复杂度。论文首先回顾了DOA估计在MIMO系统中的重要性，尤其是在多用户环境下的性能优化。然后，详细介绍了新方法的设计原理，可能包括利用自相关矩阵、协方差矩阵或者基于深度学习的特征提取技术来识别信号的方向特性。接着，作者通过理论分析和仿真结果展示了他们的方法在实际应用场景中的优势，比如在信噪比较低或用户数量众多的情况下，相较于传统方法，新方法具有更高的分辨率和更稳定的性能。在实验部分，论文可能提供了对比实验，将新方法与已有的DOA估计算法如最小均方误差（MSE）、 ESPRIT或 MUSIC进行比较，以量化其在估计精度、计算复杂度以及鲁棒性方面的改进。此外，还可能探讨了算法的稳健性和适应性，尤其是在处理阵列失配、干扰和动态环境变化时的表现。关键词部分，"Largescale", "multi-user", "MIMO", 和 "DOAestimation" 强调了论文的主要关注点，表明了研究的焦点集中在如何在大规模多用户MIMO系统中克服DOA估计的难题，以实现高效和准确的通信服务。总结来说，这篇研究论文通过引入基于相关性的DOA估计策略，为大规模多用户MIMO系统的性能优化提供了一种创新且高效的解决方案，这将对未来的无线通信系统设计和优化具有重要意义。同时，它也向业界展示了在面对复杂通信环境时，如何巧妙地利用阵列结构特点以解决实际问题。

Correlation Based Direction of Arrival Estimation

for the Large Scale Multi-user MIMO System

Xiao Wei, Wei Peng, and Tao Jiang

School of Electronics Information and Communications,

Huazhong University of Science and Technology, Wuhan, China 430074

E-mail: weixiao1991@hust.edu.cn; pengwei@hust.edu.cn; taojiang@hust.edu.cn

Abstract—It is well known that accurate direction of arrival

(DOA) estimation can help to improve the performance of

MIMO systems. However, when large scale MIMO systems are

considered, the DOA estimation becomes very difﬁcult due to

the large dimension of DOAs. Based on the observation that

correlation exists between the neighboring antennas due to the

limited size of the antenna array, we propose a correlation based

DOA estimation method for the large scale multi-user (MU)

MIMO system in this paper. It is veriﬁed that the proposed

DOA estimation method can obtain a better performance than the

existing methods with a much lower computational complexity.

Keywords—Large scale, multi-user, MIMO, DOA estimation.

I. INTRODUCTION

Large scale MIMO technology is a powerful candidate

for the future wireless communication and many research

results have been reported in the literature [1]–[6]. It has been

conﬁrmed that large scale MIMO technology can improve the

system energy efﬁciency (EE) and spectrum efﬁciency (SE)

[7]–[9], which is highly desirable to make a better use of the

limited power and bandwidth. Note that, in a massive MIMO

system, the antenna array elements are densely placed and the

distance between the neighboring antennas is usually less than

half of the wavelength of the signal carrier [10]. Therefore,

the channel fading on each antenna is characterized by the

correlation which depends on the array placement as well as

the direction of arrival (DOA) of the signal waveform [11].

Large scale MIMO can provide great diversity gain, how-

ever, its performance will be limited by the accuracy of

the channel estimator, especially, the accuracy of the DOA

estimator. Study on the DOA estimation has a long histo-

ry. The existing methods for DOA estimation include the

maximum likelihood estimation method [12], the weighted

subspace ﬁtting method [13], multiple signal classiﬁcation

(MUSIC) method [14] and the estimation of signal parameters

via rotational invariance technique (ESPRIT) [15]. Among

these algorithms, the ESPRIT is so far the best since it has

the same accuracy as the MUSIC method but with a much

lower computational complexity. However, the performance

of ESPRIT degrades rapidly as the number of parameters to

be estimated increases. In addition, in the large scale MIMO

system, the ESPRIT also suffers from the high computational

complexity.

In this paper, the DOA estimation problem in the large scale

MU MIMO system is considered. It is assumed that correlation

exists between the neighboring antennas due to the limited

space [16]. Based on the assumption of correlated antennas,

we propose a correlation based DOA estimation method. It

is proved that our proposed DOA estimator is a unbiased

estimator. Numerical results show that, compared with the

ESPRIT, the proposed DOA estimation method has a better

performance and a lower computational complexity, especially

when a large number of antennas are used.

The rest of the paper is organized as follows. The large

scale MU MIMO system model is given in Section II. In

Section III, we brieﬂy introduce the traditional ESPRIT DOA

estimation and then propose the correlation based DOA esti-

mation method in Section IV. The performance of the proposed

DOA estimation method is analyzed in Section V. Numerical

results are presented in Section VI, and ﬁnally the paper is

concluded in Section VII.

II. SYSTEM MODEL

A. Large scale MU MIMO

In this paper, the uplink transmission in a large scale MU

MIMO system is considered. In the large scale MU MIMO

system, a large number of antennas at the base station (BS)

serve a much smaller number of users. It is assumed that there

are M antennas at the BS and the number of single-antenna

users is K where M ≫ K, as shown in Fig. 1. It is also

assumed that the distance between the neighboring antennas

is less than the half wavelength of the carrier. As a result, the

channel fadings between each user and the antennas at the BS

are correlated.

At time t, the baseband equivalent received signal at the

BS is given as

Y(t) = HS + W(t), (1)

where Y(t) ∈ C

M×K

is the received signal vector, S ∈ C

K×K

is the pilot signal vector, H ∈ C

M×K

represents the channel

matrix, and W(t) ∈ C

M×K

is the independent and identically

distributed additive noise, its elements follows the Gaussian

distribution with zero mean and σ

variance. Note that, this

model is general for single-antenna users as well as the users

with multiple antennas. In the case of multiple-antenna users,

K would be the total number of antennas of all the active

users.

B. DOA Model

The signal waveform of one user often arrives at the BS

antennas from a given range of angles or beamwidth, as shown

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