L形阵列二维DOA估计：解决匹配与估计问题

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"这篇文献是IEEE Transactions on Antennas and Propagation杂志上发表的一篇关于L形阵列的二维到达角度（DOA）估计的文章，作者是Nizar Tayem和Hyuck M. Kwon。文章详细探讨了利用传播者方法（Propagator Method, PM）解决二维DOA估计的问题，并着重解决了PM在平行阵列中的一些显著缺点。" 在无线通信和雷达系统中，DOA估计是一项关键的技术，它用于确定信号源相对于接收阵列的方向。L形阵列因其结构特点和性能优势，在二维DOA估计中得到了广泛应用。文献指出，与MUSIC（Multiple Signal Classification）和ESPRIT（Estimation of Signal Parameters via Rotational Invariance Techniques）等其他算法相比，PM的计算负载显著较低，因为它不需要进行交叉相关矩阵的特征值分解（EVD）或接收到的数据的奇异值分解（SVD）。然而，PM在平行阵列中的应用存在两个主要问题：1) 2D方位角和仰角估计之间的配对匹配需要一个耗时的穷举搜索过程；2) 当仰角处于70到90度之间时，会出现估计失败的问题。为了解决这些问题，该论文提出了一种使用一或两个L形阵列的新方法，以克服上述PM的局限性，同时不增加额外的计算负担。通过模拟结果验证，采用L形配置的PM能够有效地消除这两个问题，从而提高DOA估计的精度和可靠性。这为实际应用中，尤其是在资源有限的系统中，提供了更高效且准确的DOA估计方案。该研究对于进一步优化天线阵列设计和提高无线通信系统的性能具有重要的理论和实践意义。

1622 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 5, MAY 2005

L-Shape 2-Dimensional Arrival Angle Estimation

With Propagator Method

Nizar Tayem and Hyuck M. Kwon, Senior Member, IEEE

Abstract—It is known that computational loads of the propa-

gator method (PM) can be signiﬁcantly smaller, e.g., one or two

order, than those of MUSIC and ESPRIT because the PM does not

require any eigenvalue decomposition (EVD) of the cross-correla-

tion matrix and singular value decomposition (SVD) of the received

data. However, the PM of the parallel shape array has nonnegli-

gible drawbacks such as 1) requirement of pair matching between

the 2-D azimuth and elevation angle estimation which is an exhaus-

tive search and 2) estimation failure problems when elevation an-

gles are between 70

and 90 . The purpose of this paper is to show

a way to remove these problems in the PM without additional com-

putational loads. This paper will employ one or two L-shape arrays

because the parallel shape used in the PM may cause the aforesaid

problems. Simulation results verify that the PM with one or two

L-shape conﬁgurations can remove these problems and improve

the performance of the PM signiﬁcantly, e.g., almost 5 dB in signal

to noise ratio for the parameters used in this paper.

Index Terms—Antenna array, direction-of-arrival angle (DOA)

estimation, propagator method (PM), Smart antenna.

I. INTRODUCTION

STIMATION of two-dimensional (2-D) direction-of-ar-

rival angles (DOA) has received a signiﬁcant amount of

attention over the last several decades. It has also played an

important role in array signal processing areas such as radar,

sonar, radio astronomy, and mobile communication systems.

The most popular techniques for DOA estimations are the

classical subspace methods such as the MUSIC [1]–[4] and

ESPRIT [5]–[8] algorithms. But these algorithms employ either

the eigenvalue decomposition (EVD) of cross spectral matrix

(CSM) or singular value decomposition (SVD) of the received

data matrix (RMD). Using these techniques, the computational

complexity is costly and high especially when the number of

sources and antenna elements are large. The computational

complexity of ESPRIT can be in the order of

multiplication in calculating the eigen decomposition for a

covariance matrix with an

-element array and snapshots.

Marcos and co-workers [9]–[12] have suggested the so-called

“propagator” method (PM) for array signal processing without

any eigen decomposition. The computational load of the PM is

, where is the number of incident sources.

Manuscript received June 10, 2004; revised October 20, 2004. This work was

supported by the U.S. Army Research Laboratory and the U.S. Army Research

Ofﬁce under the Grant DAAD19-01-10537.

The authors are with the Department of Electrical and Computer Engineering,

Wichita State University, Wichita, KS 67260-0044 USA (e-mail: natayem@wi-

chita.edu; hyuck.kwon@wichita.edu).

Digital Object Identiﬁer 10.1109/TAP.2005.846804

However, the PM of the parallel-shape array in [13] requires

pair matching between the 2-D azimuth and elevation angle esti-

mation

and can have an estimation failure

problem when

elevation angles are between 70

and 90 . The elevation angle

in typical mobile communications is in the range of 70

and

. Thus, the application of the PM of the parallel-shape array

to mobile communications should be reconsidered. The parallel

shape array used in the PM [13] may cause the aforesaid prob-

lems.

The idea of using L-shaped arrays is not new, e.g., [14]. But,

the L-shape array in our paper is different from that in [14]. In

our paper, the elements are placed on the

or axes

whereas the elements in [14] are on the

axis. In addition,

the L-shape in [[14], (10)] uses the same DOA estimation equa-

tions as the ones in [13, eq. (14)] and [15, (18)]. Therefore, the

L-shape in [14] has the same pair matching and failure problems

as the ones in [13] and [15].

The purpose of this paper is to show how to remove these

problems in the PM without additional computational loads.

This paper will employ a conﬁguration of one or two L-shape

arrays, which allow no pair matching between the azimuth angle

estimate

for source and the elevation angle estimate for

source

. In addition, using an L-shape array shows no elevation

angle estimation failure even if the elevation angle is between

and 90 . Furthermore, the one L-shape array in the

plane shows several other advantages over the parallel-shape

array but has a failure problem similar to the one in [13] when

the azimuth angle is between 0

and 20 . However, with the pro-

posed two L-shape arrays in the

and planes, we can

completely remove the failure problem and reduce the RMSE

signiﬁcantly.

Section II presents the system model and a proposed algo-

rithm, i.e., the PM with the one L-shape array conﬁguration in

the

plane. Section III presents another proposed algorithm,

i.e., the PM with two L-shape arrays in the

and planes.

Section IV shows simulation results. And Section V concludes

the paper.

II. P

ROPOSED PM W

ITH O

NE L-SHAPE ARRAY

Fig. 1(a) shows the one L-shape array conﬁguration which

uses the

plane instead of the plane used in [14]. Each

linear array consists of

elements. The element placed at

the origin is common for referencing purpose. Let

and be

the two sub-arrays of the linear array in the

axis, and let and

be the two sub-arrays of the linear array in the axis. Each

The deﬁnition of estimation failure is the event that the estimated angle is in

a complex form instead of a real. This happens when the absolute argument of

the arc-sine or arc-cosine function is greater than 1.

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