4-D极化MUSIC算法性能分析与应用

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"4-D快速极化MUSIC算法分析——一种利用信号极化状态增强DOA估计性能的方法" 在无线通信和雷达系统中，方向-of-arrival (DOA) 的估计是一项关键技术，它对于信号源定位、多径效应的抑制以及通信系统的性能优化具有重要意义。4-D快速极化MUSIC（Multiple Signal Classification）算法是一种针对极化信号的DOA估计方法，其核心在于充分利用信号的极化特性来提升分辨率和估计精度，同时保持相对较低的计算复杂度。传统的MUSIC算法基于噪声子空间理论，通过对数据矩阵进行特征分解来估计DOA。然而，这种算法对于处理极化信号的性能有限，无法充分利用极化信息。4-D快速极化MUSIC算法则在此基础上进行了改进，将信号的四维极化状态（幅度、相位、偏振方向和极化角）纳入考虑，从而在高分辨率估计近邻信号源方向时表现出更优的性能。该文深入分析了4-D快速极化MUSIC算法在以下三个方面的主要特点： 1. **估计精度**：通过结合极化信息，该算法能够提高DOA估计的精度。在模拟实验中，它展现出对弱信号和紧密信号源的精确检测能力，降低了因近邻信号干扰而导致的估计误差。 2. **分辨率**：4-D快速极化MUSIC算法显著提升了信号分辨率，尤其是在信号密度高、各信号源之间角度接近的情况下。这使得在复杂的电磁环境中，算法也能有效地分辨出多个信号源。 3. **计算复杂性**：尽管增加了极化维度，但算法的计算复杂性仍然保持在可接受范围内。通过对算法步骤的优化，减少了不必要的计算，确保了实时性和实用性。文章通过仿真结果验证了这些分析，展示了4-D快速极化MUSIC算法在不同场景下的表现，并与传统MUSIC算法和其他极化DOA估计方法进行了比较。这些模拟实验不仅证实了算法的优越性，也为实际应用提供了理论依据。 4-D快速极化MUSIC算法是极化DOA估计领域的一个重要进展，它有效地结合了信号的极化特性，提高了估计性能，特别是在处理紧密信号源时的分辨率和精度，而计算复杂性的控制使其在实际系统中具有较高的应用价值。这一算法对于无线通信、雷达探测等领域的研究和发展具有重要的参考意义。

Analysis for 4-D Fast Polarization MUSIC Algorithm

Guo Ran, Mao Xing-peng, Li Shao-bin, Lin Zhi-min, Deng Wei-bo, Jiang Peng

School of Electronics and Information Engineering

Harbin Institute of Technology

Harbin, Heilongjiang Province, China

mxp@hit.edu.cn

Abstract—Fast Polarization MUSIC is an algorithm which

can utilize the advantage of the signals polarization state to

estimate their directions. Its capacity in resolving close signals is

considerably enhanced, with acceptable computation complexity.

In this paper, analysis of this algorithm's performance in

estimation precision, resolution of close signals and computation

complexity are presented. Relating simulations are also provided.

I. INTRODUCTION

The estimation of the direction of arrivals (DOA) is of

great importance in various fields. Many algorithms have been

devised, and a class known as noise subspace algorithms are

being most widely studied, for their excellent performance and

acceptable computation complexity. These include multiple

emitter location and signal parameter estimation (MUSIC) [1],

estimation of signal parameters via rotational invariance

techniques (ESPRIT)[2], and some other algorithms.

However, in applications, the space for the array are often

limited, so ESPRIT which must exert on a uniform linear

array (ULA), usually cannot be adopted. As the resolution of

MUSIC largely depends on the aperture of arrays, small arrays

may well fail to resolve close signals. To obtain better

resolution, we need assistance from somewhere else. The

polarization diversity of signals have been utilized to separate

them in radar system, and is also expected to enhance the

resolution of noise subspace algorithms. In [3], [4], Jian Li

managed to embed ESPRIT algorithm in polarization sensitive

ULA. But to explore polarization in MUSIC, which provides

estimation for both azimuth and elevation, a 4-D peak search

is required, which incurs vast amount of computation.

Reference [8] proposed a fast algorithm, called 4-D Fast

Polarization MUSIC (FP-MUSIC) here. It reduces the amount

of calculation considerably, while still benefits from the

polarization. In this article, we offer the analysis on its

performance. In the simulation, the performance of FP-

MUSIC is compared with that of conventional MUSIC.

II. B

ASIC PRINCIPLE OF MUSIC AND FP-MUSIC

Consider an array consists of

non-polarization-

sensitive sensors.

narrow-band signals of the same central

frequency arrive from various directions. The output is:

() () ()

ttt=+XASN

(1)

The covariance matrix of

()

iii

∑

Ree

(2)

Here

is the ith eigen value of

, which is arranged as

1+1

NMn

λλλσ

≥⋅⋅⋅≥ ⋅⋅⋅ =

, and

is the power of the white

noise.

is the corresponding eigen vector of

. In MUSIC,

the space spectrum is defined as follows:

=+1

1=1

P =

∑

ae aU

(3)

The token

•

denotes the Frobenius norm, and

()

, ,...,

=Ueee

()

, ,...,

NNN M++

=Uee e

(4)

The vector

is called steering vector. In the conventional

MUSIC algorithm, only the direction parameters, such as the

azimuth

and the elevation

, are involved in

. A peak

search through

and

will locate directions of the arrivals.

To enhance the performance in resolution, the polarization

sensitive array can be adopted. Here we use the polarization

angle

and polarization phase difference

to determine the

signals' polarization state, and the steering vector becomes

()()()

iiii P i iii S ii

,, ,,, ,

ϕγ

ηθ

ϕγ

ηθ

=⊗aa a

(5)

where

⊗

means the Kronecker product. The column vector

()

Sii

is the component of spatial direction and the effect

of polarization is manifested in the vector

()

Piiii

ϕγ

Using the

()

iiii

ϕγ

in expression (5) to substitute the

steering vector

in expression (3), a new form of joint space

spectrum will be obtained, which can be written as

() ()

,,, 1 ,,,

JSPN

θϕγη θϕγη

= aU

(6)

Theoretically, by the positions of the 'peaks' in

()

,,,

ϕγ

, the direction and polarization parameters of the

arrivals can be estimated. A straightforward method is to exert

a 4-D search through the ranges of all parameters, which is,

however, extremely computation exhaustive.

To reduce the amount of calculation, the geometric

characters of

()

,,,

ϕγ

need to be studied. Its expression is:

()() ()

,,, ,,, ,,,

PZ MU

θϕγη θϕγη θϕγη

−

==−

⎡⎤

⎣⎦

(7)

Here

()

,,,Z

ϕγ

is called zero spectrum, and

This project is sponsored by the National Natural Science Foundation o

China (No. 61171180 and No.61001093), and Natural Scientific Researc

Innovation Foundation in Harbin Institute of Technology (HIT.

SRIF.2011117).

2013 IEEE Radar Conference (RadarCon13)

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