单基地MIMO雷达的高效实数域MUSIC算法：基于多项式求根与计算复杂度降低

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本文探讨了"基于实多项式求根的单基地MIMO雷达的计算有效频谱MUSIC算法"，由西北工业大学电子与信息学院的XULiqin和LIYong两位作者共同提出。该研究主要关注在单站多输入多输出（Monostatic MIMO）雷达系统中，如何提升算法的计算效率，同时保持目标方向角（Direction of Arrival, DOA）估计的精度。首先，作者提出了一种计算上高效的实值化MUSIC算法。在处理接收到的数据矩阵时，通过降维变换，有效地降低了数据的维度，这在减少计算负担的同时，保持了信号处理的有效性。传统的MUSIC算法通常依赖于复数协方差矩阵，而这篇论文将这一过程转化为一个实值操作，通过单位ary变换，将复数协方差矩阵转换为易于处理的实数矩阵。为了进一步降低算法的复杂性，作者引入了一种基于实数多项式的根寻找技术。这种方法替代了昂贵的谱搜索过程，能够快速定位与目标DOA相关的局部最大值。实多项式求根技术的优势在于它能够在保证查找精度的同时，显著减少了计算量，这对于大规模数据处理的雷达系统尤为重要。通过仿真结果，作者证实了该算法在计算效率提升的同时，对DOA估计的准确性几乎没有妥协。这表明，采用实多项式求根的计算有效频谱MUSIC算法不仅在理论上提供了优化的解决方案，而且在实际应用中也展现出了良好的性能。关键词包括：多输入多输出雷达、实多项式求根、计算效率、频谱MUSIC算法、方向角估计、降维变换和单位ary变换。这篇文章的研究成果对于推动MIMO雷达技术在实时、高效率环境下的应用具有重要意义。

Computationally effective spectral MUSIC algorithm

for monostatic MIMO radar using real

polynomial rooting

XU Liqin, LI Yong

School of Electronics and Information

Northwestern Polytechnical University

Xi’an, China

xuliqin@xupt.edu.cn, ruikel@nwpu.edu.cn

Abstract—A computationally effective real-valued variant of

multiple signal classification (MUSIC) algorithm for monostatic

multiple-input multiple-output (MIMO) radar is presented.

Reduced-dimension transformation is utilized to reduce the

dimension of the received data matrix at first, and then the

unitary transformation is employed to transform the complex

covariance matrix of the received data into a real-valued one. To

further reduce the computational complexity, a real polynomial

rooting technique is presented to determine the local maxima of

the MUSIC spectrum that corresponding to the DOAs of the

targets instead of the computationally-expensive spectrum search.

Simulations results demonstrate that the presented algorithm can

greatly reduce the computational complexity without sacrificing

the estimation accuracy.

Keywords—multiple input multiple output (MIMO) radar;

direction of arrival (DOA) estimation ; multiple signal classification

(MUSIC)

I. I

NTRODUCTION

Multiple-input multiple-output (MIMO) radar transmits

mutually orthogonal waveforms by using multiple transmit

antennas and receives the reflected signals by using multiple

receive antennas

[1]

. It possesses many potential advantages

over the traditional phase-array radar, such as higher accuracy

of angle estimation, more degree of freedom and better

parameter identification performance

[2]

. Direction of arrival

(DOA) estimation, as an important issue in MIMO radar, has

attracted considerable attention and intensive research

[3-7].

Multiple signal classification (MUSIC) is a widely used high-

resolution DOA estimation algorithm. However, it requires

time-consuming two-dimensional (2-D) spatial spectrum

search to obtain the estimation of DODs and DOAs of the

targets when applied to a MIMO radar system. High accuracy

of angle estimation requires a very fine grid search, resulting in

high computational costs. Also, the computational complexity

of MUSIC increases dramatically with the number of array

sensors, which is particularly prominent in the MIMO radar

system. Many scholars dedicated to reduce the computational

complexity of MUSIC for MIMO radar

[8-13]

. In [8], a reduced-

dimensional MUSIC algorithm is proposed. It only needs 1-D

spectrum search to obtain automatically paired DODs and

DOAs. In [9] and [10], the root-MUSIC algorithm is proposed

for bistatic MIMO radar, in which polynomial root finding

technique is utilized to obtain the DOAs and DODs of the

targets, completely avoiding the computational expensive

spectrum search. However, it still has relatively high

complexity as it needs to find the roots of a high-order

complex polynomial. Reduced complexity unitary root-

MUSIC algorithm is presented in [11], in which reduced-

dimension transformation and unitary transformation are

jointly used to reduce the computational complexity. In [12], a

beamspace root-MUSIC algorithm is presented for bistatic

MIMO radar. The computational burden is relieved by

mapping the received data into lower-dimensional beamspace.

In [13], a beamspace spectral MUSIC algorithm is proposed to

reduce the computational load by using a combination of

reduced-dimension transformation and beamspace processing.

However, it needs to know the priori information about the

rough location of the targets and a 1-D spectrum search is still

required.

In this paper, we present a computationally efficient

spectral MUSIC angle estimation algorithm for monostatic

MIMO radar. The algorithm firstly utilizes reduced-dimension

transformation to transform the observed data into a lower-

dimensional space and then employs unitary transformation to

reduce the computational load in the eigen-decomposition

stage. Finally, a real polynomial rooting technique is used

instead of the expensive spectrum search to determine the

local maxima of the MUSIC spectrum. The presented

algorithm can greatly reduce the computational load without

sacrificing the accuracy of angle estimation.

II. S

IGNAL

ODEL

Consider a narrowband monostatic MIMO radar system

composed of uniform linear arrays. Assume that the

transmit antennas and

receive antennas are spaced half-

wavelength apart. At the transmitting end, transmit antennas

transmit mutually orthogonal encoded pulse signals. Assume

that there are

non-coherent targets located in the

directions

,,,

θθ θ

, respectively. Echo signals reflected by

the

targets are received by the multiple antennas in the

receiver. After matched filtering, the observed data can be

expressed as

This work was supported by the National Natural Science foundation o

China (61602377)

2182

978-1-5386-3758-6/18/$31.00

2018 IEEE

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