全色MIMO雷达波形的Toeplitz矩阵设计：SINR优化关键

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本文探讨了在全色MIMO雷达系统中，通过优化波形传输协方差矩阵（Transmit Covariance Matrix, TCM）来最大化信号与干扰加噪声比（Signal-to-Interference-and-Noise Ratio, SINR）。作者Wei Xiong、Maria Greco、Fulvio Gini和Gong Zhang等人来自南京航空航天大学和意大利比萨大学的研究团队，他们的研究集中在利用对称Toeplitz矩阵形式的TCM设计，这种结构具有以下关键特性： 1. **Toeplitz矩阵的优势**：Toeplitz矩阵以其在频域中的局部相关性而闻名，这在MIMO雷达中特别有价值。通过这种结构，波形的多样性得以充分挖掘，有助于减少多个发射通道之间的互调干扰，从而提高系统的整体性能。 2. **全色MIMO雷达**：全色意味着雷达能够同时发送多种波长或频率的信号，这增加了探测范围和目标识别能力。在 colocated MIMO配置下，所有天线元素共用一个或多个发射波形，这样可以有效利用空间多径效应。 3. **SINR最大化目标**：研究的核心是设计TCM以最大化SINR，这是决定雷达性能的关键指标。通过控制波形的功率分布和相位关系，可以有效地抑制干扰，提高接收信号的质量，尤其是在复杂环境中。 4. **矩阵的构造**：提出的TCM R采用对称Toeplitz矩阵形式，确保了矩阵的秩，这意味着它具有足够的自由度来调整波形，同时保持信号的多样性，这对于抑制干扰至关重要。 5. **干扰抑制策略**：通过设计合理的Toeplitz结构，能够在不牺牲波形多样性的情况下，最大程度地抑制最大数量的干扰源，这对于在高干扰环境下保持雷达性能至关重要。总结来说，这篇研究论文提出了一种创新的TCM设计方法，结合了MIMO雷达的波形多样性优势和Toeplitz矩阵的结构特性，旨在通过优化波形传输来提升全色MIMO雷达的SINR，从而增强其抗干扰能力和目标检测性能。作者们强调了这种技术对于现代雷达系统在复杂电磁环境中的实用性，并展示了其在干扰抑制和性能优化方面的潜力。

TOEPLITZ MATRIX-BASED TRANSMIT COVARIANCE MATRIX OF COLOCATED

MIMO RADAR WAVEFORMS FOR SINR MAXIMIZATION

Wei Xiong

, Maria Greco

, Fulvio Gini

, Gong Zhang

, Zhenni Peng

1 Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing

University of Aeronautics and Astronautics, Nanjing 211106, China

2 Dipartimento di Ingegneria dell’ Informazione, University of Pisa, Pisa 56122, Italy

3 Key Laboratory of Advanced Technology for Small and Medium-sized UAV, Ministry of Industry and

Information Technology, Nanjing 210016, China

Emails: wxiong_nuaa@sina.com; m.greco@iet.unipi.it; f.gini@ing.unipi.it; gzhang@nuaa.edu.cn

ABSTRACT

Focusing on the signal-to interference-plus-noise ratio

(SINR) maximization in colocated multiple-input multiple-

output (MIMO) radars, using the covariance matrix design

of transmitted waveforms, we propose a kind of transmit

covariance matrix (TCM)

with the form of symmetrical

Toeplitz matrix, whose full rank characteristic firstly can

sufficiently exploit the waveform diversity advantage of

MIMO radar to further suppress the maximum number of

interfering sources. Meanwhile, the positive semi-definition

characteristic of

 

sin 2



guarantees that these TCMs

can be synthesized with binary phase shift keying (BPSK)

waveforms in closed form. Furthermore, employing certain

proposed TCM, higher SINR level can be yielded, and

lower sidelobe levels (SLLs) can be obtained for the

unwanted sidelobe interference suppression. Simulation

results validate the better performance of our proposed

TCMs in comparison with the phased array, omnidirectional

MIMO radar and the recently proposed TCMs.

Index Terms—colocated MIMO radar, transmit

covariance matrix, Toeplitz matrix, SINR maximization

1. INTRODUCTION



For the multiple-input multiple-output (MIMO) radar,

waveform design always is one of the most important issues

[1-14], which generally can be classified into the direct or

indirect methods. In the direct design approaches [1-6], the

transmitted signal symbols are directly calculated and some



W. Xiong’s work was supported by the National Natural Science

Foundation of China under grants 61471191, 61501233, 61671241 and

61501228, Aeronautical Science Foundation of China under grant

20152052026, the Funding of Jiangsu Innovation Program for Graduate

Education under grant KYZZ16_0169, the Fundamental Research Funds

for the Central University under grant 3082017NP2017421, the Base

Research Foundation under grant NS2015040 and also funded by the

Natural Science Foundation of Jiangsu under grant BK20140825 .

special waveform characteristics must be considered to be

satisfied, such as orthogonality, low peak-to-average power

ratio, constant modulus, similarity constraints and so on [6].

However, due to the flexibility and lower system design

complexity, the indirect MIMO waveform design has

recently received much attention [7-13], where the transmit

covariance matrix (TCM) R of the transmitted signals is

first designed, and then the transmitted waveform symbols

are generated. As shown in [7][8], for a given positive semi-

definite R, binary phase shift keying (BPSK) waveforms

can be synthesized to realize R in closed form. Focusing on

the TCM-based waveform design, some methods have been

proposed [9-13]. In [9], a TCM R

using a cosine Toeplitz

matrix is presented and yield gains in SINR level. Though

the sidelobe levels (SLLs) of receive beampattern using R

are lower, the rank of R

is only 2, that is, the most

important degree of freedom (DOF) advantage cannot be

exploited for the interference suppression. Moreover,

 

sin 2



is not positive semi-definite [9][10], which

cannot guarantee to synthesize R

with BPSK in closed

form. Considering the full-rank constraint of R and positive

semi-definition of

 

sin 2



, two Toeplitz matrices

and

are proposed as TCMs to achieve higher SINR

levels in [10], however, the full rank property of these two

TCMs is not proofed rigorously and the achieved SINR is

not the optimum with the prior knowledge of locations.

In this paper, we have extended the two matrices in [10]

to a kind of more general symmetrical Toeplitz matrix

as the TCMs, where

 

0 3 1

t t

m M M  

is the control

parameter and

M 

denotes the number of transmit

antennas. It is demonstrated that

is full-ranked and

 

sin 2



is also positive semi-definite. Moreover,

the

with smaller m yields higher SINR level, and even

gets closed to the one of phased array. While the

with

certain larger m (e.g. m =1.5 or 2) could obtain the receive

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