# Information–Theoretic Radar Waveform Design under the SINR Constraint

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## Abstract

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## 1. Introduction

- (1)
- Based on the nonnegativity of relative entropy, a model constraint relationship between the MI, the KLD, and the SINR is established in the frequency domain. It may be inferred that the maximum MI value range is bounded by SINR, and the maximum KLD value range is between 0 and the J-divergence value.
- (2)
- The effect of the SINR value range on maximizing MI and KLD under the energy constraint is derived, which is considered in the presence or absence of clutter, respectively.
- (3)
- Under the constraints of energy and SINR, a radar waveform optimal method based on maximizing MI and maximizing KLD is proposed.

## 2. Signal Model

## 3. A Relationship among the MI, KLD, and SINR

#### 3.1. MI and KLD Value Range

#### 3.2. Constraints between the MI and KLD with SINR

## 4. Information–Theoretic Optimal Radar Waveform Design

#### 4.1. SINR Constraint Formulation

#### 4.2. Waveform Design Using Mutual Information

#### 4.2.1. Without SINR Constraints

#### 4.2.2. With SINR Constraints

#### 4.3. Waveform Design Using Relative Entropy

#### 4.3.1. Without SINR Constraints

#### 4.3.2. With SINR Constraints

#### 4.4. SINR Value Range

## 5. Simulation and Results

#### 5.1. MI-Based Waveform and Value Range

#### 5.2. KLD-Based Waveform and Value Range

#### 5.3. Comparison of Detection Performance

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The maximum mutual information (MI) value versus signal-to-interference-plus-noise ratio (SINR) in the presence or absence of clutter.

**Figure 3.**The maximum Kullback–Leibler divergence (KLD) value versus SINR in the presence or absence of clutter.

**Figure 5.**Detection probability curves corresponding to optimal waveforms and linear frequency modulated (LFM) waveforms.

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**MDPI and ACS Style**

Xiao, Y.; Deng, Z.; Wu, T.
Information–Theoretic Radar Waveform Design under the SINR Constraint. *Entropy* **2020**, *22*, 1182.
https://doi.org/10.3390/e22101182

**AMA Style**

Xiao Y, Deng Z, Wu T.
Information–Theoretic Radar Waveform Design under the SINR Constraint. *Entropy*. 2020; 22(10):1182.
https://doi.org/10.3390/e22101182

**Chicago/Turabian Style**

Xiao, Yu, Zhenghong Deng, and Tao Wu.
2020. "Information–Theoretic Radar Waveform Design under the SINR Constraint" *Entropy* 22, no. 10: 1182.
https://doi.org/10.3390/e22101182