# Radar-to-Radar Interference Suppression for Distributed Radar Sensor Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Radar-to-Radar Interference Suppression

#### 2.1. Radar-to-Radar Interference

_{m}(t) is waveform transmitted by the m-th transmitting radar, α

_{m,n}is the channel coefficient for the m-th transmitting radar and the n-th receiving radar, τ

_{m,n}is the time for the signal propagating from the m-th transmitting antenna to the n-th receiving antenna and n(t) is the additive noise (no statistical assumptions are made on the characteristics of the noise at this time other than being independent of the radar returns).

^{*}being the conjugate operator to extract the returns associated with the first radar signal, s

_{1}(t), in the n-th radar:

_{1,n}s

_{1}(t − τ

_{1,n}) ⊗ h

_{1}(t) is the desired matched filtering output, n(t)⊗h

_{1}(t) is the unavoidable output associated with various system noise and ${\sum}_{m=2}^{M}{\alpha}_{m,n}\hspace{0.17em}{s}_{m}(t-{\tau}_{m,n})\otimes {h}_{1}(t)$ is just the radar-to-radar interferences that we want to suppress in this paper.

#### 2.2. Iterative Suppression Algorithm

_{1}(t) from the mixed multiple radar returns, we firstly match filtered the returns to the second radar signal, s

_{2}(t):

_{2}(t). Obviously, the first term α

_{2,1}s

_{2}(t − τ

_{2,1}) ⊗ h

_{2}(t) will have peaks, because it is the matched filtering results associated with the second radar signal, s

_{2}(t), and the remaining terms are the interferences coming from other radars.

_{1,2}(t), is greater than the decision threshold, δ, the signal components that are greater than the threshold will be equal to zero. That is to say, we do not need to know the expression of the impulse response, h(t). Therefore, it is not necessary to derive the impulse response function, h(t). The selection of the decision threshold, δ, is conceptually similar to that of stop-band attention in the classic bandpass filter design [34]. In this paper, the decision threshold is adaptively determined by the mean of the matched filtering output. That is:

_{1,2}

_{f}(ω), S

_{1}(ω − ω

_{1,1}), H

_{2}(ω) and S

_{m}(ω − ω

_{m,1}) denote, respectively, the Fourier transforming representations of the Y

_{1,2f}(t), s

_{1}(t − τ

_{1,1}), h

_{2}(t) and s

_{m}(t − τ

_{m,1}), with ω

_{1,1}and ω

_{m,1}being the frequency shifts associated with the time shifts, τ

_{1,1}and τ

_{3,1}. The above equation can be further filtered by an inverse filter in the frequency domain with the transfer function, 1/H

_{2}(ω)[27]:

_{2}(t), have been suppressed at this step.

_{1,2}

_{i}(t) to the third radar signal, s

_{3}(t):

_{3}(t). Similarly, the second term can be removed by the specific filter, h(t):

_{3}(ω) is the Fourier transforming representation of h

_{3}(t).

_{3}(ω):

#### 2.3. Interference Suppression Ratio

_{m}(t). The corresponding matched filtering result without employing the interference suppression algorithm is:

_{m}(t) is the matched filtering reference function for the first radar signal, s

_{m}(t). In contrast, when the interference suppression method is employed, according to (17) and (18), the final matched filtering result for the first radar will be:

## 3. Numerical Simulation Examples

#### Example 1: Two Radars Using the Down-Chirp and Up-Chirp Waveforms

_{s1}= 100 MHz, f

_{s2}= 0 Hz, equal chirp bandwidth B

_{r}= 100 MHz and equal chirp duration T

_{p}= 10 μs. Figure 4 shows the comparative pulse compression processing results, where we want to extract the first radar’s returns and suppress the mutual interference of the second radar. It can be noticed that the radar-to-radar interferences have been significantly suppressed by the interference suppression algorithm. Figure 5 gives the simulated interference suppression ratio. The interference levels have been suppressed at least by 20 dB. This improvement factor is important for detecting weak targets; otherwise, some weak targets will be submerged in the sidelobes and cannot be successfully detected by the radar processor.

#### Example 2: Three Radars Using the Partially Overlapped or Inverse Chirp Rate Waveforms

_{s1}= 50 MHz, f

_{s2}= 0 Hz, f

_{s3}= 100 MHz, equal chirp bandwidth B

_{r}= 100 MHz and equal chirp duration T

_{p}= 10 μs; Figure 7 shows the comparative pulse compression results, where we want to extract the first radar’s returns. The returns associated with the second and third signals are undesired radar-to-radar interferences. It can be noticed from Figure 7a that there are unacceptable large sidelobes due to the interferences coming from the second and third radars. After suppressing the second radar signals with the proposed algorithm, it can be noticed from Figure 7c that the sidelobes are significantly reduced, but there still are high sidelobes in the two sides. It can be noticed from Figure 7d that these high sidelobes are further reduced after suppressing the mutual interferences associated with the third radar. It can be noticed from the interference suppression ratio shown in Figure 8 that the mutual interferences have been suppressed by about 20 dB.

#### Example 3: Two Radars Using the OFDM Chirp Waveforms

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 4.**Comparative pulse compression results for the two radars with down-chirp and up-chirp waveforms. (

**a**) Ideal result and mutual interference; (

**b**) pulse compression using the second waveform as the reference function; (

**c**) after being processed by the iterative suppression algorithm; (

**d**) final matched filtering results for the first radar.

**Figure 7.**Comparative pulse compression results for the three radars with partially overlapped frequency or inverse chirp rate waveforms. (

**a**) Ideal result and mutual interference; (

**b**) after being pulse compressed by using the second waveform as the reference function and processed by the specific filter; (

**c**) pulse compression after suppressing the second interference; (

**d**) final matched filtering result for the first radar.

**Figure 9.**Illustration of orthogonal frequency division multiplexing (OFDM) chirp diverse waveforms.

**Figure 10.**Comparative pulse compression results for two radars using the OFDM chirp diverse waveforms: (

**a**) without applying the mutual interference suppression algorithm; (

**b**) with applying the mutual interference suppression algorithm.

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Wang, W.-Q.; Shao, H. Radar-to-Radar Interference Suppression for Distributed Radar Sensor Networks. *Remote Sens.* **2014**, *6*, 740-755.
https://doi.org/10.3390/rs6010740

**AMA Style**

Wang W-Q, Shao H. Radar-to-Radar Interference Suppression for Distributed Radar Sensor Networks. *Remote Sensing*. 2014; 6(1):740-755.
https://doi.org/10.3390/rs6010740

**Chicago/Turabian Style**

Wang, Wen-Qin, and Huaizong Shao. 2014. "Radar-to-Radar Interference Suppression for Distributed Radar Sensor Networks" *Remote Sensing* 6, no. 1: 740-755.
https://doi.org/10.3390/rs6010740