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Radar sensor networks, including bi- and multi-static radars, provide several operational advantages, like reduced vulnerability, good system flexibility and an increased radar cross-section. However, radar-to-radar interference suppression is a major problem in distributed radar sensor networks. In this paper, we present a cross-matched filtering-based radar-to-radar interference suppression algorithm. This algorithm first uses an iterative filtering algorithm to suppress the radar-to-radar interferences and, then, separately matched filtering for each radar. Besides the detailed algorithm derivation, extensive numerical simulation examples are performed with the down-chirp and up-chirp waveforms, partially overlapped or inverse chirp rate linearly frequency modulation (LFM) waveforms and orthogonal frequency division multiplexing (ODFM) chirp diverse waveforms. The effectiveness of the algorithm is verified by the simulation results.

In recent years, radar sensor networks, including bi- and multi-static radars, have received much attention [

However, besides the time, phase and antenna synchronization [

There exists several interference suppression methods that are reported to have good performance [

An amplitude limiting algorithm is proposed in [

As shown in

Although directional beamforming can be steered towards the direction of the desired signal to reduce interferences, the desired radar will receive other radars’ returns from its antenna main beam and sidelobes. The signals received by the _{m}_{m,n}_{m,n}

In typical radars, the overlapped returns expressed in ^{*} being the conjugate operator to extract the returns associated with the first radar signal, _{1}(_{1,n}_{1}(_{1,n}) ⊗ _{1}(_{1}(

If the waveforms used in the radar sensor network are perfectly orthogonal, then:

In distributed radar sensor networks, a conventional matched filtering algorithm may be significantly impacted by the radar-to-radar interferences, due to imperfect waveform orthogonality. To resolve this problem, we present an iterative suppression algorithm based on the cross-filtering idea discussed in [

For simplicity and without loss of generality, the additive noise, namely _{1}(_{2}(_{2}(_{2,1} _{2}(_{2,1}) ⊗ _{2}(_{2}(

The interferences can be removed by a specific filter, the impulse response function, _{1,2}(

Using this specific filter, we can get:

Fourier transforming with respect to the variable, _{1,2}_{f}_{1}(_{1,1}), _{2}(_{m}_{m,1}) denote, respectively, the Fourier transforming representations of the _{1,2f} (_{1}(_{1,1}), _{2}(_{m}_{m,1}), with _{1,1} and _{m,1} being the frequency shifts associated with the time shifts, _{1,1} and _{3,1}. The above equation can be further filtered by an inverse filter in the frequency domain with the transfer function, 1/_{2}(_{2}(

In the same manner, we further match filtered _{1,2}_{i}_{3}(_{3}(_{3}(_{3}(

It is further filtered by a filter in the frequency domain with the transfer function, 1/_{3}(

It can be noticed that the interferences of the second and third radars corresponding to the second and third transmitted waveforms have been suppressed at this step. The remaining interferences associated with other radars can be suppressed by iteratively applying the above suppression algorithm. In doing so, we then have:

It is necessary to further investigate the interference suppression performance. Suppose we want to extract the returns associated with the _{m}_{m}_{m}

To evaluate the quantitative performance of the radar-to-radar interference suppression algorithm for distributed radar sensor networks, we performed several numerical simulations with different radar waveforms.

To reduce radar-to-radar interferences, each radar in the distributed radar sensor networks should transmit a unique waveform, orthogonal to the waveforms transmitted by other radars. We simulate first the down-chirp and up-chirp waveforms, which are the most practical orthogonal waveforms in radar society. Suppose the two radars in the network use, respectively, the down-chirp and up-chirp waveforms (see _{s1} = 100 MHz, _{s2} = 0 Hz, equal chirp bandwidth _{r}_{p}

Although the down-chirp and up-chirp waveforms have good orthogonality, they offer only two orthogonal waveforms. We concluded in [

Consider the following parameters: _{s1} = 50 MHz, _{s2} = 0 Hz, _{s3} = 100 MHz, equal chirp bandwidth _{r}_{p}

Orthogonal frequency division multiplexing (OFDM) is also a popular choice for distributed radar sensor networks, because OFDM offers advantages, such as robustness against multipath fading and relatively simple synchronization processing. OFDM-like waveforms have been shown to be suitable for radar applications [

Due to the operational advantages, like reduced vulnerability, good system flexibility and increased radar cross-section, distributed radar sensor networks have received much attention in recent years. However, radar-to-radar interference is a major problem in radar sensor networks. In this paper, we propose an iterative radar-to-radar interference suppression algorithm based on the cross-matched filtering for distributed radar sensor networks. After analyzing the impacts of radar-to-radar interferences in distributed radar sensor networks, we derived the radar-to-radar interference suppression algorithm. This algorithm can be iteratively processed to suppress the radar-to-radar interferences one by one. We performed extensive numerical simulations with different waveforms that can be used in distributed radar sensor networks, such as down-chirp and up-chirp waveforms, the partially overlapped or inverse chirp rate LFM waveform and the OFDM chirp diverse waveform. The effectiveness of the proposed suppression algorithm is verified by simulation results. Note that the suppression algorithm is also suitable for other waveforms, e.g., polyphase code and noise waveform, not just the waveforms discussed in this paper, because no specific assumptions on the waveforms are assumed in deriving the algorithm.

This work was supported in part by the National Natural Science Foundation of China under grant No. 41101317, the Program for New Century Excellent Talents in University under grant No. NCET-12-0095, the Program for Distinguished Young Scholars in Sichuan Province under grant No. 2013JQ0003 and the Program for Young Scholars of Distinction of UESTC.

The authors have equal contributions to this paper.

The authors declare no conflicts of interest.

The radar-to-radar interferences in a distributed radar sensor network.

Block diagram of the interference suppression algorithm.

Illustration of down-chirp and up-chirp waveforms.

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

Result of the interference suppression ratio.

Illustration of three waveforms with overlapped frequency.

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

Result of the interference suppression ratio.

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

Comparative pulse compression results for two radars using the OFDM chirp diverse waveforms: (

Result of the interference suppression ratio.