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According to the Tag application with function of covert communication, a method for sparse frequency waveform design based on radar-embedded communication is proposed. Firstly, sparse frequency waveforms are designed based on power spectral density fitting and quasi-Newton method. Secondly, the eigenvalue decomposition of the sparse frequency waveform sequence is used to get the dominant space. Finally the communication waveforms are designed through the projection of orthogonal pseudorandom vectors in the vertical subspace. Compared with the linear frequency modulation waveform, the sparse frequency waveform can further improve the bandwidth occupation of communication signals, thus achieving higher communication rate. A certain correlation exists between the reciprocally orthogonal communication signals samples and the sparse frequency waveform, which guarantees the low SER (signal error rate) and LPI (low probability of intercept). The simulation results verify the effectiveness of this method.

The purpose of general radar-communication integration design is to achieve high bandwidth data communications between radar platforms by using radar transmitter/receiver subsystem. Different from former methods, Blunt proposed a method of intrapulse radar-embedded communication applied to the Tag [

Radar-embedded communications applied to the Tag.

Researches of intrapulse radar-embedded communications in [

Sparse frequency waveform design is an important research direction of the radar waveform design. For the radar system, sparse frequency waveforms have advantages of suppressing interference and improving detection performance. To design a specific sparse frequency waveform, power spectral density fitting can be used to get the objective function [

The Tag device in detection range of pulse radar receives radar signals and embeds communication signals by remodulation. Then the output signals are mixed with echo of surrounding scene and return to the radar receiver. The received signals can be expressed as

To ensure the concealment (low probability of intercept) of communication signals, the power of

As communication receiving is relatively simple (embedding only one of

The maximum likelihood receiver of formula (

A sparse frequency waveform with specific passband and stopband could be obtained by power spectrum fitting. Given the distribution of power spectral density

The objective function (

The objective function (

The derivative with respect to

Specific iterative steps of sparse frequency waveform design are as follows.

Initialize

Set the search direction

If

Calculate

Set an appropriate value of

First of all, the eigenvalue decomposition of the sparse frequency waveform sequence designed is used to get the dominant space. Then

Set the length of sparse frequency radar waveform sequence

After the eigenvalue decomposition of

A sequence will be obtained if the eigenvalues are sorted in ascending order and it clearly exhibits a demarcation that the large eigenvalues in the sequence correspond to the passband while small eigenvalues correspond to the stopband. Assuming that the space spanned by eigenvectors corresponding to the first

First of all, generate a set of

Then the second communication sample can be designed as

An important indicator of covert communication is interception [

Then, normalized correlation of the

Set the length of the sparse frequency radar waveform sequence

Power spectral density of radar waveform after communication signal

As the sparse frequency waveforms have been obtained, communication waveforms can be designed through the method discussed in Section

Sparse frequency radar waveform in time domain. (a) The real part before

Figures

After obtaining the radar-embedded communication waveforms, we can further analyze the SER with the variation of SNR. This design method contains

Error rate after communication signal

As is shown, when the SNR is −8 dB, SER can achieve 10^{−3} by using a decorrelator receiver, far less than that of the intercept receiver. It demonstrates that the communication waveform has good concealment. Figure

The interception of communication waveforms is further analyzed. Set the SNR to −15 dB. While calculating the normalized correlation, the number of large eigenvalues of the intercept receiver

Normalized correlation curve by computation of waveform

In Figure

The impact of embedded communication signals into radar signal by autocorrelation function is further analyzed. Figure

ACF of sparse frequency radar-embedded communication waveform. (a) Before

It can be seen that the autocorrelation performances are similar before or after the communication waveform

In this paper, we propose the sparse frequency waveform design based on radar-embedded communication to improve the performance of the existing radar Tag system with the function of covert communication. Firstly, sparse frequency waveforms are designed based on power spectral density fitting with the quasi-Newton method and the eigenvalue decomposition is used to get the dominant space of the waveform sequence. Secondly, the communication waveforms are designed through the projection of orthogonal pseudorandom vectors in the nondominant subspace. In the end, we analyze the error rate and the interception of sparse frequency waveform in which communication waveform samples are embedded under different SNR conditions in simulation. The result shows that using sparse frequency waveform can improve the bandwidth occupation of communication signals. Thus, a higher communication rate can be gained. Furthermore, these samples are orthogonal to each other, which guarantees low SER and LPI. It is also verified that the autocorrelation performance of radar signals would not be degraded by embedding communication signals.

The authors declare that they have no competing interests.

This work was supported by the National Natural Science Foundation of China (Grant no. 61471019).