# Development of a digital twin for an early-warning radar system

### Abstract

### Keywords

#### For citation:

Balakin D.A., Kersky E.V. Development of a digital twin for an early-warning radar system. *Journal of «Almaz – Antey» Air and Space Defence Corporation*. 2020;(1):10-18.
https://doi.org/10.38013/2542-0542-2020-1-10-18

## Introduction

The modern pace of industry development demands fast and precise radar prototyping to enhance the development quality. This task can be accomplished using the digital twin concept. Digital twin is a binary model that simulates operation of a radar and its components in detail. Development of a radar system digital twin is an urgent task, as it allows to verify as many practical solutions as possible in minimal time and to prove them at the FEED stage. The digital twin must offer the properties of simulation modelling and answer the main question: how major operational characteristics (OC) of an article will change in various operation conditions. For instance, how to see the change in angular coordinate estimate, when each receive channel of the antenna is out of phase, or how to estimate degrading of anti-jamming algorithm when AFR of the receiver is non-linear. Prompt responses to such questions substantially save time for decision-making by the customer, chief designer or developer of the equipment.

In addition, the digital twin can be helpful to debug new radar control concepts and to promptly implement them into the standard operation mode. Besides, the digital twin makes it possible to verify new digital signal processing methods and algorithms without the presence at the test object, which substantially saves time and la- hour costs. The digital twin also enables multiple repetition of various experiments in antijamming, detection and identification of complex targets and much more.

Certainly, development of a digital twin for an early-warning radar system is a complex and labour-intensive process that may be comparable to the process of development of a real radar system in terms of time. However, the above advantages are worth the time and money spent. The article considers a simplified verification model (SVM) that is an initial approximation to the digital twin. The key advantage of an SVM is the fact that it reflects design and physical peculiarities of hardware of the early-warning radar system being developed. Design features may include: radar dimensions, general structure and type of antenna curtain, in particular, type of emitters and distance between them, switching of analogue and digital signals of transceivers, radiation pattern generation method (the digital method as applied to this model) and much more. Physical features include the parameters determined in technical specifications for analogue and digital transceivers: transmission ratios of the transceiver channel, AFR and PFR of the transceiver path, noise factor, etc. The SVM was developed in the Matrix Laboratory (MATLAB) package. Due to the elaborated mathematical tool, MATLAB is well suited to simulate not just individual radar components, but also the article as a whole. In particular, MATLAB package also includes libraries, such as Phased Array system toolbox, Antenna toolbox, DSP system toolbox and much more, to facilitate fast and precise simulation of features of the article being developed [1]. It is also worth noting that MATLAB programming language itself became a tool of communication among the scientific community all over the world [2].

From the simulation perspective, the most notable is Simulink utility that is a part of MATLAB package. Simulink enables simulation of an article and its components in a visual form. This, in turn, enables a high level of understanding of general operation principles of the radar system being developed.

Let us consider the SVM architecture.

## SVM architecture

The SVM block diagram is shown in Figure 1.

The major structural element of SVM is antenna radar complex (RC) (RC appearance is shown in Fig. 2b) that consists of both analogue transceiver modules (ATRMs) and digital transceiver modules (DTRMs). Essentially, RC is a design unit of the radar system (Fig. 2a). A set of tens or hundreds of RCs can simulate a full-fledged radar system. Therefore, based on the Simulink utility, we have developed an RC library unit (Fig. 3), that makes it possible to use it together with standard units provided for in Simulink, e. g., target, environment, and antenna and feeder device (AFD). In turn, RC is based on the ATRM and DTRM that determine physical features of radar system operation. They are also implemented in the form of library elements (Fig. 3).

It should be noted that one RC contains 64 ATRMs and 32 DTRMs, and there are about thousands of them in a full-fledged radar system. The functional diagram shows a computer system (CS) that generates control commands for model components. The CS also analyses the received status commands for functional check of the article. The computer system is an abstract element of the model, which represents a set of algorithms and methods of analysis. In particular, the CS makes it possible to generate sensing signal, to perform digital processing of received signal. The CS will be further considered in more detail. In addition to the CS and RC, the AFD unit, propagation environment unit and target unit are shown in the functional diagram. Within the framework of this article, these units will not be considered in detail, as they are implemented using standard tools of the Simulink utility. However, we provided for integration of own methods and algorithms to implement functionality of the units, in order to consider various target, environment and AFD features in more detail.

**Fig. 1**. Functional diagram of the model of the radar system consisting of one RC in the target engagement mode

**Fig. 2**. Appearance of radar system (a) and radar complex (b)

**Fig. 3**. Appearance of library base units: a - RC, b - ATRM, c - DTRM

For general understanding of SVM operation principles, let us consider Figures 4 and 5. Figure 4 shows SVM implemented using Simulink tools. It corresponds to canonical scheme [3] determined in the radar technology theory. Figure 5 discloses the RC diagram (transceiver, hardware portion of the RC, i.e. subsystem 9) in more detail as applicable to Simulink model.

**Fig. 4**. Scheme of simplified verification model generation

The signal generator generates a sensing signal (SS) in two polarizations (thus, the model has the total of 128 channels: 64 horizontal and 64 vertical), while the type and parameters of the SS are set both by standard Simulink generators and using the CS where a SS of arbitrary type can be generated. Further, the SS is received in the transmit path of the RC trough DTRM to the ATRM (in Figure 4, this is the transmitter). Propagation of the SS in DTRM and ATRM lines is provided by subsystem 6 in Figure 5. Subsystem 7 further propagates the signal from the RC transmit path to environment and target units (an interference component is included in units and modules). Then, reflected signal is received by the RC receive path (receiver in Figure 4) from ATRM to DTRM. In turn, signal propagation through the RC receive path is provided by subsystem 5. Subsystem 8 propagates the reflected signal for further analysis using the CS (signal processing).

**Fig. 5**. Radar complex divided by subsystems

Figure 5 shows 8 analogue units (corresponds to 1) and 4 digital units (corresponds to 2). Note that signals from two analogue units are received in one digital unit, and, in a similar way, outputs of the digital unit provide two analogue units. In turn, each of the units contains 8 ATRMs and DTRMs shown in Figure 3. Development of additional subsystems of analogue and digital units is conditioned upon improvement of model readability. The analogue transceiver module performs the following functions: filtering, attenuation, and pre-amplification. It also considers non-linear elements and noise effects. The digital transceiver module provides digital-to-analogue conversion, analogue-to-digital conversion, attenuation, frequency conversion, signal filtering, and multi-rate processing [4]. The DTRM also features compensation algorithms for signal delays that may arise in the transceiver path. Calculation of signal delays of transmit and receive paths of the PAA is performed by the external emitter/receiver and is implemented in the computer system.

Control parameters are distributed by each ATRM and DTRM using subsystem 3.

Let us simulate the following case: an SS is sent to the RC from an external source through the environment. Due to mismatch of cable lengths or ADC mal-synchronisation, sudden delays may occur in each of the receive channels, which, in turn, may impact the receive radiation pattern. Using such operation mode, the radar system calibration and phasing situation can be simulated (Fig. 6a and b).

The SVM provides for various methods for calculation of signal delays. Let us consider them briefly (in all methods, one signal is the reference to calculate the delay):

- the method based on cross-correlation integral calculation [5] (hereinafter referred to as the correlation method);
- the method based on spectral analysis calculates spectra of two signals, further finds numbers of filters with maximum spectra, and inserts them as indices into the calculation of difference between phase frequency characteristics [5] (hereinafter referred to as the spectral method);
- the method based on Hilbert transformation performs Hilbert transformation of signals, further calculates the phase of ratio between transformation results [5] (hereinafter referred to as the Hilbert method);
- the method based on properties of the LFM signal performs heterodyning between the reference signal and the delayed signal, further calculates the spectrum where it finds the maximum filter value, by the value of which the signal delay is calculated (hereinafter referred to as the LFM method).

Figure 7 shows the results of processing using the above methods.

Model operation results suggest the following conclusions: the correlation method provides the highest error of signal delay calculation (Fig. 7a, the dot-and-dash line). The advantage of this method is its simple implementation. The spectral method and Hilbert method provide very close estimates of signal delay (Fig. 7b), but these methods fail to accomplish the task, when the delay exceeds the whole signal cycle. In addition, these methods are very sensitive to noise and interference components. The method based on LFM signal properties is free from the above shortcomings, however it is more difficult to implement.

As an LFM signal is used as the SS, we turn our attention to the LFM method for further analysis. After calculation of signal delays in the transceiver path, they need to be compensated. The compensation is performed in DTRM. The delay matrix was calculated for this purpose (Fig. 8).

Each column of the matrix is a set of signal delays in all channels, the column number stands for the channel, which the delays are compensated for. Thus, the elements of selected column are recorded to DTRM, where compensation for signal delay is performed. The results of time delay compensation are shown in Figures 6c and d.

**Fig. 6**. operation results: a and c - receive signal, b and d - radiation pattern

**Fig. 7**. Model operation results: a - delay calculation, b - calculation of delay around channel 25; 1 - true signal delay, 2 - delay calculated using the correlation method, 3 - delay calculated using the spectral method, 4 - delay calculated using the Hilbert method, 5 - delay calculated using the LFM method; Ch - channel number, T - signal delay

**Fig. 8**. Delay matrix

Further, let us consider the SVM control structure and interface.

## SVM control structure and interface

The developed simplified verification model is controlled using a special structure, i. e. control structure. Essentially, the control structure is an array of structures, where the RC number is the index. In turn, the RC structure includes the following components:

- the array of ATRM control structures, where each structure stores own value of control parameters of one ATRM, such as transmission ratio, filter ratios, AFR, etc. Therefore, in the SVM model, each ATRM may have its control parameters, to adapt modules to features of real ATRMs, thus, approximating SVM to a real radar system;
- the array of DTRM control structures, where, just like in ATRMs, each DTRM can be controlled separately, e.g., through adjusting the transceiver signal delay, setting digital filter ratios, and adjusting the signal bandwidth;
- the target structure that contains target control parameters: RCS, range, velocity, etc.;
- the environment structure that contains propagation environment control parameters: ground reflection factor, delays, number of bands, etc.

Further, let us consider the control interface shown in Figure 9.

Essentially, the shown interface represents the CS shell. As you can see, the control interface has quite an extensive set of options to preset various modes of received information display through enabling or disabling of both ATRM and DTRM, and much more. The Model List tab calls its control interface: generation of sensing signal, target, environment, antenna, RC, ATRM and DTRM. It also provides for the target engagement mode, where standard units of Simulink utility are used as the propagation environment and the target. As an example, let us consider the following case: two targets with different RCS are located at various distances. The first target was located at a distance of approximately 1,000 m, another target was located at 2,000 m, while radial velocity of the targets was different. The received signal was processed and displayed using standard units of Simulink utility. The processing result is shown in Figure 10.

**Fig. 9**. Appearance of SVM control interface

**Fig. 10**. Target engagement mode

## Conclusion

At the initial stage of a radar station digital twin development, the simplified verification model was created, where one antenna RC and its components, i. e., ATRM and DTRM, were simulated. The model of target, radio waves propagation environment, and AFD was used from Simulink environment. The features of Simulink utility made the model illustrative and reflecting the design features of the article being designed. The model is controlled by and the results of its operation are displayed using the application developed in MATLAB language. Therefore, the model has a flexible structure that enables adaptation of each individual module to the actual characteristics of the article being developed. The following tasks were accomplished. general understanding of article operation principles was provided, hardware and software control parameters were determined, the transceiver path calibration mode was worked through by external calibration signal, and the target detection mode was worked through.

It should be noted that the model looks rough and will be further expanded to accomplish other tasks. The priority development areas of the model are as follows. an increase of the number of RCs (increase of antenna dimensions), specifying the target motion equation, and engagement of complex targets. We also consider the possibility of semi-realistic simulation, using the SDR (Software-Defined Radio) technology.

The model is being developed in parallel with the development of a full-scale RC, therefore, further direction shall consist in comparing the parameters obtained during simulation to the RC test results.

## References

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3. Леонов А. И., Васенов В. Н., Гайдуков Ю. И. и др. Моделирование в радиолокации. М.: Советское радио, 1979. 264 с.

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### About the Authors

**D. A. Balakin**Balakin Dmitry Aleksandrovich – Engineer of the 1st category

Research interests: mathematical modelling in radar technologies, digital signal processing, methods and algorithms for the diagnostics of the state of dynamic systems.

**E. V. Kersky**Kersky Evgeny Viktorovich – Laboratory Head

Research interests: mathematical modelling in radar technologies, object-oriented programming, digital processing algorithms.

#### For citation:

Balakin D.A., Kersky E.V. Development of a digital twin for an early-warning radar system. *Journal of «Almaz – Antey» Air and Space Defence Corporation*. 2020;(1):10-18.
https://doi.org/10.38013/2542-0542-2020-1-10-18