A Novel Electromagnetic Compatibility Evaluation Method for Receivers Working under Pulsed Signal Interference Environment

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The proposed electromagnetic compatibility (EMC) evaluation method of receiver subject to pulsed signal interference environment based on bit error rate (BER) is an improvement of the existing EMC test and evaluation standards. The quantitative characterization of the relationship between the electromagnetic characteristics of pulse signal and the BER of the receiver is established, which serves for the evaluation of the receiver EMC under different types of pulsed signal interference environment. This method can significantly improve the reliability and engineering applicability of the EMC evaluation under a pulsed signal interference environment and can be extended to the EMC design evaluation of different types of receivers, providing technical support for their EMC design.

Abstract

For wireless communication systems, receivers usually work under complex electromagnetic environments and are often susceptible to electromagnetic interference (EMI). With the wide application of pulse signals in various fields, the impact of pulse signals on the receivers of communication system has not been extensively studied. On the one hand, the existing receiver electromagnetic sensitivity (EMS) interference coupling effect is mainly analyzed from the perspective of energy only, without considering of different electromagnetic parameter characteristics of pulse signal, such as pulse width, repetition period, duty cycle and so on. On the other hand, there is a lack of quantitative characterization of typical performance indexes of receiver subject to pulsed interference environment, resulting in insufficient reliability and accuracy of receiver interference degree prediction and electromagnetic compatibility (EMC) evaluation. This paper focuses on the EMS interference coupling effect analysis and EMC evaluation method of receiver under pulsed interference environment. First, based on the analysis of the interference mechanism of the pulse signal on receivers, the formula for the bit error ratio (BER) is derived. Then a system model is proposed to verify the theoretical analysis results through numerical simulation. With the established relationship between the parameters of the pulsed interference and the BER performance of the receiver, a novel EMC evaluation method has been proposed. As a practical application example, the evaluation method is verified via a well-designed experiment on BeiDou Navigation Satellite System (BDS). The experiment shows that the observed phenomena are in good agreement with the conclusions of the proposed evaluation method, proving that the method is applicable to the EMC evaluation of receiver under pulsed signal interference environment.

1. Introduction

With the development and application of pulse signals in radar, remote sensing, electronic measurement, high-power microwave and other fields, pulse signal has become an important part of the working electromagnetic environment of electronic systems. Depending on the different uses and operation modes of the system, there are many sources and types of pulse signals, such as the pantograph arc radiation generated during high-speed railroad operation and the external radiation from radar, etc. Taking the pulse signal in radar as an example, it has the characteristics of high-power density in energy domain, large spectrum occupation in frequency domain, wide distribution range in airspace [1,2]. The pulse signal can usually be characterized by parameters such as pulse width, pulse power, carrier frequency, repetition period (related to duty cycle and pulse width) and so on [3]. When the carrier frequency of the pulse signal is in the same frequency band as the operating frequency of the receiver, it is easy to cause in-band interference to the receiver. In addition, it may cause out-of-band interference to the receiver considering the operating characteristics of the receiver’s back-end circuit and the received pulse signal power.

As a key component of electronic systems, whether the receiver could operate normally in the electromagnetic environment determines the performance of electronic systems. For example, through the information interaction between the navigation receiver and BDS, the user can realize the stable tracking of satellite navigation signals. The railway traffic management system completes the communication between the train and the dispatching center through Global System for Mobile Communications-Railway (GSM-R). However, when the receiver encounters EMI during operation, the main performance indicators of the receiver could be affected. This can result in the reduction of signal-to-interference ratio (SIR), the increase of BER, signal reception delay, etc., and eventually leading to the degradation or even damage of the receiver performance. In ref. [4], the narrowband and ultra wide-band (UWB) radiated interference tests were conducted on a GPS receiver. When the interference signal was continuous wave (CW), the interference threshold of the receiver was far lower than the level required by EMC standard [5]. For pulse and high-level UWB signals, it was easy to interfere and even cause permanent damage to the receiver. According to the analysis of ref. [6], the external electromagnetic environment with multiple harmonics has a great impact on the BER, resulting in the reduction of system immunity. In ref. [7,8], through experiments and theoretical analysis, it was concluded that EMC design should fully consider the simultaneous interference of multiple radiation sources to improve EMC safety margin. In ref. [9], a probability evaluation tool for electromagnetic effect was proposed and verified by experiments. This could be used to statistically evaluate the safety margin of the system in high-power electromagnetic environment. Based on acceptance sampling and confidence interval, the authors in [10] introduced several statistical methods to evaluate the quality of hemp test and verified by experiments, which could improve the significance of the conclusions. In ref. [11], the EMS evaluation method of servomotor under intentional RF pulsed interference environment was studied. The authors in [12] proposed an impulse noise test method suitable for vehicle network, which can operate on a high detection probability with low false alarm probability. Through a large amount of tests and test data analysis, the authors in [13] improved the regression analysis method and fitted the amplitude-frequency characteristic curve of the arc in the frequency band of the omnidirectional beacon. The effect of arc electromagnetic emission on the airport omnidirectional beacon was analyzed. The authors in [14,15] studied the time domain, frequency domain and joint time-frequency domain characteristics of arc radiation interference. Through the test of typical indexes of GSM-R, the influence of arc radiation interference on the performance of GSM-R was analyzed. By establishing the GSM-R communication chain model, the authors in [16] analyzed the influence of EMI on BER.

According to the use requirements of receivers in different military and civil fields, the existing receiver EMC test and evaluation methods mainly refer to military standards such as GJB151B-2013, MIL-STD-461G or civil standards such as CISPR 16-1-1, ETSI EN 303 413 [5,17,18,19,20,21], which is essentially a static method. The EMC test is carried out on the receiver according to the specified waveform formulated in the standard, and the EMC evaluation is carried out according to the test results. The above method is difficult to meet the dynamic and complex electromagnetic environment faced by the receiver operating in real life. Therefore, research has been conducted in the construction of the EMI model, the construction method of electromagnetic environment, EMS threshold test method to improve the existing EMC test and evaluation methods. In ref. [22], combined with the characteristics and actual situation of EMI scene, the research on the construction of EMI effect model was carried out at the system level. The paper [23] presented a network-based methodology for system-level EMC analysis. The network framework was comprised of an EMC network and a network of the system physical architecture. The nodes and edges of the final network model were defined by corresponding parameters, which could be transferred from the origin to the destination through calculation, simulation, and measurement, respectively. A novel EMI risk analysis method was proposed in [24], including EMI risk management process and threat scenario, effect and criticality analysis. The above research can be extended to the EMC analysis of different types of systems. Through analyzing the electromagnetic characteristics of CW of high and low power, the authors in [25,26] studied the typical performance and the sensitive characteristics of the receiver under CW interference environment. The electromagnetic environment confronted by the receiver is dynamic and diverse. Therefore, the dynamic integrity construction of the electromagnetic environment in the test stage is particularly important for the EMC evaluation of the receiver. Starting from the physical characteristics of electronic equipment and the coupling mechanism of space electromagnetic field acting on electronic equipment, the theoretical method of EMC element set was proposed in [27]. The authors in [28] proposed the concept of the complexity degree of the electromagnetic environment and tried to use it to evaluate the interference signal. Starting from the response of typical ports to electromagnetic environment, the authors in [29] proposed a novel equivalent construction method of electromagnetic environment and EMS threshold test method. The accuracy and engineering applicability of the proposed method are verified by theoretical and experimental analysis. The EMC of receiver usually needs to be analyzed and evaluated according to the results of radiation sensitivity (RS) test and conduction sensitivity (CS) test. The different coupling mechanisms and advantages of RS and CS test are analyzed through the research of experiment and modeling methods [30,31,32,33,34]. The EMC evaluation of electronic systems are inseparable from theoretical analysis and experimental test. The measurement data and theoretical model, measurement data and numerical simulation results, measurement data and standard specifications will bring uncertainty to EMC evaluation. Therefore, through the statistical evaluation of test results and the uncertainty quantification of random variables, the accuracy and reliability of EMC evaluation of electronic systems could be improved [35,36,37,38].

We believe that the existing research has mainly analyzed the characteristics of pulse signals in the time domain, frequency domain and energy domain. Through simulation and testing, the analysis of the receiver EMS effect and EMC evaluation under a pulsed interference environment is carried out from the perspective of energy (usually the signal power received in the receiver’s working frequency band, which can range from a 3 or 6 dB bandwidth depending on the receiver’s performance index) for specific scenarios. However, the impact of the electromagnetic parameters of pulse signals on electronic systems has not been well understood. There is a lack of analysis and quantitative characterization of the EMI effect of typical parameters of pulse signals on receivers, which is difficult to meet the requirement of receiver EMC evaluation under dynamic and diverse environment.

Inspired by previous research, in this paper, we select the BER as the typical performance index of the receiver. By analyzing the electromagnetic characteristics of the pulse signal, we carry out the quantitative characterization modeling of the interference effect of the receiver based on BER. Based on characterization of BER, a novel EMC test and evaluation method for the receiver under pulsed interference environment is proposed in this paper. The accuracy and engineering applicability of the proposed model and method are verified by numerical simulation and experimental analysis.

The novelty of this paper is embodied into two major aspects. On the one hand, based on the electromagnetic characteristics of pulsed interference signals, the modeling approach for quantitative characterization of receiver interference effect under pulsed environment is carried out. By establishing the quantization relationship between BER and pulse width, repetition period, ISR, duty cycle and signal period, the generalized receiver interference effect quantization characterization model is constructed. The model can be extended and applied according to different modulation and coding methods of the receiver, and the receiver EMS can be analyzed according to different electromagnetic parameter characteristics of the pulse signal; on the other hand, the research on the receiver EMC testing and evaluation method under pulsed interference environment is carried out according to BER, which can improve the reliability and accuracy of receiver interference degree prediction and EMC evaluation.

The remainder of this paper is organized as follows. In Section 2, based on the traditional BER theory, where Gaussian white noise (GWN) is considered, we derive the BER formula for the receiver when pulse signals are considered as the noise. Then, numerical simulation is designed to verify the theoretical conclusions in Section 3. As a practical example, the proposed EMC evaluation method is applied to BDS in Section 4, the predictions given by the method are compared with the measured results obtained in the laboratory. Finally, in Section 5, we conclude this paper with a summary of the proposed methods and some follow-up research outlooks.

2. Modeling of Receiver Pulsed Environment Interference Effect Based on BER

2.1. Signal Processing in Communication Receiver

Although the communication system has a variety of division modes, such as frequency band, modulation mode, coding mode, etc., and different types of communication systems use different technologies, they all have the basic structure of the receiver [39] as shown in Figure 1. The characteristics of its components need to be determined according to the performance of the communication system. The flow of signal processing is that the functional signal enters the receiver through the receiving antenna and band-pass filter together with the interference signal. After mixed processing, the processed signal is converted to the baseband through down-conversion circuit, which include low-pass filter and sampling decimator.

Now let us consider interference signals from the electromagnetic environment. For the interference signal, the out-of-band signals are filtered out after passing through the antenna and band-pass filter due to the frequency selection characteristics. The pulse signal near the working frequency band of the antenna or the band-pass filter is coupled into the receiver and enters the low-noise amplifier. Due to the non-linear characteristics of the low-noise amplifier and other devices, the frequency of the interference signal is converted to the tuning frequency of the receiver. By mixing and demodulating with the useful signal, it will eventually cause the input waveform of the sampling divider to rise or fall, resulting in sampling and judgment errors, and ultimately making decoding errors. Thus, the communication efficiency is affected, and at the same time, it is manifested as an increase of the BER.

From the perspective of EMC between systems, we focus on the impact of pulse signals in the same frequency band on the BER of receiver, which can be carried out in two steps:

(1)

Analyze the interference mechanism of the pulse signal in the receiver;

(2)

Establish the quantitative characterization model of BER and the electromagnetic parameters of the pulse signal.

2.2. BER Analysis under GWN Interference

At the first stage, let us consider GWN as the only interference and the BER can be calculated as follows. Digital modulation is mainly divided into amplitude modulation, frequency modulation and phase modulation, which correspond to three modes: amplitude-shift keying (ASK), frequency-shift keying (FSK) and phase-shift keying (PSK). If binary form is adopted, it corresponds to binary amplitude-shift keying (2ASK), binary frequency-shift keying (2FSK) and binary phase-shift keying (2PSK) respectively. The difference between the three modulation modes is mainly the different ways in which the digital signal controls the change of parameters. 2ASK is the modulation mode in which the digital signal controls the change of carrier amplitude. 2FSK is the modulation mode in which the digital signal controls the change of carrier frequency, and 2PSK is the modulation mode in which the digital signal controls the change of carrier phase.

As an example, let us assume the 2ASK has been used as the modulation scheme and the filter at the front end of the receiver has ideal rectangular frequency selection characteristics, then its output signal can be expressed as:

$$y(t)=\left\{\begin{array}{cc}a\cos {\omega }_{c}t+n(t)& when sending “1”\\ n(t)& when sending “0”\end{array}\right.$$

(1)

where $n(t)$ is the narrowband GWN of the output after the filter, and $n(t)$ can be denoted as the sum of the in-phase part and quadrature part.

$$n(t)=n_c(t)\cos {\omega }_{c}t-n_s(t)\sin {\omega }_{c}t$$

(2)

After substituting it to (1), it is mixed with the coherent carrier of the same frequency and phase, and then the signal is filtered through a low-pass filter to remove frequency components outside the pass-band, and the filtered signal is used as the input signal of the sampling decision device. The mathematical expression of the input is:

$$x(t)=\left\{\begin{array}{cc}a+n_c(t)& when sending “1”\\ n_c(t)& when sending “0”\end{array}\right.$$

(3)

where $a$ is the component of the useful signal, $n_c(t)~N(0,{\sigma }_n^2)$, so it is obvious that $x(t)$ also obeys a Gaussian distribution. Thus, $x(t)$ is sampled as:

$$x=x(k{T}_B)=\left\{\begin{array}{cc}a+n_c(k{T}_B)& when sending “1”\\ n_c(k{T}_B)& when sending “0”\end{array}\right.$$

(4)

Thus the $k_{th}$ sampled value also obeys Gaussian distribution, and the probability distribution function is:

$$\begin{array}{l}{f}_1(x)=\frac{1}{\sqrt{2\pi }{\sigma }_n}\exp \{-\frac{{(x-a)}^2}{2{\sigma }_n{}^2}\}\\ f_0(x)=\frac{1}{\sqrt{2\pi }{\sigma }_n}\exp \{-\frac{x^2}{2{\sigma }_n{}^2}\}\end{array}$$

(5)

The BER of the system is:

$$P_e=P(1)P(0/1)+P(0)P(1/0)=P(1){\displaystyle \underset{-\infty }{\overset{b}{\int }}{f}_1(x)dx}+P(0){\displaystyle \underset{b}{\overset{\infty }{\int }}{f}_0(x)dx}$$

(6)

where $b$ is the detection threshold. If $P(0)=P(1)=1/2$, the best value of b equals to $b^{*}=a/2$, finally the BER is:

$$P_e=\frac{1}{2}erfc(\frac{a}{2\sqrt{2}{\sigma }_n})=\frac{1}{2}erfc(\sqrt{\frac{r}{4}})$$

(7)

where $erfc(x)=1-erf(x)=\frac{2}{\sqrt{\pi }}{\displaystyle \underset{x}{\overset{\infty }{\int }}{e}^{-{\eta }^2}d\eta }$.

2.3. BER Formula under Pulse Signal Interference

According to the typical working type of radar, three types of radar pulse signals are selected as interference signals, namely simple pulse, linear frequency modulation (LFM) pulse and bi-phase-coded pulse [40]. Among them, the carrier frequency, repetition period and pulse width of simple pulse are fixed. Square wave is usually used to modulate the amplitude of high-frequency carrier to generate simple pulse, as shown in (8).

$$s(t)=A(t)\exp \{j[2\pi f_{c}t+{\theta }_0+\phi (t)]\},t\in (0,T]$$

(8)

where $T$ is the pulse width, $A(t)$ is the amplitude function, $f_c$ is the carrier frequency, ${\theta }_0$ is the initial phase and $\phi (t)$ is the phase function.

The carrier frequency of LFM pulse changes linearly with time. The basic digital module can be used to generate continuous LFM signal, and then the square wave can be used to modulate the continuous LFM signal, as shown in (9). In the application field of radar measurement and positioning, the LFM signal can be used to obtain higher average transmission power and larger pulse width, so as to greatly increase the working coverage of radar. Moreover, due to the wide spectrum of LFM signal, it can also ensure that the radar system has high range resolution during ranging.

$$F(t)=A\left(t\right)\cos ({\omega }_{c}t+\frac{1}{2}·\mu ·t^2)$$

(9)

where ${\omega }_c$ is the carrier angular frequency, and $\mu =\raisebox{1ex}{$d\omega $}\!\left/ \!\raisebox{-1ex}{$dt$}\right.$ is the chirp rate.

The phase coded pulse has a fixed carrier frequency, and the absolute value of the phase is switched at a certain phase interval within the pulse duration. When the absolute value of the phase change in the pulse is two phases of opposite polarity, it is called bi-phase-coded pulse, as shown in (10). In radar positioning technology, bi-phase-coded pulse has been widely used in short-range communication because of its convenient phase synchronization extraction and narrow spectrum bandwidth [41]. Here, we choose the most commonly used binary code, the Barker code [22], which is meaningful only when the meaning of each code type is known.

$$\begin{array}{l}x(t)={\displaystyle {\sum }_{n=0}^{N-1}{x}_n(t-n{\tau }_c)}\\ x_n(t)=\left\{\begin{array}{cc}\exp (j{\varphi }_n),& 0\le t\le {\tau }_c\\ 0,& \mathrm{other}\end{array}\right.\end{array}$$

(10)

where $n{\tau }_c$ is pulse width.

The simulation flow of bi-phase-coded pulse is shown in Figure 2. Firstly, the RF signal source generates the high-frequency carrier. After quadrature modulation, the polarity of the RF signal is controlled through the encoded digital signal source to show the same change law as that of the Barker code. Finally, the continuous signal is converted into a pulse signal through the digital pulse module, and finally the bi-phase-coded pulse is output.

In Figure 3, Figure 4 and Figure 5, the time distribution and frequency domain characteristics of the simple pulse, LFM pulse and bi-phase-coded pulse are shown respectively.

Based on above analysis, let us take a further step to consider the BER formula under pulse signal interference. Figure 6 shows a schematic diagram of the influence of the pulse signal on the receiver when the pulse width is smaller than the symbol period. The rectangular sequence in the figure represents the receiver symbol sequence, i.e., the gray rectangles represent the disturbed symbol, and the white rectangles represent the undisturbed symbol. Through in-depth analysis, the impact of the pulse signal on the symbol is significantly different from that of the GWN signal. The GWN signal is random in the time domain and interferes with every symbol. Whether or not an error occurs mainly depends on the amplitude of the GWN at the decision time. From a statistical point of view, the level is mainly determined by the power spectral density of the GWN signal. The pulsed interference signal is periodic in the time domain, so it only interferes with part of symbols, and it is considered whether there will be a misjudgment under the condition that the symbols are interfered. So, the calculation step of the receiver’s BER under pulsed interference is the conditional probability calculation: firstly consider the probability of symbol interfered, and secondly consider the probability of misjudgment generated by the symbol under the condition of interference. For different interference patterns, the derivation idea of BER formula under pulsed signal interference mentioned in this paper can still be used.

Different parameters of the pulse signal and receiver will make the repetition period and the receiver symbol period have a different relative magnitude relationship. When the pulse width is smaller than the symbol period of the receiver, the pulse signal will interfere with at least one symbol and at most two symbols; when the pulse width is larger than the symbol period, the pulse signal will interfere with multiple symbols. After mathematical deduction, fortunately, in the case of long pulse and short pulse, the calculation results of interference probability are consistent:

$$P_1=\frac{W+T_s}{T_{PRP}}$$

(11)

where $W$ is the pulse width, $T_s$ is the symbol period, $T_{PRP}$ is the repetition period.

Under the condition that the symbol is determined to be interfered, the interference signal at this time can be equivalent to noise, and the probability of misjudgment can be deduced according to the traditional theory. Finally, the product of the two, $P_e=P_1·P_2$, is used as the BER formula of the receiver under pulse signal interference.

For example, assuming that the receiver adopts Quadrature Amplitude Modulation (QAM) or Quadrature Phase Shift Keying (QPSK) modulation and coherent demodulation, when only the pulse signal interference is considered and the symbol is determined to be interfered, the probability of misjudgment can be derived as:

$$P_2=\frac{1}{2}erfc\sqrt{\frac{1}{2}·SIR}$$

(12)

$$erfc(x)=1-erf(x)=\frac{1}{\sqrt{\pi }}{\displaystyle \underset{x}{\overset{\infty }{\int }}{e}^{-{\eta }^2}d\eta }$$

(13)

where $SIR$ is the signal-to-interference ratio. It is considered that during the operation of the receiver, the receiver will not only receive functional signals, but also receive interference signals in the external electromagnetic environment. The SIR is usually used to characterize the relationship between the function signal and the interference signal from the perspective of energy, which can be expressed as follows:

$$SIR=P_{signal}\left(dB\right)-P_{interference}\left(dB\right)$$

(14)

where $P_{signal}$ is the received function signal power, and $P_{interference}$ is the received interference signal power. SIR is related to the performance of the receiver itself. When SIR is higher than a certain value, according to Formula (14), that is, when the functional signal power is higher than a certain value of the interference signal power, the receiver can work normally. Otherwise, it cannot work normally, which means interference occurs. The interference effect of pulse signal amplitude on the receiver can be analyzed by SIR.

Therefore, the BER of the receiver adopting QAM under pulsed interference $P_{e,QAM}$ can be expressed as follows:

$$P_{e,QAM}=P_1·P_2=\frac{1}{2}erfc\sqrt{\frac{1}{2}·SIR}\frac{W+T_S}{T_{PRP}}$$

(15)

For the probability of it being interfered, it can be decomposed into the following two parts:

$$P_{e,QAM}=\frac{1}{2}erfc\sqrt{\frac{1}{2}·SIR}(\frac{W}{T_{PRP}}+\frac{T_s}{T_{PRP}})$$

(16)

where $\frac{W}{T_{PRP}}$ is the duty cycle, and $\frac{T_s}{T_{PRP}}$ is the ratio of the receiver symbol period to the interference repetition period.

According to the mathematical character of (17)

$$\underset{x\to 0}{\lim }erfc(x)=1$$

(17)

we can derive:

$$\underset{SIR\to 0}{\lim }{P}_{e,QAM}=\frac{1}{2}\frac{W+T_s}{T_{PRP}}$$

(18)

Its physical meaning is that when the SIR tends to zero, that is, when the interfering signal tends to infinite, the BER under this condition reaches the maximum value only related to the pulse duty cycle and the receiver symbol period.

3. Numerical Verification of Received Pulsed Environment Interference Model Based on BER

In order to verify the theoretical results proposed in Section 2, we establish a simulation model of the BDS interfered by pulse signal, which is shown in Figure 7. Based on the frame shown in Figure 7, we can divide the whole system into five parts, the pulsed signal interference source, the radio transmitter, the channel, the radio receiver and BER calculation module.

Based on the system model in Figure 7, the behavioral model and model parameters of each module are established in the Advanced Design System (ADS) platform, as shown in Figure 8. By adjusting the functional parameters in the behavioral model, different types of receivers can be simulated. Firstly, a complete BDS functional model is established, including radio transmitter, channel and radio receiver. BER is one of the important indexes to evaluate whether the receiver is disturbed. The BER of BDS receiver can be displayed by the BER calculation module. In the case of no interference, the main cause of BER is channel noise, when under pulsed signal interference environment, pulses with different parameter or modulation are radiated to the receiver, which is collected and post processed by the BDS receiver antenna together with the functional signal through different transmission channels. Changing the parameters of pulse signal and analyzing the BER by using the method proposed in this paper, the interference degree of BDS receiver under the pulsed signal interference environment with different parameters can be evaluated by observing the change trend of BDS BER.

In the radio transmitter, we use a module to read the signal and code it with 16-bits pulse code modulation (PCM) then convert the output integer data to binary non-return-to-zero code (NRZ). As the ideal rectangle bit flow has a very broad spectrum after modulation, we divide it to two routes and let it go through a low-pass filter, in order to narrow the bandwidth. We then set the stop frequency of the raised cosine low pass filter to Nyquist sampling frequency, and then modulate the signal by 4QAM. The output signal is expressed in (19), which we can make it clear that the QAM output signal can be regarded as a signal that is controlled of its range and its phase.

$$V_3(t)=V_1(t)\cos {\omega }_{c}t+V_2(t)\sin {\omega }_{c}t$$

(19)

According to the Friis transmission formula proposed in [42], as shown in Figure 9 and formula (20), in the channel, if we use $P_t$ as the transmit power, $P_r$ as the received power, and converting it into a logarithmic form, then we get the system loss $L_{\mathrm{s}}$ as (21).

$$P_r=\frac{P_t·G_t·G_r·{\lambda }^2}{{\left(4\pi R\right)}^2}$$

(20)

$$L_s=10\lg \left(\frac{P_t}{P_r}\right)=L_p-G_t-G_r$$

(21)

$L_p$ represents the loss of electromagnetic field in free space, which can be calculated by (22).

$$L_p=\frac{{\left(4\pi R\right)}^2}{{\lambda }^2}=\frac{{\left(4\pi Rf\right)}^2}{{\mathrm{c}}^2}=32.45+20\lg f(\mathrm{MHz})+20\lg R(\mathrm{km})\left(\mathrm{Logarithmic} \mathrm{representation}\right)$$

(22)

where $G_t$ presents the transmit antenna gain, $G_r$ presents the receiving antenna gain, $f$ is the working frequency, R is the transmission distance.

Except the loss module in the channel, we also need to consider the interference. The exterior interference for navigation receiver points to all kinds of noise picked up by the receive antenna, such as artificial interference, the atmospheric noise, jamming and the universe noise, etc. The interior interference indicates the devices’ own noise, it is easy to filter out, so we do not consider about it generally. In this part, we add exterior interference to the system, which is similar to the GWN in the receiver’s pass-band. Thus, the received power and the noise can be weighed by signal-to-noise ratio (SNR), as shown in (23). Set the SNR to 10 dB, we can figure out that the noise in the channel should be less than −60 dBm if the output power is 100 W (50 dBm). For the signal bandwidth is 640 kHz, according to (24), the calculated noise density (ND) should be −118 dBm/Hz.

The SNR is used to characterize the relationship between signal and noise in the system. The expression is as follows:

$$SNR\left(\mathrm{d}B\right)=P_{signal}-P_{noise}$$

(23)

where $P_{signal}$ is the signal power and $P_{noise}$ is the noise power.

The ND refers to the noise power corresponding to each Hertz frequency in the system operating frequency band, which reflects the noise energy level of 1 Hz bandwidth. The ND can be used to estimate the total noise power within the operating bandwidth of the system, as follows:

$$ND\left(\mathrm{dB}/\mathrm{Hz}\right)=P_{total}-SNR-10\log \left(\frac{F_S}{2}\right)$$

(24)

where $P_{total}$ is the total noise power, and $F_S$ is the Nyquist sampling frequency.

In the radio receiver, it consists of heterodyne receiver and the demodulate module. Then the signal passes through the demodulation part, and the digital processor that includes the judging circuit and the code-switching module, and we use a decode module before exporting the signal out.

In the pulse signal interference source, we establish the sources generating simple pulses, LFM pulses and bi-phase coded pulses respectively. By modifying the parameters of the pulses and observing the variation of the BER, the degree of interference of different pulses can be figured out.

According to the simulation experiment based on the behavioral model, as is shown in Figure 10 and Figure 11, the curve is drawn according to the Formula (15), which represents the ideal curve of the BER changing with the SIR under different duty cycles. The discrete points in the figure are the measured values obtained from the simulation experiment based on the above model. The measured values all fall on the theoretical curves obtained from the simulation, indicating that the measured results are consistent with the theoretical results, and verify the correctness of the model proposed in Section 2.

At the same time, it can also be obtained from the curve that, according to the property in (17), i.e., the function value tends to 1 when the independent variable of the error function tends to 0, it is deduced that there is an upper bound for the BER. In this model, calculated according to the set parameters, at a 30% duty cycle, the upper bound of the BER is 0.364. When the SIR is the same, the higher the duty cycle of the interference pulse is, the higher BER can achieve, and the higher the corresponding upper bound of the BER can be. The above simulation results are consistent with the theoretical derivation results, further verifying the correctness of the theoretical derivation.

As is shown in Figure 12, under the pulsed interference of different modulation, the relationship between the BER and the pulse duty cycle is simulated. As the SIR increases, interference to the receiver from simple pulse and bi-phase-coded pulse with the same pulse parameters is significant and there is a similar change in receiver BER. In contrast, with LFM pulse interference, the receiver BER is always at a low level. In other words, the interference of LFM pulses to the receiver is not apparent. The theoretical analysis of the reasons is as follows:

The LFM pulse has no fixed carrier frequency, and the pulse signal energy is less distributed in the working frequency band of the receiver, so the interference to the receiver is not apparent. According to the spectrum distribution of the three pulse signals, the simple pulse energy is the most concentrated, mainly at the carrier frequency of the pulse signal. The spectrum of bi-phase-coded pulse widens to a certain extent due to phase discontinuity, but the overall spectrum trend is similar to the basic pulse spectrum, and the energy is mainly concentrated at the carrier frequency. The frequency spectrum of LFM pulse is approximately rectangular in frequency modulation band, and the energy is evenly distributed in frequency modulation band. Therefore, when the pulse parameters are the same, the energy of the simple pulse and the bi-phase-coded pulse falling into the passband of the receiver is roughly the same. It is higher than that of the LFM pulse falling into the passband of the receiver.

4. EMC Evaluation Method for Communication Receiver

According to [43], the BER of BDS is closely related to its working performance. Whether it works normally can be judged by the number of BDS stable tracking satellites (in this paper, it can be observed by the upper computer). According to the system data released by the China Satellite Navigation System Management Office, when the BER is lower than ${10}^{-5}$, BDS is not disturbed and can work normally. At this time, the number of satellites that BDS can stably track is more than 10. When the number of satellites that BDS can stably track is 8–10, the interference to BDS is not apparent at this time and BDS can still work normally. When the BER is higher than ${10}^{-5}$ and lower than ${10}^{-3}$, BDS is apparently disturbed. At this time, the number of satellites that BDS can stably track is 5–8, and BDS cannot work normally. When the BER is higher than ${10}^{-3}$, BDS stops working. At this time, the number of satellites that BDS can stably track is less than 5. Therefore, we can evaluate the performance of the BDS receiver through the value of the BER.

In the experimental verification, we choose BDS receiver as the test object, on the one hand, because the minimum power level of the B3I signal transmitted by the satellite to the antenna of the receiver is −163 dBw, which is −133 dBm according to (25). Therefore, the sensitivity of receiver is very low, which leads to the disturbance phenomenon, and its EMC problem needs to be solved urgently. On the other hand, through a large number of experiments, it is found that when the BDS receiver is interfered, with the increase of the degree of interference, the number of satellite signals received by BDS receiver will decrease. Therefore, the interference degree of BDS receiver can be quantified through this phenomenon.

$$P_{\mathrm{d}B\mathrm{m}}=P_{\mathrm{d}B\mathrm{w}}+30$$

(25)

Equation (25) gives the relationship between power values in different units, where $P_{\mathrm{d}B\mathrm{m}}$ is the power value in dBm and $P_{\mathrm{d}B\mathrm{w}}$ is the power value in dBw.

According to the system parameters disclosed in the B3 section interface document [44] published by the Beidou Navigation Satellite Office of China, the code rate of B3I signal ranging code is 10.23 Mcps and the ranging code length $L=10.230$. Therefore, when calculating the BER of the receiver, the bit rate of the receiver needs to take the chip rate of 10.23 Mcps after spread spectrum, that is, $T_{chip}=1/10.23\mathrm{Mcps}$, each information symbol period in the receiver is $T_b$, the ranging code period is $T_c$, and the spread spectrum multiple is $N=T_b/T_c$, and the physical meaning is the anti-interference gain obtained after expanding the frequency band. It can also be explained that the received signal of the navigation satellite is very weak, and the spread spectrum gain is very large. Compared with other communication systems, it uses very low bit rate for high anti-interference performance.

The BER of spread spectrum communication can be expressed as:

$$P_e=Q(\sqrt{4\frac{W_L/R}{P_j/P_{av}}})=Q(\sqrt{4\frac{W_L}{R\times SIR}})$$

(26)

$$Q(x)=\frac{1}{\sqrt{2\pi }}{\displaystyle \underset{x}{\overset{\infty }{\int }}{e}^{-t^2/2}}dt,x\ge 0$$

(27)

where R is the information transmission rate, $W_L=W/2=1/T_c=R_p$, $R_p$ is the pseudo code rate, $P_j$ is the average power of interference signal, $P_{av}$ is the average power of useful signal.

The formula for the BER of the BDS receiver subjected to pulsed interference can be derived as:

$$P_e=Q(\sqrt{\frac{2}{\frac{1}{SNR}+\frac{2d·SIR}{N}}})\frac{T_{chip}+W}{T_{PRP}}$$

(28)

$$d=\frac{1}{B_j}{\displaystyle \underset{f_j-B_j/2}{\overset{f_j+B_j/2}{\int }}\sin c^2[(f_0-f)\frac{2}{B}]df}$$

(29)

Considering that the main energy of pulse signals in the same frequency band falls on the passband of the receiver, the above BER can be approximated as:

$$P_e=Q(\sqrt{4\frac{R_p}{R·SIR}})\frac{T_{chip}+W}{T_{PRP}}$$

(30)

The block diagram of the experimental design of the BDS subject to pulsed signal interference is shown in Figure 13. It mainly includes satellite navigation signal repeater, satellite navigation signal receiving/transmitting antenna, interference signal generator, interference signal transmitting antenna, interference signal receiving antenna, spectrum analyzer, oscilloscope, BDS receiving antenna and upper computer. We mainly judge whether the BDS receiver is disturbed by observing the change of the number of satellites in the upper computer.

The flow chart of receiver EMC evaluation method is shown in Figure 14. The experiment operation details are as follows:

(1) Establish stable functional link of BDS. To prevent the external electromagnetic environment from affecting the experimental results, the experiment was carried out in the microwave anechoic chamber. Considering that the BDS in the microwave anechoic chamber cannot receive the satellite navigation signal, the satellite navigation signal repeater can be used to forward the satellite navigation signal to the microwave anechoic chamber. The number of satellites displayed on the upper computer can be used to judge whether the BDS has established a stable functional link. The upper computer is connected with the BDS receiving antenna through the data line. By post-processing the received signal, it can display the working status information of the BDS receiving satellite, including the number of satellites, the longitude, latitude and altitude of the receiver position, time, working mode, etc. During the experiment, when the number of satellites displayed by the upper computer is stable at 10, we believe that BDS establishes a stable functional link.

(2) Measure the SIR. With the BDS in stable operation, the environmental receiving antenna is connected to the spectrum analyzer. The signal power received by the BDS receive antenna is measured in the experimental environment. Turn on the interference signal generator, adjust the external output signal power, and radiate the pulsed interference signal in the microwave anechoic chamber through the interference signal transmitting antenna. The power value of interference signal received by BDS can be read through the upper computer. During the experiment, the external output power of the interference signal generator remains unchanged, and the SIR of BDS can be calculated according to Equation (14), which is 46.5 dB.

(3) Measure the pulse width and repetition period. With the BDS in stable operation, turn on the interference signal generator, measure the pulse width and repetition period through spectrum analyzer. By adjusting the pulse width and repetition period of the external output pulse signal, the number of satellites that can be stably tracked by the BDS is recorded and displayed on the upper computer.

(4) Calculate the value of BER. Changing the pulse width and repetition period of the pulse interference signal can affect the BER of BDS. Using the method proposed in this paper, the BER of BDS is calculated according to Equations (11)–(18), (25)–(30).

(5) Evaluate the EMC of the BDS. The BER of BDS is calculated through step (4). According to [43], the interference degree of BDS by pulse signal can be predicted through the BER. The accuracy and reliability of the method proposed in this paper are verified by comparing with the display results of upper computer. The evaluation results are shown in

Table 1. EMC evaluation experiment results of BDS when changing pulse width.

SIR (dB)	Duty Cycle	W (us)	$\frac{{\mathit{T}}_{\mathit{c}\mathit{h}\mathit{i}\mathit{p}}+\mathit{W}}{{\mathit{T}}_{\mathit{P}\mathit{R}\mathit{P}}}$	BER	Evaluation	Number of Satellites
46.5	50%	1	0.0015	2.03 × 10−6	No interference	10
		10	0.0105	1.42 × 10−5	Interference	9
		100	0.1005	1.36 × 10−4	Interference	7
		500	0.5005	6.76 × 10−4	Interference	5
		1000	1	1.35 × 10−3	Stop working	0

and

Table 2. EMC evaluation experiment results of BDS when changing repetition period.

SIR (dB)	Duty Cycle	${\mathit{T}}_{\mathit{P}\mathit{R}\mathit{P}} \left(\mathbf{us}\right)$	$\frac{{\mathit{T}}_{\mathit{c}\mathit{h}\mathit{i}\mathit{p}}+\mathit{W}}{{\mathit{T}}_{\mathit{P}\mathit{R}\mathit{P}}}$	BER	Evaluation	Number of Satellites
46.5	50%	104	0.001	1.35 × 10−6	No interference	10
		103	0.0101	1.37 × 10−5	Interference	9
		102	0.101	1.36 × 10−4	Interference	7
		50	0.202	2.73 × 10−4	Interference	6
		10.9	1	1.35 × 10−3	Stop working	0

.

The experiment layout for EMC evaluation of BDS is shown in Figure 15. In this experiment, the SIR is the actual measured value, which is 46.5 dB, and the pulse signal duty cycle is 50%. SIR and pulse signal duty cycle remains unchanged during this experiment. Change the pulse width W, thereby the BER value varies. The experimental results are shown in Table 1. It can be read from Table 1 that when no interference is predicted, the number of satellites remains unchanged at 10 satellites. When the predicted interference occurs, the number of satellites gradually decreases, and when the navigation receiver is predicted to stop working, the number of satellites becomes zero.

Similarly, keep the SIR of the receiver at 46.5 dB and the pulse width $W=10 \mathrm{us}$, the pulse signal duty cycle is 50%. By changing the repetition period $T_{PRP}$, the value of BER is affected. The experimental results are shown in Table 2. It can be read from Table 2 that when no interference is predicted, the number of satellites remains unchanged at 10 satellites. When the predicted interference occurs, the number of satellites gradually decreases, and when the navigation receiver is predicted to stop working, the number of satellites becomes zero.

It can be seen that in this experiment, the interference phenomenon of the BDS receiver is accurately evaluated by estimating the BER of the receiver. When the evaluation result is “no interference”, the measured number of satellites is 10, indicating that there is no obvious interference. When the evaluation result is “interference”, the number of measured satellites decreases significantly, and the higher the BER, the fewer the number of measured satellites, and the more apparent the interference phenomenon. When the evaluation result is “stop working”, the upper computer displays that the number of satellites is zero, and the BDS receiver stops working. Through experimental verification, the evaluation results are in good agreement with the measured interference phenomenon of BDS receiver, which verifies the effectiveness of the evaluation method proposed in this paper.

5. Conclusions

The operating performance of an electronic system is closely related to the electromagnetic environment. With the widespread use of pulse signals in various fields, they have become an important part of electromagnetic environment. Therefore, in the development and test stage of electronic system, fully analyzing the impact of pulse signal on equipment EMC and accurately evaluating equipment EMC under pulsed signal interference environment are the keys to reduce equipment performance risk. In this paper, based on the analysis of the interference mechanism of the pulse signal on receiver, we proposed the modelling method for the quantitative characterization of receiver interference effect under pulsed environment. The quantitative relationship between BER and pulse width, repetition period, ISR, duty cycle and signal period is established. The model allows quantitative analysis of the receiver EMS based on the characteristics of different electromagnetic parameters of the pulse signal. A system model is then presented to verify the results of the theoretical analysis through numerical simulations. With the established relationship between the parameters of the pulsed interference and the BER performance of the receiver, a novel EMC evaluation method has been proposed. The quantitative evaluation of the receiver EMC under pulsed interference environment can be achieved. As a practical application example, the evaluation method is verified via a well-designed experiment on BDS. The experiments show that the measured values are in good conformity with the theoretical values, proving the applicability of the method to receiver EMS analysis and EMC evaluation under pulsed interference environment.

In further work, we will continue to study the modeling method of the receiver EMI effect and EMC evaluation method according to the relationship between typical performance indexes of receiver and the electromagnetic characteristics of pulsed interference signals in different scenarios to make them better for engineering applications.