A conducted emission mitigation method for software-defined radios through vector signal cancellation

Siyu XIA, Qi WU

School of Electronics and Information Engineering, Beihang University, Beijing 100191, China

KEYWORDS

Abstract Recently, Software-Defined Radio (SDR) has gained great popularity owing to its attractive merits, such as flexible signals configuration in multiple channels.However, commercial SDR equipment also has large spurious emissions in the Transmitting(Tx)channel.This paper presents a cascaded model for the Conducted Emission (CE) properties of a general SDR platform,which captures all the key components with high precision.Based on a deeper understanding of the CE properties, a mitigation method is proposed for suppressing the spurious emissions of an SDR Tx channel.This method is based on an efficient vector signal cancellation scheme, in which multiple SDR channels are adopted to suppress the second-and third-order harmonic signals simultaneously.A hardware prototype with dual SDR channels is built and measured for verification.Experimental results show that the suppression level of the third-order harmonic signal is 24 dB on average in the frequency range of 100 MHz to 3000 MHz.The theoretic limit of the suppression level is related to the magnitude and phase errors, and the suppression level may be further improved by calibrating each SDR channel.

1.Introduction

Traditional radio systems are based on a full-hardware structure with minimum reconfigurable capability.Conducted Emission (CE) of such a hardware radio contains a target radio signal (useful signal) as well as spurious ones (harmful signals), such as harmonic and intermodulation components.Spurious signals are mainly generated by nonlinear components,1,2the jitter of a reference clock, and the phase noise of a Phase-Locked Loop(PLL).3,4Spurious signals deteriorate the quality of useful signals and may also cause serious Electromagnetic Interference (EMI) issues to nearby radio systems.5,6Therefore, wireless communication standards predefine strict limits on the spurious signal levels of radio systems, and state-of-the-art filter techniques are adopted to suppress those signals7,8.

With the rapid development of Digital Signal Processing(DSP) hardware,the baseband function of wireless transceivers is gradually transferred to the digital domain.This development improves largely the flexibility of radio systems and potentially reduces Research and Development (R&D) costs.This concept is known as an SDR which contains both hardware and software parts.9–11Generally speaking,an SDR consists of hardware components that contain a configurable frontend and a DSP circuit to generate and receive wireless signals, as well as a software configuration that controls key parameters of the radio such as the operating frequency,signal bandwidth,modulation scheme,and so forth.Therefore,SDR solutions are attractive for both commercial and military communication systems.12,13For instance, an SDR platform was used in a real-time, ray-based emulator of Unmanned Aerial Vehicle (UAV) communication channels.14

In most cases, a general SDR platform does not contain a tunable filter in the last stage between the power amplifier and antenna as illustrated in Fig.1, e.g., the architecture in Ref.15This is due to the motivation that an SDR shall achieve a small size and low fabrication cost simultaneously.As a result,it is inevitable that an SDR platform would have a large amount of CE in the form of harmonics and spurious signals with relatively large magnitudes.Therefore, it would be difficult for a general SDR platform to satisfy wireless communication standards or Electromagnetic Compatibility (EMC)standards.In addition, an elaborate CE model of general SDR equipment is not available in literature,and effective mitigation methods are also under development.16

To suppress spurious emissions of general SDR equipment,some innovative works were reported in literature.For instance, improving the linearity of an SDR receiver alleviates the issues of performance degradation and reduces potential interferences existing in adjacent bands.17In addition,a reconfigurable SDR frontend was proposed to manage the attenuation ratio adaptively with the input power, which could limit the output power to alleviate potential interferences to other equipment.18Combined with a low-noise Transconductance Amplifier (TCA), a raised-cosine signal was used to suppress the harmonics of a Local Oscillator (LO),19and the usage of an adaptive gain controller could do a similar job.20Moreover,a similar SDR concept was adopted in a radar system, which created software-controlled waveforms to provide better interference suppression performance through a proper definition of the channel bandwidth.21In addition, SDR receivers may rely on the degrees of freedom in Multi-Input, Multi-Output(MIMO) transmission in order to suppress a number of interfering streams, at the expense of a spatial multiplexing gain.22However, the above-mentioned techniques focus more on the improvement of analog circuits.Additionally, most of the modified hardware architectures are no longer reconfigurable and hence reduce largely the adaptability of an SDR platform.

According to the structural diagram of a general SDR,suppression of spurious signals can also be achieved in the digital domain.For instance,an adaptive filter can be implemented in the digital domain to eliminate unwanted echo signals.23A digitally supported harmonic injection scheme was proposed to cancel out modulated harmonics by providing frequency reconfigurability.24Moreover, a digital cancellation prototype was implemented to cancel out an interference signal, which operated in the latter stage of an Analog-to-Digital Circuit(ADC).25Different narrowband interference cancellation procedures were analyzed for an Orthogonal Frequency Division Multiplexing (OFDM) scheme, with potential SDR applications.26It is noted that the reported algorithms in the digital domain usually cannot handle hardware issues within a transceiver, such as I-Q mismatch, carrier leakage, and nonlinearities of components.In addition, those schemes require usually substantial signal processing computation, which requires powerful DSP hardware integrated in an SDR platform.This would increase the complexity and power consumption of such an SDR platform.Detailed comparisons between the reported techniques are shown in Table 1.It is seen that the proposed scheme is flexible for use and introduces an extra gain through the superposition of multiple SDR channels.

Different from the reported works in literature, an additional SDR radio channel is adopted to suppress spurious signals in this paper.This method avoids the usage of a tunable filter that can cover only a limited frequency range but introduce a high insertion loss.It is noted that most commercial SDR platforms have multiple channels, and this method can make full use of them.In addition, extra SDR radio channels also increase the output power of the whole system, which is useful in many wireless communication systems.As will be proven in this paper, the proposed method is applicable in a wide frequency range, without affecting the frequency reconfigurable characteristics of an SDR platform.

The remaining parts of this paper are organized as follows.Section 2 establishes a cascaded CE model of a general SDR platform, and the accuracy of this model is verified by measurements.A cancellation method is demonstrated through dual- and quadruple-channel schemes in Section 3.Section 4 demonstrates the experimental setup of vector signal cancellation in a commercial SDR platform for verification.Finally,this paper is concluded in Section 5, which also discusses the pros and cons of this method.

Fig.1 Block diagram of a general SDR platform (transmitter part).

Table 1 Comparison between different suppression schemes.

2.Conducted emission model for a general SDR platform

2.1.Analysis of a general SDR architecture

Fig.1 shows the block diagram of a general SDR platform.27The architecture is derived from Radio Frequency (RF) agile transceivers like the AD9361 chipset.The Transmitting (Tx)signal path collects two sets of complement data in the I-Q format from the digital interface, and each channel contains a Finite Impulse Response (FIR) filter and an interpolating filter.These digital filters provide a bandwidth limiting function and translate the required data rate prior to the Digital-to-Analog Conversion (DAC) circuit.In the latter stages of the DAC circuit, an analog low-pass filter can reduce spurious signals by removing sampling artifacts.Finally, an analog signal is injected into an up-conversion mixer for RF transmission.

To more clearly demonstrate spurious signals in the output port of the SDR platform,output spectra of the AD9361 chipset carried by FMCOMMS3 are captured and shown in Fig.2.The AD9361 chipset is selected owing to its popularity in commercial products.It is a high-performance RF agile transceiver, which integrates a frequency synthesizer, a mixer, and a reconfigurable digital interface in one chip.28Without losing the generality,the baseband signal is set to be 10 MHz,the carrier frequency to be 500 MHz, and the output magnitude to be - 10 dBm.The direct frequency conversion circuit is a key component to achieving a high modulation accuracy and a low transition noise.Nevertheless, it can be clearly observed from Fig.2(a)that the output signals have other spurious signals with relatively large magnitudes.Those spurious signals have an equal frequency interval that is equal to multiples of the baseband frequency.Therefore, they are regarded as the LO leakage, image frequency, and harmonic components of the baseband signal after the up-conversion process, respectively.Some odd multiples of the carrier frequency can also be observed when broadening the frequency spectrum chart.As shown in Figs.2 (b) and (c), the observation range covers three and five multiplies of the carrier frequency, respectively.The measured curves are similar to those shown in Fig.2 (a).The higher-order harmonics and the resulting modulated signals yield a reduced magnitude in a high-frequency range.It should be mentioned that this SDR circuit adopts a square wave as the LO signal as shown in Fig.3, which can provide a larger transconductance than that of the same circuit that adopts a sine wave as the LO signal.However,the square wave has rich harmonic components, which cause more spurious emissions as shown in Figs.2 (b) and (c).

2.2.Modelling of CE curves

To better understand the output spectrum of SDR devices, a cascaded model of the CE curves is established through a two-step approach.Firstly,a nonlinear model of the baseband signal is established.Then an up-conversion model is cascaded with the nonlinear model to get an accurate output spectrum.The baseband signal x(t) with a single-frequency component can be expressed as

where ωBBis the angular frequency of the baseband signal.A power-series model is useful to model the nonlinearity of a Power Amplifier (PA) used in a general SDR platform, and the amplified baseband signal yBB(t) is

Fig.2 Output spectra of a general SDR platform.

Fig.3 Illustration of Tx signal path in a general SDR platform(LO signal is square wave).

where kiis the expansion coefficients of the ith-order component, and n is the total order of the power series.A threeorder model (n = 3) is adopted in this paper, which simplifies the model and also ensures the model’s accuracy in a general SDR platform.29

The AD9361 chipset adopts a direct-conversion Zero-IF(ZIF) architecture, in which a direct-conversion circuit mixes the baseband signals of dual DAC channels with the LO signals to obtain an RF signal in a single step.The square wave is used as the LO signals, and its frequency spectrum is the superposition of many odd carrier harmonics as

Fig.4 Predicted CE curves of SDR platform by model in Eq.(5)(fLO =500 MHz).

Therefore, the up-conversion signal should include harmonic components of the LO signals as

where ωLOis the angular frequency of the LO signals, while xLOI(t) and xLOQ(t) are the LO signals used in the I and Q channels, respectively.It is seen that the up-conversed signal contains the odd-order harmonics of the square wave mixed with the baseband signal.Contrarily, usage of sine wave as the LO signals will not introduce such extra harmonic components.

Dual channels are required to generate the I-Q data, and some in-band distortions caused by channels mismatch cannot be filtered out by digital filters.After being converted to analog signals, the mixer transfers the baseband signal to an RF one.If taking the channels mismatch between I and Q paths into consideration, a CE model of a general SDR platform can be found as

Based on the established model, the output signal can be readily obtained through simple algebra.In order to include the influences of room temperature, time jitter, and other factors on the SDR hardware, model coefficients are obtained by a curve fitting process of the experimental results.The predicted output spectrum of the SDR platform is shown in Fig.4.The errors between the predicted and experimental results are provided in Table 2.Compared with the experimental results, the prediction error of the target signal is less than 1.0 dB, and the errors of the harmonic signals are below 2.5 dB.Therefore, the accuracy of the established CE model is satisfactory, which can be used in the following part.

3.Suppression of spurious emissions for a general SDR platform

Recently, several methods were proposed to suppress the spurious response of a general SDR platform operating in a receiver mode, such as an 8-phase harmonic recombination receiver, an adaptive digital feed-forward linearization structure, and an integrated circulator to cancel reciprocal mixing noises.30–32Those advancements can facilitate the reduction of spurious emissions of an SDR platform in a transmitter mode.In this section, the suppression of harmonic signals is achieved by the summation of vector signals from additional SDR channels.

Table 2 Comparison between predicted and measured results.

3.1.Dual channels

According to the datasheet of the SDR RF chipset(AD9361),it can be clearly observed that two Tx paths share one common LO signal to generate an RF signal.33Therefore,the generated signals at the two Tx paths are coherent, and hence inherent distortions of the SDR hardware may be cancelled by superposition of the two Tx signals.In this paper, the third harmonic signal is selected for suppression, since it is close to the target signal and can hardly be filtered out by other methods.The detailed approach can be summarized as follows.The target signal is derived from two separate paths with the same frequency, but different phases through a linear superposition.Through proper treatments of the two paths, the target signal can be enhanced in magnitude while the third-order harmonic signals are suppressed.Figs.5(a)and(b)demonstrate a superposition scheme of two vector signals.The two vector signals xBB1and xBB2are

where θ is the phase difference between the two vector signals,A is the amplitude of the signals, and α and β are the amplification coefficients of the two SDR channels, respectively.It is required that α and β are identical to achieve an ideal cancellation, which may be accomplished by channel calibration as discussed in the next section.

According to Eq.(6), it can be concluded that θ provides the necessary condition for suppressing the third-order harmonic component.The following parameters satisfy such requirements as

It is seen that the third-order harmonic component of Signal 2 has a phase difference of 3θ if compared with that of Signal 1, and hence they cancel out each other.An advantage of vector cancellation is to provide an extra gain to the target signal.To quantify the gain factor of the target signal, the two vector signals are normalized and arranged with an ideal phase difference of 60°.Therefore, the amplitude vector of the two signals is A= [ρ,ρ],and hence the amplitude of the target signal ASYNequals to

Theoretically,the amplitude of the synthesized target signal is increased by 2.38 dB.

Fig.5 Superposition of two signals with different phases.

3.2.Quadruple channels

The last part presents suppression of the third-order harmonic signal through vector cancellation.It is possible to suppress both the second- and third-order harmonic signals simultaneously, with extra SDR channels.In this part, this function is achieved by utilizing quadruple channels.Similar to the treatment discussed in the previous part, the four vector signals from quadruple channels should have an identical amplitude but deliberately allocated phases.It is required that the harmonic components of the four vector signals are allocated uniformly in the four quadrants as demonstrated in Fig.6.Fig.6(a) shows the permitted angular range of the four vector signals so that their second-order harmonic signals are distributed in each quadrant.Fig.6(b)shows the permitted angular range of the corresponding third-order harmonic signals.Considering the intersection region of the two graphs, the required phase settings of the four vector signals θ1,θ2,θ3,θ4are given as follows:

For instance, the following phase set θ1= 30?,θ2=90?,θ3=120?,θ4=180?satisfies the requirements shown in Fig.6, and hence it will be used for demonstrating the main concept.As shown in Fig.7 and Table 3, both the secondand third-order harmonic signals can be cancelled simultaneously.For the second-order harmonic signals, the signal of channel 1 is cancelled out by the signal of channel 3, and channels 2 and 4 also cancel out each other in the same manner.Additionally, the third-order harmonic components are suppressed in a similar way.It is seen that at least four SDR channels are required for cancelling out the second- and third-order harmonics simultaneously.

Fig.6 Permitted angular range of four vector signals.

Fig.7 Superposition of quadruple signals.

Table 3 Signal pairs for cancellation of second- and third-order harmonic signals.

Taking into account all the signal contributions, the quadruple signals are described as

Therefore, the combined signal is derived as

Compared with the target signal with a single SDR channel,the amplitude of the combined target signal is increased by 3.89 dB.

4.Hardware and software implementation

4.1.Simulation results with multiple SDR channels

In this section, the effects of the proposed method are verified by simulations, which are implemented in the MATLAB environment.The third-order nonlinear model is adopted to validate the theoretical method.The output spectra of one SDR channel and two combined SDR channels with proper phase setting are shown in Figs.8(a)and(b),respectively.According to the simulated results, it can be found that usage of the two SDR channels cancels out the third-order harmonic signal completely.

Moreover, the second-order harmonic component can be added in the nonlinear model.In this case, quadruplechannels are necessary for offsetting both the second- and third-order harmonic signals.Fig.9 exhibits a comparison between the original signal in one single SDR channel and the synthesized signal through quadruple channels.The obtained results are convincing for suppressing the spurious signals.Based on the two results, it can be concluded that the proposed cancellation method is effective to obtain a pure frequency spectrum containing only the target signal theoretically.

4.2.Experimental setup and results of a dual-channel scheme

To validate the performance of the proposed multi-channel cancellation scheme, a dual-channel SDR platform was established as demonstrated in Fig.10.The SDR platform was composed of an AD-FMCOMMS3-EBZ RF frontend and a ZC702 Field Programmable Gate Array (FPGA).The two Tx channels connect an external power combiner to obtain the synthesized signal that is captured and measured by an R&S FSV3044 spectrum analyzer.

The LO frequency is swept from 100 MHz to 3000 MHz with a uniform frequency step of 100 MHz in the experiment.The baseband frequency is 10 MHz,and the magnitude of each channel is - 10 dBm.It is noted that the sampling frequency and bandwidth also affect slightly the signal magnitude, and thus the SDR settings remain unchanged during the frequency sweep.As shown in Fig.11, the green and purple lines show the third-order harmonic signals of the two SDR channels,respectively.The red line shows the synthesized signal of the two channels.It is observed that the third-order harmonic signal has been suppressed effectively by the vector signals synthesis procedure.An average reduction effect of 15 dB has been achieved in the frequency range of 100 MHz to 3 GHz.Additionally, the maximum reduction level reaches 30.4 dB.

Fig.8 Simulated output spectra.

Fig.9 Simulated results of the quadruple-channel scheme.

Fig.10 Experimental setting with a dual-channel SDR platform and a power combiner.

Fig.11 Magnitudes of the third-order harmonic signals of two SDR channels and the synthesized one.

Theoretically, the cancellation effect of multiple vector signals is valid in the whole frequency band of the SDR platform.In practice, its performance is limited by the calibration accuracy of each SDR channel and the performance of the power combiner.The adopted power combiner covers the frequency range of 0.01–3.0 GHz, and hence low-band signals are selected for verification in this paper.

4.3.Error analysis

Multi-channel superposition offers a promising method for suppressing the spurious signal of a general SDR platform.It should be noted that the suppressing effect is also sensitive to mismatching of magnitude and phase.34,35Therefore, an accurate calibration of each SDR channel should be performed.Moreover,it is helpful to find the required calibration accuracy for any targeted suppression levels.In this part, this issue is treated for a dual-channel scheme as shown in Fig.12.

The vector signal of channel 1 is set as a benchmark, and the phase error between channels 1 and 2 is denoted as φ.The adverse effects of the phase error can be calculated as

Fig.12 Superposition errors of two vector signals.

where Poffsetis the third-order harmonic power of the synthesized signal before calibration, and Poriginalis the original harmonic power of channel 1.Similarly, the effects of the magnitude error can be evaluated by

where adis the magnitude difference between channels 1 and 2,with the magnitude of channel 1 being regarded as a reference.The LO signal generation is the main contributor to a phase error.According to the datasheet of the SDR chipset(AD9361), a fractional-N PLL with a high frequency resolution is adopted.Additionally, an on-board power monitor can estimate the transmitted power with high precision, and hence the effect of the magnitude error is not significant.Therefore, the main focus is the phase error that affects more the achievable cancellation levels.As shown in Fig.13, the phase error has an adverse effect on the theoretic cancellation limits.For instance, the theoretic limit of suppression reduces to about-20 dB with a phase error of 2°.This curve gives an approximate requirement of calibration accuracy for each SDR channel.

Fig.14 depicts the cancellation of the third-order harmonic signal after phase calibration of two SDR channels.An improvement of about 8.8 dB is achieved on average, and the maximum suppression value of the third-order harmonic signal is increased by about 13.6 dB, as shown in Table 4.The experimental results show that the phase error has a great influence on the cancellation effect,which is consistent with the theoretic analysis discussed above.

Fig.13 Theoretic cancellation limit with regard to phase error.

Fig.14 Magnitudes of third-order harmonic signals after phase calibration.

Table 4 Measured suppression levels of third-order harmonic signals.

According to the measured results shown in Fig.13,the following error analysis can be performed.From the SDR software control interface, the phase stepping of the baseband signal is 1°.According to Eq.(12),the cancellation effect with two SDR channels is - 24.2 dB.The experimental results do not achieve the theoretic accuracy, but with a difference of ～7 dB.This may be caused by the synchronization issues of the two channels, i.e., the clocks of the two channels are not strictly synchronized.In addition,the electrical path difference between the two SDR channels in the Printed Circuit Board (PCB) may also contribute to some errors.

5.Conclusions

A harmonic suppression method through superposition of multiple channels is proposed in this paper.This method takes advantage of the multi-channel architecture of a general SDR platform and improves the CE performance through vector signal cancellation.A cascaded model is also established for describing the CE curves, from which a deeper understanding of the transmitting behavior is achieved.The principle of vector signal cancellation is presented, and the theoretic limit is also discussed.It is found that the phase errors have a larger effect on the theoretic cancellation limit.A hardware prototype is also built and measured for verifying the presented method.The suppression level of third harmonic signals is 24 dB on average, in a wide frequency spectrum of 100–3000 MHz.This method is potentially useful for solving EMC issues of a general SDR platform.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Nos.U2141230 and 61971018).