Yannian Lou,Chaojie Zhang,Xiaojun Jin,and Zhonghe Jin

Micro-Satellite Research Center,Zhejiang University,Hangzhou 310027,China

Application and improvementofwaveletpacketde-noising in satellite transponder

Yannian Lou,Chaojie Zhang*,Xiaojun Jin,and Zhonghe Jin

Micro-Satellite Research Center,Zhejiang University,Hangzhou 310027,China

The satellite transponder is a widely used module in satellite missions,and the most concerned issue is to reduce the noise of the transferred signal.Otherwise,the telemetry signalwill be polluted by the noise contained in the transferred signal,and the additionalpower willbe consumed.Therefore,a method based on waveletpacketde-noising(WPD)is introduced.Compared with other techniques,there are two features making WPD more suitable to be applied to satellite transponders:one is the capability to deal with time-varying signals without any priori information of the input signals;the other is the capability to reduce the noise in band,even if the noise overlaps with signals in the frequency domain,which provides a greatde-noising performance especially for wideband signals.Besides,an oscillation detector and an averaging filter are added to decrease the partialoscillation caused by the thresholding process of WPD.Simulation results show that the proposed algorithm can reduce more noises and make less distortions of the signals than other techniques.In addition,up to 12 dB additional power consumption can be reduced at–10 dB signal-to-noise ratio(SNR).

wavelet packet de-noising(WPD),satellite transponder,power consumption reduction,real-time de-noising.

1.Introduction

In satellite missions such as the satellite communication system[1],the satellite video transfer system[2],the two way satellite time and frequency transfer(TWSTFT)system[3]and the satellite coherent ranging system(SCRS) [4],the transponder is an important module which allows the signal to be transmitted from an earth station to another through the satellite.When the signalpasses through the transponder,it is important to reduce the noise for two reasons.On one hand,it prevents the telemetry signals generated by the satellite from being polluted by the noise contained in the transferred signal.On the other hand,the noise will increase the power consumption because the noise is amplified and transmitted as well.

There are many methods to reduce the noise,such as finite impulse response(FIR)filtering,fast Fourier transform(FFT)based de-noising,Kalman filtering,averaging filtering,median filtering and wavelet packet de-noising (WPD).Among these methods,FIRfiltering is widely used in satellite transponders for its linear phase characteristic, stability and simple structure[5].If the approximate frequency band of the input signal is known in advance,it is easy to design an FIR filter to reduce the noise out of band.Besides,in some missions such as the SCRS,it requires that the group delays of different side-tone signals are identicalwhich can be metby the FIRfilterforits linear phase characteristic.However,the de-noising performance decays for wideband signals,as the FIR filtering can only reduce the noise outofband.

FFT based de-noising is an alternative way to reduce noise[6].It transforms the signal into frequency domain and selects a suitable threshold to deal with the coefficients.All the coefficients below the threshold are set to zero.This method can be used only when all frequency coefficients of the signal are much larger than the coefficients of noise.Otherwise,itwillcause distortions.Moreover,the de-noising performance is limited for wideband signals because only few coefficients are setto zero.

Kalman filtering is a modern method of de-noising, which has a great performance[7].However,itis complicated and much prioriinformation ofthe inputsignalneeds to be informed in advance to setup the state-transition matrix,the measurementmatrix and some other functions.If the priori information is insufficient or inaccurate,it will cost much time for the convergence process.Moreover,if the characteristic of the input signal changes,it will also costsome time for the convergence process.

Averaging filtering is a kind of time-domain filtering.It replaces the currentvalue with the mean value ofits neighboring values.Thus,it can reduce high frequency noise,but some details of the signal will be eliminated as well, leading to distortions.

Median filtering is also a kind of time-domain filtering. Different from averaging filtering,it replaces the current value with the median value of some neighboring values. Its low-passcharacteristic willalso cause some details loss.

WPD is a modern de-noising method based on wavelet packet transform,developed from wavelet de-noising which was proposed by Donoho and Johnstone[8–10].It has been widely used in image de-noising[11,12],speech signal de-noising[13–16]and sensing signal de-noising [17–19].There is also application potential in satellite communication systems and satellite navigation systems [20,21].The principle of WPD is that the energy of signals is concentrated in a limited number of coefficients in the wavelet packet domain,while the energy of noise is distributed in the entire waveletpacketdomain.Therefore, afterthe waveletpacketdecomposition,the waveletpacket coefficients of signals are larger than the coefficients of noise,leading to the separation of the signals and the noise [11].Then a threshold is set for allcoefficients.The coefficients below the threshold is set to zero,so the noise can be reduced effectively.Compared with other techniques, WPD can reduce noise in band,and avoid signal detail loss.However,partial oscillation caused by the nonlinear process of thresholding is a major disadvantage.

As WPD has some particular advantages,we propose our satellite transponder de-noising algorithm based on WPD which overcomes the drawback by combining WPD with averaging filtering.

The remainderofthis paperis structured as follows.The typical structure of a satellite transponder is introduced in Section 2.Section 3 concentrates on the algorithm,including the basic WPD,the selection of threshold and threshold function,the elimination of partial oscillations,the time consumption evaluation and the workflow.Section 4 shows the simulation results compared with other denoising techniques,both on the de-noising performance, the distortion performance and the powerreduction performance.Finally,Section 5 concludes this paper.

2.Structure ofsatellite transponder

Fig.1 shows the typical structure of a satellite transponder and the signal characteristics of all nodes.Atfirst,the received signal as in Fig.1(a)is mixed with the local oscillator signal to move the signal to the baseband,like Fig.1(b).Then,some amplifiers are used to amplify the signal,and the noise is amplified as well,as in Fig.1(c). Afteramplified,the signalpasses through a filter to reduce the noise outof band,shown in Fig.1(d).Then,demodulation is carried out to get the transferred signal(see Fig. 1(e)).The de-noised signal(see Fig.1(f))is modulated on the downlink carrier together with the telemetry signal as in Fig.1(g).After the modulation,a series of amplifiers are adopted to amplify the signal,as in Fig.1(h),and an up-converter is adopted to move the signal to the radio frequency(RF)band,as in Fig.1(i).In order to reduce the noise outof band and the mirror signalcaused by frequency mixing,an RF band-pass filter is adopted,as in Fig.1(j).The last level is a power amplifier(PA),which makes the signalstrong enough to be sentback to the earth station,as in Fig.1(k).

Fig.1 Satellite transponder

From Fig.1 and above introduction,two issues come up.First,the telemetry signalwillbe polluted by the noise contained in the transferred signal,leading to the increase of the bit error rate(BER).Moreover,this problem cannot be solved by increasing the signal power because the noise power will also increase and the signal-to-noise ratio(SNR)remains the same.Second,the noise is amplified several times and transmitted together with the signals,which will cost additional power,especially for the PA module.The satellite transponderdeveloped by Microsatellite Research Center of Zhejiang University is discussed as an example.The total gain of this transponder is from 70 dB to 135 dB.Assuming thatthe bandwidth is 2 MHz(63 dBHz)and noise level is–174 dBm/Hz,the outputpower ofthe noise willbe up to 24 dBm(251 mW), calculated by(1).With the PA efficiency of 20%,the additional power consumption caused by noise is 1.255 W. It is unacceptable as the total power consumption of the transponder is only 3.5 W.It means that if no de-noising method is adopted,35.9%additional power will be consumed.In(1),Pnoiseis the power of outputnoise.

Therefore,we have to find a method to avoid the additionalpower consumption caused by the noise and to prevent the telemetry signal being polluted by the noise in satellite transponders.These requirements lead to the application of WPD in satellite transponders.

3.Algorithm and improvement

3.1 WPD algorithm

Assume thatthe signalis

where f(k)is the input signal,s(k)is the original signal, σis the noise leveland n(k)is a uniform white noise.

Fig.2 shows the de-noising process and the signal features.Itcan be divided into foursteps.

Fig.2 Workflow of WPD

Step 1The inputsignalis decomposed to L levels with a certain kind of wavelet function.In Fig.2,it is decomposed in three levels.

Step 2Selecta group of optimalwaveletpacket basis based on the entropy ofevery node in the decomposed tree.

Step 3Dealthe wavelet packetcoefficient wj,kwith a threshold and a threshold function.Then getthe de-noised coefficient?wj,k.

Step 4Reconstructthe signalfrom?wj,kby the inverse waveletpackettransform.

3.2 Threshold and threshold function

As the WPD algorithm has been discussed several times [11–14,22],we do not cover every aspect of it.Instead, only threshold and threshold function are discussed in this paper,as the performance of WPD mostly depends on them.For the threshold,if it is too aggressive,some parts of signals will be eliminated,leading to distortions.However,if it is too conservative,the de-nosing performance willbe limited.The threshold function decides how to deal the coefficients with the threshold,so it is also important in WPD.Besides,the requirements of differentapplication areas vary from each other,so the threshold and the threshold function should be selected according to calculation resources,distortion tolerance,de-noising requirement and working SNR in different applications.This is why they are discussed in our satellite transponderapplication.

In[11–13],severalthresholds,such as sqtwolog,minimaxi,rigrsure,heursure,mean value and median value,are introduced.

For rigrsure and heursure,the process of risk calculation is complicated,calculation complexity is too high for the limited computing resources in the satellite transponder,so they cannot be adopted.The mean value method and the median value method do not take the SNR into consideration so they can only be used in the high SNR situation.The remaining methods as sqtwolog and minimaxi are compared in Fig.3 when SNR is–6 dB.From Fig.3,itis obvious thatthe sqtwolog threshold has a better de-noising performance,but it is too aggressive,causing more distortion.The minimaxi threshold is more conservative which leaves more noise and less distortion.

Fig.3 Comparison between minimaxi and sqtwolog

Define the mean square error(MSE):

whereσstands for the standard deviation of the noise,and n is the number of inputsignalpoints.

Table 1 Comparison between minimaxi and sqtwolog

After the selection of the threshold,threshold functions are discussed.In[14],threshold functions are summarized as follows.

Hard threshold function is

Softthreshold function is

Improved threshold function 1 is

Improved threshold function 2 is

whereμis defined as follows:

Improved threshold function 3 is

In all the threshold functions,λis the threshold,sgn(·)is the sign function,is the resultcoefficient.

Fig.4 shows the behaviors of threshold functions with thresholdλ=10.As the coefficients larger than the threshold are kept unchanged in hard threshold function, the distortion caused by de-noising is the smallest among all the threshold functions.This assumption is supported by the simulation results shown in Table 2.The inputsignal in this simulation is a multi-tone signalwith frequencies of 16 kHz,100 kHz and 200 kHz,and the SNR is 0 dB.It shows thatthe hard threshold function makes the leastdistortion at all frequencies.Moreover,since de-noising is a nonlinear process,the distortions of 16 kHz,100 kHz and 200 kHz are atdifferentlevels,which makes the distortions more unacceptable in satellite transponders.Therefore,the hard threshold function is selected.

Fig.4 Behaviors of different threshold functions

Table 2 Distortion value of different functions

Besides,the hard threshold function is the simplestone among allfunctions.Every coefficientshould be dealtwith the threshold function,so a little difference in the complexity of functions will cause a big difference in computing resources and time consumption.The computing time and resources are limited in satellite transponders,which is the other reason why the hard threshold function is selected.

3.3 Eliminate partialoscillation

In Fig.4,itis shown thatthe hard threshold function is the only one which is discontinuous atλ.This drawback leads to more partial oscillations in time-domain,as shown in Fig.5.

Fig.5 Partialoscillations in time-domain

These oscillations may cause many problems in satellite transponders,such as bit error for data transmission, loss of lock for phase lock loop(PLL),and fake information for images.Thus,it is important to reduce them in satellite transponders.To reduce these oscillations,we have two choices:one is to selectother threshold functions instead,atthe costofmore distortions and more computing resources;the other is to detect and eliminate these oscillations after the de-noising process.Since we do not want to compromise on the distortions,the latter one is selected.

Atfirst,we need to detectthe oscillations as follows:

(i)Divide the de-noised signal into several time intervals.

(ii)Calculate the number of peaks in each time interval.

(iii)Compare the number of peaks in an interval with the average value of its eight neighboring intervals.If it has three more peaks,the oscillation is confirmed.

As the signals through satellite transponders are modulated and band-limited,the number of peaks will not change rapidly among neighboring intervals.However,if the oscillation occurs,the number of peaks in an interval will increase rapidly,as shown in Fig.6.Thus,the above process can detectthe oscillations effectively.Once the oscillation is detected,we need to find a method to eliminate it.The averaging filter is a good choice for its low-pass characteristic.Only the intervals thatthe oscillation occurs are dealt with the averaging filter,to avoid the detail loss of signals in otherintervals.

After the process,the signal shown in Fig.5 is converted to the signal shown in Fig.7,with the oscillation decreased.

Fig.6 Number of peaks in an interval

Fig.7 Result of eliminating partialoscillation

3.4 Time consumption evaluation

Since the transponder is a real-time system and WPD is a frame-based system,the signal should be buffered at the length n and then be dealtwith WPD.The de-noising performance increases with n increasing.However,the requirement of real-time means that n cannot increase unlimitedly.

The time delay of WPD includes three parts:buffering, processing and unbuffering.Assuming thatthe sample frequency is fs,the buffering delay is n/fs.The processing delay is determined by the complexity ofthe algorithm and the ability of processor.If the field programmable gate array(FPGA)is adopted to carry on parallelprocesses with high speed,the processing delay is quite small and can be ignored.Different from buffering,the unbuffering is to convertthe signalfrom frame-based to time-based with only one clock delay,so the delay is also small and can be ignored.As a result,n is determined by the sample frequency fsand the totaldelay tolerance tdas follows: In this paper,the signal length n is set to 213,and the sample frequency is 10 MHz.Therefore,the corresponding time delay is 0.82 ms.

3.5 Workflow of algorithm

The workflow is introduced as shown in Fig.8 based on the above discussions.

Step 1Atfirst,buffer the signalto length n;

Step 2Decompose the signal with optimal basis and calculate the threshold with estimated noise power in parallel,to getthe coefficients and threshold atthe same time;

Step 3Deal the coefficients with minimaxi threshold and hard threshold function;

Step 4Reconstructthe signalby inverse waveletpacket transformation;

Step 5Divide the reconstructed signalinto severaltime intervals;

Step 6Calculate the numberof peaks in every interval;

Step 7For all intervals,detect whether the oscillation occurs;

Step 8If the oscillation occurs,dealthe intervalwith an averaging filter to eliminate the oscillation;

Step 9After all the intervals has been processed,repeat the Step 6–Step 8,until there is no new oscillation detected.

Step 10Unbufferthe frame-based signalto time series.

Fig.8 Workflow of the proposed algorithm

4.Simulation results

Two kinds of signals are adopted in simulation,shown in Fig.9.Fig.9(a)is a multi-tone signal,with frequencies of 16 kHz,100 kHz and 200 kHz,representing for narrowband signals.Fig.9(b)is a phase modulation(PM)signal, with carrier frequency of 500 kHz and modulation depth of 400 rad,representing for wideband signals.

Fig.9 Signals in simulation

To explain the performance of the proposed method,we compare it with an averaging filter,a median filter,a FIR filterand the originalWPD.The comparison is on the MSE performance and the power reduction performance.

Fig.10(a)shows the MSE performances of the multitone signal.It can be seen thatwhen the SNR is low,FIR performs best,because most noise is out of band for narrowband signals,which can be eliminated by FIR effectively.The performance of the improved WPD is close to FIR because itcan also eliminate noise out of band effectively and the partial oscillations of the improved WPD can be decreased notably.The performance of the original WPDis worse than the improved WPDbecause the oscillations occurfrequently when SNRis low.The performances of median filtering and averaging filtering are notso good as they can only eliminate noise athigh frequencies.

When the SNR is high,the performance of FIR is degraded.The reason is as follows.The frequency response of FIR is not absolute flat in the passband,and narrowerpassband leads to largerfluctuation,which willcause more distortions.For the multi-tone signal,the passband is very narrow,so the distortion becomes the major part of the MSE instead of noise,when SNR increases.As a result, the MSE is degraded.With the high SNR,the improved WPDperforms bestas the distortion is limited by selecting optimal threshold and threshold function.The MSE performance gap between improved WPD and original WPD is narrowed as the number of oscillations decreasing with SNR increasing.

For the wideband signal in Fig.10(b),things are different.When the SNR is low,the improved WPD performs best,and the performance is similar to the result in Fig. 10(a).The reason is that the improved WPD can eliminate not only the noise out of band,but also the noise in band.Thus,the bandwidth of the signalwillnotaffectthe de-noising performance too much.The MSE performance gap between the improved WPD and the original WPD is still owing to the oscillations.For FIR,only the noise out of band can be eliminated,so compared with the narrowband signal,the performance is degraded forthe wideband PMsignal.

Fig.10 Comparison of MSE performances

When the SNRis high,the MSEs ofmedian filtering and averaging filtering are degraded much.The reason is that the wideband PM signal has some high frequency parts, which will be wiped out by median filtering and averaging filtering for their low-pass characteristics.Therefore, distortions occur and the MSEs are degraded.For FIR,the passband is relative wide so the frequency response is relative flat,resulting in very smalldistortions.The improved WPD stillperforms best,as itcan keep high frequency details and avoid distortions concurrently.

Fig.11 shows the powerreduction performances of different methods.In the simulation,the power of signals is set to 24 dBm.The results show that the improved WPD can reduce most power for both the wideband signal and the narrowband signal.When the SNR is–10 dB,up to 12 dBpowerconsumption can be reduced by the improved WPD.The main reason is thatmostpowerof noise is eliminated by the improved WPD,and even a small part of signals’power is eliminated as well,especially at the low SNR.Besides,the averaging filter added in the improved WPD eliminates the power of oscillations.

Fig.11 Comparison of outputpower

However,some weak parts of signals willbe eliminated by the improved WPD at the low SNR,leading to somepowerloss,which can be seen in Fig.11(b).This is a drawback of the improved WPD.Fortunately,the power loss is less than 1.5 dB and the MSE performance is not affected too much.Thus,this drawback can be tolerated forsatellite transponders.

In Fig.11(b),there is also power loss for averaging filtering and median filtering.Itis because the high frequency parts of the signalthatis eliminated by averaging filtering and median filtering for their low-pass characteristic.

In summary,the simulation results show that the improved WPD performs best on de-noising,distortion and power reduction,for both narrowband and wideband signals.

5.Conclusions

In this paper,a de-noising method based on WPD is introduced and used to satellite transponders.An oscillation detector and an averaging filter has been added into the method,in order to decrease the oscillation caused by the WPDand some applicability adjustments are carried outto meetthe specific requirements of satellite transponders.

With the proposed method used to satellite transponders,many benefits are achieved.As WPD can deal with all kinds of signals with a single system without any priori information,it improves the versatility of satellite transponders.The satellite transponders can transfer differentsignals withoutany changes if the proposed method is adopted.This is an importantbenefitbroughtby WPD. Besides,the capability of reducing the noise in band ensures the de-noising performance for wideband signals,so the powerconsumption is reduced and the telemetry signal is prevented from being polluted.Moreover,the oscillations caused by WPD can be eliminated by partial averaging filtering effectively,while mostdetails of signals are kept,which improvesthe detaildistortion performance further.These benefits make a greatpotentialforthe proposed method to be applied to satellite transponders.

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Biographies

Yannian Louwas born in 1987.He received his B.E.degree in information engineering from Zhejiang University in 2010,and he is a Ph.D.candidate in Zhejiang University now.He is a memberof Micro-Satellite Research Center,Zhejiang University.His research interests are satellite communication and navigation systems.

E-mail:yannis@zju.edu.cn

Chaojie Zhangwas born in 1982.He received his B.E.and Ph.D.degrees from Zhejiang University in 2004 and 2009,respectively.Now he is a lecturer of Zhejiang University.He is a member of Micro-Satellite Research Center.His research interests include micro satellite and software defined radio technologies.

E-mail:zhangcj@zju.edu.cn

Xiaojun Jinwas born in 1977.He received his B.E. M.E.and Ph.D.degrees from Zhejiang University in 2001,2004 and 2007,respectively.He joined the faculty of Zhejiang University in 2009,and has been an associate professor since 2010.His research interests include relative ranging,formation flying and navigation of micro satellite.

E-mail:axemaster@zju.edu.cn

Zhonghe Jinwas born in 1970.He received his Ph.D.degree in microelectronics and solid electronics from Zhejiang University in 1998.Since 2002,he has been a professor with the Department of Information and Electronics Engineering, Zhejiang University.His research interests include micro satellite,optical sensors and MEMS/NEMS technologies.

E-mail:jinzh@zju.edu.cn

10.1109/JSEE.2015.00074

Manuscript received March 07,2014.

*Corresponding author.

This work was supported by the National Natural Science Foundation of China(61401389).