Continuous-Wave Interference Mitigation for Acquisition Method in Unified Carrier TT&C Systems

Yunyun Wu, Xiuli Yu and Yongqing Wang,

(1.School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China; 2.Beijing Institute of Astronautical Systems Engineering, Beijing 100076, China)

Abstract: An interference mitigation for acquisition method, based on both energy center and spectrum symmetry detection, has been proposed as a possible solution to the problem of signal acquisition susceptibility to continuous-wave interference (CWI)in unified carrier telemetry, tracking, and command (TT&C) systems.With subcarrier modulation index as a priori condition, the existence of CWI is determined by comparing the energy center with the symmetric center.In the presence of interference, the interference frequency point is assumed and culled; sequentially， the spectral symmetry is used to verify whether the signal acquisition is realized. Theoretical analysis, simulations, and experimental results demonstrate that the method can realize the acquisition of the main carrier target signal with an interference-to-signal ratio of 31 dB, which represents an improvement over the existing continuous-wave interference mitigation for acquisition methods.

Key words: unified carrier telemetry tracking and command (TT&C); interference mitigation; signal acquisition; spectrum symmetry

Unified carrier system technology is widely used in commercial satellite and deep space telemetry, tracking, and command (TT&C) systems. Unified carrier TT&C systems are characterized by their phase modulation of multiple communication subcarriers on the main carrier which has numerous applications, including tracking, telemetry, remote control, speed and distance measurement,and other communication functions[1]. According to the characteristics of signal modulation, the main carrier is vital to achieving acquisition. The key to signal acquisition under this system is to acquire the main carrier.At present, unified carrier system technology is open and most satellites have limited anti-interference capabilities[2].In addition, spacecraft utilize wide beam antennas which have difficulty achieving space filtering[3]and are vulnerable to interference, resulting inacquisition failure. Ref.[4] assumed a white Gaussian noise(WGN) interference protection threshold for a deep space TT&C station. However,continuous wave interference differsfrom WGN. CWI is a type of strong, suppressive jamming that is easy to produce and use. When strong CWI exists, the conventional carrier acquisition algorithm is no longer applicable.Ref. [5] analyzed the losses in both ranging accuracy and error rate fora deep space communication network that is caused by the presence of CWI. When the interference signal’s power is greater than the system’s anti-interference margin, the system acquisition performance deteriorates dramatically, the acquisition time grows, and the false alarm probability increases[6]. Studying a unified carrier acquisition algorithm with continuous wave interference mitigation is of practical significance.

Early mature unified carrier TT&C systems, such as America’s Apollo landing system[7]and China’s unified S-band (USB)[8], utilized frequency scanning that searched for Doppler frequencies for signal acquisition.However,their search steps were limited by the bandwidth of the loop filter, scanning was slow, their acquisition times were long, and their phases were unstable[9]. With the development of digital signal processing technology, more attention has been paid to the spectral characteristics of signals to improve signal acquisition performance. There are two primary aspects of the spectral characteristics of unified carrier TT&C signals.One is that the modulation index determines the distribution of the signal’s energy. The greater the modulation index, the less the main carrier energy and the greater the subcarrier energy. The second is that the subcarrier signal spectra are symmetrical about the main carrier. When the modulation index is smaller than 1.4, the spectral peak of the modulation signal is located at the main carrier and can be acquired with the maximum value decision algorithm[9-10].However, this is not the case for a large modulation index.

Ref.[11] demonstrates that the use of the smallest error judgment method with pseudo-symmetric points allows the influence of the modulationindex to be ignored.However, their algorithm needs to consider every point in the Doppler frequency range to determine the symmetry, which results in a huge computation cost and is not conducive to the achievement of the implementation. The acquisition method based on the spectrum energy center in Ref. [12] requires a moderate amount of computation.However, it can only beapplied when both the carrier energy and spectrum symmetry centers are consistent, and this is not the case when interference is present.An acquisition method based on circular self-convolution acquisition using spectral symmetry is proposed in Ref.[13]. Its computational load is small, and it is easy to realize, but it also relies on the premise of spectrum symmetry. When CWI exists, the spectrum symmetry condition is no longer satisfied. Therefore, this study proposes a CWI mitigation acquisition method in which the positional relationship between the energy and symmetry centers is utilized to verify the existence of interference. In the presence of CWI, the frequency of the suspected interference is determined and eliminated.Both the symmetrical center and the interference are obtained simultaneously, allowing main carrier acquisition to be achieved.

1 Signal Model

The unified carrier TT&C system utilizes phase modulation (PM), and a common expression for the receiver’s input signal is

(1)

whereAis the carrier’s amplitude,ωcis the main carrier’s angular frequency,midenotes the phase modulation index of theith subcarrier, andωidenotes the angular frequency of theith subcarrier. The frequency domain expression for the PM signal is obtainedvia Fourier transform (FT) as

(2)

In the unified carrier TT&C system, the uplink telecomm(TC) space data signal typically includes a PCM-BPSK-PM modulated TC subcarrier and a PCM-BPSK-CDMA modulated ranging subcarrier. Under the influence of both CWI and Gaussian noise, the input baseband signal can be expressed as

s(t)=Acos [ωct+m1X1(t)+m2X2(t)]+
J(t)+v(t)

(3)

wherem1is the modulation index of the TC signals which have a restrained value because small values of this index make it difficult to command signal synchronization[12]while large values result in downlink modulation losses[14]. The Consultative Committee for Space Data Systems (CCSDS)blue book has standardized this value to the range of 0.2-2 rad[15]. Meanwhile,m2is the modulation index of a ranging signal, with a range of 0-1.4 rad[15]. The TC signalX1(t) is represented as

(4)

whereωscis the angular frequency of the subcarrier,d(t) represents the command data with possible values of ±1,p(t) is the unit impulse response, andR1is the data rate of the command. Moreover, the ranging signalX2(t) is represented as

(5)

wherec(t) is pseudo-random(PN) code with possible values of ±1 andR2is the data rate of the PN code.

Finally, the CWI signalJ(t) is represented as

J(t)=Ajcos (ωjt)

(6)

whereAjis the interference’s amplitude,ωjis the interference’s angular frequency, andv(t) represents Gaussian noise with mean 0.

Based on the Bessel function, if the ordern>m1, the value ofJn(m1) decreases rapidly. Furthermore, whenm1>1.4, the peak value of the unified carrier signal is no longer the main carrier but becomes the subcarrier. Therefore, the algorithm needs to considerm1with the value of 1.4 as a boundary. Whenm1≤1.4, only the side frequency components,n=1, need to be considered, and when 1.4

Whenm1is less than or equal to 1.4, the single power spectrum corresponding to Eq.(3) ignores the frequency components higher than the first order and can be expressed as

(7)

The first to the fifth terms of Eq.(7) are the power spectrum of the main carrier, command subcarrier, ranging subcarrier, CWI, and Gaussian noise, respectively.

When 1.4

(8)

The third term of Eq.(8) is the second-order frequency component of the remote control command subcarrier, and the other terms are consistent with Eq.(7).

The total power of each frequency component of the PM signal is equal to the power of the unmodulated carrier, and the modulation assigns carrier power to each component in accordance with the modulation index.

Total transmit power is given by

(9)

The modulation loss is defined as the ratio of the service power to the unmodulated carrier power.In addition, the main carrier modulation loss(CML) is

(10)

The first-order TC subcarrier modulation loss (SCML) is

(11)

The second-order TC subcarrier modulation loss(SC2ML) is

(12)

and the ranging subcarrier modulation loss (RCML ) is

(13)

The interference-to-signal ratio (ISR) is the ratio of the CWI’s power to the total transmitted power.

Without any loss of generality, the modulation index of the TC subcarrier is set to values of 1 and 2, while the ranging subcarrier modulation index is set to 0.43. The modulation loss of each carrier component is shown in Tab.1.

Tab.1 Modulation losses for carrier components

As Tab.1 and Fig.1 illustrates, whenm1=1, the main carrier amplitude is greater than that of the first-order subcarrier.Therefore, if the ISR is greater than -3.15 dB, the conventional maximum value detection method leads to false acquisition, and when it is greater than -4.9 dB, the symmetry is destroyed and the circular self-convolution method cannot be used.

As both Tab.1 and Fig.2 illustrate, when the modulation indexm1=2, the TC subcarrier’s first-order amplitude is greater than that of its second order, and each of theseis greater than that the main carrier. For this case, the maximum value method is inapplicable. Moreover, when the ISR is greater than -13.8 dB, the convolutional method cannot be used.

Fig.1 Spectrum for m1=1 with ISR=-3.15 dB

Fig.2 Spectrum for m1=2 with ISR=-2.6 dB

By contrast, we can obtain clear relationships between the amplitudes and locations of the main carrier and the subcarriers. In addition, we observe that the diluted spectrum ranging signals are nearly submerged in noise and thus can be ignored.

2 Methods

2.1 CWI detection algorithm based on energy center

The CWI signal does not always need to be removed, since it does not affect the acquisition of the main carrier either when the interference falls outside of the band or when the interference’s power is small. Interference mitigation operations increase the complexity of the algorithm and prolong the acquisition time, so it is necessary to detect the presence of interference. The interference only needs to be eliminated if the presence of acquisition-affecting CWI is verified.

The received signal is sampled by an analog-to-digital (A/D) converter and down-converted to a baseband signalx(n). Then anN-point fast Fourier transform (FFT) is performed, whereNis a power exponent of 2, and the result is squared to obtain the energy as

E(k)=|X(k)|2,k=1,2,…N

(14)

By analyzing the structure of the PM signal’s spectrum, it is determined that the signal’s energy is symmetrical when there is no CWI, and the energy center is the center of symmetryor the main carrier location. When CWI is present, the symmetry is broken, and the energy center deviates from the center of symmetry and moves closer to the position of the interference. Therefore, by defining whether the energy center of the received signal is at the center of symmetry or not, the CWI signal can be determined.

The energy center of the received signal can be obtained by using

(15)

The modulation indexm1of the subcarrier is required as a priori information to calculate the signal’s center of symmetry, with 1.4 used as a boundary. Whenm1<1.4, the highest peak of theE(k) spectrum is assumed to be the center of symmetry, and its frequency is recorded ask′c. When 1.4

Then, the energy centerkcis compared with the center of symmetryk′c. Ifk′c=kc, then either no interference exists or the interference’s power is too small to affect the carrier acquisition,kcis the position of the main carrier, and acquisition is achieved. Whenk′c≠kc, i.e. CWI exists, both interference detection and elimination is required for subsequent acquisition operations, and the spectrum symmetry acquisition method with interference mitigation continues to be used.A flowchart of the proposed method is shown in Fig.3.

Fig.3 Flowchart of proposed method

2.2 CWI mitigation for acquisition algorithm based on spectral symmetry

If interference is identified, it needs to be detected and eliminated. It is also necessary to consider the subcarrier modulation indexm1and deal with it differently for different values.

①m1<1.4

Whenm1<1.4, the single sideband power spectrum of the received signal is shown as Eq.(7) and ignores the harmonic component of the subcarrier. For this case, the ranging subcarrier uses a PN code to spread the spectrum, which submerges the signal in noise and has no influence on the determination of symmetry. Therefore,the range code is considered unmodulated and thus, only the main carrier, the first-order subcarrier, and the CWI signal need to be considered. The steps for doing so are as follows.

(a)Use the peak detection method to iteratively select four lines and arrange them in order of frequency fromp1top4.

(b)Assuming thatpi(with an initialivalue of 1) is the interference, setE(pi)=0, which eliminates the interference, and set the three remaining frequency points aspmin,pmedandpmax.

(c)Determine if the three lines satisfy both symmetry and the two judgment conditions:

(16)

Term ① ensures that the maximum valuepmaxand the minimum valuepminare symmetrical aboutpmed, while term ② guarantees thatpmaxandpminhave equal amplitudes. Before judgment,α-βsmoothing filter algorithm is used to judge the amount of |pmin+pmax-2pmed| and |E(pmin)-E(pmax)| to reduce the impact of noise on the decision[17].

(d)If the symmetry condition in (c) is satisfied, consider the eliminatedpithe true interference frequency,and considerpmedthe main carrier to be acquired.In addition, output both the interference’s frequency and the acquisition results. If not, seti=i+1 and repeat steps (b)-(d) until the symmetry condition is satisfied.

② 1.4

When 1.4

(a)Use the peak detection method to iteratively select six lines and arrange them in order of frequency fromp1top6.

(b)Assuming thatpi(with an initialivalue of 1) is the interference, setE(pi)=0, eliminates it, and set the remaining five frequency points aspmin,ps_min,pmed,ps_max, andpmax.

(c)Determine whether symmetry is satisfied or not by using the two conditions from Eq.(16).

(d)Repeat steps (b)-(d) form1<1.4.

2.3 Acquisition probability

A square-law detector is used with a decision quantity ofE(k)=z=I2+Q2. Under the assumption ofH0, when no CWI exists,zobeys the centralχ2distribution with two degrees of freedom, and the probability density function is

(17)

Under the assumption ofH1, when the CWI exists,zobeys the non-centralχ2distribution with two degrees of freedom, and the probability density function is

(18)

whereAjrepresents the interference’s amplitude andI0is the Bessel function of the first kind.

The distribution of |Ei-Ej|

(19)

The location constraint can be obtained from the secondary judgment of Ref.[18]. The probability that |pi+pj-pk|≤lis denoted asp1. That is, from the integer setφ1(φ1={0,1,…，N}), the three integerspi,pjandpkare extracted randomly, and the probability that they satisfy |pi+pj-pk|≤lis denoted asp1; this can be written as

(20)

In addition, the total false alarm probabilityPFAis

PFA=1-pl(1-pfa1)

(21)

Using CFAR detection, the decision thresholdVis obtained by determining both the two constantsPFAandl, and the NFFT points. The detection probability is

(22)

The acquisition probability of the proposed algorithm is 90% whenPFA= 10-6under the location constraintl=5.

3 Results

A simulation of the TC space data uplink of a unified carrier TT&C system was performed with a sampling frequency of 60 MHz. The main carrier frequency of the baseband signal was 100 kHz. The values for the TC signal subcarrier modulation index were selected to be 1 and 2 under a frequency of 32 kHz and a command data rate of 2 bit/s. In addition, the ranging subcarrier modulation index was 0.43, the PN code rate was 1.023 Mbit/s, and the number of FFT points was 65 536. Finally, the carrier-to-noise ratio was 60 dB.

3.1 Simulation

After both the FFT and squaring of the baseband signal, the signal’s energy spectrumwas obtained. An interference detection algorithm based on the energy center was used to determine the presence of CWI in the signal. The conventional maximum value detection method was adopted when no interference existed. Otherwise,an interference mitigation method based on symmetry was used to eliminate the interference.

To validate the proposed method, it was compared to both the maximum value decision and circular self-convolution algorithms.Moreover, the theoretical performance in the ideal condition of the improved algorithm is also compared.Whenm1=1, all three algorithms were compared. However, the maximum value decision algorithm could not be applied whenm1=2, so only the other two algorithms were compared. Fig.4 and Fig.5 provide the acquisition probability results achieved over 100 Monte-Carlo simulations for which the subcarrier modulation indexwas eitherm1=1 orm1=2, the CWI frequency was a random value in the range -100 kHz-100 kHz and the ISR ranged from -20 dB-45 dB.

Fig.4 shows that the circular self-convolution algorithm was the most sensitive to CWI. Additionally, when symmetry was destroyed (at an ISR higher than -6 dB), the acquisition probability dropped from 95% to 2%. Maximum value detection was invalid when the interference’s power was greater than that of the main carrier (the ISR was higher than -4 dB). In this case, the probability was only 40%, and faulty acquisition occurred. However, when the ISR was 34 dB, the acquisition probability was still able to reach 90% using proposed method, which is consistent with the findings of the theoretical analysis. Furthermore, when the ISR was lower than -13 dB, the algorithm determined that CWI was absent.

Fig.4 Algorithm performances for m1=1

Fig.5 shows that when the ISR was higher than -4 dB, the circular convolution algorithm’s acquisition probability was 87% and the CWI point was incorrectly acquired. The acquisition probability of the method proposed in this study was as high as 90% when the ISR was 31 dB.Within an acceptable range, the simulation results were consistent with those of the theoretical analysis.

Compared with the conventional maximum value detection method and circular self-convolution algorithm, the CWI mitigation acquisition method based on both the energy center and symmetry is not affected by either the modulation index or interference. This method can determine whether there is interference in the received signal or not.If the interference does not affect acquisition, the mitigation algorithm is not run, thereby reducing the overall complexity of the algorithm. If the algorithm determines that the interference affects acquisition, our method eliminates it. Simulation results show that the proposed method performs well against CWI. In summary, the experimental results demonstrated the feasibility of the algorithm.

Fig.5 Algorithm performances for m1=2

3.2 FPGA implementation

The proposed method has been implemented on the Xilinx xc7k325t field-programmable gate array (FPGA). An (8192-points pipelined) FFT module was first used to complete the acquisition algorithm and then to calculate the signal energy. After that, the energy center coordinates were calculated by using a multiplier and a divider, and RAM was used to store the data.Both the FPGA resources consumed by these methods as well as the total available FPGA resources[19]are shown in Tab.2.

Tab.2 FPGA resource consumption

The resources consumed by the proposed acquisition method represented 4.7% of the FPGA’s slice registers and 10.8% of its slice look-up tables (LUTs).

In the cases of different modulation indices, the algorithm based on FPGA implementation was used to obtain 30 dB ISR interference. The Doppler frequency was set to 30 kHz, and 100 trials were performed at each target frequency point.

Tab.3 shows the performance of the proposed method with a modulation indexset from 1 to 2 and a target Doppler frequency of 130 kHz. The acquisition probability reached as least 90% in each case, which is consistent with the MATLAB simulation results. In addition, the frequency root mean square error was smaller than 500 Hz, which is sufficient to meet the tracking demand.

Tab.3 Performance of implemented method

4 Conclusions

In this paper, a unified carrier TT&C signal acquisition method with CWI mitigation is proposed. The algorithm is based on an energy center algorithm and is less sensitive to the modulation index than the maximum value detection algorithm. Moreover, the symmetry of the signal spectrum is destroyed by CWI. Using this feature, the interference can be detected and eliminated, and the main carrier of the target signal can be acquired successfully under interference. The proposed method exhibits superior interference suppression compared to the circular self-convolution method. Theoretical analysis and verification show that the acquisition probability can reach as high as 90% at ISR≤31 dB, and the method’s consumption of FPGA resources is moderate.

This algorithm is implemented in the unified carrier TT&C signal. the premise is that the signal spectrum has symmetry. Therefore, this method can be extended and applied to other signal formats with symmetry characteristics.However, the method does have some application limitations. There is spectrum leakage in the presence of strong interference. When interference and signal overlap or close, interference will produce the “pollution” of spectral signal, which influence detecting the spectrum. In this case, the performance of the algorithm will be greatly attenuated.Further research is needed.