# Adaptive Threshold Energy Detection Spectrum Sensing Method for L-Band Digital Aeronautical Communication System

Authors: Lei Wang; Mingli Liu; Jin Zhang; Dongxia Li
Journal: Security and Communication Networks
 (2022)

---

## Abstract

Air travel is growing at an alarming rate. However, according to the latest research report by Eurocontrol on European aviation, the growth of air traffic will be limited by the available spectrum resources. As one of the means to provide air/ground (A/G) broadband communication, the L-band digital aeronautical communication system (LDACS) is becoming the preferred model for final deployment and has received continuous attention. Based on various spectrum measurement studies, the international civil aviation organization (ICAO) has identified multiple 1 MHz vacant bands between adjacent distance measuring equipment (DME) signals for LDACS. In order to improve spectrum efficiency, the concept of dynamic spectrum access (DSA) can be applied to the LDACS, which requires the use of spectrum sensing methods to detect the spectrum holes of DME users. In this paper, an adaptive threshold energy detection spectrum sensing method is proposed based on the characteristics of DME pulse signals. Firstly, the energy of the received signal is estimated to construct the detection statistics, and the equations of detection probability and false alarm probability are established. Secondly, the adaptive threshold is calculated using the maximum likelihood decision criterion under the assumption of a constant probability of false alarm. Thirdly, the detection statistic is compared to the adaptive threshold to determine the spectrum occupancy state in the decision-making stage. Finally, the result is transmitted back to the transmitter for the best spectrum resource allocation. According to the simulation analysis, the adaptive threshold energy detection-based sensing method outperforms the energy-difference detection method under low signal-to-noise ratio (SNR) conditions. Meanwhile, it has superior adaptability since the adaptive threshold can be adaptively changed according to the channel.


---

## Body

## 1. Introduction

To increase the capacity of aeronautical communication systems, the International Civil Aviation Organization (ICAO) recommends that a part of the L-band (960 MHz to 1164 MHz) can be used for air-to-ground (A/G) communications, and two candidate systems are being investigated concurrently [1]: L-band digital aeronautical communication system type 1 (LDACS1) [2] and L-band digital aeronautical communication system type 2 (LDACS2) [3] are used to modernize the air traffic management (ATM). LDACS1 is a frequency division duplexing (FDD)-based system with orthogonal frequency division multiplexing (OFDM) as the modulation scheme [4, 5]. LDACS2 is a time division duplex (TDD)-based system with Gaussian minimum frequency shift keying (GMSK) as the modulation scheme. Compared to LDACS2, LDACS1 is the most promising and mature choice for future A/G communication [6] due to its high spectrum efficiency, large transmission capacity, high throughput, and multicarrier transmission. Hence, the work presented in this paper will focus on LDACS1, and it will be referred as LDACS hereafter. The spectrum occupancy of L-band is shown in Figure 1. Various legacy or incumbent users in L-band are DME system (960–1215 MHz), radar-based multifunctional information distribution system, universal access transceiver system (978 MHz), secondary surveillance radar (1030 MHz), and airborne collision avoidance system (1090 MHz). According to the traditional static spectrum allocation scheme for aeronautical communication, ground station and aircraft are required to synchronize in advance and agree on a common frequency. As the spectrum must be allocated before use and maintained for a period of time, the spectrum resources will be idle in different degrees in time and space. Especially in the increasingly saturated LDACS, it is easy to cause the waste of spectrum resources, which will result in the low utilization rate of spectrum resources.Figure 1
Spectrum distribution of L band.To improve the quality of ATM, the spectrum is required to be used efficiently. Cognitive radio (CR)-based methods have been proposed to improve spectrum efficiency and communication capacity. Energy detection, cyclic stationary characteristics detection, and matching filter detection are now the most widely used spectrum sensing methods [7]. Energy detection is a simple and effective method to sense the environment in a blind way. Cyclic stationary characteristics detection may need some information on the primary user such as statistical property, while matched filter detection needs complete information about the primary user. In addition, there are spectrum sensing methods based on the signal covariance matrix, wavelet transform, signal characteristic value, and so on. Also, related spectrum sensing methods on L-band in the field of aeronautical communication, such as the energy difference method [8], low-power correlator method [9], and cyclic prefix assisted method [10], are used to sense OFDM signal of L-band. Furthermore, coherence detection [11] and power detection [12] are used for detecting DME signals [13, 14]. The former employs the repetitive structure of DME pulse pairs and proposes a correlation of parts of the received signal with shifted parts. But the operation is relatively complicated because of the difference of correlation between OFDM and DME signals. The latter employs the Gaussian shaped interference spectrum and can be applied when employing LDACS as an inlay system. However, it ignores the effect of the OFDM signal and has poor adaptability. This paper proposed an adaptive threshold energy detection method for detecting the DME signal. The DME signal is used as the primary user signal, while the OFDM signal is used as the authorized user signal. The received signal includes the DME signal, OFDM signal, and noise.The paper is organized as follows: in Section2, the characteristic of DME and OFDM transmissions is presented. In Section 3, the adaptive threshold energy detection-based spectrum sensing scheme for the DME signal is described. Section 4 presents the simulation results. Section 5 concludes the paper.


## 2. The Signal Characteristic

### 2.1. DME Signal

DME is a kind of radio navigation equipment which calculates the distance between the ground station (GS) and the airborne station (AS). There are 252 possible channels in this system, 126 X channels and 126 Y channels. The airborne inquiry frequency is 1025–1150 MHz, and the ground response frequency is 962–1213 MHz. The channel frequency interval is 1 MHz.Figure2 clarifies the shape of one DME pulse pair and the given parameters. As can be seen from it, the interval between pulse pairs is 12μs, and the half-width of the Gaussian-shaped pulses is 3.5μs.Figure 2
The time domain waveform of the baseband DME signal.For the OFDM receiver of LDACS, it may receive several DME signals from multiple DME platforms, and this paper only analyzes the DME signal transmitted from one DME platform. DME works in the way of transmitting pulse pairs, and it consists of pairs of Gaussian-shaped pulses with intervalΔt. Mathematically, a DME signal consists of pairs of Gaussian-shaped pulses which are described by(1)bt=e−ε/2t2+e−ε/2t−Δt2,where ε=4.5×10111/s2, the interval of Gaussian-shaped pulse pair Δt is determined by the transmission mode of DME, and the possible value is 12μs or 36μs.According to (1), the model of the pulse interference signal of DME is further given as follows:(2)it=∑i=0N1−1∑u=0NU,i−1AiDMEbt−ti,uej2πfc,it+jφi,u.Among them,N1 represents the number of interference sources of DME, i represents the serial number of interference source of DME, u represents the serial number of DME pulse pair, NU,irepresents the total number of pulse pairs generated by the ith interference source of DME during the observation time, ti,urepresents the moment when the uth pulse pair generated by the ith interference source of DME appears, and ti,ucan be modeled as a random variable with a Poisson distribution. fc,i represents the offset of the carrier frequency of the signal transmitted by the ith interference source of DME; φi,u represents the initial phase of the carrier signal transmitted by the ith interference source of DME, φi,u is modeled as a random variable uniformly distributed between 0,2π; φiDME represents the peak power of the pulse signal transmitted by the ith interference source of DME, AiDME represents the peak amplitude of the pulse signal emitted by the ith interference source of DME, and AiDME=ψiDME,i=0,…,N1−1. The time domain waveform and spectrum are shown in Figures 3 and 4:Figure 3
The time domain waveform of DME signal.Figure 4
The frequency domain waveform of DME signal.


### 2.2. OFDM Signal of LDACS

The modulation mode of the forward link of LDACS is OFDM, and the subcarrier modulation mode is QPSK, so the baseband OFDM signal can be expressed as(3)rt=∑n=−∞∞cnqt−nTs−t0=∑n=−∞∞∑k=−Nc/2Nc/2ck,nej2πΔft−nTs−t0qt−nTs−t0,where n represents the serial number of the modulation symbol, k represents the subcarrier serial number, Nc represents the number of subcarriers, ck,n represents the nth modulation symbol on the kth subcarrier, Δf=1/TFFT (TFFT=Ts+TCP, Ts is the symbol length of OFDM signal, and TCP is the cycle prefix), and qt represents the shaping pulse. ck,n needs to satisfy ck,n∈ej2πp/4p=14, Eck,n=Eck,n∗=0, Eck,nck,n∗=δk−k′δn−n′, Eck′,n′=0.The modulated OFDM signal [15] can be described by(4)xt=Rertej2πfct=rtcos2πfct=12rte−j2πfct+rtej2πfct.


## 2.1. DME Signal

DME is a kind of radio navigation equipment which calculates the distance between the ground station (GS) and the airborne station (AS). There are 252 possible channels in this system, 126 X channels and 126 Y channels. The airborne inquiry frequency is 1025–1150 MHz, and the ground response frequency is 962–1213 MHz. The channel frequency interval is 1 MHz.Figure2 clarifies the shape of one DME pulse pair and the given parameters. As can be seen from it, the interval between pulse pairs is 12μs, and the half-width of the Gaussian-shaped pulses is 3.5μs.Figure 2
The time domain waveform of the baseband DME signal.For the OFDM receiver of LDACS, it may receive several DME signals from multiple DME platforms, and this paper only analyzes the DME signal transmitted from one DME platform. DME works in the way of transmitting pulse pairs, and it consists of pairs of Gaussian-shaped pulses with intervalΔt. Mathematically, a DME signal consists of pairs of Gaussian-shaped pulses which are described by(1)bt=e−ε/2t2+e−ε/2t−Δt2,where ε=4.5×10111/s2, the interval of Gaussian-shaped pulse pair Δt is determined by the transmission mode of DME, and the possible value is 12μs or 36μs.According to (1), the model of the pulse interference signal of DME is further given as follows:(2)it=∑i=0N1−1∑u=0NU,i−1AiDMEbt−ti,uej2πfc,it+jφi,u.Among them,N1 represents the number of interference sources of DME, i represents the serial number of interference source of DME, u represents the serial number of DME pulse pair, NU,irepresents the total number of pulse pairs generated by the ith interference source of DME during the observation time, ti,urepresents the moment when the uth pulse pair generated by the ith interference source of DME appears, and ti,ucan be modeled as a random variable with a Poisson distribution. fc,i represents the offset of the carrier frequency of the signal transmitted by the ith interference source of DME; φi,u represents the initial phase of the carrier signal transmitted by the ith interference source of DME, φi,u is modeled as a random variable uniformly distributed between 0,2π; φiDME represents the peak power of the pulse signal transmitted by the ith interference source of DME, AiDME represents the peak amplitude of the pulse signal emitted by the ith interference source of DME, and AiDME=ψiDME,i=0,…,N1−1. The time domain waveform and spectrum are shown in Figures 3 and 4:Figure 3
The time domain waveform of DME signal.Figure 4
The frequency domain waveform of DME signal.


## 2.2. OFDM Signal of LDACS

The modulation mode of the forward link of LDACS is OFDM, and the subcarrier modulation mode is QPSK, so the baseband OFDM signal can be expressed as(3)rt=∑n=−∞∞cnqt−nTs−t0=∑n=−∞∞∑k=−Nc/2Nc/2ck,nej2πΔft−nTs−t0qt−nTs−t0,where n represents the serial number of the modulation symbol, k represents the subcarrier serial number, Nc represents the number of subcarriers, ck,n represents the nth modulation symbol on the kth subcarrier, Δf=1/TFFT (TFFT=Ts+TCP, Ts is the symbol length of OFDM signal, and TCP is the cycle prefix), and qt represents the shaping pulse. ck,n needs to satisfy ck,n∈ej2πp/4p=14, Eck,n=Eck,n∗=0, Eck,nck,n∗=δk−k′δn−n′, Eck′,n′=0.The modulated OFDM signal [15] can be described by(4)xt=Rertej2πfct=rtcos2πfct=12rte−j2πfct+rtej2πfct.


## 3. Adaptive Threshold Energy Detection Spectrum Sensing Method

With the presence of noise and the OFDM signal, the spectrum sensing problem can be modeled as a binary hypothesis problem with two hypothesesH0 and H1 to represent the absence and presence of the DME signal in the channel, respectively.(5)yn=h∗xn+wn,H0,h∗xn+sn+wn,H1,where sn is the sampling sequence of the DME signal, and xn is the OFDM signal transmitted through L-band. According to the central limit theorem(CLT), the sum of independent and identically distributed random variables follows the Gaussian distribution. wn is additive white Gaussian noise (AWGN), which follows Gaussian distribution with a mean value of 0 and variance of σ2. h is the ideal channel gain and is constant.The important index to measure the performance of spectrum sensing is the probability of detection, probability of false alarm, and probability of missing. The formulas of these three indicators are as follows:(6)Pd=PH1|H1,Pf=PH1|H0,Pm=PH0|H1.In the spectrum sensing method of CR, Harry Urkowitz researched the energy detection method of unknown deterministic signals. On the basis of its research, this paper proposes an energy detection method based on adaptive threshold to sense the DME signal. The steps involved in the proposed method are shown in Figure5. The received signal is scanned and then sent through a band pass filter (BPF) to filter and separate DME and OFDM signals based on their center frequency. The split DME signal and noise are then transmitted to the A/D transformer. The energy of the received signal is computed. Finally, the detector selects the hypothesis in comparison with the threshold [16], with the results being transmitted back to the transmitter for reallocation of spectral resources.Figure 5
Model of the adaptive threshold energy detection.The definition of detection statistic under different cases is derived as follows:(7)T=∑n=1Nyn2=∑n=1Nwn2,H0,∑n=1Nh∗sn+wn2,H1,where σ2 represents the noise variance, σs2 represents the average power of the DME signal, and N is the number of received signal samples. Based on the CLT, the distribution of the test statistic [17] under H0 and H1 can be given as(8)T∼NcNσ2,2Nσ4,H0,NcNσ2+δσs2,2Nσ2+δσs22,H1,where Ncμ,σ2 stands for Gaussian distribution with mean μ and variance σ2, and the gain of the channel δ can be expressed by the following formula, where p represents the number of paths:(9)δ=∑l=1pEhl2.From (8), the probability density function of T in two cases can be given as(10)fT|H0=14πNσ41/2exp−T−Nσ224Nσ4,fT|H1=14πNσ2+δσs221/2exp−T−Nσ2+δσs224Nσ2+δσs22.Therefore, the probability of detection, the probability of false alarm, and the probability of missed alarm can be derived.(11)Pd=PT>λ|H1=Qλ−Nσ2+δσs22Nσ2+δσs2,Pf=PT>λ|H0=Qλ−Nσ22Nσ2,Pm=PT<λ|H1=1−Pd=1−Qλ−Nσ2+δσs22Nσ2+δσs2,where λ is the adaptive decision threshold and Q (·) is the right tail function of the standard normal distribution, also known as the standard Gaussian complementary cumulative distribution function [18, 19]. Conventionally, the threshold is chosen to limit Pf to an acceptable value.The decision thresholdλ for a particular false alarm rate is given as(12)λ=σ22NQ−1Pf+N.


## 4. Simulations and Analysis

### 4.1. Simulation Setup

According to the relevant specifications of the ICAO, the simulation parameters are set in Table1 and Table 2.Table 1
LDACS signal.
ItemsValuesCarrier frequency/GHz1Transmission bandwidth/MHz0.49805Sampling interval/μs1.6Channel modelAWGN/multipathfading channelNumber of significant subcarriers50Modulation modeQPSKTable 2
DME signal.
ItemsValuesSignal start time/ms2Carrier frequency/GHz0.5Sampling interval/μs1.6Channel modelAWGN/multipath fading channel


### 4.2. Simulation Results and Analysis

To verify the performance of the adaptive threshold energy detection method in spectrum sensing of the L-band DME signal, this section conducts simulation with MATLAB under different conditions. The results are all averaged over 1000 realizations, and the number of samples for detection isN = 16200.Simulation 1: the SNR is set to −20 dB, −18 dB, and -15 dB. The connection curve between the probability of detection and the probability of false alarm is shown in Figure6. As shown in Figure 6, the probability of false alarm has less impact on detection performance, while the change in SNR has a greater impact on it. The probability of detection steadily rises as the SNR increases. When SNR = −15 dB, the probability of detection can reach 100% at about Pf = 0.05. But when SNR = −20 dB, the probability of detection needs to reach 100% at about Pf = 0.35.Figure 6
The relation curve between the detection probability and the false alarm probability under different SNRs.Simulation 2: to verify the effect of the change in SNR on detection performance, we set the SNR range from −20 dB to −5 dB for observation, and the effect of SNR for the adaptive threshold energy detection method of the DME signal is shown in Figure7. It can be seen that when SNR is above −12 dB, the probability of detection can reach 100%; when the SNR is below −12 dB, the detection performance drops sharply. At the same time, the detection performance of Pf = 0.1 is clearly better than that of Pf = 0.01 and Pf = 0.05.Figure 7
Curve of detection performance with SNR.Simulation 3: to verify the superiority of the adaptive threshold energy detection method for DME signal detection, the method is simulated under the same probability of false alarm and SNR as the energy difference detection method (the energy difference of the signals received in different channels is compared with the decision threshold). We set the SNR range from −20 dB to −5 dB under two false alarm rates (Pf = 0.1 and Pf = 0.01). It can be seen from Figure 8, in the same probability of false alarm and SNR, the proposed method’s probability of detection is clearly higher than that of the energy difference detection method. With the increase of SNR, both methods’ probability of detection increases, but the probability of detection based on the adaptive threshold energy detection method has priority to reach 100%.Figure 8
Comparison of adaptive threshold energy detection and energy difference detection.Simulation 4: to verify the practicability of the adaptive threshold detection method for the DME signal, the detection process is simulated in multipath channel and compared with the energy difference detection method. Under the setting of simulation 3, the number of paths is 8, the Doppler frequency shift is 1250 Hz, the delay of each path is {0, 0.4, 0.8, 1.2, 1.6, 2,2.4, and 2.8}μs, and the power attenuation of each path is {0, −1.7373, −3.4744, −5.2115, −6.9487, −8.6859, −10.4231, and -12.1602}dB. Combining Figures 8 and 9, it can be seen that at Pf = 0.01, under the AWGN channel, the probability of detection reaches 100% when the SNR is −13 dB, and under the multipath channel, the probability of detection reaches 100% at SNR = −11 dB, but the probability of detection based on adaptive threshold energy detection is still higher than that of energy difference detection.Figure 9
Comparison of adaptive threshold energy detection and energy difference detection in the multipath channel.


## 4.1. Simulation Setup

According to the relevant specifications of the ICAO, the simulation parameters are set in Table1 and Table 2.Table 1
LDACS signal.
ItemsValuesCarrier frequency/GHz1Transmission bandwidth/MHz0.49805Sampling interval/μs1.6Channel modelAWGN/multipathfading channelNumber of significant subcarriers50Modulation modeQPSKTable 2
DME signal.
ItemsValuesSignal start time/ms2Carrier frequency/GHz0.5Sampling interval/μs1.6Channel modelAWGN/multipath fading channel


## 4.2. Simulation Results and Analysis

To verify the performance of the adaptive threshold energy detection method in spectrum sensing of the L-band DME signal, this section conducts simulation with MATLAB under different conditions. The results are all averaged over 1000 realizations, and the number of samples for detection isN = 16200.Simulation 1: the SNR is set to −20 dB, −18 dB, and -15 dB. The connection curve between the probability of detection and the probability of false alarm is shown in Figure6. As shown in Figure 6, the probability of false alarm has less impact on detection performance, while the change in SNR has a greater impact on it. The probability of detection steadily rises as the SNR increases. When SNR = −15 dB, the probability of detection can reach 100% at about Pf = 0.05. But when SNR = −20 dB, the probability of detection needs to reach 100% at about Pf = 0.35.Figure 6
The relation curve between the detection probability and the false alarm probability under different SNRs.Simulation 2: to verify the effect of the change in SNR on detection performance, we set the SNR range from −20 dB to −5 dB for observation, and the effect of SNR for the adaptive threshold energy detection method of the DME signal is shown in Figure7. It can be seen that when SNR is above −12 dB, the probability of detection can reach 100%; when the SNR is below −12 dB, the detection performance drops sharply. At the same time, the detection performance of Pf = 0.1 is clearly better than that of Pf = 0.01 and Pf = 0.05.Figure 7
Curve of detection performance with SNR.Simulation 3: to verify the superiority of the adaptive threshold energy detection method for DME signal detection, the method is simulated under the same probability of false alarm and SNR as the energy difference detection method (the energy difference of the signals received in different channels is compared with the decision threshold). We set the SNR range from −20 dB to −5 dB under two false alarm rates (Pf = 0.1 and Pf = 0.01). It can be seen from Figure 8, in the same probability of false alarm and SNR, the proposed method’s probability of detection is clearly higher than that of the energy difference detection method. With the increase of SNR, both methods’ probability of detection increases, but the probability of detection based on the adaptive threshold energy detection method has priority to reach 100%.Figure 8
Comparison of adaptive threshold energy detection and energy difference detection.Simulation 4: to verify the practicability of the adaptive threshold detection method for the DME signal, the detection process is simulated in multipath channel and compared with the energy difference detection method. Under the setting of simulation 3, the number of paths is 8, the Doppler frequency shift is 1250 Hz, the delay of each path is {0, 0.4, 0.8, 1.2, 1.6, 2,2.4, and 2.8}μs, and the power attenuation of each path is {0, −1.7373, −3.4744, −5.2115, −6.9487, −8.6859, −10.4231, and -12.1602}dB. Combining Figures 8 and 9, it can be seen that at Pf = 0.01, under the AWGN channel, the probability of detection reaches 100% when the SNR is −13 dB, and under the multipath channel, the probability of detection reaches 100% at SNR = −11 dB, but the probability of detection based on adaptive threshold energy detection is still higher than that of energy difference detection.Figure 9
Comparison of adaptive threshold energy detection and energy difference detection in the multipath channel.


## 5. Conclusions

LDACS is considered as a promising candidate for the future air-to-ground links, which is recommended to operate on the lower half of theL band as an inlay system between the two neighboring DME channels. Spectrum utilization efficiency of LDACS can be improved by enabling dynamic spectrum access (DSA) in the system. In this paper, an adaptive threshold energy detection spectrum sensing method based on the constant false alarm rate for the DME signal is proposed. The method does not need the prior information of the primary user (refers to DME in the text) signal, such as the prior probability, signal power, waveform, and so on. It has the characteristics of short detection time and low algorithm complexity. The impact of the probability of false alarm, SNR, and channel fading on the probability of detection is verified in the simulations. In addition, the detection performance of the proposed method is compared with that of the energy difference detection in simulation, with results showing that the proposed method is superior to the energy difference detection method in terms of flexibility and detection performance.



---

*Source: 4325515-2022-10-17.xml*