International Journal of Electronics and Communications (AEÜ)

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1 Int. J. Electron. Commun. (AEÜ) 66 (018) Contents lists available at SciVerse ScienceDirect International Journal o Electronics and Communications (AEÜ) journal homepage: w w w. e lsevier. de/ a e ue Anti-chirp-jamming communication based on the cognitive cycle Yingtao Niu, Fuqiang Yao, Mingyue Wang, Jianzhong Chen Nanjing elecommunication echnology Institute, No. 18 Houbiaoying Street, P.O. Box 37, Nanjing 10007, China a r t i c l e i n o a b s t r a c t Article history: Received 7 May 017 Accepted 14 November 017 Keywords: Chirp jamming Anti-jamming Cognitive cycle Conventional wireless communication systems are hardly reliable in a chirp-jamming environment. hus, an anti-chirp-jamming communication (ACJC) scheme based on the cognitive cycle is proposed in this paper. he scheme includes three main modules, namely, chirp-jamming sensing, anti-chirp-jamming decision-making, and adaptive adjustment o communication requency and transmission power which compose the cognitive cycle or chirp jamming. he chirp jamming sensing module detects and predicts the parameters o chirp jamming by periodogram and Kalman ilter. Based on the estimated chirp-jamming parameters, the anti-chirp-jamming decision-making module makes decisions on communication requency and transmission power by simple arithmetical computation. Finally, the ACJC system communicates with the given communication requency and transmission power. Simulation results show that the ACJC scheme can unction even with strong chirp jamming in the same band, and enable reliable communication, eectively avoiding attacks rom malicious jammers. 017 Elsevier GmbH. All rights reserved. 1. Introduction Wireless communication has been increasingly deployed in wider applications over the last ew decades. However, the open eature o the wireless channel makes wireless communication prone to man-made intererence, which can be classiied into two dierent types: unintended and intended. Unintended intererence is caused by radiation or out-o-band radiation o all kinds o wireless equipment such as communication, radars, navigation, broadcast equipment, and so on. his type o intererence is not aimed at any particular wireless system. ypical examples include the intererence that occurred in the subway control communication system [1] in Guangzhou, China in 008 and the intererence that occurred in the aviation communication system [] in Hubei, China in 016. In comparison, intended intererence aims to interrupt the inormation transmission o a wireless communication system. his type o intererence is also called jamming. ypical examples o jamming incidents include that o the South Korean GPS in 017 [3], that o China elecom in Hainan in 016 [4], and the aair o AsiaSat-3s in 004 [5]. Malicious jamming is more popular in military communication. All kinds o intererence seriously aect the eiciency and reliability o communication. Intererence includes several kinds o patterns [6], in which chirp jamming (linear or nonlinear requency modulation intererence) is popular and important because it can occupy and jam wide-band spectrum. Such jamming pattern is caused by unintended equipment and Corresponding author. el.: address: niuyingtao78@hotmail.com (Y. Niu). oten by malicious users, which may be dangerous or the communication system especially in military communication. hereore, eective anti-jamming measures must be used to ensure the reliability o a wireless communication system in a chirp-jamming environment. he main anti-jamming technology o the requency domain is spread spectrum technology [7]. his technology mainly includes the requency hopping spread spectrum (FHSS) and the direct sequence spread spectrum (DSSS), both o which remarkably improve communication reliability. In the two technologies, FHSS is used most widely in military applications. he communication channel o conventional FHSS hops pseudorandomly in a hopset. I 30% o all channels in the hopset are jammed, the voice communication breaks because too many packets are lost [6,7]. Adaptive requency hopping (AFH) is proposed to overcome this shortcoming [8,9]. he AFH deletes jammed channels rom the hopset and communicates in channels without jamming or intererence. hus, AFH can prevent the eect o requency-static or slow time-varying intererence, making it suitable or military applications and others [10]. However, due to its limited intererence detection ability, conventional AFH cannot adapt easily to ast time-varying environments [11] and can hardly deal with dynamic jamming such as chirp jamming. Only a strong transmission power should be used to suppress the eect o chirp jamming; otherwise, the band occupied by chirp jamming is abandoned in the FH or AFH systems. hese two approaches lead to high power or spectrum cost. hereore, ensuring communication reliability in a chirp-jamming environment with low power and spectrum costs should be investigated. Cognitive radio (CR) [1] has emerged as a possible solution to the anti-jamming problem. CR establishes a cognitive cycle or an /$ see ront matter 018 Elsevier GmbH. All rights reserved. doi: /j.aeue

2 548 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) electromagnetic environment, ater which it reuses the spectrum rule or AFH has been ormulated in [11], which can prevent hole that primary users do not use. In this manner, CR achieves ei- sel-intererence o dierent Bluetooth equipment. Another study cient spectrum utilization without intererence or primary users. [17] has grouped Bluetooth channels according to the channel allo- I the cognition concept is introduced to the anti-jamming ield and cation o WLAN. In this work, a moving average technique has been the cognitive cycle or chirp jamming is established, the commu- used to estimate the status o channels in groups with better pernication system can have strong adaptability to the chirp-jamming ormance than conventional schemes. From these works, existing environment. Anti-jamming costs, particularly those o spectrum AFH schemes have shown sensing abilities and adaptabilities to and power consumption, can also be remarkably lower. slow time-varying environments. However, the schemes can hardly A novel scheme called anti-chirp-jamming communication track ast time-varying environments, largely because the schemes (ACJC) based on the cognitive cycle is proposed. he main sense the spectrum and communicate in a public architecture, application o ACJC is in military communication in the ultra- which limits its sensing ability. Current engineering practices have high requency (UHF) band. However, ACJC can also be used also veriied that AFH is unable to meet the desired perormance in by civilians, such as or Bluetooth or industrial wireless sensor a strong chirp-jamming environment [10]. network (WSN) applications. hree main modules are covered Real-time sensing or highly dynamic chirp jamming is crucial in the proposed scheme. First, chirp-jamming sensing serves to ACJC. Several techniques or sensing or detection o chirp signals as the anti-chirp-jamming oundation. Second, the core o the have been suggested in literature. In [18], an online detection algoscheme is anti-chirp-jamming decision-making. hird, the means rithm or a long and weak chirp signal based on Hough transorm o anti-chirp-jamming comprises an adaptive adjustment o com- has been proposed. In [19], a radar chirp signal detection method munication requency and transmission power. In general, the ACJC based on dierent wavelet transorms has also been proposed. attempts to dodge chirp jamming in real time to ensure communi- Simultaneous detection and parameter estimation o multiple chirp cation reliability with low spectrum cost and power consumption signals based on evolutionary algorithms have been proposed in in an environment with chirp jamming. he rest o the paper is [0]. his method can estimate the start and stop requencies o organized as ollows. Related works are presented in Section, each chirp signal. In another study [1], detection methods or weak and the system model o the proposed ACJC is described with its binary chirp signals in a noisy environment have been presented, underlying assumptions in Section 3. he chirp-jamming sensing whereas in [1], both coherent and incoherent reception cases scheme o the ACJC is introduced in detail in Section 4. he decision- have been considered. In [], the combination o local polynomial making approach or anti-chirp jamming is investigated in Section Fourier transorm and Hough transorm to detect chirp signals has 5. Simulation results are provided in Section 6, and conclusions are been presented. In [3], a chirp signal detection algorithm based presented in Section 7. he notations used in the remainder o the on kurtosis detection and iltering in ractional Fourier domain has paper are listed in the Appendix A. been presented. Finally, in [4] a method or sensing chirp signal by Focusing on the dynamic characteristics o chirp jamming, the a narrow band energy detector combined with a requency scannovel eatures o the proposed ACJC scheme are summarized as ner has been presented. However, none o the present methods are ollows. First, the cognitive cycle is introduced to the anti-jamming suitable or ACJC system because o the ollowed problem. communication ield, providing a new kind o wireless resource: jamming knowledge or communication systems. Second, a realtime sensing algorithm or chirp jamming based on a modiied periodogram is proposed to help achieve chirp jamming parameter estimation and prediction with low complexity. Based on the sensing results, the system can determine where (in the requency domain) and when spectrum holes exist. hird, a simple antichirp-jamming decision-making approach is proposed, which can adapt time-stressed decision-making in a dynamic chirp-jamming environment. Based on the decision-making results, the system can adjust its communication requency and power in real time. Simulation results show that the ACJC scheme can maintain com- (a) Existing methods ocused mainly on the detection o weak chirp signals in noisy environments or applications in radar, communication, and medicine. However, chirp jamming, which threatens the communication system, is usually a strong signal. (b) Existing methods ocused mainly on the global characteristics o chirp signals. Most o these methods cannot detect the instantaneous characteristics o chirp signals that are inevitable to anti-jamming communication in real time. (c) Most o existing methods have high complexity, which increase their processing delay or calculation time. he real-time property o the algorithms is also important in anti-chirp-jamming. munication reliability in the chirp-jamming environment. 3. System model o the ACJC. Related works (a) Real-time sensing ability or chirp jamming. Communication systems should be able to detect and predict instantaneous chirp jamming requency and power. Other parameters o chirp jamming, including sweeping rate and start and stop re- quencies, should also be estimated. he real-time property is In this section, relevant studies related to ACJC are reviewed including AFH and chirp signal detection technology. In the early stages o AFH development, studies have ocused on AFH in high requency (HF) duplex communication [9,13]. In the AFH o [9,13], link quality is periodically analyzed and ed back to avoid bad requency, which remarkably enhances reliability and quality o communication. Res. [14,15] have proposed an AFH scheme or Bluetooth, which can coexist with wireless local area network (WLAN). Another study [16] has proposed an AFH based on adaptive channel code and adaptive power adjustment, which eeds back BER instead o the measure channel. his scheme can compensate or slow environment change, i.e., the spectral environment remains invariable while the AFH system detects environment and deletes jammed channels rom the hopset. Generally, conventional AFH scheme cannot easily adapt to requency-dynamic intererence [11]. hus, etiquette he characteristics o chirp jamming are listed below. (a) he instantaneous spectrum o chirp jamming moves rapidly in the requency domain. he sweeping rate is up to several GHz/s. (b) he dynamic range o chirp jamming in the requency domain is quite large and is usually larger than the hopset o FHSS or bandwidth o DSSS. (c) Chirp jamming power is usually very high, seriously aecting the reliability o communication. o eliminate the eect o chirp jamming, communication systems should have the ollowing abilities:

3 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) (c) he scanning requency range o chirp jamming is assumed in the work requency band o ACJC. Fig. 1. Function block diagram o the proposed ACJC scheme. necessary to ensure reliable communication, which produces high demand or the complexity o sensing algorithm. (b) Real-time decision-making ability. Appropriate communication requency and power should be decided according to the sensing results. hus, real-time property o the decision-making algorithm is also very important. his is typical time-stressed decision making. (c) Frequency and power agility. he communication system should adjust communication requency and transmission power according to the decision-making results to help avoid collision with chirp jamming. o obtain the aorementioned abilities, the cognitive cycle o cognitive radio [1,5] is introduced into the anti-jamming ield and the cognitive cycle or chirp jamming is established. Based on the requirements, the cognitive cycle or anti-chirp-jamming should have several basic unctions. hese unctions include chirpjamming sensing, anti-chirp-jamming decision-making, adaptive communication parameters adjustment, and so on. he unction block diagram o ACJC is given in Fig. 1. From Fig. 1, the power spectrum density (PSD) o the target band is computed irst. hen, the parameters o chirp jamming are estimated and stored in the working memory. Some instantaneous parameters o chirp jamming can be predicted. Using the predicted and stored parameters, the decision-making unction can choose the communication requency and transmission power. Finally, ACJC communicates using the given parameters. he proposed ACJC model is shown in Fig. in accordance with the unction block diagram. he ACJC scheme includes the general components o a wireless communication system such as digital modulator, upconverter, power ampliier, and so on. he chirp-jamming sensing and antichirp-jamming decision-making modules are also included (Fig. ). he ollowing assumptions are given in the paper. (a) Generally, the cognitive cycle needs a eedback channel to connect the receiver to the transmitter [1]. hereore, ACJC is assumed to be a duplex communication system, in which the receiver can convey cognitive inormation to the transmitter. (b) he carrier requency and transmission power are assumed to be adjusted by the decision-making module. Maximum allowable transmission power is regulated or all requency bands and all wireless communication systems, so assume that the ACJC transmits under the maximum allowable transmission power. Spectrum sensing can be perormed through two dierent architecture, public sensing and independent sensing (i.e., single-radio chain and dual-radio chain in [6]). In public sensing architecture, inormation reception and spectrum sensing use the same radio chain alternately by time division. he obvious advantage o this architecture is its simplicity and low cost. However, only speciic time slots are allocated or spectrum sensing, thereby limiting its sensing capability. In addition, the system can hardly track ast environment changes i a lower ratio o time slots is used or sensing. he communication eiciency decreases i a higher ratio o time slots is used or sensing instead o inormation transmission. In independent sensing architecture, one radio chain is dedicated to inormation transmission and reception, and another chain is devoted to spectrum sensing. his architecture is apt in sensing and ollowing ast environment changes. Spectrum sensing and communication do not aect each other, and a complex sensing strategy is not essential to the system. However, independent sensing architecture also has disadvantages due to its high complexity and cost. In considering the highly dynamic characteristics o chirp jamming and the time-stressed sensing and decision-making unctions, ACJC adopts the second architecture, as shown in Fig. 3. In the chirp-jamming sensing module, a broadband radio requency (RF) ront end with a bandwidth that covers all channels should be equipped. he automatic gain control (AGC) is not exploited in the RF ront end to detect the actual signal power. hereore, the gain o RF ront end is ixed without AGC. By designing the appropriate gain o RF ront end, strong chirp jamming will all on the linear range o RF ront end. Furthermore, the linear output range o RF ront end should match the lexible analog input range o analog-to-digital converter (ADC). he weak chirp jamming that does not aect communication perormance will be ignored. he very strong chirp jamming that exceeds the linear range o RF ront end will be limited by its amplitude. By this approach, the actual chirp jamming power that seriously aects communication is detected. Ater the received signal is processed by the RF ront end, downconverter, and ADC, chirp jamming is sensed at an intermediate requency. he channel between transmitter and receiver o ACJC is assumed to be a slow time-varying requencyselective ading channel. Slow time-varying indicates that the channel remains invariable during a period o chirp jamming. he requency-selective ading channel is modeled as a inite impulse L 1 response (FIR) ilter with L order, such as h(n) = hlı(n n l), l=0 where hl is the lth channel tap gain, h(n) denotes the impulse response o channel in n time slot. hereore, the discrete time received signal ater processing by ADC is given by the ollowing equation: L 1 r(n) = hls(n n l) + c(n) + v(n) (1) l=0 where v(n) is AWGN, s(n) is the linearly modulated communication signal, and c(n) is the single-tone chirp jamming. s(n) and c(n) can be given as jcn s(n) = ame, 0 n N s () c(n) = exp[j chirp(n)n], 0 n N c (3) where Ns is the sample number in one symbol period o s(n), am is the amplitude o s(n), c is the carrier requency o s(n), Nc is the sample number in one period o c(n), and chirp(n) is the

4 550 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) Fig.. System model o the proposed ACJC scheme. Fig. 3. Block diagram o chirp-jamming sensing based on independent sensing architecture. instantaneous requency o c(n) in n time slot. I c(n) is linear chirp jamming, chirp(n) is given by H L chirp(n) = L + n, 0 n N c (4) Nc where L and H are the start and stop requency o chirp jamming, respectively. I c(n) is nonlinear chirp jamming, such as the quadratic chirp jamming, chirp is given by H L chirp(n) = L + n, 0 n N (5) N c c I c(n) is another nonlinear chirp jamming, i.e., logarithmic chirp jamming, chirp is given by [( ) 1/Nc] n H chirp(n) = L, 0 n N c (6) L 4. Chirp-jamming sensing Chirp jamming is sensed ater the received signal is processed by the RF ront end, downconverter, and ADC. he tasks o chirp-jamming sensing include PSD computation, chirp jamming parameters estimation, and prediction Computation and processing o PSD Chirp-jamming sensing based on PSD is used in ACJC. he most popular PSD calculation algorithm is periodogram, which has very low complexity. hereore, the modiied periodogram is explored in the proposed scheme. he modiied periodogram is deined as ollows [7]: N (1/NF s) wlr(l)e j l i l=1 S( i) =, i = 1,,..., N (7) 1 N N l=1 w l where wl is a window, Fs is the sample requency, and N is the point number o PSD. In the proposed sensing scheme, PSD is calculated every second. However, one o the shortcomings o the periodogram is the large luctuation in the generated PSD, which must be smoothened. A moving average ilter is exploited. Compared with other smoothened algorithms (e.g., Local regression using weighted linear least squares and a polynomial model, Savitzky- Golay ilter, etc.), moving average ilter has very low complexity, which can lower the processing delay. he ilter can be written as ollows: 1 M S sm( i) = S( i j ) (8) M + 1 j= M where S sm( i) is the smoothened PSD in i. In this ilter, M is an important parameter because an excessively small M has poor smoothening eect, whereas an excessively large M yields a good smoothening eect and produces high errors in PSD with large curvature. In the proposed scheme, M = is used. he PSD vector ater smoothening at n time slot is written as S (, n) = [S (, n), S (, n),..., S (, n)] smooth sm sm sm N 1 he eect o static spectrum signal should be eliminated to identiy chirp jamming and estimate its parameters. he background subtraction o moving target detection in image processing is used to solve this problem. S smooth(, n) is processed as a dual value and is assumed to be a decision threshold. I S sm( i, n), then S ( i, n) = 1; otherwise, S ( i, n) = 0. is an important parameter that aects the sensing perormance greatly. In the paper, is determined by simulation. First, the PSD vector S smooth(, n) is sorted in descending order. Second, a mean value mean is computed by 0% largest values o PSD. Finally, is set to be proportional to mean. he simulation result is shown in Fig. 4. In Fig. 4, the X-axis denotes the proportion between and mean. he Y-axis denotes the normalized MSE o the detected value o instantaneous requency o chirp jamming. From Fig. 4, normalized MSE is smallest when lies between 10% and 150% o mean.

5 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) Fig. 5. Inherent estimation error o start and stop requency o chirp jamming. Fig. 4. Relation between decision threshold and normalized MSE. hereore, = 0.7 mean is obtained. Next, the dierence operation o S (, n) at n and n + 1 time slot is obtained as ollows: S (, n) = S (, n + 1) S (, n) (9) Perorming the above computation helps eliminate the eect o static spectrum signal. I chirp jamming exists, then S (, n) is composed o the instantaneous dual-value spectrum peak o the chirp jamming at n and n + 1 time slot (Fig. 9(d)). he instantaneous requencies chirp(n) and chirp(n + 1) at the n and n + 1 time slots, respectively, can be obtained by calculating the center requency o the two spectrum peaks. Repeating this operation can yield the instantaneous requency vector chirp = [ chirp(1), chirp(),..., chirp(n 1)], where N1 is the number o detected instantaneous requencies. I chirp(n), chirp(n + 1), and chirp(n + ) monotonously increase, then chirp jamming can be identiied. 4.. Parameter estimation o chirp jamming he chirp jamming parameters requiring estimation include sweeping rate, start/stop requency, sweeping bandwidth, instantaneous bandwidth, and instantaneous power Estimation o sweeping rate I is the PSD detection interval, the sweeping rate at n time slot v (n) can be approximately calculated as ollows: chirp(n) chirp(n 1) v (n) = 4... Estimation o start and stop requency I the duration o the chirp-jamming sensing module operation exceeds the chirp jamming period, the start and stop requency is approximately estimated as ollows: ˆ L = min( chirp) ˆ H = max( chirp) (10) where min ( ) and max ( ) denote the obtained minimum and maximum value, respectively. However, besides random estimation error, the estimated value also exhibits an inherent estimation error, where min ( chirp) and max ( chirp) are viewed as start requency L and stop requency H, respectively, because the PSD detection time is not ininitesimal. Fig. 5 shows the inherent estimation error o L and H. o analyze the inherent error, the ollowed assumptions are given. (a) PSD detection time is assumed to be equal to PSD detection interval. (b) he starting time o PSD detection is assumed to be equal to the starting time o chirp jamming. (c) he NP PSD detection periods are included in one chirp jamming period, i.e., NP c < (N P + 1). From Fig. 5, ˆ ˆ L is larger than L, and H is smaller than H. I c = NP, the inherent error o ˆ L is L = L L = v (/), and the inherent error o ˆ H is H = H H = v (/). I NP < c < (N P + 1), the inherent error o ˆ L is L = L L = v (/), and the inherent error o ˆ H is H = H H = v (/) + v (c NP). Ater analysis o L and H, the inherent error can be compensated partly to reduce estimation error o L and H. hereore, the estimation o L and H ater compensation are: ˆ L = min( chirp) v (11) ˆ H = max( chirp) + v (1) Estimation o sweeping bandwidth he sweeping bandwidth is given approximately as B ˆ ˆ ˆ chirp = H L = max( chirp) min( chirp) + v (13) Estimation o instantaneous bandwidth he instantaneous bandwidth o chirp jamming can be calculated as the width o the spectrum peak, which is greater than the detection threshold. his can be written as B ins(n) = BW[ S (, n)] (14) where B ins(n) is the estimated value o the instantaneous bandwidth o the chirp jamming in n time slot and BW[ ] denotes the obtained bandwidth o the irst spectrum peak o S (, n) Estimation o instantaneous power he instantaneous power o chirp jamming can be calculated using the summation o PSD within the instantaneous bandwidth and is given by P chirp(n) = S sm( i, n) (15) i Bins(n) where P chirp(n) is the instantaneous power o chirp jamming at n time slot and is the resolution o PSD.

6 55 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) Parameters prediction o chirp jamming Some parameters o chirp jamming should be predicted to ensure that the communication signal can coexist in the same band. hese parameters include instantaneous requency and power. In this section, the prediction algorithm based on the Kalman ilter is discussed. In contrast to other prediction algorithms, the status update o the Kalman prediction algorithm is decided only by the latest previously estimated data and the newest detected data. hereore, only the latest previously estimated data are stored. he instantaneous requency and sweeping rate o chirp jamming at n time slot are assumed as chirp(n) and v (n), respectively. he instantaneous requency o linear chirp jamming linearly changes with time. hereore, the relationship is given by chirp(n + 1) = chirp(n) + v (n) (16) with zero mean and variances o and, respectively. he mea- 1 sure equations can be written in vector/matrix orm as x(n) = Hs(n) + v(n) (3) [ ] where x(n) = [x (n), x (n)] , H =, and v(n) = be computed as Q(n) = E[w(n)w (n)] = d [ ] dp R(n) = E[v(n)v 0 (n)] = 1 0 I the PSD detection interval is short enough, the change o instantaneous requency o nonlinear chirp jamming can be considered approximately as linear change during n time slot and n + 1 In practice, R(n) is decided by system characteristics such as sample rate, quantization level, and so on. Q(n) can be estimated by the previously detected N (N ) values as ollows: time slot. hereore, (16) is also tenable or nonlinear chirp jam- N 1 ming i is short enough. = [d (k)] d Random error o parameters estimation o chirp jamming N k=1 (4) always exists because o noise and ading channels. hereore, N although the transmission power o chirp jamming is invariable, the 1 estimated value o power in dierent time slots varies. he power = [d dp P(k)] N shit rate between P chirp(n) and P chirp(n + 1) can be assumed as v P(n). k=1 (5) I the PSD detection period is small enough, an approximate relationship exists, such as he iterative initial value should be estimated beore s(n) is predicted by the Kalman ilter. chirp(n) and P chirp(n) are detected in n = 1 P chirp(n + 1) = P chirp(n) + v P(n) (17) and n =, respectively. In obtaining x 1(1), x (1), x 1(), and x (), the initial state variables s(1) can be estimated as Similarly, the estimated values o v (n) and v (n) in dierent P x 1(1) time slots vary because random estimation errors always exist. I ˆchirp(1) 1 d (n) and d (n) are assumed to be the changes o v (n) and v (n) [x 1() x 1(1)] P P v ˆ ˆ (1) s(1) = during, respectively, the relationships can be expressed as P ˆ = chirp(1) x (1) v ˆ (1) 1 p v [x () x (1)] (n + 1) = v (n) + d (n) (18) v he initial value o one-step update value ˆs(1 1) can be estimated P(n + 1) = v P(n) + d P(n) (19) approximately as ˆs(1 1) = ˆs(1). hen, the initial value o minimum However, although the values o v (n), v P(n), d (n) and d P(n) are MSE matrix can be computed as dierent per time slot, the rate o change (similar to acceleration) o ˆ ˆ ˆ ˆ v (n), v P(n), d (n) and d P(n) is quite small. Additionally, their changes M(1 1) = E{[s(1) E(s(1))][s(1) E(s(1))] } seem random. hereore, these values can be assumed as station ary stochastic variables (simulation results presented in Section = v veriy the validity o this assumption). he variances o d (n) and 0 0 P 0 d (n) are and, respectively. heir mean values are assumed P d dp vp to be zero. he chirp(n), v (n), P chirp(n), and v P(n) can be viewed as where,,, and are the variances o chirp(n), v (n), P chirp(n), our state variables. hereore, the system state equation is com- v v P P posed o (16) (19). In vector/matrix orm, the equation is expressed and v P(n), respectively. hese values can be estimated using the as previously detected N (N ) values o chirp(n), v (n), P chirp(n), and v P(n). From ˆs(1 1) and M(1 1), the iterative calculation can be s(n + 1) = As(n) + w(n) (0) perormed using the Kalman ilter [8] through the ollowing steps: (a) he one step predictive value o state vector ˆs(n n 1) is computed using: where s(n) = [ chirp(n), v (n), P chirp(n), v P(n)], A = s(n n ˆ 1) = As(n ˆ 1 n 1) (6) and w(n) = [0, d (n), 0, d (n)] p. w(n) is viewed as the state noise. (b) he minimum predictive MSE M(n n 1) is calculated using: I x 1(n) and x (n) are the measure values o chirp(n) and P chirp(n), respectively, the measure equations can be written as M(n n 1) = AM(n 1 n 1)A + Q(n) (7) x 1(n) = chirp(n) + v 1(n) (1) x (n) = P chirp(n) + v (n) () where v 1(n) and v (n) are the measure noise o chirp(n) and P chirp(n), respectively. he measure noise are assumed to be stationary noise, [v (n), v (n)]. he autocorrelation matrices o w(n) and v(n) can (c) Kalman gain K(n) is then obtained using: 1 K(n) = M(n n 1)H [R(n) + HM(n n 1)H ] (8) (d) he one-step update value ˆs(n n) is determined using: s(n n) ˆ = s(n n ˆ 1) + K(n)[x(n) Hs(n n ˆ 1)] (9)

7 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) (e) he minimum MSE M(n n) is calculated using (30), and then Step (a) is repeated. M(n n) = [I K(n)H]M(n n 1) (30) Step (a) predicts the state variables, and the other steps are iterative steps o the Kalman ilter. he shortcoming o Kalman ilter is that i the measure value x(n) changes suddenly (or example, x(n) in stop requency, whereas x(n + 1) in start requency), the one step predictive value ˆs(n n 1) yields a very large error and converges slowly. o address this problem, some modiied Kalman ilters have been proposed. However, these algorithms are very complex. In the paper, the problem is solved by a simple method. A sudden change o x(n) will induce the one-step update value ˆs(n n) to change remarkably. I the change o ˆs(n n) exceeds a threshold K, ˆs(n n) will be set as zero. In the next time slot, the one-step predictive value ˆs(n + 1 n) will converge at a proper value with small error, or example, the error is less than 1% rom Fig. 10(a). he threshold K can be decided by simulation. In theory, the abovementioned chirp-jamming sensing scheme, which mainly includes parameter estimation and prediction o chirp jamming, can adapt to the sensing o linear chirp jamming and to nonlinear chirp jamming, such as quadratic or logarithmic chirp jamming. he simulation results in Section 6.1 veriied this point. Fig. 6. Carrier requency o ACJC under linear chirp jamming. 5. Anti-chirp-jamming decision-making Fig. 7. Carrier requency o ACJC under nonlinear chirp jamming Decision-making o communication requency he main task o communication requency decision-making is to ind the appropriate communication requency to avoid collision between communication signal and chirp jamming. Furthermore, the rational switch rule o communication requency should be designed to reduce the complexity o the system control. Hence, this section irst investigates the conditions that prevent communication signal and chirp-jamming collision. he communication requency and its switch rule are then designed rom an engineering viewpoint. In theory, i the communication signal o the ACJC system is to prevent collision with chirp jamming, the communication signal should be orthogonal to chirp jamming in the requency domain, i.e., their inner product is zero. he continuous-time complex chirp jamming c(t) and linearly modulated communication signal s(t) are given by c(t) = exp[j chirp(t)t], 0 t c s(t) = am exp(jct), 0 t s where chirp(t) is the instantaneous requency o chirp jamming, c is the period o c(t), s is the symbol period o s(t), am is the amplitude o s(t), and c is the carrier requency o s(t). I s(t) does not collide with c(t) during c, the inner product o s(t) and c(t) should meet as c c s(t), c(t) 0 = s(t)c (t)dt = 0 (31) 0 However, c is diicult to solve in 0 t c because the solution o s(t), c(t) c = 0 is not the elementary orm unction. Hence, an 0 approximate method is used to determine the communication requency c, which does not collide with chirp jamming. Compared with c, s is small enough such that chirp(t) can be considered unchanged during s. he communication signal bandwidth is calculated approximately as BW s = 1/ s. he inner product o s(t) and c(t) in 0 t s can be written as s s(t), c(t) s 0 = am exp(jct) exp[ j chirp(t)t]dt 0 s = am exp{[j[c chirp(t)]t]}dt (3) 0 I (3) is set as zero, then the minimum requency interval between communication signal and chirp jamming can be easily calculated by [9] sc = c chirp(t) = BW s (33) hat is, i the instantaneous requency interval between communication and chirp jamming satisies sc BW s, then chirp jamming does not interere with the communication signal. From (3) and (33), the linear or nonlinear property o chirp(t) does not aect the conclusion; thus, it adapts linear and nonlinear chirp jamming. his is not a stringent condition. However, in engineering, the ollowing points are considered to ensure the stability o communication quality. (a) c should maintain a large interval with chirp(t). (b) he switch times o c should be lower possibly to decrease time overhead imposed by the requency switch. (c) he requency switch time interval o c should be even to simpliy the design o the system protocol. Considering the abovementioned points and the behavior o chirp jamming, ACJC should have a signal orm as an adaptive FH signal. I the chirp jamming is linear, the communication signal o ACJC should hop in at least two carrier requencies (c1 and c) to coexist with chirp jamming, as shown in Fig. 6. In this condition, the requency switch times are at their minimum during c, so the time overhead o requency switch is also at

8 554 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) a minimum. is assumed to be the time o irst requency change. 1 It is calculated rom point (c) as c 1 = c 1; i.e., 1 = hereore, the switch times o the carrier requency in one chirpjamming period are c/ and c. he hop period is h = c/. In c/, c1, and c should be kept away rom the chirp-jamming instantaneous requency chirp( c/). In c, c1, and c should be kept away rom H and L. Hence, c1 is at the midpoint between chirp( c/) and L, and c is at the midpoint between chirp( c/) and H. hese are expressed as L + chirp( c/) c1 = + ( /) c = H chirp c (34) For linear chirp jamming, chirp( c/) = (1/)( H + L). hereore, c1 = ( H + 3 L)/4, c = (3 H + L)/4. For nonlinear chirp jamming, chirp( c/) = / (H + L)/. I even or uniorm hop period o ACJC is also adopted, i.e., h = c/, c1 and c should be computed according to the detected value o chirp( c/) and (34) and (35), as shown in Fig. 7. In summary, the communication signal orm o ACJC should be an adaptive FH signal. he hop period is hal o the chirp-jamming period, and the communication requency ulils (34) and (35). However, ACJC is dierent rom the existing FH system. ACJC has no standard or ixed hop period. he hop period o ACJC can be adjusted according to the period o chirp jamming, unless the period o chirp jamming is too short to exceed the shortest limitation o the hop period o ACJC. On the other hand, ACJC has not hopset. ACJC can select any requency in its license band according to the requency o the chirp jamming. 5.. Decision-making o transmission power (35) As mentioned previously, the ACJC system switches its communication requency according to the behavior o chirp jamming. However, the requency switch introduces time overhead to the system. he time overhead o the requency switch includes requency switch time and transmission time o auxiliary inormation such as synchronization and signaling inormation. he time overhead cannot transmit useul inormation and decreases eective signal-to-noise ratio (SNR). hus, transmission power must be adjusted to compensate, which is the task o the decision-making unction o the transmission power. heoretically, i the duration o the requency switch is ignored and transmission power is kept constant in dierent carrier requencies, the BER perormance o the ACJC system remains the same as that o a ixed requency system o continuous transmission. However, seamless hopping is impossible or the ACJC system. he requency switch, synchronization, and system signaling, among others, inevitably generate time overhead. In the paper, the eect o time overhead on system perormance is analyzed using the perormance analysis method o the FH system [10]. Only the time overhead o the requency switch and transmission o auxiliary inormation are considered in the analysis. he hop period o the ACJC system has two sections: (a) Dwell time dw. he ACJC system transmits inormation during dwell time. Auxiliary inormation such as synchronization and signaling inormation is also transmitted. he transmission time o useul inormation and the time overhead o auxiliary inormation are represented as inor and au, respectively. (b) Frequency switch time sw. sw includes dead, rise, and all times. Fig. 8. Block diagram o anti-chirp-jamming decision-making. Hence, one hop period can be divided as h = dw + sw = inor + au + sw = inor + oh (36) where oh = au + sw is the time overhead that cannot transmit useul inormation. Here, R1 is assumed to be the continuous transmission rate o inormation sequence, whereas R is assumed to be the transmission rate during inor. he ACJC system must transmit all useul inormation discontinuously within inor at rate R, with average or eective transmission rate R1 within h. According to the inormation balance principle, the ollowing equation must be satisied: R1 h = R inor (37) h R = R1 > R 1 (38) inor hereore, the practical rate o useul inormation is R, which is higher than the average transmission rate R 1. I the transmission power is constant, the energy per bit in the ACJC system is less than that in a continuous transmission system. hereore, the ACJC system has worse BER perormance than the continuous transmission system. he energy per bit in the continuous transmission system with R1 is assumed as E b1. he energy per bit in the ACJC system with average rate R1 and practical rate R is assumed as E b. he transmission power is P t. hus: Pt E b1 = R1 P t E b = R I noise v(n) is assumed to be a white Gaussian random process N with zero mean and PSD 0, SNR per bit is calculated by E SNR b1 = b1 = P t N 0 R1N0 Eb SNR b = = P t N0 RN0 Pt = inor R1N0 h inor = SNR b1 h (39) I SNR per bit is denoted as db, the loss o SNR per bit in the ACJC system is computed as SNR b(db) = SNR b1(db) SNR b(db) h = 10lg (db) inor c = 10lg (db) c oh (40) (41) Here, oh is related to hardware perormance and communication protocol. It is generally a ixed value. hereore, SNRb is mainly related to c. A larger c means a smaller SNR b. I the BER perormance in the ACJC system is the same as that in the continuous transmission system, the transmission power o the ormer

9 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) Fig. 9. PSD o received signal: (a) PSD in the n time slot; (b) dual-value PSD in the n time slot; (c) dual-value PSD in the n + 1 time slot; (d) dierence operation o S (, n) and S (, n + 1). should increase to maintain the same SNR per bit. his principle is expressed as P t1 = P t R 1 N 0 RN0 R c P t = Pt1 = Pt1 R1 c oh (4) where Pt1 is the transmission power in the continuous transmission system and Pt is the transmission power in the ACJC system. From (4), the transmission power o the ACJC system is larger than that o the ixed requency communication system in the same SNR due to the time overhead o the requency switch. he ACJC system necessarily transmits under maximum allowable transmission power. I the maximum allowable transmission power is reached, other methods which can reduce the transmission power requirement such as channel code, diversity, and so on, are exploited to maintain the BER perormance. A block diagram o the anti-chirp-jamming decision-making module is shown in Fig. 8. he module employs a simple arithmetical computation with very low complexity. 6. Simulation results he simulation is perormed in intermediate requency. Modulations o the ACJC system are 10 kbps BPSK and 0 kbps QPSK. Sampling requency, PSD detection duration, and PSD detection period are 0 MHz, 100 s and 100 s, respectively. he start and stop requencies o chirp jamming are L = 1 MHz and H = 6 MHz, respectively. he transmission power o chirp jamming is 1 W and ree space propagation loss is not considered. he chirp-jamming period is 5 ms. Single-tone jamming with 500 khz, broadband jamming with central requency o 8 MHz, bandwidth o 3 MHz, and AWGN exist in the wireless environment. he channel models are considered as AWGN channel and COS 07 in typical urban (U) [30] Sense perormance o chirp jamming Fig. 9(a) shows the smoothened PSD S smooth(, n) in n time slot. Instantaneous PSD o single-tone jamming, broadband jamming, and chirp jamming can be ound in the igure. Fig. 9(b) and (c) shows the dual-value PSD S (, n) in n and n + 1 time slots, respectively. PSD o single-tone and broadband jamming does not change with time. However, chirp jamming PSD clearly changes. hereore, the dierence between S (, n) and S (, n + 1) is obtained as Fig. 9(d). Static spectrum signals such as single-tone and broadband jamming are eliminated, and dual-value PSD peaks o chirp jamming in n and n + 1 time slots are obtained in the igure. By calculating the central requency o dual-value PSD peaks o chirp jamming, instantaneous requencies chirp(n) and chirp(n + 1) are derived. Based on chirp(n) and chirp(n + 1), the instantaneous requency o the next time slot chirp(n + ) can be predicted. Fig. 10 shows the MSE perormance o sweeping rate o linear chirp jamming. From Fig. 10, the MSE perormance o sweeping rate keeps steady and has enough precision or anti-jamming decisionmaking when JNR 1 db (JNR, jamming-to-noise ratio).

10 556 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) Fig. 10. Estimation perormance o sweeping rate o chirp jamming versus JNR. Fig. 1. Estimation perormance o stop requency o chirp jamming versus JNR. Fig. 11 shows the MSE perormance o start requency. From Fig. 11, MSE perormance keep steady until JNR = 1 db. Fig. 1 shows the MSE perormance o stop requency. Similar to start requency, MSE perormance o stop requency keep steady until JNR = 1 db. Fig. 13 shows the MSE perormance o sweeping bandwidth. From Fig. 13, MSE o sweeping bandwidth reaches 10 6 at JNR = 1 db. hen the MSE decrease gradually with the increase o JNR. Fig. 14 shows the MSE perormance o instantaneous requency. Similar to the other parameters MSE, MSE o instantaneous requency keep steady until JNR = 13 db. Fig. 15 shows the MSE perormance o instantaneous power. Since the existence o noise power, the MSE o instantaneous power decrease approximately linearly with the increase o JNR. Fig. 16(a) shows the curves o detected and predicted values o the linear chirp-jamming instantaneous requency. Except or the chirp-jamming stop requency, the predicted requency value using the Kalman ilter coincides precisely with the detected value. Fig. 16(b) shows the prediction error o instantaneous requency chirp. he steady-state prediction error is less than 0.01 MHz except or the chirp-jamming stop requency. Fig. 13. Estimation perormance o sweeping bandwidth o chirp jamming versus JNR. Fig. 11. Estimation perormance o start requency o chirp jamming versus JNR. Fig. 14. Estimation perormance o instantaneous requency o chirp jamming versus JNR.

11 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) assumption that v (n), P chirp(n), v P(n), d (n), and d P(n) are stationary stochastic variables is logical. Fig. 18(a) shows the curves o detected and predicted values o the nonlinear chirp jamming instantaneous requency. Fig. 18(b) shows the prediction error o instantaneous requency chirp. Similar conclusions with Fig. 16 are drawn. It indicates that (10) and (16) are also tenable or nonlinear chirp jamming i is short enough. Fig. 19(a) shows the curve o detected and predicted values o the nonlinear chirp jamming instantaneous power. Fig. 19(b) shows the prediction error o instantaneous power P chirp. Similar conclusions with Fig. 17 are drawn. From Figs , the chirp-jamming sensing scheme is ound to sense both linear and nonlinear chirp jamming, respectively. he sensing perormance can meet the requirement o anti-chirpjamming decision-making. Fig. 15. Estimation perormance o instantaneous power o chirp jamming versus JNR. Fig. 17(a) shows the curve o detected and predicted values o the linear chirp-jamming instantaneous power. Fig. 17(b) shows the prediction error o instantaneous power P chirp. From Fig. 17(b), the absolute and relative prediction errors o power are less than 0.0 W and %, respectively. Since instantaneous requency and power is predicted precisely by the Kalman ilter, the 6.. BER perormance o ACJC In this section, BER perormance o ACJC system, the ixed requency communication system with continuous transmission, and the FH system without adaptive strategy (also called blind FH system) are simulated. All systems in the simulations are equipped with a band-pass ilter to suppress out-o-band radiation. he signal-to-jamming ratio (SJR) is the power ratio o the communication signal to chirp jamming. Fig. 0 shows the time and requency distribution o PSD in a wireless environment. he ACJC signal hops adaptively according Fig. 16. Prediction o linear chirp jamming instantaneous requency and prediction error: (a) prediction o chirp jamming instantaneous requency; (b) prediction error o instantaneous requency. Fig. 17. Prediction o linear chirp jamming instantaneous power and prediction error: (a) prediction o chirp jamming instantaneous power; (b) prediction error o instantaneous power.

12 558 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) Fig. 18. Prediction o nonlinear chirp jamming instantaneous requency and prediction error: (a) prediction o chirp jamming instantaneous requency; (b) prediction error o instantaneous requency. Fig. 19. Prediction o nonlinear chirp jamming instantaneous power and prediction error: (a) prediction o chirp jamming instantaneous power; (b) prediction error o instantaneous power. to chirp jamming. he adaptive hopping strategy avoids collision and achieves coexistence o the ACJC signal and chirp jamming. Fig. 1 compares the BER perormance o the ixed requency communication system with continuous transmission, blind FH system, and the ACJC system with QPSK in AWGN channel. In Fig. 1, SNR is assumed to be 13 db. Fig. presents the BER perormance comparison with BPSK in AWGN channel. In Fig., SNR is assumed to be 10 db. he intrusion o chirp jamming has no signiicant eect on the BER perormance o the ACJC system as shown in Figs. 1 and. he ACJC system perormance is determined mainly by SNR. However, the ixed requency communication and the blind FH systems show poor BER perormance under strong chirp jamming. Fig. 3 compares the BER perormance o the ixed requency communication system with continuous transmission, the blind FH system, and the ACJC system with QPSK in COS 07 U channel. SNR is assumed to be 30 db. he intrusion o chirp jamming is ound to have no signiicant eect on the BER perormance o the ACJC system. he perormance o the ACJC system is determined mainly by the ading channel and AWGN. Fig. 0. Frequency and time distribution o PSD in a wireless environment. Fig. 1. BER comparison o ACJC, blind FH, and ixed requency communication systems with QPSK in an AWGN channel.

13 Y. Niu et al. / Int. J. Electron. Commun. (AEÜ) 66 (018) able 1 Summary o the notations used in the paper Fig.. BER comparison o ACJC, blind FH, and ixed requency communication systems with BPSK in AWGN channel. Fig. 3. BER comparison o ACJC, blind FH, and ixed requency communication systems with QPSK in COS 07 U channel. Notation r(n) s(n) c(n) v(n) Nc chirp(n) chirp S( i) wl Fs N S sm(i) M Ssmooth(, n) S (, n) v (n) ˆ L ˆ H Bˆ chirp B ˆ ins(n) P chirp(n) v p(n) d (n) d p(n) s(n) A w(n) x 1(n) x (n) v 1(n) v (n) Q(n) R(n) s(n n ˆ 1) M(n n 1) K(n) s(n n) ˆ M(n n) c s c h R1 R Pt1 Pt Deinition Discrete-time received signal Linearly modulated communication signal Single-tone chirp jamming AWGN Sample number o chirp jamming in one period Instantaneous requency o the chirp jamming in n time slot Instantaneous requency vector PSD in i Window Sample requency Point number o PSD ime interval o PSD computation Smoothened PSD in i he length o smooth PSD vector ater smoothening at n time slot Dual-value PSD vector at n time slot Sweeping rate at n time slot Estimated value o start requency Estimated value o stop requency Estimated value o sweeping bandwidth Estimated value o the instantaneous bandwidth o the chirp jamming in the n time slot Instantaneous power o the chirp jamming in the n time slot Power shit rate between n and n + 1 time slots Change o v (n) during with variance d Change o v p(n) during with variance dp State vector o Kalman predictor State transition matrix o Kalman predictor State noise o Kalman predictor Measure values o chirp(n) Measure values o P chirp(n) Measure noise o chirp(n) with variance 1 Measure noise o P chirp(n) with variance Autocorrelation matrices o w(n) Autocorrelation matrices o v(n) One step predictive value o state vector Minimum predictive MSE Kalman gain One-step update value Minimum MSE Period o the chirp jamming Symbol period o ACJC signal Carrier requency o ACJC signal Hop period o ACJC signal Eective or average transmission rate o system ransmission rate in ransmission time o useul inormation ransmission power in the continuous transmission system ransmission power in ACJC system Fig. 4. Perormance loss induced by time overhead: (a) relationship between the loss o SNR and time overhead; (b) BER under dierent time overhead.