Chirp-Based FHSS Receiver with Recursive Symbol ... - MDPI

sensors Article

Chirp-Based FHSS Receiver with Recursive Symbol Synchronization for Underwater Acoustic Communication Geunhyeok Lee 1 , Woongjin Park 1 , Taewoong Kang 1 , Kiman Kim 1, * and Wanjin Kim 2 1 2

*

Department of the Radio Communication Engineering, Korea Maritime and Ocean University, Busan 49112, Korea; [email protected] (G.L.); [email protected] (W.P.); [email protected] (T.K.) Agency for Defense Development, Changwon 51678, Korea; [email protected] Correspondence: [email protected]

Received: 18 October 2018; Accepted: 11 December 2018; Published: 19 December 2018







Abstract: In this paper, we propose a covert underwater acoustic communication method that is robust to fading using a chirp signal combined with a frequency-hopping spread spectrum scheme. A fractional Fourier transform, which estimates the slope of the signal frequency variation, is applied to the receiver to enable a robust and reliable symbol estimation with respect to the frequency and irregular phase variations. In addition, since the recursive symbol synchronization can be implemented using a chirp signal, compression and expansion effects due to the Doppler shift can be mitigated. Simulation and lake trials were performed to verify the performance of the proposed method. The simulation was performed by two different methods. Keywords: covert underwater acoustic communication; frequency-hopping spread spectrum; symbol synchronization; Doppler fading; fractional Fourier transform; underwater channel simulator

1. Introduction The upcoming 5G communication standard has been an active area of research in recent years, focusing on terrestrial communications. However, progress in underwater communications has been comparatively much slower. The underwater acoustic environment is much more challenging, with far greater dispersion and multipath effects, limiting the potential use of the classical 5G scheme in the underwater domain [1]. Some research in developing underwater technology has taken place with a focus on orthogonal frequency division multiplexing (OFDM) and single-carrier frequency division multiple access (SC-FDMA) schemes [2,3]. In general, the underwater acoustic communication community has focused on increasing transmission distance, improving bandwidth efficiency, and reducing the rate of error in the complex time–space-varying underwater channel [4,5]. Covert underwater acoustic communication has been studied for military purposes to hide positioning information or data information. Although it is not an acoustic signal, underwater optical communication using a blue–green laser has also been aimed at enhancing covertness through the use of the strong directivity of lasers [6]. In addition, biomimetic signaling has been studied as a scheme for underwater acoustic communications, but the subject is in the early stages [7,8]. On the other hand, the spread spectrum schemes are widely used in the field to achieve covert communication. There are two typical spread spectrum schemes. One is a direct-sequence spread spectrum (DSSS) method in which the data are multiplied by a spread factor [9–12]. The other is a frequency-hopping spread spectrum (FHSS) method in which the frequency band is shifted using a spread code [13]. The FHSS method is randomly hopped according to the hopping pattern. By this method, an interceptor who does not know the hopping pattern cannot recover the signal. Furthermore, if any jamming is executed with malicious

Sensors 2018, 18, 4498; doi:10.3390/s18124498

www.mdpi.com/journal/sensors

Sensors 2018, 18, 4498

2 of 18

intent, the signal performance will be maintained because the center frequency will be continuously changed. This capability is called anti-jamming [14,15]. A simple multiple-access underwater acoustic communication protocol called JANUS was designed and tested as a NATO standard. It was a binary frequency shift keying (BFSK)-based FH method [16]. A covert underwater acoustic communication scheme between an unmanned underwater vehicle (UUV) and a distant mother platform using an OFDM had been studied [17]. However, the previous FHSS method was of the form in which a single center frequency was hopped. A chirp-based method utilizes a data-modulated signal, which has its energy spread over a bandwidth that is greater than the rate of information being sent, like all spread spectrum systems. The chirp-based method is one in which the binary information modulates the slope of a linear chirp, with chirps representing zeros or ones. This method alone can be considered a covert underwater acoustic communication technology. Due to the wide bandwidth in the chirp-based method, immunity against various frequency-selective fading and a frequency diversity effect may be expected [18,19]. Fractional Fourier transform (FrFT) is a generalized analysis method of the existing Fourier transform concept [20,21]. In particular, when a chirp signal has a linear characteristic in the time–frequency domain, robust detection is possible in a noisy or reverberant environment, as the FrFT results can obtain a concentrated energy spectrum. The FrFT has been applied in various fields, such as radar, image processing and communication [22–25]. Since underwater acoustic communication signals must typically pass through poor underwater channels, the coherent methods that are sensitive to phase shifts complicate the structure of the receiver. On the other hand, the non-coherent methods, such as the FrFT, can mitigate the fading effects with a relatively simple receiver structure. The chirp signal combined with FHSS and demodulated by the FrFT method was studied in recent times [26]. This method simultaneously transmitted two chirp signals in one symbol duration and demodulated the received frequency-hopped signals in the FrFD (fractional Fourier domain) of the FrFT spectrum. As the up-slope chirp signal and the down-slope chirp signal were applied in one symbol duration, a parallel receiver should have retrieved the different transform orders. In this paper, we propose the single chirp-based FHSS method demodulated by the non-coherent FrFT method. In the proposed method, either the up-slope chirp signal or the down-slope chirp signal is transmitted within one symbol duration, and does not require the parallel demodulator. There is also a difference from the conventional method in symbol demapping using the FrFT spectrum. The conventional method was independently demodulated using different orders for the up-slope chirp and the down-slope chirp without considering the negative frequency domain in the fractional frequency domain. On the other hand, since the proposed method uses the symmetrical characteristic of the frequency (having the positive frequency and negative frequency), there is a difference in the form represented by the FrFT due to the slope inversion of the positive and the negative frequency domains. In addition, as only a single transform order is required, a simpler receiver structure can be used. Due to the movement, a Doppler shift can occur to the received signal, and the Doppler frequency will be relatively large due to the slow acoustic velocity in water compared to the propagation velocity on the ground [27]. Since the received signal is expanded and compressed by the Doppler shift, a method of implementing symbol synchronization recursively using an autocorrelation function of the estimated chirp signal should be employed. To consider the performance of the proposed method, we conducted simulations based on an underwater channel propagation model and conducted a lake trial to verify its validity. The remainder of this paper is organized as follows: In the next section, the principle of the single chirp-based FHSS scheme is presented. Section 3 describes the receiver based on the FrFT. Sections 4 and 5 then show the performance of the proposed method as evaluated via simulations and lake trials. Section 6 provides the conclusion.

Sensors 2018, 18, 4498

3 of 18

2. Chirp-Based FHSS Scheme Sensors 2019, 19 FOR PEER REVIEW

The basic chirp signal used in the proposed method is expressed in Equation (1) as

3

2. Chirp-Based FHSS Scheme

   k s(t) = exp j2π f 0 t + t2 , The basic chirp signal used in the proposed method is2expressed in Equation (1) as

(1)

𝑘 where f 0 is the initial frequency ands(𝑡) k is = the chirp Equation the exp 𝑗2𝜋rate. 𝑓𝑡+ 𝑡 , (1) can be rewritten to express(1) 2 chirp signal as follows, f max − f min(1) can be rewritten to express the where 𝑓 is the initial frequency is the chirp su (and t) =𝑘exp [ j2πt ( f minrate. + Equation t)], (2) T chirp signal as follows, f − f max t)], (3) sd𝑠(t(𝑡) ( f max ++ min ) ==exp exp[ j2πt [𝑗2𝜋𝑡(𝑓 𝑡)], (2) T where f min is the minimum frequency f max is the + maximum frequency. T is the duration of(3) the 𝑠 (𝑡) =and exp[𝑗2𝜋𝑡(𝑓 𝑡)], symbol. Equation (2) represents a signal that has an up-slope frequency with an initial frequency where 𝑓 is the minimum afrequency is the maximum frequency. 𝑇 is the duration of. f min . Equation (3) represents signal thatand has𝑓a down-slope frequency with an initial frequency f max the symbol.the Equation (2) represents a signal the thatabove has anequations up-slopecan frequency with an To express chirp signal in real numbers, be expressed asinitial frequency 𝑓 . Equation (3) represents a signal that has a down-slope frequency with an initial frequency 𝑓 . Su (the t) =above Re{suequations (4) (t)}, To express the chirp signal in real numbers, can be expressed as

= Re 𝑅𝑒{s𝑠 ((𝑡) , S𝑆d ((𝑡) t) = d t )}.

(4) (5)

(5) (𝑡) = 𝑅𝑒 𝑠 (𝑡) . The chirp-based scheme selects one of𝑆the chirp symbols of Equation (4) using the binary sequence bi . Therefore, the chirp-based t) with the chirp symbolsymbols period TofisEquation expressed(4) as [28] The chirp-based schemesignal selectssc (one of the using the binary sequence 𝑏 . Therefore, the chirp-based signal s (𝑡) with the symbol period T is expressed as [28] ( S u ( t ) , i f bi = 0 𝑆 (𝑡), 𝑖𝑓 𝑏 = 0 , nT ≤ t ≤ (n + 1) T. sc (t) = (6) 𝑠 (𝑡) = Sd (t), i f bi = 1 , n𝑇 𝑡 (n + 1)𝑇. (6) 𝑆 (𝑡), 𝑖𝑓 𝑏 = 1 This This equation equation implies implies assigning assigning aa binary binary value value “1” “1” to to aa signal signal with with an an up-slope up-slope frequency, frequency, and assigning assigning aa binary binary value value “0” “0” to a signal with a down-slope frequency. During During the the duration duration of of the symbol, the chirp signal is mapped by the binary bit stream. The The received received signal is is usually usually used used by by aa correlator receiver. Figure Figure 11 shows shows the the basic basic structure structure of of the the hopping hopping scheme scheme in in aa chirp-based chirp-based FHSS. FHSS. In In this this case, case, since the hopping hopping duration is longer longer than than the the symbol symbol duration, duration, there there are several symbols in the single single hopping interval.

Figure 1. Basic Basic scheme scheme of of the the chirp-based chirp-based FHSS. Figure

Sensors 2018, 18, 4498

4 of 18

Sensors Sensors2019, 2019,1919FOR FORPEER PEERREVIEW REVIEW

44

3. Receiver Receiver Design Based Based on Fractional Fractional Fourier Transform Transform 3. 3. ReceiverDesign Design Basedon on FractionalFourier Fourier Transform Figure 22 shows shows a block diagram diagram of the proposed proposed method. Firstly, Firstly, a hopping pattern pattern is generated Figure Figure 2 showsa ablock block diagramofofthe the proposedmethod. method. Firstly,a ahopping hopping patternisisgenerated generated and multiplied by the modulated transmission signal to perform frequency hopping, and the the receiver receiver and multiplied by the modulated transmission signal to perform frequency hopping, and and multiplied by the modulated transmission signal to perform frequency hopping, and the receiver utilizes aa bandpass filter with a known hopping pattern. Then, the compression or expansion effect of utilizes utilizes abandpass bandpassfilter filterwith witha aknown knownhopping hoppingpattern. pattern.Then, Then,the thecompression compressionororexpansion expansioneffect effect the signal due to the Doppler shift can be corrected by introducing the matched filter results between ofofthe thesignal signaldue duetotothe theDoppler Dopplershift shiftcan canbebecorrected correctedby byintroducing introducingthe thematched matchedfilter filterresults results the symbol estimation through the FrFT spectrum and the received signal. between the symbol estimation through the FrFT spectrum and the received signal. between the symbol estimation through the FrFT spectrum and the received signal.

Figure Block diagram Figure2.2.Block Blockdiagram diagramofofthe theproposed proposedmethod. method.

Figure 1,1,there there are four symbols ininaaasingle single hopping frequency interval. InInthe theexample exampleshown shownininFigure Figure1, thereare arefour foursymbols symbolsin singlehopping hoppingfrequency frequencyinterval. interval. symbol is divided into a low-frequency band and a high-frequency band. The symbol with Each symbol is divided into a low-frequency band and a high-frequency band. The symbol with an Each symbol is divided into a low-frequency band and a high-frequency band. The symbol with an an up-slope in the low-frequency band is called “Symbol Mapping #1”, and the symbol with a up-slope up-slopeininthe thelow-frequency low-frequencyband bandisiscalled called“Symbol “SymbolMapping Mapping#1”, #1”,and andthe thesymbol symbolwith witha adowndowndown-slope is “Symbol called “Symbol Mapping #2”. The symbol with up-slope in the high-frequency is slope Mapping #2”. symbol with ininthe band slopeisiscalled called “Symbol Mapping #2”.The The symbol withup-slope up-slope thehigh-frequency high-frequency bandisband iscalled called called “Symbol Mapping #3”, and the symbol with down-slope is called “Symbol Mapping #4”. “Symbol Mapping #3”, and the symbol with down-slope is called “Symbol Mapping #4”. “Symbol Mapping #3”, and the symbol with down-slope is called “Symbol Mapping #4”. Figure Figure3a3ashows showsthe thematched matchedfilter filterresult, result,which whichisisfrom fromthe theauto-correlation auto-correlationfunction functionofofthe the “Symbol #1” in any hopping pattern. It can be seen that the output of the matched filter “Symbol Mapping #1” in any hopping pattern. It can be seen that the output of the matched filter has “Symbol Mapping #1” in any hopping pattern. It can be seen that the output of the matched filter has a maximum value atideal the ideal point. Figure 3b shows the matched filter result, iscrossthe ahas value atatthe point. Figure 3b3bshows the filter which isisthe amaximum maximum value the ideal point. Figure shows thematched matched filterresult, result, whichwhich thecrosscross-correlation function between the “Symbol Mapping #1” and “Symbol Mapping #2” in any correlation between the Mapping #1” “Symbol Mapping #2” hopping correlationfunction function between the“Symbol “Symbol Mapping #1”and and “Symbol Mapping #2”ininany any hopping hopping pattern. Since “Symbol Mapping #1” and “Symbol Mapping #2” have different slopes, the pattern. Since “Symbol Mapping #1” and “Symbol Mapping #2” have different slopes, the maximum pattern. Since “Symbol Mapping #1” and “Symbol Mapping #2” have different slopes, the maximum maximum point of the matched filter result cannot be correctly represented, and the magnitude is less point pointofofthe thematched matchedfilter filterresult resultcannot cannotbebecorrectly correctlyrepresented, represented,and andthe themagnitude magnitudeisisless lessthan thanthe the than ideal value [29]. ideal value [29]. idealthe value [29]. 1400 1400

ㅡㅡ Matched filtering Result, Symbol : [#1 #1] Matched filtering Result, Symbol : [#1 #1]

Matched filtering result Matched filtering result Maximum Point Maximum Point Correct Line Correct Line

1200 1200

Amplitude Amplitude

1000 1000 800 800 600 600 400 400 200 200 0 0

1920 1920

Sample Position [N][N] Sample Position

(a) (a) Figure 3. Cont.

Sensors 2018, 18, 4498

5 of 18

Sensors 2019, 2019, 19 19 FOR FOR PEER PEER REVIEW REVIEW Sensors

55 1400 1400

ㅡ #2] Matched filtering filtering Result, Result, Symbol Symbol :: [#1 [#1ㅡ #2] Matched

Matchedfiltering filteringresult result Matched MaximumPoint Point Maximum CorrectLine Line Correct

1200 1200

Amplitude Amplitude

1000 1000 800 800 600 600 400 400 200 200 00

663 663

Sample Position Position [N] [N] Sample

(b) (b) Figure 3. Matched filter output in the same frequency band. (a) The same slope symbol; (b) different Figure 3. 3. Matched filter output inin the same frequency band. (a)(a) The same slope symbol; (b) different Figure Matched filter output the same frequency band. The same slope symbol; (b) different slope symbols. slope symbols. slope symbols.

Figure 4a4a shows the matched filter result from the cross-correlation function between “Symbol Figure 4a shows the matched filter result from the cross-correlation function between “Symbol Figure shows the matched filter result from the cross-correlation function between “Symbol Mapping #1” and “Symbol Mapping #3” in any hopping pattern. The mapping types have the Mapping #1” and “Symbol Mapping #3” in any hopping pattern. The mapping types have the same Mapping #1” and “Symbol Mapping #3” in any hopping pattern. The mapping types have thesame same slopes but show a lower magnitude because the frequency bands are different. Figure 4b shows the slopes but but show show aa lower lower magnitude magnitude because because the the frequency frequency bands bands are are different. different. Figure Figure 4b 4b shows shows the slopes the matched a across-correlation function between matchedfilter filterresult resultasas as a cross-correlation cross-correlation function between“Symbol “SymbolMapping Mapping#1” #1”and and“Symbol “Symbol matched filter result function between “Symbol Mapping #1” and “Symbol Mapping #4” inin any hopping pattern. but show lower Mapping #4” in any hopping pattern.The Themapping mappingtypes typeshave havethe thesame samefrequency, frequency, but show lower Mapping #4” any hopping pattern. The mapping types have the same frequency, but show lower values due toto their different slopes. values due to their different slopes. values due their different slopes. 1400 1400

ㅡ #3] Matched filtering filtering Result, Result, Symbol Symbol :: [#1 [#1ㅡ #3] Matched

Matchedfiltering filteringresult result Matched MaximumPoint Point Maximum CorrectLine Line Correct

1200 1200

Amplitude Amplitude

1000 1000 800 800 600 600 400 400 200 200 00

Sample Position Position [N] [N] Sample

3507 3507

(a) (a) 1400 1400

ㅡ #4] Matched filtering filtering Result, Result, Symbol Symbol :: [#1 [#1ㅡ #4] Matched

Matchedfiltering filteringresult result Matched MaximumPoint Point Maximum CorrectLine Line Correct

1200 1200

Amplitude Amplitude

1000 1000 800 800 600 600 400 400 200 200 00

1919 1919

Sample Position Position [N] [N] Sample

(b) (b) Figure 4. Matched filter output in different frequency bands. (a) The same slope symbol; (b) different Figure Matched filter output different frequency bands. The same slope symbol; (b) different Figure 4.4. Matched filter output inin different frequency bands. (a)(a) The same slope symbol; (b) different slope symbols. slope symbols. slope symbols.

In this this paper, paper, we we propose propose aa method method to to estimate estimate the the symbol symbol in in the the received received signal signal by by applying applying In the FrFT FrFT scheme. scheme. The The FrFT FrFT is is aa generalization generalization of of the the conventional conventional Fourier Fourier transform transform concept, concept, which which the makes itit possible possible to to convert convert the the time time domain domain signal signal into into aa time–frequency time–frequency intermediate intermediate domain. domain. That That makes

Sensors 2018, 18, 4498

6 of 18

In this paper, we propose a method to estimate the symbol in the received signal by applying the FrFT scheme. The FrFT is a generalization of the conventional Fourier transform concept, which makes it possible to convert the time domain signal into a time–frequency intermediate domain. That is, when the time domain is represented by the x-axis and the frequency domain by the y-axis, the FrFT is the result obtained by rotating an arbitrary angle ∅ in the counterclockwise direction. The FrFT can obtain the spectra with various characteristics depending on the transform orders defined as α = 2∅/π. If the different signals have different frequency slopes, the signals will have peaks at different positions with different transform orders on the FrFT spectrum. In this way, the correct transform order with peaks in each FrFT spectrum is called the optimal transform order, which is denoted by αopt [27,30]. The FrFT equation is Z Fa f (u) =

Kα (u, x ) f ( x )dx,

(7)

where the term Kα (u, x ) is expressed as   
 2 2   Aα exp iπ cot(α) x + u − 2 csc(α)ux , (α 6= nπ ) Kα (u, x ) = , δ(u − x ) (α = 2nπ )   δ(u + x ) (α = (2n ± 1)π )

(8)

p where Aα is the amplitude factor defined as 1 − icot(α). If ∅ = π/2, the FrFT is equivalent to the Fourier transform. Next, the optimal transform order in a discrete region can be expressed as αopt

  2 2 −1 Mk , = ∅ = cot π π fs2

(9)

where f s is the sampling frequency, k is the chirp rate, and M represents the sampling point. If the sampling points and sampling frequency are fixed, the optimal transform order is determined from the value k. Figure 5a shows a conceptual diagram of the FrFT for a chirp signal. In this case, we can assume that the chirp signal xu (t) with the up-slope characteristic exists for the analysis period T, and the chirp signal xu (t) has the initial frequency f 0 at the start time (kτ − ∆T/2) and the frequency f 1 at the end time (kτ + ∆T/2) (generally, the frequency f 1 is higher than the frequency f 0 ). Therefore, the point ou which is the middle point between pu = [(kτ − ∆T/2)/s, f 0 s] and point qu = [(kτ + ∆T/2)/s, f 1 s] can be expressed as [kτ/s, f m s], where f m is the center frequency and s is the rescaling factor, and is defined as s = T/ f s . The k is the symbol number. The vector u0 , which is the point ou that corresponds to the u-axis, is     kτ π π u0 = |ou | sin αopt = fms − sin αopt . (10) 2 s 2 When the starting point for the signal xu (t) is τ = 0, the vector u0 can be written as: u0 = ( f m s) sin (αopt

π ). 2

(11)

When considered in the frequency domain, the signal also has a negative frequency that is inversely proportional to the positive frequency. The negative frequency exists symmetrically with the positive frequency and forms a relatively wide and low spectrum on the FrFT as [p0u to q0u ] in Figure 5a. On the other hand, in Figure 5b, the chirp signal xd (t) with the down-slope characteristic will appear symmetrically with the signal xu (t). Therefore, the vector u1 can be written as
 π u1 = − f m0 s sin αopt , 2

(12)

Sensors 2018, 18, 4498

7 of 18

where f m0 is the center frequency of the signal xd (t). If the signal xu (t) and xd (t) are in the same frequency band and have the same slope, the vector u1 can be rewritten as  π = − u0 . u1 = (− f m s) sin αopt 2

(13)

The opposite characteristics of FrFT can be seen from Equation (13). If the center frequency and the frequency variation are same, the positions of the vectors u0 and u1 are the opposite and the Sensorsvalue. 2019, 19 FOR PEER REVIEW 7 same

(a)

(b) Figure5.5.Relation Relationbetween betweenthe the chirp signal and FrFT coefficient α. The (a) The up-slope signal; (b) Figure chirp signal and FrFT coefficient α. (a) up-slope chirpchirp signal; (b) the the down-slope signal. down-slope chirpchirp signal.

Figure Figure6a 6ashows showsthe thesymmetrical symmetricalcharacteristics characteristicsininthe thefractional fractionaldomain domaintotodistinguish distinguishbetween between the theup-slope up-slopeand andthe thedown-slope. down-slope. This This isis an an example example of ofthe theFrFT FrFTspectrum spectrumfor forFigure Figure5a. 5a. In Inthe the proposed method, with respect to the middle line of the fractional spectrum, the left side is the proposed method, with respect to the middle line of the fractional spectrum, the left side is the positive domain, andand the right side isside the negative frequency domain (theoretically existing). positivefrequency frequency domain, the right is the negative frequency domain (theoretically Therefore, in the up-slope state (like Figure 5a), the energies are energies concentrated on the left side, in existing). Therefore, in the up-slope state (like Figure 5a), the are concentrated on and the left the down-slope (like Figure energies areenergies concentrated on the righton side. On the other side, and in the state down-slope state 5b), (likethe Figure 5b), the are concentrated the right side. On the other hand, Figure 6b shows the FrFT spectrum of the conventional method that coexists with the up-slope and the down-slope in the symbol duration. Unlike the proposed method, the conventional method is processed only in the positive frequency domain and distinguishes between the up-slope and the down-slope by using the two transform orders which are dependent on each symbol. This means that the conventional receiver must have the parallel structures. In this paper, we propose the

Sensors 2018, 18, 4498

8 of 18

hand, Figure 6b shows the FrFT spectrum of the conventional method that coexists with the up-slope and the down-slope in the symbol duration. Unlike the proposed method, the conventional method is processed only in the positive frequency domain and distinguishes between the up-slope and the down-slope by using the two transform orders which are dependent on each symbol. This means that the conventional must have the parallel structures. In this paper, we propose the FrFT receiver8 Sensors 2019, 19 FOR receiver PEER REVIEW using only one transform order. 20 Proposed method

Amplitude

15

10

5

0 -300

-200

-100 0 100 FrFT bin [u x fs]

200

300

(a) 20 Conventional method

Amplitude

15

10

5

0 -300

-200

-100 0 100 FrFT bin [u x fs]

200

300

(b) spectrum comparison between (a) the proposed method, (b) the Figure 6.6.FrFTFrFT spectrum comparison between (a) the proposed method, and (b) the and conventional conventional method. method.

In the the proposed proposed method, method,when whenthe thefrequency-hopping frequency-hoppinginterval intervalisis𝑓f wd, ,the thevector vector𝑢uhn regarding In regarding the hopped frequency f is written as the hopped frequency 𝑓hn is written as

=𝑓 +n 𝑛𝑓f wd . f𝑓hn = fm + Then, Then,

(14) (14)


sin 𝛼αopt𝜋π2 𝑠)s)sin 𝑢uhn==(𝑓( f hn
(15) = [( f m + n f wd )s] sin αopt2 π2
π𝜋 = u + n f s sin α , ( ) = [(𝑓0 + 𝑛𝑓wd )𝑠] sin opt 𝛼 2 (15) 2 where n represents the number of hopped intervals. The signals hop due to f wd , which means that 𝜋 𝑢 FrFT + (𝑛𝑓spectrum. 𝑠) sin 𝛼Using ,the above property, regardless of the they are spaced at regular intervals in=the 2 frequency band of the hopping, a ‘decision section’ for estimating a symbol can be formed because where 𝑛 represents the number of hopped intervals. The signals hop due to 𝑓 , which means that they are spaced at regular intervals in the FrFT spectrum. Using the above property, regardless of the frequency band of the hopping, a ‘decision section’ for estimating a symbol can be formed because the FrFT bin formed for each symbol is always regular. That is, the FrFT bin is obtained for the received signal through Equation (15), and the symbol is estimated by the demapping method which

Sensors 2018, 18, 4498

9 of 18

the FrFT bin formed for each symbol is always regular. That is, the FrFT bin is obtained for the received signal through Equation (15), and the symbol is estimated by the demapping method which distinguishes the FrFT bin in the decision section. Since the estimated symbol can be implemented as Sensors 2019, 19 FOR PEER REVIEW an ideal form of the signal, it is possible to perform a matched filter between the received signal and99 Sensors 2019, 19 FOR PEER REVIEW the ideal signal. The synchronization error can be obtained between the results of the above procedure procedure and the results of the matched filter in the ideal case. When compensating for the next and the results matched filter in the ideal When for the next symbol procedure and of thethe results of the matched filtercase. in the idealcompensating case. When compensating for thealong next symbol along with the weight, it is possible to implement symbol synchronization to correct the with thealong weight, it isthe possible to it implement symbol synchronization correct the errors associated symbol with weight, is possible to implement symbol to synchronization to correct the errors associated with the Doppler shift. with Doppler with shift.the Doppler shift. errorsthe associated Figure 7 is a plot of the FrFT spectrum for all frequency-hopping bands in a single space. From Figure forfor allall frequency-hopping bands in ainsingle space. From the Figure 77 isisaaplot plotofofthe theFrFT FrFTspectrum spectrum frequency-hopping bands a single space. From the relation given in Equation (15), it can be seen that the spectrum is formed regularly in proportion relation given in Equation (15),(15), it can be seen thatthat thethe spectrum is formed regularly in proportion to the relation given in Equation it can be seen spectrum is formed regularly in proportion to the frequency-hopping interval. Based on this, even if an arbitrary frequency hopping is the frequency-hopping interval. Based Based on this,on even if an arbitrary is performed, it to the frequency-hopping interval. this, even if anfrequency arbitraryhopping frequency hopping is performed, it will be completed in the above spectrum section. That is, in the case that any hopped will be completed above spectrum section. That is,section. in the case that hopped symbol input, performed, it will in bethe completed in the above spectrum That is, any in the case that any is hopped symbol is input, it can be estimated through the section of the spectrum. it can beisestimated through the section of thethe spectrum. symbol input, it can be estimated through section of the spectrum. 20 20

amplitude amplitude

15 15

FrFT spectrum : Spectrum overlapping FrFT spectrum : Spectrum overlapping FrFT spectrum FrFT Left :spectrum up-slope Left : up-slope Right : down-slope Right : down-slope

10 10

5 5

0 -300 0 -300

-200 -200

-100 0 100 200 300 -100 0 [u x fs] 100 200 300 FrFT bin FrFT bin [u x fs] Figure 7. Aggregate FrFT spectra for all frequency bins. Figure 7. Aggregate FrFT spectra for all frequency bins.

4. Simulation Simulation and and Results Results 4. 4. Simulation and Results Weperformed performedthe the simulation to analyze the performance the proposed method. We simulation to analyze the performance of theofproposed method. Figure Figure 8 shows8 We performed the simulation to analyze the performance of the proposed method. Figure 8 shows a packet structure of a transmission signal designed for the simulation. We used 1080 bits per a packet structure of a transmission signal designed for the simulation. We used 1080 bits per frame, a shows a packet structure of a transmission signal designed for the simulation. We used 1080 bits per frame, a center frequency of 16 kHz, a sampling frequency of 192 kHz, and a data rate of 100 bps. center frequency of 16 kHz, a sampling frequency of 192 kHz, and a data rate of 100 bps. One chirp frame, a center frequency of 16 kHz, a sampling frequency of 192 kHz, and a data rate of 100 bps. One chirp symbol is 1.2the kHz and the is total band is approximately 10LFM kHz.(linear The LFM (linear symbol band is 1.2 band kHz and total band approximately 10 kHz. The frequency One chirp symbol band is 1.2 kHz and the total band is approximately 10 kHz. The LFM (linear frequency modulation) signals are used to distinguish the packets. The signal length is 0.1 s and the modulation) signals are used to distinguish packets. the Thepackets. signal length is 0.1 slength and the is frequency modulation) signals are used to the distinguish The signal is bandwidth 0.1 s and the bandwidth is 4interval kHz. A of guard interval ofto1 prevent s is arranged to prevent antointerference duepseudo-noise to the signal. 4bandwidth kHz. A guard 1 s is arranged an interference due the signal. The is 4 kHz. A guard interval of 1 s is arranged to prevent an interference due to the signal. The pseudo-noise code uses 512 bits for 0.512coding s, and no channel coding technique is applied. code uses 512 bits for 0.512 andbits no for channel technique applied. The pseudo-noise code usess,512 0.512 s, and no channeliscoding technique is applied.

Figure 8. Packet design. Figure 8. Packet design. Figure 8. Packet design.

There are several software packages for simulating channel transfer characteristics in There are several software packages for simulating channel transfer characteristics in underwater environments. Norwegian FFI provides the Watermark software that simulates underwater environments. Norwegian FFI provides the Watermark software that simulates transmission information in several underwater channels [31]. However, to verify the performance transmission information in several underwater channels [31]. However, to verify the performance of the proposed method, a channel is simulated by applying the sound velocity distribution measured

Sensors 2018, 18, 4498

10 of 18

There are several software packages for simulating channel transfer characteristics in underwater environments. Norwegian FFI provides the Watermark software that simulates transmission information in several underwater channels [31]. However, to verify the performance of the proposed Sensors 2019, 19 FOR is PEER REVIEW by applying the sound velocity distribution measured in the South Sea,10 method, a channel simulated Sensors 2019, 19 FOR PEER REVIEW 10 South Korea, to the VirTEX (Virtual Time Series Experiment), which is a Bellhop-based underwater based underwater channel modeling program developed and released by the Scripps Institution of channel modelingchannel program developed and released by and the Scripps Institution of Oceanography based underwater modeling program developed released by the Scripps Institution of Oceanography (SIO) [32,33]. The simulation environment is shown in Figure 9. In the simulation, it (SIO) [32,33]. The simulation environment shown in Figure 9. In the simulation, it issimulation, assumed that Oceanography (SIO) [32,33]. The simulationisenvironment is shown in Figure 9. In the it is sea assumed the sea afloor is of inclined at athe depth of 30 mtofrom transmitter to 40 mposition from the floorthat isthat inclined depth 30 mat from mthe from the receiver. isthe assumed the seaatfloor is inclined a depthtransmitter of 30 m from40the transmitter to 40 The m from the receiver. The position of the receiver is placed at a depth of 30 m and the transmitter is assumed to of the receiver is placed of is 30placed m andat the to be moving receiver. The position of at thea depth receiver a transmitter depth of 30 is massumed and the transmitter is horizontally assumed to be moving horizontally with a fixed depth of 5 m. It is assumed that the distance between the with a fixedhorizontally depth of 5 m.with It is aassumed that the between thethat transmitter and receiver moves be moving fixed depth of distance 5 m. It is assumed the distance between the transmitter and receiver moves from 300 m to 200 m linearly at approximately 12 knots towards the from 300 mand to 200 m linearly atfrom approximately 12 m knots towards the receiver and then moves inthe the transmitter receiver moves 300 m to 200 linearly at approximately 12 knots towards receiver and then moves in the opposite direction at the same speed from 200 m to 300 m. oppositeand direction at the in same from 200 m to receiver then moves the speed opposite direction at300 the m. same speed from 200 m to 300 m. 0

Depth(m) Depth(m)

10 20 30 40

Sound Speed Profile Sound Speed Profile

0 10 20 30 40

50 50 1500 1505 1510 1515 1520 1525 1530 1535 1500 1505 1510 Sound 1515 Speed(m/s) 1520 1525 1530 1535 Sound Speed(m/s) Figure 9. Sound velocity profile for the simulation. Figure9.9.Sound Soundvelocity velocityprofile profilefor forthe thesimulation. simulation. Figure

Thechannel channelresponse responsecharacteristics characteristicsfor forthe thesimulation simulationare areshown showninin Figure Thechannel channel The Figure 10.10. The The channel response characteristics for the simulation are shown in Figure 10. The channel impulse response shows that not only the direct path, but also the sub-path, are reflected from the impulseresponse responseshows showsthat thatnot notonly onlythe thedirect directpath, path,but butalso alsothe thesub-path, sub-path,are arereflected reflectedfrom from the the impulse surface and the floor. surfaceand andthe thefloor. floor. surface -3

1

x -3 10 x110

0.8 0.8 Amplitude Amplitude

0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.194 0.194

0.196 0.196

0.198 0.2 0.198 Arrival time 0.2 (s) Arrival time (s)

0.202 0.202

Figure 10.10. Channel impulse response forfor simulation. Figure Channel impulse response simulation. Figure 10. Channel impulse response for simulation.

Figure 11a shows the result of the matched filter for the termination by overlapping the received Figure 11a shows the result of the matched filter for the termination by overlapping the received signal and the ideal signal when approaching between the transmitter and the receiver. As shown in signal and the ideal signal when approaching between the transmitter and the receiver. As shown in Figure 11a, the signal is compressed since it is positioned backward, even though the packet Figure 11a, the signal is compressed since it is positioned backward, even though the packet synchronization is initially adjusted due to the Doppler frequency, which is caused by the mobility synchronization is initially adjusted due to the Doppler frequency, which is caused by the mobility of the transmitter. The synchronization error due to the compression is approximately 0.056 s, and of the transmitter. The synchronization error due to the compression is approximately 0.056 s, and

Sensors 2018, 18, 4498

11 of 18

Sensors 2019, 19 FOR PEER REVIEW

11

Figure 11a shows the result of the matched filter for the termination by overlapping the received signal and the ideal signal when approaching between the transmitter and the receiver. As shown On the other hand, Figure 11b shows an overlapping of the received signal and the ideal signal in Figure 11a, the signal is compressed since it is positioned backward, even though the packet in the case of retreating, which expands the signal due to the Doppler frequency. The synchronization synchronization is initially adjusted due to the Doppler frequency, which is caused by the mobility error due to the expansion is approximately 0.055 s and has an error of approximately 5 to 6 symbols, of the transmitter. The synchronization error due to the compression is approximately 0.056 s, and as in the previous case. assuming a transmission rate of 100 bps, the error is approximately 5–6 symbols. 1.5 Received data Ideal Data Maximum point

Amplitude

1 0.5 0 -0.5 -1 -1.5

14.1143 14.17

Time (s)

(a) 1.5 Received data Ideal Data Maximum point

1

Amplitude

0.5 0 -0.5 -1 -1.5

14.17 14.2257

Time (s)

(b) Figure outputfor forthe thereceived received data and ideal data. (a)approach; The approach; Figure11. 11. Matched Matched filtering output data and thethe ideal data. (a) The (b) the (b)retreat. the retreat.

On the other hand, 11b rate shows an overlapping of the receivedratio signal and the ideal signal inor Table 1 shows theFigure bit error according to the signal-to-noise (SNR) in the presence the case of of retreating, which expands the signal to the length Doppler frequency. The synchronization absence the symbol synchronization. Thedue symbol changes continuously due to the error due to the expansion is approximately 0.055 s and has an error of approximately 5 to 6 symbols, a compression and expansion of the signal. Accordingly, if the synchronization is not performed, aslarge in theerror previous case. occurs. On the other hand, when the symbol synchronization is performed using the Table 1 shows the bit error bit rateerror according to the signal-to-noise in the presence proposed method, the uncoded rate (BER) is considerably low.ratio The (SNR) simulation results show orthat absence of the symbol synchronization. The symbol length changes continuously due to the the proposed method is robust to multipath delays and variability due to the Doppler shift. compression and expansion of the signal. Accordingly, if the synchronization is not performed, a large error occurs. On the other hand, when the symbol synchronization is performed using the proposed Table 1. Uncoded bit error rate in the simulation. method, the uncoded bit error rate (BER) is considerably low. The simulation results show that the SNR (dB) Non-Sync Method Sync Method proposed method is robust to multipath delays and variability due to the Doppler shift. 15 0.49 0.000 10 0.48 0.002 5 0.49 0.004 0 0.48 0.050

The second simulation was performed using the underwater channel software released by FFI. Watermark is a benchmark for physical-layer schemes of underwater acoustic communications. It contains data with five different channel characteristics, and we used a channel (named as NCS1)

Sensors 2018, 18, 4498

12 of 18

Table 1. Uncoded bit error rate in the simulation. SNR (dB)

Non-Sync Method

Sync Method

15 10 5 0

0.49 0.48 0.49 0.48

0.000 0.002 0.004 0.050

The second simulation Sensors 2019, 19 FOR PEER REVIEWwas performed using the underwater channel software released by 12 FFI. Watermark is a benchmark for physical-layer schemes of underwater acoustic communications. measured Norway. This is the channel which broad Doppler spreading occurs and repeats for It contains in data with five different channelincharacteristics, and we used a channel (named as NCS1) 60 cycles. We set the Doppler shiftchannel higher to the spreading performance difference of the measured in Norway. This is the in make whichmore broadvisible Doppler occurs and repeats proposed method. Other is to provided in thevisible reference Figure 12 difference shows the for 60 cycles. We set thedetailed Dopplerinformation shift higher make more the [31]. performance bitthe error rate. Themethod. horizontal axis detailed of the figure refers to the number of The bit [31]. error rate of the of proposed Other information is provided in cycles. the reference Figure 12 proposed approximately 0.07,axis which shows better performance thanofthe conventional shows the method bit errorisrate. The horizontal of the figure refers to the number cycles. The bit method. error rate of the proposed method is approximately 0.07, which shows better performance than the conventional method. Sync method Non-Sync method

0.6

Bit error rate

0.5 0.4 0.3 0.2 0.1 0 0

10

20 30 40 Number of cycles

50

60

Figure Figure 12. 12. Simulation result using Watermark Watermark benchmark benchmarkmodel. model.

5. Lake Trials 5. Lake Trials To investigate the performance of the proposed method in a real environment, lake trials were To investigate the performance of the proposed method in a real environment, lake trials were conducted at Kyungcheon Lake, Mungyeong City. The first and second experiments were conducted conducted at Kyungcheon Lake, Mungyeong City. The first and second experiments were conducted at the beginning and end of May 2018, respectively. The water depth of the lake was approximately at the beginning and end of May 2018, respectively. The water depth of the lake was approximately 30–40 m, and the transmitters were located approximately 5 m from the boat. The receiver was 30–40 m, and the transmitters were located approximately 5 m from the boat. The receiver was located located at a depth of 30 m, and the boat was steered randomly from 100 m to approximately 400 m at a depth of 30 m, and the boat was steered randomly from 100 m to approximately 400 m from the from the receiver. The boat moved at speeds of 2 knots and 4 knots, and the configuration of the receiver. The boat moved at speeds of 2 knots and 4 knots, and the configuration of the signals used signals used was the same as those of the previous simulations. However, in the second experiment, was the same as those of the previous simulations. However, in the second experiment, which was which was conducted at the end of May, the hopping rate designed a half-spacing signal for each conducted at the end of May, the hopping rate designed a half-spacing signal for each hopping hopping frequency. Because of the overlap of the hopping frequencies, the ISI can degrade the frequency. Because of the overlap of the hopping frequencies, the ISI can degrade the communication communication performance due to multipath delay. However, this can be overcome by using the performance due to multipath delay. However, this can be overcome by using the FrFT and bandpass FrFT and bandpass filtering. Additionally, by designing with the above method, the frequency band filtering. Additionally, by designing with the above method, the frequency band can be used more can be used more efficiently. A Neptune D/17/BB model projector was used as the transmitter and efficiently. A Neptune D/17/BB model projector was used as the transmitter and a B&K 8106 a B&K 8106 hydrophone was used as the receiver. The Neptune D/17/BB model that was used as a hydrophone was used as the receiver. The Neptune D/17/BB model that was used as a transmitter is transmitter is a broadband projector with a bandwidth of approximately 10 kHz [34,35]. a broadband projector with a bandwidth of approximately 10 kHz [34,35]. Figure 13 shows the channel impulse response and Figure 14 shows the scattering function used Figure 13 shows the channel impulse response and Figure 14 shows the scattering function used for the Doppler estimation. Figure 13a shows the measured channel response in the first experiment for the Doppler estimation. Figure 13a shows the measured channel response in the first experiment performed at the beginning of May, and Figure 13b is the result of the second experiment performed at performed at the beginning of May, and Figure 13b is the result of the second experiment performed the end of May. As shown in Figure 13, the difference in the reception time occurs as the transmitter at the end of May. As shown in Figure 13, the difference in the reception time occurs as the transmitter moves, which generates a slope. Figure 13b shows there are more complex delay profiles. Figure 14a moves, which generates a slope. Figure 13b shows there are more complex delay profiles. Figure 14a shows that the Doppler frequency is approximately −16 Hz to −22 Hz, and Figure 14b shows that the Doppler frequency is approximately −10 Hz to −5 Hz, where the (−) sign means that the distance between the transceivers gradually increased. However, there seems to be an issue with the scattering function in Figure 14b, as a main Doppler shift cannot be detected and the multipath arrival is entirely

Sensors 2018, 18, 4498

13 of 18

shows that the Doppler frequency is approximately −16 Hz to −22 Hz, and Figure 14b shows that the Doppler frequency is approximately −10 Hz to −5 Hz, where the (−) sign means that the distance between the transceivers gradually increased. However, there seems to be an issue with the scattering function in Figure 14b, as a main Doppler shift cannot be detected and the multipath arrival is entirely smeared. This was a result of the increased level of noise due to minor equipment problems and Sensors 2019, 19 FOR PEER REVIEW 13 because the channel conditions Sensors 2019, 19 FOR PEER REVIEW in the second experiment were relatively poor due to stronger winds. 13

-6 -8 -8 -8

0.2 0.2

0.2

-10 -10

14

-10

-2 -2

0

-2 -4

-4

-4 -6

-6

-6 -8

Power density (dB)(dB) Power density

-4 -6 -6

13

0 0

0 0 2 02 4 24 6 4 6 8 6 8 10 8 10 12 10 12 14 12 14 0

Power density (dB)

-2 -4 -4

Transmitted Time (sec) Transmitted Time (sec) Transmitted Time (sec)

-2 0 -2

Power density Power density (dB)(dB)(dB) Power density

Transmitted Time (sec) Transmitted Time (sec)

0 0

Transmitted Time (sec)

CIR2 Sensors 2019, 19 FOR PEER REVIEW 0 CIR2 0 CIR2 2 2 0 4 4 2 6 4 6 8 6 8 10 8 10 12 10 12 14 12 14 0 0.05 0.1 0.15 Time (s) 0.15 014 0.05 Arrival0.1 0 0.05 0.1 (s) 0.15 Arrival Time (a)

-8 -8

-10 0.2 -10 0.2 -10

0.05 0.1 0.15 Time (s) 0.15 0.05 Arrival0.1 0.05 Arrival 0.1Time (s) (b) 0.15

0

0

Arrival Time (s)

0.2

Arrival Time (s)

(a)

(b)

(a) (b)(b) the second lake trial. Figure 13. Measured channel impulse responses for (a) the first lake trial and Figure Measuredchannel channelimpulse impulse responses responses for (a) the second lake trial. Figure 13.13. Measured (a) the thefirst firstlake laketrial trialand and(b) (b) the second lake trial. Figure 13. Measured channel impulse responses for (a) the first lake trial and (b) the second lake trial.

-1

-10 -5 -10

-1 -1

-50 -5

-1.5

05 0

-1.5 -1.5

5 5 10

-2

10 15 10

-2 -2

-2.5

15 20 15 25 025 0 0

0.05

0.1

0.15

0.05 0.1 Arrival 0.1 Time 0.05

0.15 (s) 0.15 Arrival Time(s) (s) Arrival Time (a)

0.2 0.2 0.2

-15 -10 -15

-1

-10 -5 -10

-1 -1

-50 -5

-1.5

005

-1.5 -1.5

-2

55 10

-2 -2

10 10 15

-2.5 -2.5 -2.5

20 20

25

-3

25 25 0 00

-3 -3

-0.5

-0.5 -0.5

15 15 20

-2.5 -2.5

20 25 20

0

Power density (dB)

-15 -10 -15

-20

-15 -20

Frq. (Hz) Doppler Frq.Frq. (Hz)(Hz) Doppler

-0.5 -0.5

0

-25

-0.5

Doppler Frq. (Hz)

Doppler Frq.Frq. (Hz)(Hz) Doppler

-25 -20

0

-25

-20 -15 -20

Power density (dB)(dB) density (dB) Power density

-25 -20

0

-25

0

Power density (dB)(dB) Power density

0

-25

0.05

0.15

0.2

0.10.1 Arrival Time (s)0.15 0.15 Arrival (s) ArrivalTime Time (b)(s)

0.1

0.2 0.2

0.05 0.05

-3 -3 -3

(a) (b) (a) (b) Figure 14. Scattering function for the Dopplerfrequency frequencyestimation estimationfor for(a) (a)the thefirst firstlake laketrial trialand and(b) (b)the Figure 14. Scattering function for the Doppler Figure 14. Scattering function for the Doppler frequency estimation for (a) the first lake trial and (b) Figure 14. trial. Scattering the second lake trial. function for the Doppler frequency estimation for (a) the first lake trial and (b) second lake the second lake trial. the second lake trial.

Figures 15a and 16a show spectrograms of the transmitted signal, and Figures 15b and 16b show Figures 15a and 16a show spectrograms transmittedsignal, signal, and Figures 15b and 16b show Figures 15a and 16a show spectrograms of of the transmitted and Figures 15b and 16b show Figures of 15a and 16a show spectrograms of the transmitted signal, andthe Figures 15bwe and 16b show spectrograms of the received signal through the experiments. From figures, can see that spectrograms the received signal through the lake experiments. From the figures, we can see spectrograms of the received signal through the lake experiments. From the figures, we can see that that spectrograms of thefading received signal throughsignals the lake experiments. From the figures, we can see that there is is considerable fading the received due multipath propagation delay. there is considerable ininin the due tomultipath multipath propagation delay. there considerable fading thereceived receivedsignals signals due to propagation delay. there is considerable fading in the received signals due to multipath propagation delay. 4

4 x 10 x 10 3 3 4 x 10 3

Spectrogram Spectrogramofofthe theideal idealdata data

4 4

10 xx10 33 4

Spectrogram of the ideal data

3

2.52.5

Frequency [Hz] Frequency [Hz][Hz] Frequency

Frequency [Hz]

Frequency [Hz][Hz] Frequency

Spectrogram of the received data

x 10

2.5 2.5

2.5 2 2

2 1.5

1.5

1.5 1

Spectrogram received data Spectrogram of of thethe received data

1

2.5 22

2 1.5

1.5

1.5 1

1

1

1 0.5

0.85 0.9 0.95 1 1.05 0.5 0.8 0.8 0.85 0.9 0.95 Time 1 [s]1.05 0.5 Time [s] 0.8 0.85 0.9 0.95 1 1.05

(a)

1.1

1.15

1.1

1.15

1.1

1.15

1.2

1.2

1.2

0.5 0.8 0.5

0.8 0.5 0.8

0.85

0.85

0.85

0.9

0.9

0.9

0.95

1

0.95 1 Time [s]

0.95

1.05

Time [s]

(b)

1

1.05

1.05

1.1

1.15

1.2

1.1

1.15

1.2

1.1

1.15

1.2

Time [s] Time [s] (a) (b) (a) (b) Figure 15. Spectrogram thetransmitted transmitted signal, received signal in the trial. trial. Figure 15. Spectrogram ofof (a)(a)the signal,and and(b) (b)the the received signal in first the first

Figure 15. Spectrogram of (a) the transmitted signal, and (b) the received signal in the first trial. Figure 15. Spectrogram of (a) the transmitted signal, and (b) the received signal in the first trial.

Sensors 2018, 18, 4498 Sensors2019, 2019,19 19FOR FORPEER PEERREVIEW REVIEW Sensors 4

14 of 18 14 14 4

Spectrogramof ofIdeal Idealdata data Spectrogram

104 xx10 33

104 xx10 33

2.5 2.5 Frequency Frequency[Hz] [Hz]

Frequency Frequency[Hz] [Hz]

2.5 2.5

Spectrogramof ofReceive Receivedata data Spectrogram

22

1.5 1.5

11

22

1.5 1.5

11

0.5 0.5 0.8 0.8

0.85 0.85

0.9 0.9

0.95 0.95

11

Time[s] [s] Time

1.05 1.05

1.1 1.1

1.15 1.15

1.2 1.2

(a) (a)

0.5 0.5 0.8 0.8

0.85 0.85

0.9 0.9

0.95 0.95

11

Time[s] [s] Time

1.05 1.05

1.1 1.1

1.15 1.15

1.2 1.2

(b) (b)

Figure 16. Spectrogram of (a) the transmitted signal, and (b) the received signal in the second trial. Figure Figure16. 16.Spectrogram Spectrogramof of(a) (a)the thetransmitted transmittedsignal, signal,and and(b) (b)the thereceived receivedsignal signalin inthe thesecond secondtrial. trial.

Since the received signal experiences substantial fading as passes through the underwater underwater Since the the received received signal signal experiences experiencessubstantial substantialfading fadingas asitit it passes passes through through the underwater Since channel, the delay due to multipath propagation or the slope change due to the Doppler frequency channel, the delay due to multipath propagation or the slope change due to the Doppler frequency channel, the delay due to multipath propagation or the slope change due to the Doppler frequency should beconsidered. considered.Therefore, Therefore, is necessary necessary to calculate calculate the adjacent range adjacent adjacent to the thetransform optimal should be it is to calculate the range to the optimal should considered. Therefore, ititnecessary is to the range to optimal transform order for the the application application of the the FrFT FrFT scheme atFigure the receiver. receiver. Figure 17 shows shows the the order for the application of the FrFT scheme at thescheme receiver.at 17 shows the accumulation of transform order for of the Figure 17 accumulation of the spectra of the received signal that is obtained from the optimal transform order the spectra of the received signal that is obtained from the optimal transform order to the adjacent accumulation of the spectra of the received signal that is obtained from the optimal transform order to the adjacent adjacent range. When the optimal optimal transform order is is 𝛼𝛼spectrum = 0.996, 0.996, the spectrum spectrum is spread spread by range. When the optimal transform ordertransform is αopt = order 0.996, the is spread by the delay caused to the range. When the = the is by the delay caused by multipath propagation in the range adjacent to the order. However, due to the by multipath propagation in the range adjacent to the order. However, due to the property of the the delay caused by multipath propagation in the range adjacent to the order. However, due to the property of the the chirp signal, the multipath has little effect on on the estimation. estimation. Figure 17a shows shows the chirp signal, thechirp multipath has little effect onhas thelittle estimation. Figure 17a shows the correctly estimated property of signal, the multipath effect the Figure 17a the correctly estimated symbol, which is on on the right side in the FrFT FrFT bin and fixed fixed on number 240 of symbol, which is on the right side is in thethe FrFT binside andin fixed on the number 240on of the the number FrFT bin240 point. correctly estimated symbol, which right the bin and of the FrFT bin point. We can determine from this symbol that the down-slope chirp signal has a center We can determine from this symbol that the down-slope chirp signal has a center frequency of 1.2 kHz. the FrFT bin point. We can determine from this symbol that the down-slope chirp signal has a center frequency of 1.2 1.2 kHz. On the the other hand, Figure 17b 17b estimated shows the thesymbol. incorrectly estimated symbol. The The On the other hand, Figure 17bother shows the incorrectly Theestimated receiver estimates to a frequency of kHz. On hand, Figure shows incorrectly symbol. receiver estimates to a different point. The transmitted signal has the transform order 𝛼 = 0.996, different point. The transmitted signal has the transform order α = 0.996, but the received signal opt receiver estimates to a different point. The transmitted signal has the transform order 𝛼 = 0.996, but the received signal hasthe the approximate value “1”. Thismeans means that thereceiver receiver cannotleft distinguish hasthe thereceived approximate value “1”.approximate This means value that the receiver cannot distinguish between and right. but signal has “1”. This that the cannot distinguish between left and right. Therefore, Therefore, we determined determined thiscenter symbol as the the correct correct center frequency and the Therefore, we determined this symbol as the correct frequency and the incorrect slope. In the this between left and right. we this symbol as center frequency and incorrect slope. In this case, the received symbol was affected by the serious Doppler effect beyond case, the received symbol was affected by the serious Doppler effect beyond the Doppler tolerance of incorrect slope. In this case, the received symbol was affected by the serious Doppler effect beyond the Doppler tolerance of of the the chirp chirp signal. signal. theDoppler chirp signal. the tolerance The eestim stimaate tedd point point The

1.004 1.004 1.002 1.002

FrFT FrFTorder order αα

11 0.998 0.998 0.996 0.996 0.994 0.994 0.992 0.992 0.99 0.99 0.988 0.988 220 220

240 240

260 260

280 280

FrFT bin bin [u [u xx fs] fs] FrFT

(a) (a)

300 300

320 320

(b) (b)

Figure 17. Color Colorintensity intensity of the FrFT results in (a) the correctly correctly estimated symbol and (b) the the Figure 17. 17. ofof thethe FrFT results in (a)in the(a) correctly estimated symbol and (b) the incorrectly Figure Color intensity FrFT results the estimated symbol and (b) estimated symbol. incorrectly estimated symbol. incorrectly estimated symbol.

Figure 18 18 shows shows the the cumulative cumulative error error rate rate per per elapsed elapsed symbol symbol to to analyze analyze the the synchronizing synchronizing Figure 18 shows the cumulative error rate per elapsed symbol to analyze the synchronizing Figure effectof ofthe theproposed proposedmethod. method.IfIf Ifthe thesymbol symbolsynchronization synchronizationis isnot notperformed, performed,the thecumulative cumulativeerrors errors effect of the proposed method. the symbol synchronization is not performed, the cumulative errors effect increase because the symbol is compressed or expanded over time. Conversely, performance of increase because the symbol is compressed or expanded over time. Conversely, the performance of increase because the symbol is compressed or expanded over time. Conversely, the performance of the synchronized synchronized symbol symbol is is good. good. As As aa result, result, the the FrFT FrFT receiver receiver can can be be aa system system used used to to efficiently efficiently the demodulate chirp signals that are robust and resistant to fading and Doppler effects. demodulate chirp signals that are robust and resistant to fading and Doppler effects.

Sensors 2018, 18, 4498

15 of 18

the synchronized symbol is good. As a result, the FrFT receiver can be a system used to efficiently Sensors 2019, 19chirp FOR PEER REVIEW 15 demodulate signals that are robust and resistant to fading and Doppler effects. Synchronized symbol Non-Synchronized symbol

Accumulated error rate

0.25 0.2 0.15

0.1 0.05 0 0

20

40

60

80

100

Elapsed symbol (%) Figure Figure 18. 18. Synchronization Synchronization performance. performance.

Tables Tables 22 and and 33 show show the the results results of of the the uncoded uncoded bit bit error error rate rate obtained obtained by by demodulating demodulating the the received signal from the lake experiment, where the transmitted signal is not applied received signal from the lake experiment, where the transmitted signal is not applied to to the the channel channel coding. Tables 22 and and 33 show show the the cases caseswhere wherethe themoving movingspeed speedofofthe thetransmitter transmitterisisapproximately approximately2 coding. Tables 2knots knotsand and4 4knots, knots,respectively. respectively.Some Someexperiments experimentswere were performed performed in in an an environment environment where where the the weather condition was relatively poor, and the corresponding performance may be lower than those of weather condition was relatively poor, and the corresponding performance may be lower than those other cases. Nevertheless, according of other cases. Nevertheless, accordingtotothe theproposed proposedmethod, method,the thebit biterror errorrate rate is is reduced reduced to to 36.4% 36.4% after iterative symbol synchronization. Therefore, we verified that the proposed method improves after iterative symbol synchronization. Therefore, we verified that the proposed method improves the The chirp chirp signal signal has has properties properties that that are are robust the performance. performance. The robust to to fading fading and and Doppler Doppler effects, effects, and and the proposed method showed that it was possible to maintain these advantages through efficient the proposed method showed that it was possible to maintain these advantages through efficient demodulation. To compare we compared times for for each demodulation. To compare the the computations, computations, we compared the the computation computation times each of of the the arbitrary symbols designed with the proposed method and the conventional method. The parameters arbitrary symbols designed with the proposed method and the conventional method. The parameters of of symbols symbols were were set set to to be be similar similar to to those those shown shown in in Figure Figure 6. 6. In In this this case, case, by by using using the the MATLAB MATLAB function “Tic − Toc”, the running program time was measured and compared. The proposed function “Tic − Toc”, the running program time was measured and compared. The proposed method method used a single receiver and scanned the value around the transform order to obtain the spectrum used a single receiver and scanned the value around the transform order to obtain the spectrum (see (see Figure 17).the Onother the other hand, the conventional method at least two receivers, which means Figure 17). On hand, the conventional method usedused at least two receivers, which means that that transform orders be calculated. a result of a relative computation comparison two two transform orders mustmust be calculated. As a As result of a relative computation time time comparison with with a computer equipped with an Core Intel i7-6700/4 Core i7-6700/4 GHz processor, the proposed method took a computer equipped with an Intel GHz processor, the proposed method took 0.2277 0.2277 s while the conventional method took 0.4717 s. s while the conventional method took 0.4717 s. Table 2. Uncoded bit error rate at 2 knots. Table 2. Uncoded bit error rate at 2 knots. First Trial

Trial Trial

11 22 3 34 45 56 6

First Trial Non-SyncMethod Method Sync Sync Method Method Non-Sync 0.23 0.09 0.23 0.09 0.24 0.09 0.24 0.09 0.28 0.001 0.28 0.001 0.12 0.09 0.12 0.09 0.22 0.11 0.09 0.01 0.22 0.11 0.09 0.01

Second Trial

Second Trial Non-Sync Method Non-Sync Method Sync SyncMethod Method 0.19 0.08 0.19 0.08 0.35 0.11 0.35 0.11 0.10 0.09 0.10 0.09 0.08 0.07 0.08 0.07 0.10 0.01 0.07 0.06 0.10 0.01 0.07 0.06

Table 3. Uncoded bit error rate at 4 knots.

Trial 1 2

Non-Sync Method 0.17 0.26

Sync Method 0.04 0.05

Sensors 2018, 18, 4498

16 of 18

Table 3. Uncoded bit error rate at 4 knots. Trial

Non-Sync Method

Sync Method

1 2

0.17 0.26

0.04 0.05

6. Conclusions In this paper, we proposed a covert acoustic communication scheme that is robust to fading and Doppler effects. It consists of a single chirp-based FHSS that is resistant to delay propagation and the Doppler shift. Additionally, the receiver demodulates to the FrFT spectrum. To verify the performance of the proposed method, we estimated the signal in an environment with a multipath delay, and the Doppler frequency through simulations and lake experiments, to determine the uncoded BER. Since the chirp signal has a relatively good orthogonality, it is robust against the instability of the phase. It was also possible to estimate the slope using the FrFT spectrum, even in the case of frequency variation due to the Doppler shift. This means that the proposed method can be demodulated while maintaining the properties of the chirp signal. As a result, we could obtain high-reliability communication performance. In the conventional method, the up-sloped chirp signal and the down-sloped chirp signal existed within one symbol simultaneously, and independent demodulators with different orders were used. However, in the proposed method, either the up-sloped or down-sloped chirp signal was transmitted within one symbol, and a parallel structure, as used with the conventional method, was not required in the demodulator. To verify the performance of the proposed method, we performed various simulations. Specifically, we used the Watermark software released by FFI. In the future, it will be necessary to conduct research for efficient FrFT spectrum formation and optimization of the receiver structure. Sea trials will be performed. Author Contributions: All authors contributed significantly to the work presented in this manuscript. G.L. and K.K. proposed the method described in this paper; G.L., T.K. and K.K. conceived and designed the experiments; G.L., T.K., W.-J.K. and W.P. performed the experiments and analyzed the data; W.-J.K. provided some valuable advice. Funding: This work was supported by the Agency for Defense Development, South Korea under Grant UD170022DD and Low Frequency Underwater Research Laboratory. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7.

8.

Catipovic, J.A. Performance limitations in underwater acoustic telemetry. IEEE J. Ocean. Eng. 1990, 15, 205–216. [CrossRef] Yaacoub, E.; Dawy, Z. A survey on uplink resource allocation in OFDMA wireless networks. IEEE Commun. Surv. Tutor. 2012, 14, 322–337. [CrossRef] Tsiropoulou, E.E.; Kapoukakis, A.; Papavassiliou, S. Uplink resource allocation in SC-FDMA wireless networks: A survey and taxonomy. Comput. Netw. 2016, 96, 1–28. [CrossRef] Stojanovic, M. Underwater acoustic communications. In Proceedings of the IEEE Electro/International, Boston, MA, USA, 21–23 June 1995; pp. 435–440. Stojanovic, M.; Catipovic, J.; Proakis, J. Phase coherent digital communications for underwater acoustic channels. IEEE J. Ocean. Eng. 1994, OE-16, 100–111. [CrossRef] Kaushal, H.; Kaddoum, G. Underwater optical wireless communication. IEEE J. Mag. 2016, 4, 1518–1547. [CrossRef] ElMoslimany, A.; Zhou, M.; Duman, T.M.; Suppapplola, A.P. A new signaling scheme for underwater acoustic. In Proceedings of the IEEE Computer Society Conference on OCEANS 2013 MTS/IEEE, San Diego, CA, USA, 23–27 September 2013; pp. 1–5. Liu, S.; Qiao, G.; Ismail, A.; Liu, B.; Zhang, L. Covert underwater acoustic communication using whale noise masking on DSSS signal. In Proceedings of the OCEANS 2013 MTS/IEEE Bergen: The Challenges of the Northern Dimension, Bergen, Norway, 10–14 June 2013; pp. 1–6.

Sensors 2018, 18, 4498

9. 10.

11. 12. 13.

14. 15. 16.

17.

18. 19. 20. 21. 22.

23.

24. 25.

26. 27. 28. 29. 30.

17 of 18

Stojanovic, M.; Proakis, J.G.; Rice, J.A.; Green, M.D. Spread spectrum underwater acoustic telemetry. Proc. MTS/OCEANS 1998, 2, 650–654. Yang, T.C.; Yang, W.B. Performance analysis of direct-sequence spread-spectrum underwater acoustic communications with low signal-to-noise-ratio input signals. J. Acoust. Soc. Am. 2008, 2, 842–855. [CrossRef] [PubMed] Yang, T.C.; Yang, W.B. Low probability of detection underwater acoustic communications using direct-sequence spread spectrum. J. Acoust. Soc. Am. 2008, 6, 3632–3647. [CrossRef] Ling, J.; He, H.; Li, J.; Roberts, W.; Stoica, P. Covert underwater acoustic communications. J. Acoust. Soc. Am. 2010, 128, 2898–2909. [CrossRef] [PubMed] Freitag, L.; Stojanovic, M.; Singh, S.; Johnson, M. Analysis of channel effects on direct-sequence and frequency-hopped spread-spectrum acoustic communication. IEEE J. Ocean. Eng. 2001, 26, 586–593. [CrossRef] Kaleh, G.K. Performance comparison of frequency-diversity and frequency-hopping spread-spectrum systems. IEEE Trans. Commun. 1997, 45, 910–912. [CrossRef] Yang, W.B.; Ynag, T.C. High-frequency FH-FSK underwater acoustic communications: The environmental effect and signal processing. Proc. High Freq. Ocean Acoust. Conf. 2004, 728, 106–113. Potter, J.; Alves, J.; Green, D.; Zappa, G.; Nissen, I.; McCoy, K. The JANUS underwater communications standard. In Proceedings of the 2014 Underwater Communications and Networking (UComms), Sestri Levante, Italy, 3–5 September 2014. Walree, P.; Ludwig, T.; Solberg, C.; Sangfelt, E.; Laine, A.; Bertolotto, G.; Ishoy, A. UUV Covert Acoustic Communications. Available online: https://pdfs.semanticscholar.org/ee86/ f2f5e30a241831f7cdc32e697a541f5f1c83.pdf (accessed on 28 September 2018). Marchetti, L.; Reggiannini, R. An efficient receiver structure for sweep-spread-carrier underwater acoustic links. IEEE J. Ocean. Eng. 2016, 41, 440–449. Cook, C.E. Linear FM signal formats for beacon and communication systems. IEEE Trans. Aerosp. Electr. Syst. 1974, AES-10, 471–478. [CrossRef] Ozaktas, H.M.; Arikan, O.; Kutay, M.A.; Bozdagi, G. Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. 1996, 44, 2141–2150. [CrossRef] Almeida, L.B. The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process. 1994, 42, 3084–9091. [CrossRef] Gaglione, D.; Clemente, C.; Llioudis, C.V.; Persico, A.R.; Proudler, I.K.; Soraghan, J.J. Fractional Fourier based waveform for a joint radar-communication system. In Proceedings of the IEEE Radar Conference, Philadelphia, PA, USA, 2–6 May 2016. Qiu, X.; Sha, X.J.; Shen, Q.H.; Wu, X.L. Fractional Fourier transform based secure communication system. In Proceedings of the 2010 6th International Conference on Wireless Communications Networking and Mobile Computing, Chengdu, China, 23–25 September 2010. Yuan, F.; Wei, Q.; Cheng, E. Multiuser chirp modulation for underwater acoustic channel based on VTRM. Int. J. Navel Archit. Ocean Eng. 2017, 9, 256–265. [CrossRef] Chen, Y.; Clemente, C.; Soraghan, J.J.; Weiss, S. Partial fractional Fourier transform (PFRFT)-OFDM for underwater acoustic communication. In Proceedings of the 23rd European Signal Processing Conference, Nice, France, 31 August–4 September 2015. Tu, X.; Xu, X.; Zou, Z.; Yang, L.; Wu, J. Fractional Fourier domain hopped communication method based on chirp modulation for underwater acoustic channels. J. Syst. Eng. Electr. 2017, 28, 449–456. Sharif, B.S.; Neasham, J.; Hinton, O.R.; Adams, A.E. A computationally efficient Doppler compensation system for underwater acoustic communications. IEEE J. Ocean. Eng. 2000, 25, 52–61. [CrossRef] Kaminsky, E.J.; Simanjuntak, L. Chirp slope keying for underwater communications. Proc. SPIE Prog. Biomed. Opt. Imaging 2005, 5778, 894–905. Plumb, R.G. Matched filter response of a linear array with time-varying phase weights. IEEE Trans. Aerosp. Electr. Syst. 1993, 29, 1046–1050. [CrossRef] Kaihan, Z.; Keyu, C.; Fei, Y.; Jinwang, Y. Chirp FSK based on FRFT for underwater acoustic communication. In Proceedings of the 7th IEEE International Conference on Electronics Information and Emergency Communication (ICEIEC), Macau, China, 21–23 July 2017; pp. 49–52.

Sensors 2018, 18, 4498

31. 32. 33. 34. 35.

18 of 18

FFI. Available online: https://www.ffi.no/en/research-projects/Sider/Watermark.aspx (accessed on 28 September 2018). Kim, J.S.; Song, H.C.; Hodgkiss, W.S. Virtual time series experiment (VIRTEX) simulation tool for underwater acoustic communications. J. Acoust. Soc. Am. 2009, 10, 2174–3647. [CrossRef] Siderius, M.; Oirter, M.B. Modeling broadband ocean acoustic transmissions with time-varying sea surface. J. Acoust. Soc. Am. 2008, 124, 137–150. [CrossRef] [PubMed] NEPTUNE SONAR. Available online: http://www.neptune-sonar.co.uk/wp-content/uploads/2016/03/ Model-D17.pdf (accessed on 1 August 2018). Bruel & Kjaer. Available online: https://www.bksv.com/en/products/transducers/acoustic/microphones/ hydrophones/8106 (accessed on 1 August 2018). © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).