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Asynchronous Chirp Slope Keying for Underwater Acoustic Communication

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Asynchronous Chirp Slope Keying for Underwater Acoustic Communication Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 March 2021 doi:10.20944/preprints202103.0750.v1 Article Asynchronous Chirp Slope Keying for Underwater Acoustic Communication Dominik Jan Schott 1,†∗, Andrea Gabbrielli 2, Wenxin Xiong 2, Georg Fischer 3, Fabian Höflinger 1,3, Johannes Wendeberg2, Christian Schindelhauer 2, Stefan Johann Rupitsch 1 1 Dep. of Microsystems Engin. (IMTEK), University of Freiburg, Germany 2 Dep. of Computer Sci. (IIF), University of Freiburg, Germany 3 Fraunhofer EMI, Efringen-Kirchen, Germany * Correspondence: [email protected] † Current address: Georges-Koehler-Allee 106, 79110 Freiburg, Germany 1 Abstract: We propose an asynchronous acoustic chirp slope keying to map bit sequences on single 2 or multiple bands without preamble or error correction coding on the physical layer. Details of the 3 implementation are disclosed and discussed, the performance verified on laboratory scale in a 4 pool measurement, as well as simulated for a channel containing Rayleigh fading and Additive 5 White Gaussian Noise. For time-bandwidth products of 50 in single band mode, a raw data rate of 6 100 bit/s is simulated to achieve bit error rates below 0.001 for signal-to-noise ratios above -6 dB. 7 In dual-band mode and a data rate of 200 bit/s, this bit error level was achieved for signal-to-noise 8 ratios above 0 dB for time-bandwidth product of 25. The packet error rates follow this behavior 9 with an offset of 1 dB. 10 Keywords: Underwater Communication; Wireless Communication; Acoustic Communication; 11 Ultrasound Acoustics; Digital Signal Processing; Chirp Modulation; Chirp Slope Keying; Chirp 12 Spread Spectrum; Citation: Schott, D. J.; Gabbrielli, A.; 13 1. Introduction Xiong, W.; Fischer, G.; Höflinger, F.; 14 Shallow water still challenges communication attempts after over a hundred years Wendeberg, J.; Schindelhauer, C.; 15 of research [1–3] due to the strongly selective frequency fading, high phase noise and Rupitsch, S. J. Asynchronous Chirp 16 fast echoes and for moving nodes, due to a strong Doppler effect [4–9]. The shallower Slope Keying for Underwater 17 the channel, the more pronounced this inhibitions become. Previous investigations into Acoustic Communication . Sensors 18 the field of acoustic underwater communications have shown promising results [10–12], 2021, 1, 0. https://doi.org/ 19 but concentrated on deeper bodies of water over longer distances of several kilometer in 20 audible or sub-audible frequencies[13,14]. While high-bandwidth communication with Received: 21 large spectral efficiencies will be prone to upset the natural habitat if performed in the Accepted: 22 audible range of the maritime fauna [15,16], narrow-band methods are vulnerable the Published: 23 fading effects discussed before. The ongoing interest is a result of the strong attenuation 24 of radio signals underwater and the long distances that require to be covered. Applica- Publisher’s Note: MDPI stays neu- 25 tion examples, where underwater acoustic communication is crucial are diver tracking tral with regard to jurisdictional 26 [17,18], robot/AUV telemetry [19–22], and underwater sensor networks [23,24]. claims in published maps and insti- tutional affiliations. 27 1.1. Related Work 28 The general idea to sweep the frequency of a carrier to transmit information may be Copyright: © 2021 by the authors. 29 as old as (breathing) life on earth, but the first modern record we found is E. Hüttmann’s Submitted to Sensors for possible 30 patent for a distance measurement method from 1940 [25]. The idea to use chirps for open access publication under the 31 modulating a signal, e.g., as Chirp Slope Keying (CSK) is often attributed to M. R. Win- terms and conditions of the Cre- 32 kler’s work in the early 1960s [26], and also sometimes refered to as Linear Frequency ative Commons Attribution (CC 33 Modulation or Linear FM [27]. After the application in satellite radio transmission BY) license (https://creativecom- 34 during the Cold War era [28,29], the interest in chirp modulations mostly vanished due mons.org/licenses/by/ 4.0/). Version March 29, 2021 submitted to Sensors https://www.mdpi.com/journal/sensors © 2021 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 March 2021 doi:10.20944/preprints202103.0750.v1 Version March 29, 2021 submitted to Sensors 2 of 19 35 to the low achievable data rates. For radio communications, this changed in 2013 with 36 the establishment of the LoRa protocol as a low-power long range radio modulation for 37 small consumer applications [30,31]. Chirp modulation of acoustic signals under water 38 have gathered attention since the early 2000s [32], and is researched continuously by 39 groups around the world ever since [18,33–37]. While the achievable data rate is severely 40 limited compared to narrow-band schemes [5], CSK will be especially of interest, when 41 the data amount is low and the channel inhibitions are strong. The performance of our 42 approach in this work has partially been reported in [38]. The scope of this contribution 43 is to report on the details of our system’s inner structure and underlying algorithms. 44 This investigation zooms in on the modulation and demodulation part of typical basic 45 elements of digital communication systems [39], hence, expects coded input and will 46 return still coded output. Consequently, additional forward error correction coding will 47 improve the estimation of the overall system [40], but is not part of this investigation. 48 2. Materials and Methods 49 2.1. Basic System Structure 50 Our system is divided into functional blocks with the modulation and demodulation 51 in focus, as shown in Fig.1; more details about the structure inside those two blocks is 52 discussed in sec.2.2 and sec.2.4. d Modulate DAC PA ytx stx {N} {Ntx} {Ttx} dest Demodulate ADC AF s yrx rx {Nest} {Trx} {Nrx} Figure 1. Flow diagram of the basic communication chain: The data d is modulated, amplified before transmission, filtered and amplified at reception, and demodulated as dest. The entire analog domain is regarded as part of the communication channel. 53 The data d of length N is modulated into the digital sequence of linear up and 54 down chirps ytx, now of length Ntx, as illustrated in Fig.1. The DAC then converts this 55 into the the output stx, which is an analog continuous real-valued signal of length Ttx 56 that is boosted by a power amplifier (PA) before it is turned into an acoustic wave by a 57 piezoelectric transducer. 58 The received signal is bandpass-filtered and amplified by an analog active filter (AF) 59 into the continuous real-valued and band-limited received signal srx of length Trx. The 60 ADC samples the received signal into the sequence yrx of length Nrx. The demodulation 61 step estimates the originally sent sequence as dest given a small set of prior information 62 about the original signal, e.g., the ideal chirp parameters. We consider exclusively time discrete signals throughout this work, sampled at points n = bt · fsc 2 Z, (1) Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 March 2021 doi:10.20944/preprints202103.0750.v1 Version March 29, 2021 submitted to Sensors 3 of 19 63 where t is the time of observation and fs the sampling frequency. For simplicity we 64 assume the sampling frequency of transmitter and receiver to be equal, save an oscillator 65 frequency mismatch of D fs and phase offset of Dfs. In practical application, this is not 66 required, but only the parameters that describe the used waveform sufficiently. 67 2.2. Modulation 68 Before transmission the data d is mapped onto the slope sign of chirps and up- converted into the transmission bands, see Fig.2. Chirps DUC (0, 1) yrbb {Nref, 2} yref {Nref, Nlo, 2} d MUX CSK ytx dmux {N} {Ntx} {Nsym, Nlo} Figure 2. Modulator block in detail: The data input d is multiplexed onto Nlo sub-bands (MUX) and modulated by the up-converted chirped symbols from the Digital Up-Converter (DUC). The transmission sequence ytx is assembled by the Chirp Slope Keying (CSK) block, already in the transmission band. Simple arrow lines indicate vectors, double lines arrays. 69 70 2.2.1. Linear Chirp Creation Initially, a reference chirp yrbb is generated through ( w[n] · sin(j[n]), with, for 0 < n ≤ Nref yrbb[n] = (2) 0, else. For simplicity of calculation we normalize1 the angular frequencies w0 = 2p f0/ fs, and (3) w1 = 2p f1/ fs with the start frequency f0 and the stop frequency f1. This allows the definition of the argument j[n] for a linear chirp as w1 − w0 w[n] = w0 + n , (4) Nref and therefore Z n j[n] = j0 + w[n]dn. (5) 0 With (4) and (5), we can calculate the instantaneous phase for a linear sinusoidal chirp according to 1 2 w1 − w0 j[n] = j0 + n · w0 + 2 n · . (6) Nref The modulation will become clearer if we substitute w + w w = 1 0 , (7) c 2 1 Note that implementations in MATLAB often use the Nyquist frequency fnyq = fs/2 for normalization instead. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 30 March 2021 doi:10.20944/preprints202103.0750.v1 Version March 29, 2021 submitted to Sensors 4 of 19 Bw = jw1 − w0j, (8) and introduce z = sign(w1 − w0). (9) The instantaneous phase of the chirp from (6) then takes the form of Bw n j[n] =j0 + n · wc + z n 1 + , (10) 2 Nref 71 where each bit of the data is mapped onto the sign z.
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