AU2018452060A1 - Chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method - Google Patents

Chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method Download PDF

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AU2018452060A1
AU2018452060A1 AU2018452060A AU2018452060A AU2018452060A1 AU 2018452060 A1 AU2018452060 A1 AU 2018452060A1 AU 2018452060 A AU2018452060 A AU 2018452060A AU 2018452060 A AU2018452060 A AU 2018452060A AU 2018452060 A1 AU2018452060 A1 AU 2018452060A1
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spread spectrum
underwater acoustic
sequence
data
acoustic communication
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Pengbin KANG
Haoyuan LIU
Hui Liu
Pengyun LIU
Huibing SHAO
Xiaohu Wang
Jinqiu Wu
Hongda YAO
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Tangshan Zhaolan Marine Technology Co Ltd
Beijing Institute of Control and Electronic Technology
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Tangshan Zhaolan Marine Technology Co Ltd
Beijing Institute of Control and Electronic Technology
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B1/00Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69Spread spectrum techniques
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B13/00Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The present invention relates to the field of underwater acoustic communication, relates to a chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method, and relates to generalized frequency division multiplexing underwater acoustic communication technology and chaotic sequence spread spectrum underwater acoustic communication technology. Proposed by the present invention is a 5G multi-carrier spread spectrum underwater acoustic communication system applicable to the field of underwater acoustics, which implements effective information transmission in an underwater acoustic channel having limited bandwidth resources, and which achieves information transmission without bit errors during experimentation. The aim of the present invention is to provide an effective information transmission method in the field of underwater acoustic communication having limited channel bandwidth resources, thereby being significant in the development of underwater acoustics technology.

Description

Our Ref: OF180849D/P/AU
CHAOTIC SEQUENCE-BASED 5G MULTI-CARRIER SPREAD SPECTRUM UNDERWATER ACOUSTIC COMMUNICATION METHOD
FIELD OF THE INVENTION
The present invention relates to a chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method, belongs to the field of underwater acoustic communications, and relates to a generalized frequency division multiplexing underwater acoustic communication technology and a chaotic sequence spread spectrum underwater acoustic communication technology.
BACKGROUND OF THE INVENTION
A spread spectrum communication technology is a common technology in a long-distance underwater acoustic communication technology, and with the development of the communication technology, its communication modes can be divided into several modes like Direct Sequence Spread Spectrum (DS), Frequency-Hopping Spread Spectrum (FH), Time Hopping (TH), Chirp Modulation, and Hybrid Spread Spectrum, depending on different spectrum spreading methods. In the field of underwater acoustic communications, an effective information transmission method is required.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a chaotic sequence-based 5G !0 multi-carrier spread spectrum underwater acoustic communication system for the field of underwater acoustic communications with limited channel bandwidth resources. The present invention proposes a 5G multi-carrier spread spectrum underwater acoustic communication system suitable for the field of underwater acoustics, which realizes effective information transmission in an underwater acoustic channel with !5 limited bandwidth resources and realizes information transmission without a bit error in experiments. The object of the present invention is to provide an effective information transmission method for the field of underwater acoustic communications with limited
Our Ref: OF180849D/P/AU
channel bandwidth resources, which is of great significance for the development of underwater acoustic technologies. The present invention provides a chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method, the method comprises the following steps: step 1: at a transmitting end, encoding source data, and performing a spread spectrum operation on the encoded serial data by using a chaotic spread spectrum sequence; step 2: performing GFDM modulation on data after spread spectrum, and after that, adding a cyclic prefix to the modulated data to obtain transmitted data; step 3: at a receiving end, performing synchronization and GFDM demodulation on the data, after the modulated signals pass through an underwater acoustic channel; and step 4: despreading the demodulated data by utilizing a chaotic signal generated locally at the receiving end, and integrating the obtained signals over a duration and making a judgement to obtain data estimated by the receiving end. Preferably, the present invention further comprises features selecting any one of 1 to 4: 1. a spread spectrum process in step 1 is as below:
the transmitted data is expressed by d(t), and then the process can be
expressed as:
d(t) = Yd(n)g(t - nT,,) n
c(t)= c(n)p(t - nT)
values of d(n) and the chaotic sequence c(n) used for spreading spectrum
are 1 or -1, g(t) and p(t) are rectangular pulses of a unit amplitude with durations
T,, and T, respectively, N represents a length of the spread spectrum sequence, in
general, T,,=NT. A sequence after spread spectrum p(t) is:
Our Ref: OF180849D/P/AU
p(t) = d(t)c(t)
and a modulation process in step 2 is expressed as below:
data after the GFDM modulation is y(t), g[] is used to express a GFDM
modulation process, and then:
y(t)=g[p(t)] = g[d(t)c(t)]
and a discrete spread spectrum signal for GFDM adopting a BPSK modulation mode can be expressed as: Nc-1 M GMD
sMC-DS (t) =IIIdk [i]c [ j]p, (t -- iJ -- jT))cos[ 2rc(f + kAf')t ] k=O i=-M j=0
where d[i] is data on a k-th subcarrier, ck[j] represents a spread spectrum
sequence which is correspondingly multiplied by dj[i], N, represents a number of
subcarriers,and Af'=1/T is a subcarrier spacing.
2. a process of performing the GFDM demodulation on the received signal in step 3 is as below: at the receiving end, on the premise of correct synchronization, the GFDM
demodulation is performed on the received signal y'(t), g-'[] is used to represent the
GFDM demodulation process, and then a signal r(t) to be despread can be expressed
as:
r(t)=g-'[y'(t)].
3. a process of despreading the received signal in step 4 is as below:
r(t) is despread by utilizing a chaotic spread spectrum sequence c,(t) which
is generated locally and the same as that at the transmitting end:
m(t) = r(t)c,.(t)=g-'[y'(t)]c,.(t) = g-1[ g[d(t)c(t)]]c,(t)=d(t)c(t)c,(t)
the signal is integrated over the duration:
q(t) = I m(t)dt
Our Ref.: OF180849D/P/AU
where a pulse duration of the spread spectrum sequence c(t) is T, ,namely
f c(t)c,(t)dt = T
and therefore, q(t) can be expressed as:
T when d(t=1 when d(t)=-I
As compared with the prior art, the present invention has the following beneficial effects: a chaotic sequence-based multi-carrier spread spectrum underwater acoustic communication system is realized, and it is verified through simulation and experimentation that the system has better performance than a GFDM spread spectrum underwater acoustic communication system based on a common spread spectrum sequence, can utilize fewer initial values of the sequence (other common spread spectrum sequences require more initial values in order to generate the same number as the chaotic sequence, which increases the amount of information transmission of the communication system, occupies valuable bandwidth resources, and reduces transmission efficiency), and realizes a lower bit error rate of the entire communication system -- with a modulator structure of M=2 and K=29 taken as an example to conduct an analysis, in a Gaussian white noise channel, when a signal-to-noise ratio is -9dB, the chaotic sequence-based 5G spread spectrum underwater acoustic communication technology system described in the present invention realizes a bit error rate of the underwater acoustic communication system adopting the common spread spectrum !0 sequence to spread spectrum when the signal-to-noise ratio is 4dB, and has an improvement in performance by 13dB, and in a multipath underwater acoustic channel, when the signal-to-noise ratio is -3dB, the chaotic sequence-based 5G spread spectrum underwater acoustic communication technology system described in the present invention realizes a bit error rate of the underwater acoustic communication system utilizing the common spread spectrum sequence to spread spectrum when the signal-to-noise ratio is 6dB, and has an improvement in performance by 9dB. And, information transmission without a bit error was realized in experiments, which proves
Our Ref: OF180849D/P/AU
that the chaotic sequence-based GFDM spread spectrum underwater acoustic communication system is a fire-new and efficient communication system that can flexibly utilize a bandwidth of a transmission channel, and is more applicable to the field of underwater acoustic communications.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1: a schematic diagram of a chaotic sequence-based underwater acoustic spread spectrum system; Figure 2: (a) a principle diagram of a transmitting end of a chaotic spread spectrum underwater acoustic system and (b) a principle diagram of a receiving end of the chaotic spread spectrum underwater acoustic system; Figure 3: a comparison diagram of bit error rate performance of different spread spectrum underwater acoustic communication systems in a Gaussian white noise channel with a modulator structure of M=2 and K=29; Figure 4: a comparison diagram of bit error rate performance of different spread spectrum underwater acoustic communication systems in a multipath channel with a modulator structure of M=2 and K=29; Figure 5: a comparison diagram of bit error rate performance of different spread spectrum underwater acoustic communication systems in a Gaussian white noise channel with a modulator structure of M=29 and K=2; Figure 6: a comparison diagram of bit error rate performance of different spread spectrum underwater acoustic communication systems in a multipath channel with a modulator structure of M=29 and K=2; Figure 7: an impulse response of an experimental channel; and Figure 8: pictures of transmission and reception in an experiment: (a) a !5 transmitted image, (b) a received image of a common spread spectrum sequence underwater acoustic communication system (M=2 and K=29), a bit error rate of which is 0.0119, (c) a received image of a chaotic spread spectrum underwater acoustic communication system (M=2 and K=29), a bit error rate of which is 0.0046, and (d) a received image of a GFDM chaotic spread spectrum underwater acoustic
Our Ref: OF180849D/P/AU
communication system (M=29 and K=2).
DETAILED DESCRIPTION OF THE EMBODIMENTS
The present invention focuses on a research of a direct spread spectrum underwater acoustic communication system based on GFDM, advantages of which are as below: 1. a strong anti-interference ability, and a low bit error rate A spread spectrum communication technology is that, at a transmitting end, a spread spectrum sequence is utilized to perform spread spectrum processing on a transmitted signal to spread an original bandwidth occupied by the signal, and at a receiving end, despread processing is performed on the transmitted signal by adopting a correlation inspection method, with a noise signal in the transmission process spread into a broadband signal, and a target signal can be extracted by a narrowband filtering method, and it has a relatively high signal-to-noise ratio and can effectively improve the system's anti-interference performance and reduce the system's bit error rate. 2. good concealment performance, and a low interception probability A signal after spread spectrum is broadened as to its frequency band, can be submerged in noise, is not easy to be intercepted by an enemy, and has a small possibility of interference to a surrounding electronic device. The potential for a military application is huge, frequency-hopping radio stations in HF, VHF and UHF frequency !0 bands have been used in foreign military communication equipment, and a direct sequence spread spectrum radio station also begins to enter a practical stage. Therefore, it has good concealment performance. 3. good anti-multipath performance Because of good autocorrelation of spread spectrum codes, a signal after !5 passing through a multipath channel can be extracted conveniently and effectively. 4. good confidentiality A spread spectrum signal is submerged in noise because its power spectrum density is very low, and signals on different paths or different users' signals adopt different pseudo-random sequences to spread spectrum, and a receiver can despread
Our Ref: OF180849D/P/AU
and demodulate original information data only if it knows a correct form of the spread spectrum sequence. Therefore, the spread spectrum communication technology has high reliability and good confidentiality. Spread spectrum systems can be divided into time-domain spread spectrum communication systems and frequency-domain spread spectrum communication systems based on spread spectrum operations performed in a time domain and a frequency domain. On the one hand, because an underwater acoustic channel has limited available bandwidth resources, and on the other hand, because frequency-domain spread spectrum will destroy correlation between subcarriers, the present invention conducts a research on time-domain spread spectrum. The spread spectrum technology in the present invention adopts a chaotic sequence, and mainly has the following advantages: Firstly, lengths of traditional spread spectrum sequences are relatively fixed,
each being 2"-1 , and selectable spread spectrum codes are small in number. Because a chaotic sequence is sensitive to an initial value, a huge number of spread spectrum sequences can be obtained by changing parameter(s) and an initial value of a chaotic system, and lengths of the sequences can be set arbitrarily. Therefore, there are a very large number of spread spectrum codes available for selection, and therefore it provides better confidentiality than traditional spread spectrum sequences. Secondly, a chaotic spread spectrum sequence itself has characteristics like aperiodicity, broadband and being noise-like, and is similar to a random process, making it difficult for the sequence to be found and intercepted in an actual transmission process. Therefore, the system has a considerable degree of confidentiality, is very difficult to be deciphered, and can greatly improve safety of the communication system. Finally, generation and duplication of a chaotic sequence are very convenient, and as long as an iteration formula and an initial value of a chaotic system are given, a chaotic spread spectrum sequence can be generated. Therefore, based on the above-mentioned advantages of a chaotic sequence, a chaotic sequence is applied to a chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication technology of the present invention.
Our Ref: OF180849D/P/AU
Time-domain spread spectrum: a block diagram of multi-carrier time-domain spread spectrum transmission is as shown in Figure 1. At a transmitting end, serial-to-parallel conversion is performed on a data signal, after that, spread spectrum codes distributed in a time domain are utilized to perform a spread spectrum operation on each data symbol individually, and finally each data after spread spectrum is modulated by using a subcarrier of a different frequency, and ultimately multi-carrier time-domain spread spectrum is realized. It can be seen from the figure that all chips of each transmitted data after time-domain spread spectrum are transmitted on one subcarrier, which indicates that the system has a relatively poor ability to resist frequency-selective fading, while a length of the chips of each transmitted data after time-domain spread spectrum is the same as a length of the spread spectrum codes, and therefore the system has a relatively strong ability to resist time-selective fading. A common spread spectrum sequence underwater acoustic communication system performs GFDM modulation on N parallel signals on which spread spectrum has been performed, and in general, a number of parallel data is less than a number of subcarriers in an OFDM system. The common spread spectrum sequence underwater acoustic communication system transmits, in parallel, multiple data after direct spread spectrum, in underwater acoustic communications, the spread spectrum signals are limited by a bandwidth, and when the spread spectrum codes are relatively long, !0 transmitting the signals and performing synchronization at the receiving end both require to take a lot of time, and the receiving end of the GFDM-DS spread spectrum system adopts the method introduced above, as shown in Figure 2(b). Figures 3 and 4 compare bit error rate performance of a third-order common spread spectrum sequence underwater acoustic communication system, a fifth-order common spread spectrum sequence underwater acoustic communication system and a chaotic spread spectrum underwater acoustic communication system with a modulation matrix of M=2 and K=29, in the case of a Gaussian white noise signal and in a multipath channel, respectively, and it can be seen from the figures that when an order of an m sequence is 5 (that is, the length is 63), the common spread spectrum sequence underwater acoustic communication system can realize bit error rate performance close
Our Ref: OF180849D/P/AU
to that of the chaotic spread spectrum underwater acoustic communication system. Likewise, Figures 5 and 6 compare bit error rate performance of a third-order common spread spectrum sequence underwater acoustic communication system, a fifth-order common spread spectrum sequence underwater acoustic communication system and a chaotic spread spectrum underwater acoustic communication system with a modulation matrix of M=29 and K=2, in the case of a Gaussian white noise signal and in a multipath channel, respectively, and a similar conclusion can be drawn, and no further details are given here. The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. An experiment was performed in an anechoic pool in May 2017, the pool having a length of 25 meters, a width of 15 meters, and a height of 10 meters, anechoic wedges being arranged around the pool. A transmitting transducer, having a working frequency band of 3-8kHz, was deployed at a depth of 3 meters, a standard hydrophone was adopted as a receiving hydrophone, which was deployed at a depth of 3 meters, and a horizontal distance between the transmitting transducer and the receiving hydrophone was 5 meters. The actually measured impulse response of a channel was as shown in Figure 7, maximum multipath time delay being about 5.5ms, a sampling frequency being 48kHz, and a situation of roll-off parameter(s) in two types of spread !0 spectrum systems in which a RC filter is combined with a RRC filter bank being taken as an example to perform a comparison of experimental results. Transmission and reception of the GFDM-DS and GFDM-CSSS spread spectrum underwater acoustic communication systems are performed by adopting the RC filter and the RRC filter bank. The present invention comprises the following steps: step 1: at a transmitting end, encoding binary source data, and performing a spread spectrum operation on the encoded serial data by using a chaotic spread spectrum sequence, wherein a chaotic spread spectrum process is as below: Figure 2(a) is a principle diagram of a transmitting end and a receiving end for spreading spectrum and despreading of a GFDM spread spectrum system, in which
Our Ref: OF180849D/P/AU
time-domain spread spectrum is performed on data undergoing parallel-to-serial conversion by using the spread spectrum sequence, after that, GFDM modulation is performed according to a GFDM modulation method to obtain modulated data, and a cyclic prefix is added to obtain transmitted data. At the receiving end, the received signals are synchronized firstly, on the premise of ensuring correct synchronization, the synchronized signals are demodulated and despread, and after that, the obtained signals are integrated over a duration and judged to obtain data estimated by the
receiving end. The transmitted data is expressed by d(t ), and then the process can be
expressed as below: d(t) = d(n)g(t - nT,) n
c(t)=Y c(n)pft -n~c
values of d(n) and the chaotic sequence c(n) used for spreading spectrum
are 1 or -1, g(t) and p(t) are rectangular pulses of a unit amplitude with
durations T and T , respectively, N represents a length of the spread spectrum
sequence, and in general, T=NT. The sequence after spread spectrum p(t) is:
p(t) =d(t)c(t).
step 2: performing GFDM modulation on data after spread spectrum, and after that, adding a cyclic prefix to the modulated data to obtain transmitted data;
data after the modulation is y(t), g[] is used to express a GFDM modulation
!0 process, and then:
y(t)=g(p(t)] = g~d(t)c(t)] and a discrete spread spectrum signal for GFDM adopting a BPSK modulation mode can be expressed as: Nc-1 M GMD
sMC-DS (t) =IIIdk [i]ck [ j]p, (t - iJ - jT )cos[ 2rc(f0 + kAf')t ] k=O i=-M j=O
where d,[i] is data on a k-th subcarrier, ck[j] represents a spread spectrum
Our Ref.: OF180849D/P/AU
sequence which is correspondingly multiplied by d[i], N, represents a number of
subcarriers,and Af'=1/7T is a subcarrier spacing.
step 3: at a receiving end, performing synchronization and GFDM demodulation on the data, after the modulated signals pass through an underwater acoustic channel; at the receiving end, on the premise of correct synchronization, the GFDM
demodulation is performed on the received signal y(t), g-'[-] is used to represent the
GFDM demodulation process, and then a signal r(t) to bedespread can be expressed
as:
1 [y'(t)] r(t)=g-
step 4: despreading the demodulated data by utilizing a chaotic signal generated locally at the receiving end, and integrating the obtained signals over a duration and making a judgement to obtain data estimated by the receiving end,
r(t) is despread by utilizing a chaotic spread spectrum sequence c,(t) which
is generated locally and the same as that at the transmitting end: m(t)= r(t)c,(t)=g-y'(t)]Cr(t) = g -i(g~d(t)c(t )]]c,.(t)=d(t)c(t)c,.(t )
the signal is integrated over the duration:
(t ) = fo m(t )dt
where a pulse duration of the spread spectrum sequence c(t) is T, namely
C(t)Cr(t)dt = T
and therefore, q(t) can be expressed as:
f T, when d(t)=I t-T when d(t)=-1
Figure 8: (a) is a picture of transmission in an experiment, and (b) and (c) are received images in the case of a modulator structure of M=2 and K=29, bit error rates of
Our Ref: OF180849D/P/AU
which are 0.0119 and 0.0046, respectively. (d) is a received image of common spread spectrum sequence underwater acoustic communication system and chaotic spread spectrum underwater acoustic communication system with a modulator structure of M=29 and K=2, each having a bit error rate of 0. According to the experimental results, in the case where a transmitted signal occupies the same bandwidth and channel resources are divided equally by subcarriers included in different modulation matrix structures, as a number of the subcarriers increases, performance of both the chaotic spread spectrum underwater acoustic communication system and the common spread spectrum sequence underwater acoustic communication system decreases, because when the number of the subcarriers is large, for a non-orthogonal multi-carrier technology, main lobe overlap between various subcarriers is serious, which in turn leads to a decrease in bit error performance. Therefore, on the one hand, it is required to design a reasonable subcarrier structure to avoid inter-carrier interference, and on the other hand, it is required to research and design a reasonable channel estimation method for the GFDM's modulator structure to remove influence of the channel on the system and improve performance of the GFDM spread spectrum system. The specific instances described above are only preferred examples of the present invention and do not limit the present invention in any form, and any simple !0 modification and equivalent change made to the above examples according to the technical essence of the present invention falls within the protection scope of the present invention.

Claims (4)

Our Ref: OF180849D/P/AU WHAT IS CLAIMED IS:
1. A chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method, characterized in that the method comprises the following steps:
step 1: at a transmitting end, encoding source data, and performing a spread spectrum operation on the encoded serial data by using a chaotic spread spectrum sequence;
step 2: performing GFDM modulation on data after spread spectrum, and after that, adding a cyclic prefix to the modulated data to obtain transmitted data;
step 3: at a receiving end, performing synchronization and GFDM demodulation on the data, after the modulated signals pass through an underwater acoustic channel; and
step 4: despreading the demodulated data by utilizing a chaotic signal generated locally at the receiving end, and integrating the obtained signals over a duration and making a judgement to obtain data estimated by the receiving end.
2. The chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: a spread spectrum process in step 1 is as below:
the transmitted data is expressed by d(t ), and then the process can be expressed as:
!0 d(t)=Y d(n)g(t - nT,,)
c(t) Yc(n)p(t - nT )
values of d(n) and the chaotic sequence c(n) used for spreading spectrum are 1 or -1, g(t) and p(t) are rectangular pulses of a unit amplitude with durations T, and T7, respectively, N represents a length of the spread spectrum sequence, in general, !5 T,=NT, and a sequence after spread spectrum p(t) is:
p(t) =d(t)c(t)
and a modulation process in step 2 is expressed as below:
data after the GFDM modulation is y(t) , g[.] is used to express a GFDM modulation process, and then:
Our Ref: OF180849D/P/AU
y(t)=g(p(t)] = g~d(t)c(t)]
and a discrete spread spectrum signal for GFDM adopting a BPSK modulation mode can be expressed as: Nc-1 m GMwD
sMC-DS (t) =IIIdk [i]c [ j]p, (t -- iJ -- jT))cos[ 2rc(f + kAf')t ] k=O i=-M j=0
where d[i] is data on a k-th subcarrier, ck[j] represents a spread spectrum sequence which is correspondingly multiplied by d[i], Nc represents a number of subcarriers, and Af'=1/T is a subcarrier spacing.
3. The chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: a process of performing the GFDM demodulation on the received signal in step 3 is as below:
at the receiving end, on the premise of correct synchronization, the GFDM demodulation is performed on the received signal y'(t), g-'[-] is used to represent the GFDM demodulation process, and then a signal r(t) to be despread can be expressed as:
r(t)=g-'[y'(t)]
4. The chaotic sequence-based 5G multi-carrier spread spectrum underwater acoustic communication method according to claim 1, characterized in that: a process of !0 despreading the received signal in step 4 is as below:
r(t) is despread by utilizing a chaotic spread spectrum sequence c,(t) which is generated locally and the same as that at the transmitting end:
m(t) = r(t)c,.(t)=g-'[y'(t)]c,.(t) = g-1[ g[d(t)c(t)]]c,(t)=d(t)c(t)c,(t)
the signal is integrated over the duration:
q(t) = T m(t)dt 5 where a pulse duration of the spread spectrum sequence c(t) is T,,, namely
Our Ref.: OF180849D/P/AU
c(t)c,(t)dt = T
and therefore, q(t) can be expressed as:
T, when d(t)=1 when d(=-1
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