CN111064544A - Cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding - Google Patents

Cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding Download PDF

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CN111064544A
CN111064544A CN201910982683.8A CN201910982683A CN111064544A CN 111064544 A CN111064544 A CN 111064544A CN 201910982683 A CN201910982683 A CN 201910982683A CN 111064544 A CN111064544 A CN 111064544A
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王桢铎
周武
王超
朱小辉
张宏滔
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715th Research Institute of CSIC
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/004Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056Systems characterized by the type of code used
    • H04L1/0057Block codes
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B11/00Transmission systems employing sonic, ultrasonic or infrasonic waves
    • 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
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/004Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045Arrangements at the receiver end
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • H04L27/2626Arrangements specific to the transmitter only
    • H04L27/2627Modulators
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
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Abstract

The invention discloses a cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding, which is used for coding a physical layer signal of underwater acoustic communication filtering multi-tone modulation. In the invention, a digital fountain coding method is used for coding physical layer signals which are modulated by underwater acoustic communication filtering multitone, and sub-bands with higher average square error after equalization are erased, and the sub-bands are often subjected to severe frequency domain fading and influence the decoding performance. And collecting the selected sub-band equalization bits to perform decoding digital fountain decoding, recovering the information source transmission bits, and realizing error-free reliable transmission.

Description

Cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding
Technical Field
The invention relates to the field of underwater acoustic communication coding modulation and demodulation decoding, in particular to a cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding.
Background
The underwater acoustic communication is an important means for carrying out underwater long-distance wireless information transmission, and has wide and important application in the fields of marine scientific investigation, environmental monitoring, oil and gas exploration, exploitation and the like. However, the underwater acoustic communication channel is very challenging, has the characteristics of complex multipath effect, doppler spread, time-varying characteristics and the like, and is a typical delay-doppler dual spread channel. Meanwhile, the underwater acoustic communication system is a typical broadband wireless communication system because the available bandwidth is very limited.
In order to cope with multipath spreading of an underwater acoustic channel, a multi-carrier technology is widely applied to underwater acoustic communication, and main modulation means include Orthogonal Frequency Division Multiplexing (OFDM), filtered multi-tone modulation (FMT), and the like. The filtering multi-tone modulation divides the bandwidth into a series of sub-bands, and a guard interval exists between adjacent sub-bands, so that the interference between carriers can be greatly reduced, and the Doppler spread of an underwater acoustic channel can be effectively resisted. In addition, the filtering multi-tone modulation has lower peak-to-average ratio and is more robust under the underwater acoustic channel with delay-Doppler double expansion. From the time domain, the filtering multi-tone modulation has a short equivalent channel in a subband, and can adopt basic Decision Feedback Equalization (DFE) to recover symbols; from the aspect of frequency domain dimension, because a guard interval exists between adjacent subbands of the filtering multi-tone modulation, different subbands of the filtering multi-tone modulation experience independent frequency domain fading after passing through a channel. This provides a basis for this patent to use cross-subband coding to obtain the diversity gain in the frequency domain.
The digital fountain coding is a code-rate-free coding technology and is mainly characterized in that at a transmitting end, an unlimited number of coding symbols can be generated from a signal source, and at a receiving end, the signal source can be recovered by receiving a group of minimum number of signal source coding symbols. As a common digital fountain code, the digital fountain code based on LT codes is adopted in the patent. The digital fountain code is applied to data link layer network communication of underwater acoustic communication, and the digital fountain code is combined with FMT modulation and applied to a physical layer technology of the underwater acoustic communication.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding, which is suitable for an underwater acoustic communication channel with time delay-Doppler double expansion. The method can be used for coding and decoding, modulating and demodulating the underwater acoustic communication signals, and realizes reliable and error-free underwater acoustic communication.
The object of the present invention is achieved by the following technical means. A cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding is characterized in that the digital fountain coding method is used for coding of physical layer signals of underwater acoustic communication filtering multi-tone modulation, and by means of digital fountain coding at a sending end, filtering multi-tone modulation of coding information, received signal processing and digital fountain decoding, sub-bands which are subjected to severe frequency domain fading are erased, and the rest sub-band signals are selected for decoding to recover information source signals.
The implementation steps of the invention are mainly as follows:
1) performing LT coding-based digital fountain coding on the source bits at a transmitting end, wherein the redundancy of the coding is ξ;
2) carrying out filtering-based multi-tone modulation on the source code after LT coding, and modulating the source code into M sub-bands in the communication bandwidth, wherein a guard interval exists between adjacent sub-bands;
3) at a receiving end, the passband received signals are transferred to a baseband through complex demodulation, decision feedback equalization based on iterative least squares is carried out on each subband, and the average square error of equalization of each subband is calculated;
4) selecting sub-bands for LT decoding based on the average squared error for equalization of each sub-band, at least
Figure RE-GDA0002417434210000021
The sub-bands are used for decoding;
5) and collecting LT coded bits in the selected sub-band, and carrying out digital fountain decoding based on LT coding to complete the communication process.
The invention has the beneficial effects that: in the invention, a digital fountain coding method is used for coding physical layer signals which are modulated by underwater acoustic communication filtering multitone, and sub-bands with higher average square error after equalization are erased, and the sub-bands are often subjected to severe frequency domain fading and influence the decoding performance. And collecting the selected sub-band equalization bits to perform decoding digital fountain decoding, recovering the information source transmission bits, and realizing error-free reliable transmission.
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FIG. 1: a digital fountain code schematic diagram;
FIG. 2: oversampling filtering multitone modulation frequency domain diagram;
FIG. 3: a filtered multi-tone modulation block diagram;
FIG. 4: a recursive least squares decision feedback equalization block diagram;
FIG. 5: a digital fountain decoding schematic diagram;
FIG. 6: average square error of each sub-band;
Detailed Description
The invention will be described in detail below with reference to the following drawings:
the invention discloses a cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding, which is used for coding a physical layer signal of underwater acoustic communication filtering multi-tone modulation.
1. Sending end digital fountain code
As shown in fig. 1, the main flow of the digital fountain coding at the transmitting end is as follows:
(1) suppose that there is a source of informationK bits of information need to be transmitted, and the bits needing to be transmitted are recorded as c ═ c1,c2,…,ckThe redundancy of the source coding is ξ, that is, the number of coded source bits is L ═ K (1+ ξ), and the coded source bits are d ═ d1,d2,…dLAnd recording the code modulation matrix as G, which comprises K rows and L columns, and K multiplied by L elements;
(2) generating a coder fixed weight sequence sigma, i.e. the number of source codes that need to participate in modulo two addition
Figure RE-GDA0002417434210000031
Figure RE-GDA0002417434210000032
Refers to the smallest odd number greater than or equal to the window length;
(3) generating a window sequence of length
Figure RE-GDA0002417434210000033
(4) For the coded modulation matrix, coding is carried out iN a column-by-column mode, the current coding column index is recorded as iN, and the following six steps are mainly executed:
a) randomly searching an element in the column, recording the position of the element as loc, and taking the loc as a starting point of the sliding window;
b) randomly selecting w elements from the position of the loc element to the end position of the column;
c) randomly scrambling the positions of the w selected elements, and recording the scrambled positions of the elements as pos;
d) taking out the first sigma elements from the scrambled w elements as the iN column of source codes participating iN coding;
e) assigning the position of G (pos, iN) iN the coding matrix G to be 1, and performing modulo two summation on the corresponding source codes;
f) the same operation is performed on all the code columns, and the coded source bit d can be obtained1,d2,…dL
2. Filtered multitone modulation of coded information
Obtaining a sequence d of digital fountain codes1,d2,…dLThen, it is subjected to oversampled filtered multitone modulation. In this work an oversampled filtered multitone modulation system is used, the bandwidth of the communication system being B. As shown in fig. 2, in the oversampled filtered silver robbed modulation system, the system upsampling factor N is greater than the number of subbands M of the system. Sub-band width for oversampled filtered polyphonic systems
Figure RE-GDA0002417434210000034
And spacing of adjacent sub-bands
Figure RE-GDA0002417434210000035
As shown in fig. 3, the main process of transmitting end signal modulation is as follows:
(1) the encoded sequence d1,d2,…dLConstellation mapping and serial-parallel conversion are carried out to obtain parallel M paths of sending complex signals which are marked as s0(kT),s1(kT),…sM-1(kT) interpolating up-samples each path of signal by a factor of N, where K is the sampling interval and T is the symbol length;
(2) filtering each path of complex signals by a root raised cosine filter H (L) with the length of L, and moving the complex signals to a corresponding sub-band with the bandwidth;
(3) adding the signals in each sub-band to form a composite signal
Figure RE-GDA0002417434210000036
As follows:
Figure RE-GDA0002417434210000037
where n is the sampling interval of the transmission passband signal, fmmN/MT is the carrier frequency of the mth subband.
(4) Passband transmit signal
Figure RE-GDA0002417434210000041
Through underwater acoustic dual extension channelsThen, the signal reaches a receiving end to carry out signal processing of the receiving end;
3. and (3) received signal processing:
after passing through the underwater acoustic double-extension channel, a passband receiving signal can be obtained
Figure RE-GDA0002417434210000042
And the received signal passes through a shaping filter, so that an equivalent sub-band received signal r can be obtainedm(k' T), as follows:
Figure RE-GDA0002417434210000043
after the passband received signal is obtained, adaptive equalization may be performed at baseband. At a receiving end, according to linear frequency modulation signals at the front part and the rear part of the data block, estimated Doppler factors are obtained through calculation, the passband receiving signals are resampled, and then the passband signals are moved to a baseband through low-pass filtering. As shown in fig. 4, in the present implementation, an equalization algorithm based on the iterative least squares is used to equalize each sub-band by using a decision feedback quadratic multiple of the whole symbol interval. Feedforward filter length of NfFeedback filter length of NbAn estimate of the nth symbol of the mth subband may be obtained
Figure RE-GDA0002417434210000044
As follows:
Figure RE-GDA0002417434210000045
the error e (n) of the symbol estimation is:
e(n)=d(n)-wH(n-1)r(n),
wherein, w (n) is the filter coefficient, and the updating method comprises:
w(n)=w(n-1)+k(n)e*(n),
where k (n) updates the coefficient matrix for the coefficients of the iterative least squares. Therefore, we can obtain the equalized Mean Square Error (MSE) for the mth subband as:
Figure RE-GDA0002417434210000046
in the achievement, MSE obtained by equalization guides the selection of the alternative sub-band for the next digital fountain decoding.
4. Receiving end digital fountain decoding
(1) The obtained symbol decision
Figure RE-GDA0002417434210000047
Mapping back to bits, and performing parallel-serial conversion to obtain d'11,…d′1k,…d′M1,…d′MkWherein k is L/M is the number of the filtering polyphonic symbols;
(2) and selecting the largest r values from the MSE errors of all M sub-bands, removing the corresponding r sub-bands, and correspondingly removing the corresponding decision bits from the symbols in the previous step. Recording the rest decision bits as b with the length of L ', removing the corresponding columns of r sub-bands in a modulation matrix G to obtain a demodulation matrix G' which comprises K rows and L 'columns with the dimension of K multiplied by L', and then carrying out digital fountain bit decoding;
(3) the demodulation is divided into two steps, and for the demodulation matrix G', the decoding operation is performed column by column and row by row, respectively. Firstly, performing column-by-column decoding operation on the demodulation matrix G', and recording the index of the current decoding column as iK:
a) searching a line from a K line to an L' line in an iK column, finding out a line with a 1 appearing for the first time, and recording the serial number of the line change as i _ max;
b) exchanging the ith _ max row with the iK row, and simultaneously exchanging elements b (i _ max) and b _ (iK) in the remaining bits b to be decided;
c) in the iK-th column, the vanishing elements of G' (i _ max, iK) or less are changed to 0 by determinant transformation;
d) performing the same operation on all the coding columns iK, and converting the decoding matrix into a lower triangular matrix with a diagonal element of 1;
(4) secondly, for the demodulation matrix G', the progressive decoding operation is performed on all rows, and the index of the current decoding row is iL:
a) finding a row with only one element equal to 1 in the demodulation matrix G', and marking the index of the row as loc (ind);
b) find the column with element 1 in the loc (ind) th row, mark the index of the column as pos, and decode the element, x (pos) ═ b [ loc (ind) ]/G' [ loc (ind), pos ];
c) eliminating elements corresponding to the position [ loc (ind) ] of the demodulation matrix G 'to participate in the rest encoding of the encoding in the dimension of the column, finding out the row of the pos-th column of the demodulation matrix G' with all elements being 1, marking as loc2, and performing linear elimination element calculation, wherein b (loc2) ═ b (loc2) -A (loc2, pos) × d '(pos), wherein d' is a column vector formed by collecting all received bits;
d) and executing the operation on all the row indexes iL, converting the decoding matrix into a diagonal matrix, and finishing the decoding process.
The analysis was performed by the lake test below.
In the experiment, two underwater acoustic communication MODEMs, each with one transducer and four hydrophones, were used as the transmitting and receiving ends. The distance between the transmitting end and the receiving end is about 130m, and the water depth is about 1.5 m. The depth of water in which the MODEM is deployed is about 0.5 m. The filtered multitone signal is modulated onto 32 subbands with an oversampling factor of 40, QPSK modulation. The bandwidth is 5kHz, i.e. from 21.5kHz to 26.5 kHz. The symbol length is 10 ms. The roll-off factor of the baseband pulse forming root raised cosine filter is 0.15, and the delay width is 12 symbol lengths.
The LT code proposed based on the present invention was tested in experiments, containing 8 data packets, each including a 1280-bit source code. For LT coding, 1920 coded bits are included after LT coding, and then modulated onto 32 subbands, each containing 60 bits or 30 QPSK symbols.
To ensure a minimum set of successful decoding, LT decoding requires at least 1280 bits, so LT coding can remove up to 10 subbands. The decoding result is represented by the number of successfully decoded packets compared to the number of failed packets, the number of successfully decoded packets being earlier, e.g., 8-0 indicates that all 8 packets can be recovered, and 3-5 indicates that 3 packets can be decoded and 5 packets fail. When the non-rate coded packet is successfully recovered, the decoded information is the same as the source bits of the transmitting end. The number of erased subbands represents the number of subbands removed, which is selected according to its corresponding MSE value. In general, more packets can be successfully decoded when more subbands are removed, and decoding performance is affected by channel physical conditions. The results show that decoding performance can be improved when the number of removed subbands increases. Meanwhile, the digital fountain code has frequency domain diversity redundancy, so that the decoding can still be successfully performed in a poor channel environment.
Table 1: lake test experiment decoding result
Figure RE-GDA0002417434210000061
TABLE 1
It should be understood that equivalent substitutions and changes to the technical solution and the inventive concept of the present invention should be made by those skilled in the art to the protection scope of the appended claims.

Claims (6)

1. A cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding is characterized in that: the digital fountain coding method is used for coding physical layer signals of underwater acoustic communication filtering multi-tone modulation, the digital fountain coding is carried out through a sending end, the filtering multi-tone modulation of coding information, received signal processing and digital fountain decoding are carried out, sub-bands subjected to severe frequency domain fading are erased, and the rest sub-band signals are selected for decoding to recover information source signals.
2. The digital fountain coding-based cross-subcarrier underwater acoustic communication filtering multi-tone modulation method as claimed in claim 1, wherein: the implementation steps are mainly as follows:
1) performing LT coding-based digital fountain coding on the source bits at a transmitting end, wherein the redundancy of the coding is ξ;
2) carrying out filtering-based multi-tone modulation on the source code after LT coding, and modulating the source code into M sub-bands in the communication bandwidth, wherein a guard interval exists between adjacent sub-bands;
3) at a receiving end, the passband received signals are transferred to a baseband through complex demodulation, decision feedback equalization based on iterative least squares is carried out on each subband, and the average square error of equalization of each subband is calculated;
4) selecting sub-bands for LT decoding based on the average squared error for equalization of each sub-band, at least
Figure FDA0002235709040000011
The sub-bands are used for decoding;
5) and collecting LT coded bits in the selected sub-band, and carrying out digital fountain decoding based on LT coding to complete the communication process.
3. The digital fountain coding-based cross-subcarrier underwater acoustic communication filtering multi-tone modulation method as claimed in claim 2, wherein: the main flow of the digital fountain coding at the transmitting end is as follows:
(1) suppose that there is K bits of information to be transmitted from the source, and let the bit to be transmitted be c ═ c1,c2,…,ckThe redundancy of the source coding is ξ, that is, the number of coded source bits is L ═ K (1+ ξ), and the coded source bits are d ═ d1,d2,…dLAnd recording the code modulation matrix as G, which comprises K rows and L columns, and K multiplied by L elements;
(2) generating a coder fixed weight sequence sigma, namely the number of source codes needing to participate in modulo two addition
Figure FDA0002235709040000012
Figure FDA0002235709040000013
Refers to the smallest odd number greater than or equal to the window length;
(3)、generating a window sequence of length
Figure FDA0002235709040000014
(4) And aiming at the coded modulation matrix, coding iN a column-by-column mode, recording the current coding column index as iN, and mainly executing the following six steps:
a) randomly searching an element in the column, recording the position of the element as loc, and taking the loc as a starting point of the sliding window;
b) randomly selecting w elements from the position of the loc element to the end position of the column;
c) randomly scrambling the positions of the w selected elements, and recording the scrambled positions of the elements as pos;
d) taking out the first sigma elements from the scrambled w elements as the iN column of source codes participating iN coding;
e) assigning the position of G (pos, iN) iN the coding matrix G to be 1, and performing modulo two summation on the corresponding source codes;
f) the same operation is performed on all the code columns, and the coded source bit d can be obtained1,d2,…dL
4. The digital fountain coding-based cross-subcarrier underwater acoustic communication filtering multi-tone modulation method as claimed in claim 2, wherein: the main flow of the filtering multi-tone modulation of the coding information of the sending end is as follows:
(1) d sequence to be encoded1,d2,…dLConstellation mapping and serial-parallel conversion are carried out to obtain parallel M paths of sending complex signals which are marked as s0(kT),s1(kT),…sM-1(kT) interpolating up-samples each path of signal by a factor of N, where K is the sampling interval and T is the symbol length;
(2) filtering each path of complex signals by a root raised cosine filter H (L) with the length of L, and moving the complex signals to a corresponding sub-band with the bandwidth;
(3) adding the signals in each sub-band to form a composite signal
Figure FDA0002235709040000021
As follows:
Figure FDA0002235709040000022
where n is the sampling interval of the transmission passband signal, fmmN/MT is the carrier frequency of the mth subband;
(4) passband transmit signal
Figure FDA0002235709040000023
And the signal reaches a receiving end after passing through the underwater sound double-extension channel, and the signal processing of the receiving end is carried out.
5. The digital fountain coding-based cross-subcarrier underwater acoustic communication filtering multi-tone modulation method as claimed in claim 2, wherein: and (3) received signal processing: obtaining a passband receiving signal after passing through the underwater sound double-extension channel
Figure FDA0002235709040000024
And the received signal passes through a shaping filter, thus obtaining an equivalent sub-band received signal rm(k' T), as follows:
Figure FDA0002235709040000025
after the passband receiving signal is obtained, self-adaptive equalization is carried out at a baseband; at a receiving end, calculating to obtain an estimated Doppler factor according to linear frequency modulation signals from the front part and the rear part of a data block, resampling a passband receiving signal, and moving the passband signal to a baseband through low-pass filtering; the decision feedback quadratic multiplication based on the iterative least square with the whole symbol interval is adopted as an equalization algorithm of a receiving end to perform equalization processing on each sub-band; feedforward filter length of NfFeedback filter length of NbThe m < th > can be obtainedEstimation of the nth symbol of a subband
Figure FDA0002235709040000026
As follows:
Figure FDA0002235709040000027
the error e (n) of the symbol estimation is:
e(n)=d(n)-wH(n-1)r(n),
wherein, w (n) is the filter coefficient, and the updating method comprises:
w(n)=w(n-1)+k(n)e*(n),
where k (n) updates the coefficient matrix for the coefficients of the iterative least squares, so the Mean Square Error (MSE) of the equalization obtained for the mth subband is:
Figure FDA0002235709040000031
and the MSE obtained by equalization guides the selection of the alternative sub-band for the next digital fountain decoding.
6. The digital fountain coding-based cross-subcarrier underwater acoustic communication filtering multi-tone modulation method as claimed in claim 2, wherein: the receiving end digital fountain decoding process comprises the following steps:
(1) the obtained symbol decision
Figure FDA0002235709040000032
Mapping back to bits, and performing parallel-serial conversion to obtain d'11,…d′1k,…d′M1,…d′MkWherein k is L/M is the number of the filtering polyphonic symbols;
(2) selecting the largest r values from MSE errors of all M sub-bands, removing the corresponding r sub-bands, and correspondingly removing the corresponding decision bits from the symbols in the previous step; recording the rest decision bits as b with the length of L ', removing the corresponding columns of r sub-bands in a modulation matrix G to obtain a demodulation matrix G' which comprises K rows and L 'columns with the dimension of K multiplied by L', and then carrying out digital fountain bit decoding;
(3) the demodulation is divided into two steps, and the decoding operation is respectively carried out on the demodulation matrix G' column by column and row by row; firstly, performing column-by-column decoding operation on the demodulation matrix G', and recording the index of the current decoding column as iK:
a) searching a line from a K line to an L' line in an iK column, finding out a line with a 1 appearing for the first time, and recording the serial number of the line change as i _ max;
b) exchanging the ith _ max row with the iK row, and simultaneously exchanging elements b (i _ max) and b _ (iK) in the remaining bits b to be decided;
c) in the iK-th column, the vanishing elements of G' (i _ max, iK) or less are changed to 0 by determinant transformation;
d) performing the same operation on all the coding columns iK, and converting the decoding matrix into a lower triangular matrix with a diagonal element of 1;
(4) secondly, for the demodulation matrix G', performing a progressive decoding operation on all rows, and recording the index of the current decoding row as iL:
a) finding a row with only one element equal to 1 in the demodulation matrix G', and marking the index of the row as loc (ind);
b) find the column with element 1 in the loc (ind) th row, mark the index of the column as pos, and decode the element, x (pos) ═ b [ loc (ind) ]/G' [ loc (ind), pos ];
c) eliminating elements corresponding to the position [ loc (ind) ] of the demodulation matrix G 'to participate in the rest encoding of the encoding in the dimension of the column, finding out the row of the pos-th column of the demodulation matrix G' with all elements being 1, marking as loc2, and performing linear elimination element calculation, wherein b (loc2) ═ b (loc2) -A (loc2, pos) × d '(pos), wherein d' is a column vector formed by collecting all received bits;
d) and executing the operation on all the row indexes iL, converting the decoding matrix into a diagonal matrix, and finishing the decoding process.
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US20230055353A1 (en) * 2022-04-26 2023-02-23 Qinghai Normal University Data encoding and decoding method for underwater acoustic networks (uans) based on improved online fountain code
CN116708112A (en) * 2023-08-07 2023-09-05 中国电子科技集团公司第二十九研究所 Transmission and detection method, medium and device for reducing PAPR of FMT system

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US20230055353A1 (en) * 2022-04-26 2023-02-23 Qinghai Normal University Data encoding and decoding method for underwater acoustic networks (uans) based on improved online fountain code
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Application publication date: 20200424