A time-frequency joint equalization method and system for GMSK underwater acoustic communication

Abstract

This invention belongs to the field of underwater acoustic communication technology. Specifically, it relates to a time-frequency joint equalization method for GMSK underwater acoustic communication. The method includes: converting and mapping the transmitted signal sequence, then modulating it according to the GMSK signal modulation method based on Laurent decomposition to obtain a GMSK complex baseband signal, and modulating it onto a carrier as the final transmitted signal, which is then transmitted into the underwater acoustic channel; the underwater acoustic channel receives the final transmitted signal, uses it as the received signal, and performs bandpass filtering, two-dimensional time-frequency synchronization, matched filtering, time-frequency equalization, demapping, and decision processing on the received signal to obtain the decided symbol, thus completing the time-frequency joint equalization.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic communication technology, specifically, it relates to a time-frequency joint equalization method and equalization system for GMSK underwater acoustic communication. Background Technology

[0002] Underwater acoustic communication channels are highly complex, characterized by frequency-selective fading, time-varying characteristics, and limited bandwidth. Gaussian minimum frequency shift keying (GMSK) modulation, due to its continuous phase and constant envelope, offers excellent power and spectral efficiency, effectively improving the effectiveness and reliability of communication systems. However, the channel structure in underwater acoustic communication is extremely complex and highly time-varying; therefore, appropriate equalization techniques are needed to process the received signal.

[0003] Currently, traditional frequency domain equalization techniques can effectively address interference in complex multipath channels. However, because the equalization coefficients cannot be updated within the duration of the information block, communication performance degrades significantly in time-varying channels. Traditional time domain equalization, which uses Viterbi decoders for symbol detection, suffers from an complexity that increases exponentially with signal length and is also subject to error propagation. Summary of the Invention

[0004] To address the interference problem of complex time-varying underwater acoustic channels in existing technologies on GMSK underwater acoustic communication, this invention proposes a time-frequency joint equalization method for GMSK underwater acoustic communication, which includes:

[0005] After converting and mapping the transmitted signal sequence, the signal is modulated according to the GMSK signal modulation method based on Laurent decomposition to obtain the GMSK complex baseband signal, which is then modulated onto the carrier as the final transmitted signal and transmitted into the underwater acoustic channel.

[0006] The underwater acoustic channel receives the final transmitted signal, treats it as the received signal, and performs bandpass filtering, two-dimensional time-frequency synchronization, matched filtering, time-frequency equalization, demapping, and decision processing on the received signal to obtain the decided symbol, thus completing the joint time-frequency equalization.

[0007] As an improvement to the above technical solution, after converting and mapping the transmitted signal sequence, the signal is modulated according to the GMSK signal modulation method based on Laurent decomposition to obtain a GMSK complex baseband signal, which is then modulated onto the carrier wave as the final transmitted signal. s f ( t The signal is transmitted into the underwater acoustic channel; the specific process includes:

[0008] Transmitted signal sequence Add a cyclic prefix and tail symbol to convert it into a bipolar non-return-to-zero code signal sequence. ;

[0009] This bipolar non-return-to-zero code signal sequence As a signal block, this signal block has a signal frame structure with multiple parameters concatenated; these multiple parameters include: data block length. Information sequence length Circular prefix length The length of the tail symbol sequence is Among these, the length of the cyclic prefix sequence must be greater than the maximum channel delay; the tail symbol in this signal block must ensure that the phase state of the information sequence returns to zero;

[0010] And this bipolar non-return-to-zero code signal sequence Information-symbol mapping is performed to obtain the GMSK complex baseband signal sequence. ;

[0011] (1)

[0012] in, GMSK complex baseband signal sequence Elements in; A bipolar non-return-to-zero code signal sequence Elements in; It is an imaginary number;

[0013] The GMSK signal modulation method based on Laurent decomposition employs a phase shaping function to modulate the GMSK signal sequence. Modulation was performed to obtain the GMSK complex baseband signal. ,

[0014] (2)

[0015] And modulate it onto a carrier wave as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel;

[0016]

[0017] in, The partial impulse response is given, where j is the imaginary number and fc is the center frequency of the carrier wave.

[0018] make ;but ;

[0019] (3)

[0020] (4)

[0021] (5)

[0022] in, q ( t () is a frequency-shaped pulse g ( τ The integral function of ).

[0023] (6)

[0024] in, T For symbol intervals, B For bandwidth, L Pulse memory length;

[0025] (7)

[0026] in, or ; This is a complementary error function.

[0027] As an improvement to the above technical solution, the underwater acoustic channel receives the final transmitted signal, uses it as the received signal, and performs bandpass filtering, two-dimensional time-frequency synchronization, matched filtering, time-frequency equalization, demapping, and decision processing on the received signal to obtain the decided symbol, thus completing the joint time-frequency equalization; the specific process includes:

[0028] The underwater acoustic channel receives the final transmitted signal. , denoted as the received signal ;

[0029] (8)

[0030] in, Channel response; z(t) is the received noise;

[0031] Regarding the received signal Bandpass filtering is performed, and time-frequency two-dimensional synchronization is achieved using a synchronization sequence to obtain the synchronized signal;

[0032] The synchronized signal is subjected to matched filtering using a low-pass filter and a coherent receiver to obtain the complex baseband signal. ;

[0033]

[0034] (9)

[0035]

[0036] in, After passing through a low-pass filter, the signal is obtained. ;

[0037]

[0038] in, The signal output by the matched filter; The noise output of the matched filter; The subscript used to represent the integral; ;

[0039] (10)

[0040] (11)

[0041] Using complex baseband signals Channel estimation is performed using the cyclic prefix in the data to obtain the estimated channel;

[0042] After performing a Discrete Fourier Transform on the complex baseband signal with the cyclic prefix removed, and then combining it with the estimated channel for frequency domain equalization, we obtain... ;

[0043] (12)

[0044] in, This is the frequency domain expression of the signal after frequency domain equalization. The frequency domain expression for the output signal of the matched filter; These are the equalization coefficients of the frequency domain equalizer; For whitening noise filter, denoted as ; ;

[0045] in,

[0046] (13)

[0047] in, To estimate the frequency domain response of the channel; To estimate the frequency domain response of the channel Conjugate; Noise power spectrum;

[0048] Again Perform a discrete inverse Fourier transform to obtain the soft information after frequency domain equalization. ;

[0049] complex baseband signal The input is fed into an adaptive decision feedback equalizer to obtain the time-domain equalized soft information. ;

[0050] (14)

[0051] in, and K B These are the order of the feedforward filter and the order of the feedback filter, respectively. r n-j For sequence { r n The elements of} are the inputs to the feedforward filter. For phase offset estimation; Equalizer coefficients; For sequence The elements are used as inputs to the feedback filter;

[0052] (15)

[0053] (16)

[0054] in, , For different phase-locked loop coefficients; For updated phase offset estimation; For intermediate quantities in the calculation;

[0055] (17)

[0056] in, This is the output symbol of the feedforward filter; This represents the prior estimation error; It is an imaginary number;

[0057] in, ; ;

[0058] in, For the input of the feedback filter; For soft information after time-domain equalization Information obtained through hard judgment;

[0059] Combined with the obtained frequency domain equalization soft information Soft information after time-domain equalization Symbol estimation is performed based on maximum likelihood estimation to obtain the estimated symbol. ;

[0060] (18)

[0061] in, For estimation symbols The log-likelihood estimate; The symbol following the judgment; To define the conditional probability distribution function;

[0062] , Represented as

[0063] (19)

[0064] (20)

[0065] in, The symbols following the judgment The information obtained through mapping; For variance; for and In function F The unified representation in parentheses; The symbol number in the sequence represents the nth estimated symbol;

[0066] Using estimation symbols Perform demapping and decision-making to obtain the decided symbol. To achieve joint time-frequency equalization;

[0067] (twenty one)

[0068] in, ; For the first n One estimated symbol The symbol after demapping; For the first n -1 estimation symbol The symbol after demapping.

[0069] As an improvement to the above technical solution, the method further includes: employing an adaptive algorithm, and based on the obtained decision symbol... Update the equalizer coefficients to obtain the updated equalizer coefficients. ;

[0070] (twenty two)

[0071] in, It is the gain vector; The equalizer coefficients from the last update; This is the error from the previous reading; .

[0072] This invention also provides a time-frequency joint equalization system for GMSK underwater acoustic communication, the system comprising:

[0073] The mapping and modulation module is used to convert and map the transmitted signal sequence, then modulate it according to the GMSK signal modulation method based on Laurent decomposition to obtain a GMSK complex baseband signal, which is then modulated onto a carrier wave as the final transmitted signal and transmitted into the underwater acoustic channel; and

[0074] The filtering and equalization processing module is used to receive the final transmitted signal in the underwater acoustic channel, treat it as the received signal, and perform bandpass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and decision processing on the received signal to obtain the decided symbol and complete the time-frequency joint equalization.

[0075] As an improvement to the above technical solution, the mapping modulation module includes: a mapping unit and a modulation unit;

[0076] The mapping unit is used to map the transmitted signal sequence Add a cyclic prefix and tail symbol to convert it into a bipolar non-return-to-zero code signal sequence. ;

[0077] Among them, the bipolar non-return-to-zero code signal sequence As a signal block, this signal block has a signal frame structure with multiple parameters concatenated; these multiple parameters include: data block length. Information sequence length Circular prefix length The length of the tail symbol sequence is Among these, the length of the cyclic prefix sequence must be greater than the maximum channel delay; the tail symbol in this signal block must ensure that the phase state of the information sequence returns to zero;

[0078] This bipolar non-return-to-zero code signal sequence Information-symbol mapping is performed to obtain the GMSK complex baseband signal sequence. ;

[0079] (1)

[0080] in, GMSK complex baseband signal sequence Elements in; A bipolar non-return-to-zero code signal sequence Elements in; It is an imaginary number;

[0081] The modulation unit is used for GMSK signal modulation based on Laurent decomposition, employing a phase shaping function to modulate the GMSK signal sequence. Modulation was performed to obtain the GMSK complex baseband signal. ,

[0082] (2)

[0083] And modulate it onto a carrier wave as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel;

[0084]

[0085] in, This represents the partial impulse response, where j is an imaginary number. The center frequency of the carrier wave;

[0086] make ;but ;

[0087] (3)

[0088] (4)

[0089] (5)

[0090] in, q ( t () is a frequency-shaped pulse g ( τ The integral function of ).

[0091] (6)

[0092] in, T For symbol intervals, B For bandwidth, L Pulse memory length;

[0093] (7)

[0094] in, or ; This is a complementary error function.

[0095] As an improvement to the above technical solution, the filtering and equalization processing module includes: a filtering unit and an equalization processing unit;

[0096] The filtering unit is used to receive the final transmitted signal in the underwater acoustic channel. , denoted as the received signal ;

[0097] (8)

[0098] in, Channel response; z(t) is the received noise;

[0099] Regarding the received signal Bandpass filtering is performed, and time-frequency two-dimensional synchronization is achieved using a synchronization sequence to obtain the synchronized signal;

[0100] The synchronized signal is subjected to matched filtering using a low-pass filter and a coherent receiver to obtain the complex baseband signal. ;

[0101]

[0102] (9)

[0103]

[0104] in, After passing through a low-pass filter, the signal is obtained. ;

[0105]

[0106] in, The signal output by the matched filter; The noise output of the matched filter; The subscript used to represent the integral; ;

[0107] (10)

[0108] (11)

[0109] The equalization processing unit is used to utilize complex baseband signals Channel estimation is performed using the cyclic prefix in the data to obtain the estimated channel;

[0110] After performing a Discrete Fourier Transform on the complex baseband signal with the cyclic prefix removed, and then combining it with the estimated channel for frequency domain equalization, we obtain... ;

[0111] (12)

[0112] in, This is the frequency domain expression of the signal after frequency domain equalization. The frequency domain expression for the output signal of the matched filter; These are the equalization coefficients of the frequency domain equalizer; For whitening noise filter, denoted as ; ;

[0113] in,

[0114] (13)

[0115] in, To estimate the frequency domain response of the channel; To estimate the frequency domain response of the channel Conjugate; Noise power spectrum;

[0116] Again Perform a discrete inverse Fourier transform to obtain the soft information after frequency domain equalization. ;

[0117] complex baseband signal The input is fed into an adaptive decision feedback equalizer to obtain the time-domain equalized soft information. ;

[0118] (14)

[0119] in, and K B These are the order of the feedforward filter and the order of the feedback filter, respectively. r n-j For sequence { r n The elements of} are the inputs to the feedforward filter. For phase offset estimation; Equalizer coefficients; For sequence The elements are used as inputs to the feedback filter;

[0120] (15)

[0121] (16)

[0122] in, , For different phase-locked loop coefficients; For updated phase offset estimation; For intermediate quantities in the calculation;

[0123] (17)

[0124] in, This is the output symbol of the feedforward filter; This represents the prior estimation error; It is an imaginary number;

[0125] in, ; ;

[0126] in, For the input of the feedback filter; For soft information after time-domain equalization Information obtained through hard judgment;

[0127] Combined with the obtained frequency domain equalization soft information Soft information after time-domain equalization Symbol estimation is performed based on maximum likelihood estimation to obtain the estimated symbol. ;

[0128] (18)

[0129] in, For estimation symbols The log-likelihood estimate; The symbol following the judgment; To define the conditional probability distribution function;

[0130] , Represented as

[0131] (19)

[0132] (20)

[0133] in, The symbols following the judgment The information obtained through mapping; For variance; for and In function F The unified representation in parentheses; The symbol number in the sequence represents the nth estimated symbol;

[0134] Using estimation symbols Perform demapping and decision-making to obtain the decided symbol. To achieve joint time-frequency equalization;

[0135] (twenty one)

[0136] in, ; For the first n One estimated symbol The symbol after demapping; For the first n -1 estimation symbol The symbol after demapping.

[0137] The advantages of this invention compared to the prior art are:

[0138] 1. The method of the present invention, based on the Laurent decomposition design, can use a simple detector to replace Viterbi decoding, which greatly reduces the complexity of conventional adaptive decision feedback equalizers.

[0139] 2. In the equalizer, the method of the present invention adopts an adaptive algorithm, which can update the equalizer coefficients symbol by symbol, effectively track the time-varying underwater acoustic channel, and greatly improve the performance and environmental adaptability of GMSK communication in the time-varying underwater acoustic channel.

[0140] 3. By embedding signal block-based frequency domain equalization to correct the soft information input to the feedback filter, the error propagation of the adaptive decision feedback equalizer is reduced, thereby improving communication performance. Attached Figure Description

[0141] Figure 1 This is a data block structure of the final transmitted signal in an embodiment of the underwater acoustic signal transmission method in a time-frequency joint equalization method for GMSK underwater acoustic communication according to the present invention;

[0142] Figure 2 This is a flowchart of the underwater acoustic signal transmission method in a time-frequency joint equalization method for GMSK underwater acoustic communication according to the present invention;

[0143] Figure 3 This is a signal equalization process in one embodiment of a time-frequency joint equalization method for GMSK underwater acoustic communication according to the present invention;

[0144] Figure 4a This is a time-domain waveform diagram of the underwater acoustic GMSK signal according to the method of the present invention;

[0145] Figure 4b This is a time-frequency diagram of the underwater acoustic GMSK signal according to the method of the present invention;

[0146] Figure 5 This is a schematic diagram of the measured channel delay-normalized amplitude in a marine underwater acoustic communication experiment in one embodiment of the method of the present invention;

[0147] Figure 6a This is a time-domain waveform of the received signal after bandpass filtering in the underwater acoustic communication experiment at sea, as shown in the example.

[0148] Figure 6b This is the time-frequency diagram of the received signal after bandpass filtering in the underwater acoustic communication experiment at sea, as shown in the example.

[0149] Figure 7This is a schematic diagram of the time-domain signal delay-normalized amplitude after matched filtering in a marine underwater acoustic communication experiment, as described in an embodiment of the method of the present invention.

[0150] Figure 8 This is a schematic diagram of the equalizer output soft information symbol number and normalized amplitude in an underwater acoustic communication test in an embodiment of the method of the present invention. Detailed Implementation

[0151] The present invention will now be further described with reference to the accompanying drawings.

[0152] like Figure 1 As shown, this invention provides a time-frequency joint equalization method for GMSK underwater acoustic communication. It combines traditional frequency domain equalization technology based on Laurent decomposition and adaptive decision feedback equalization technology. By updating the equalization coefficients symbol by symbol to track changes in the channel, it reduces error propagation and thus greatly improves the transmission performance of GMSK signals in underwater acoustic time-varying channels. At the same time, it has lower complexity than traditional time domain equalization technology.

[0153] The method includes:

[0154] After converting and mapping the transmitted signal sequence, the signal is modulated according to the GMSK signal modulation method based on Laurent decomposition to obtain the GMSK complex baseband signal, which is then modulated onto the carrier wave as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel;

[0155] Specifically, the transmitted signal sequence Add a cyclic prefix and tail symbol to convert it into a bipolar non-return-to-zero code signal sequence. ;

[0156] This bipolar non-return-to-zero code signal sequence As a signal block, this signal block has a signal frame structure with multiple parameters concatenated; these multiple parameters include: data block length. Information sequence length Circular prefix length The length of the tail symbol sequence is Among them, the length of the cyclic prefix sequence must be greater than the maximum channel delay; the tail symbol in the signal block must ensure that the phase state of the information sequence returns to zero; the cyclic prefix is ​​an arbitrary sequence unrelated to the information sequence, and its phase state must start from and end at zero.

[0157] And this bipolar non-return-to-zero code signal sequence Information-symbol mapping is performed to obtain the GMSK complex baseband signal sequence. ;

[0158] (1)

[0159] in, GMSK complex baseband signal sequence Elements in; A bipolar non-return-to-zero code signal sequence Elements in; It is an imaginary number;

[0160] Based on the Laurent decomposition-based GMSK signal modulation scheme, a phase shaping function is applied to the GMSK signal sequence. Modulation was performed to obtain the GMSK complex baseband signal. ,

[0161] (2)

[0162] And modulate it onto a carrier wave as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel;

[0163]

[0164] in, It is a partial impulse response, i.e. j is an imaginary number, and fc is the center frequency of the carrier wave;

[0165] make ;but Partial impulse response can be It means that, among them, ; Frequency-shaped pulses Integral function get:

[0166] Among them, partial impulse response can be get,

[0167] (3)

[0168] (4)

[0169] (5)

[0170] in, q ( t () is a frequency-shaped pulse g ( τ The integral function of ).

[0171] (6)

[0172] in, T For symbol intervals, B For bandwidth, L Pulse memory length, It is a complementary error function;

[0173] (7)

[0174] in, or ; It is a complementary error function;

[0175] The underwater acoustic channel receives the final transmitted signal. , denoted as the received signal and the received signal Bandpass filtering, two-dimensional time-frequency synchronization, matched filtering, time-frequency equalization, demapping, and decision processing are performed to obtain the decided symbol, thus completing the joint time-frequency equalization.

[0176] Specifically, the final transmitted signal After passing through the underwater acoustic channel, the received signal is obtained after bandpass filtering and two-dimensional time-frequency synchronization at the receiving end. Among them, bandpass filtering can be handled by designing bandpass filters based on signal bandwidth, and time-frequency two-dimensional synchronization can be handled using synchronization sequences.

[0177] The underwater acoustic channel receives the final transmitted signal. , denoted as the received signal ,

[0178] (8)

[0179] in, Channel response; z(t) is the received noise;

[0180] And the received signal Bandpass filtering is performed, and time-frequency two-dimensional synchronization is achieved using a synchronization sequence to obtain the synchronized signal; bandpass filtering and synchronization are common preprocessing methods in underwater acoustic communication.

[0181] The synchronized signal is subjected to matched filtering using a low-pass filter and a coherent receiver to obtain the complex baseband signal. ;

[0182]

[0183] (9)

[0184]

[0185] in, After passing through a low-pass filter, the signal is obtained. ;

[0186]

[0187] in, The signal output by the matched filter; The noise output of the matched filter; The subscript used to represent the integral; ;

[0188] (10)

[0189] (11)

[0190] Using complex baseband signals Channel estimation is performed using the cyclic prefix in the data to obtain the estimated channel;

[0191] Complex baseband signal with header cyclic prefix removed After performing a discrete Fourier transform and then combining it with the estimated channel for frequency domain equalization, we obtain... ;

[0192] (12)

[0193] in, This is the frequency domain expression of the signal after frequency domain equalization. The frequency domain expression for the output signal of the matched filter; These are the equalization coefficients of the frequency domain equalizer; For whitening noise filter, denoted as ; ;

[0194] GMSK signal , c (0,0; l It can be approximated as {0.996, 0.513, 0.0567, 0.000654, ..., 0.000654, 0.0567, 0.513}.

[0195] in,

[0196] (13)

[0197] in, To estimate the frequency domain response of the channel; To estimate the frequency domain response of the channel Conjugate; Noise power spectrum;

[0198] Again Perform a discrete inverse Fourier transform to obtain the soft information after frequency domain equalization. ;

[0199] complex baseband signal The input is fed into an adaptive decision feedback equalizer to obtain the time-domain equalized soft information. ;

[0200] (14)

[0201] in, and K B These are the order of the feedforward filter and the order of the feedback filter, respectively. r n-j For sequence { r n The elements of} are the inputs to the feedforward filter. For phase offset estimation; Equalizer coefficients; For sequence The elements are the inputs to the feedback filter; where the two terms on the right side of the equals sign are the feedforward filter and the feedback filter, respectively.

[0202] (15)

[0203] (16)

[0204] in, , For different phase-locked loop coefficients; For updated phase offset estimation; For intermediate quantities in the calculation;

[0205] (17)

[0206] in, This is the output symbol of the feedforward filter; This represents the prior estimation error; It is an imaginary number;

[0207] in, ; ;

[0208] in, For the input of the feedback filter; For soft information after time-domain equalization Information obtained through hard judgment;

[0209] Among them, a hard judgment refers to when If the value is greater than 0, then it is determined that... =1; when If the value is less than 0, then it is determined that... =-1;

[0210] Combined with the obtained frequency domain equalization soft information Soft information after time-domain equalization Symbol estimation is performed based on maximum likelihood estimation to obtain the estimated symbol. ;

[0211] (18)

[0212] in, For estimation symbols The log-likelihood estimate; The symbol following the judgment; To define the conditional probability distribution function;

[0213] , Represented as

[0214] (19)

[0215] (20)

[0216] in, The symbols following the judgment The information obtained through mapping; For variance; for and In function F The unified representation in parentheses; The symbol number in the sequence represents the nth estimated symbol;

[0217] Using estimation symbols Perform demapping and decision-making to obtain the decided symbol. To achieve joint time-frequency equalization;

[0218] (twenty one)

[0219] in, ; For the first n One estimated symbol The symbol after demapping; For the first n -1 estimation symbol The symbol after demapping.

[0220] Using formulas (20) and (21) as equalizers, calculate thereby obtaining The process involves a symbol-by-symbol iteration, where the equalizer returns a symbol to the equalizer for equalization and then retrieves the next symbol. As a result, the detector and equalizer cannot be completely independent.

[0221] The method further includes: employing an adaptive algorithm, and based on the obtained decision symbol Update the equalizer coefficients to obtain the updated equalizer coefficients. ;

[0222] (twenty two)

[0223] in, It is the gain vector; The equalizer coefficients from the last update; This is the error from the previous reading; .

[0224] In an embodiment of the present invention, the application of the method of the present invention for underwater information transmission of GMSK signals is discussed. The signal transmission system after matching the hydroacoustic transducer with the power amplifier has a bandwidth of 4-8kHz, a center frequency of 6kHz, and a symbol period of 0.5ms during GMSK modulation, transmitting 1038 bits of original information.

[0225] The process flow of the transmitter in the method of this invention is as follows: Figure 2 First, the frame structure of the transmitted signal is designed by adding a 256-bit cyclic prefix, which is composed of special words. The final complete signal frame structure of the transmitted signal is as follows: Figure 1 As shown, it has multiple parameters, namely the data block length. Information sequence length Circular prefix length The length of the tail symbol sequence is The GMSK complex baseband signal is obtained by mapping and modulation based on the Laurent decomposition of the GMSK signal. And modulate it onto a carrier wave as the final transmitted signal. s f ( t It is transmitted into the underwater acoustic channel.

[0226] like Figure 4a As shown in the time-domain waveform of the transmitted signal, the GMSK signal has a constant envelope structure, which is insensitive to the nonlinear characteristics of the power amplifier and can effectively overcome the nonlinear distortion problem caused by the nonlinear power amplifier. Figure 4bThe spectrum of the GMSK transmitted signal shown in the figure indicates that the signal has low out-of-band energy and good frequency utilization.

[0227] The channel structure of underwater acoustic communication in the example is as follows: Figure 5 As shown, the maximum channel delay spread is 100ms, exhibiting a relatively complex multipath structure.

[0228] Method and flow reference for the receiving end Figure 2 After performing two-dimensional time-frequency synchronization using a synchronization sequence and then bandpass filtering the received signal, the filtered time-frequency diagram is shown below. Figure 6a and 6b As shown in the figure, the time-domain waveform reveals that the channel causes significant multipath interference to the signal. The time-frequency diagram of the received signal shows that the GMSK signal has low out-of-band radiation and high bandwidth efficiency.

[0229] The complex baseband signal is obtained by performing matched filtering on the bandpass filtered signal using equation (8). like Figure 7 As shown. Figure 7 This indicates a signal that has not undergone equalization; the information contained in this diagram cannot be reconstructed from the transmitted binary sequence.

[0230] refer to Figure 3 For complex baseband signals Equalization and demodulation are performed. First, channel estimation is achieved using a cyclic prefix algorithm. And for the complex baseband signal with the cyclic prefix removed Frequency domain equalization is performed to obtain frequency domain equalization output soft information. The equalization coefficients are shown in equation (11). The complex baseband signal... The output adaptive decision feedback filter is calculated using the cyclic prefix, i.e., the filter tap coefficients in formula (14). .

[0231] When the n=1th symbol passes through the equalizer, the soft information d1 output by the adaptive decision feedback filter and the soft information b1 output by the frequency domain equalization are jointly estimated based on maximum likelihood estimation, and the estimated symbol is then used... Update the filter tap coefficients, then iterate symbol by symbol. Estimated symbol of the received signal. like Figure 8 As shown, after demapping and making a decision, the complete output information is obtained. A total of 1038 bits were used to complete the entire communication process. Figure 8 Each dot in the diagram represents a symbol; a dot above a 0 can be interpreted as 1; a dot below a 0 can be interpreted as -1; thus, the transmitted binary sequence can be obtained.

[0232] The present invention also provides a time-frequency joint equalization system for GMSK underwater acoustic communication, the system comprising: a mapping modulation module and a filtering equalization processing module;

[0233] The mapping and modulation module is used to convert and map the transmitted signal sequence, then modulate it according to the GMSK signal modulation method based on Laurent decomposition to obtain a GMSK complex baseband signal, and modulate it onto the carrier as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel;

[0234] Specifically, the mapping modulation module includes: a mapping unit and a modulation unit;

[0235] The mapping unit is used to map the transmitted signal sequence Add a cyclic prefix and tail symbol to convert it into a bipolar non-return-to-zero code signal sequence. ;

[0236] This bipolar non-return-to-zero code signal sequence As a signal block, this signal block has a signal frame structure with multiple parameters concatenated; these multiple parameters include: data block length. Information sequence length Circular prefix length The length of the tail symbol sequence is Among these, the length of the cyclic prefix sequence must be greater than the maximum channel delay; the tail symbol in this signal block must ensure that the phase state of the information sequence returns to zero;

[0237] This bipolar non-return-to-zero code signal sequence Information-symbol mapping is performed to obtain the GMSK complex baseband signal sequence. ;

[0238] (1)

[0239] in, GMSK complex baseband signal sequence Elements in; A bipolar non-return-to-zero code signal sequence Elements in; It is an imaginary number;

[0240] The modulation unit is used for GMSK signal modulation based on Laurent decomposition, employing a phase shaping function to modulate the GMSK signal sequence. Modulation was performed to obtain the GMSK complex baseband signal. ,

[0241] (2)

[0242] It is then modulated onto a carrier wave as the final transmission signal and transmitted into the underwater acoustic channel;

[0243]

[0244] in, This represents the partial impulse response, where j is an imaginary number. The center frequency of the carrier wave;

[0245] make ;but ;

[0246] (3)

[0247] (4)

[0248] (5)

[0249] in, q ( t () is a frequency-shaped pulse g ( τ The integral function of ).

[0250] (6)

[0251] in, T For symbol intervals, B For bandwidth, L Pulse memory length;

[0252] (7)

[0253] in, or ; This is a complementary error function.

[0254] The filtering and equalization processing module is used to receive the final transmitted signal in the underwater acoustic channel, treat it as the received signal, and perform bandpass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and decision processing on the received signal to obtain the decided symbol and complete the time-frequency joint equalization.

[0255] Specifically, the filtering and equalization processing module includes: a filtering unit and an equalization processing unit;

[0256] The filtering unit is used to receive the final transmitted signal in the underwater acoustic channel. , denoted as the received signal ;

[0257] (8)

[0258] in, Channel response; z(t) is the received noise;

[0259] Regarding the received signal Bandpass filtering is performed, and time-frequency two-dimensional synchronization is achieved using a synchronization sequence to obtain the synchronized signal;

[0260] The synchronized signal is subjected to matched filtering using a low-pass filter and a coherent receiver to obtain the complex baseband signal. ;

[0261]

[0262] (9)

[0263]

[0264] in, After passing through a low-pass filter, the signal is obtained. ;

[0265]

[0266] in, The signal output by the matched filter; The noise output of the matched filter; The subscript used to represent the integral; ;

[0267] (10)

[0268] (11)

[0269] The equalization processing unit is used to utilize complex baseband signals Channel estimation is performed using the cyclic prefix in the data to obtain the estimated channel;

[0270] After performing a Discrete Fourier Transform on the complex baseband signal with the cyclic prefix removed, and then combining it with the estimated channel for frequency domain equalization, we obtain... ;

[0271] (12)

[0272] in, This is the frequency domain expression of the signal after frequency domain equalization. The frequency domain expression for the output signal of the matched filter; These are the equalization coefficients of the frequency domain equalizer; For whitening noise filter, denoted as ; ;

[0273] in,

[0274] (13)

[0275] in, To estimate the frequency domain response of the channel; To estimate the frequency domain response of the channel Conjugate; Noise power spectrum;

[0276] Again Perform a discrete inverse Fourier transform to obtain the soft information after frequency domain equalization. ;

[0277] complex baseband signal The input is fed into an adaptive decision feedback equalizer to obtain the time-domain equalized soft information. ;

[0278] (14)

[0279] in, and K B These are the order of the feedforward filter and the order of the feedback filter, respectively. r n-j For sequence { r n The elements of} are the inputs to the feedforward filter. For phase offset estimation; Equalizer coefficients; For sequence The elements are used as inputs to the feedback filter;

[0280] (15)

[0281] (16)

[0282] in, , For different phase-locked loop coefficients; For updated phase offset estimation; For intermediate quantities in the calculation;

[0283] (17)

[0284] in, This is the output symbol of the feedforward filter; This represents the prior estimation error; It is an imaginary number;

[0285] in, ; ;

[0286] in, For the input of the feedback filter; For soft information after time-domain equalization Information obtained through hard judgment;

[0287] Combined with the obtained frequency domain equalization soft information Soft information after time-domain equalization Symbol estimation is performed based on maximum likelihood estimation to obtain the estimated symbol. ;

[0288] (18)

[0289] in, For estimation symbols The log-likelihood estimate; The symbol following the judgment; To define the conditional probability distribution function;

[0290] , Represented as

[0291] (19)

[0292] (20)

[0293] in, The symbols following the judgment The information obtained through mapping; For variance; for and In function F The unified representation in parentheses; The symbol number in the sequence represents the nth estimated symbol;

[0294] Using estimation symbols Perform demapping and decision-making to obtain the decided symbol. To achieve joint time-frequency equalization;

[0295] (twenty one)

[0296] in, ; For the first n One estimated symbol The symbol after demapping; For the first n -1 estimation symbol The symbol after demapping.

[0297] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A time-frequency joint equalization method for GMSK underwater acoustic communication, the method comprising: After converting and mapping the transmitted signal sequence, the signal is modulated according to the GMSK signal modulation method based on Laurent decomposition to obtain the GMSK complex baseband signal, which is then modulated onto the carrier as the final transmitted signal and transmitted into the underwater acoustic channel. The underwater acoustic channel receives the final transmitted signal, uses it as the received signal, and performs bandpass filtering, two-dimensional time-frequency synchronization, matched filtering, time-frequency equalization, demapping, and decision processing on the received signal to obtain the decided symbol and complete the joint time-frequency equalization. The underwater acoustic channel receives the final transmitted signal, uses it as the received signal, and performs bandpass filtering, two-dimensional time-frequency synchronization, matched filtering, time-frequency equalization, demapping, and decision processing on the received signal to obtain the decided symbol, thus completing the joint time-frequency equalization. The specific process includes: The underwater acoustic channel receives the final transmitted signal. , denoted as the received signal ; （8） in, Channel response; z(t) is the received noise; This represents the length of the data block. T The symbol interval; Regarding the received signal Bandpass filtering is performed, and time-frequency two-dimensional synchronization is achieved using a synchronization sequence to obtain the synchronized signal; The synchronized signal is subjected to matched filtering using a low-pass filter and a coherent receiver to obtain the complex baseband signal. ; （9） in, After passing through a low-pass filter, the signal is obtained. ; It is a partial impulse response; in, The signal output by the matched filter; The noise output of the matched filter; The subscript used to represent the integral; ; （10） （11） Using complex baseband signals Channel estimation is performed using the cyclic prefix in the data to obtain the estimated channel; After performing a Discrete Fourier Transform on the complex baseband signal with the cyclic prefix removed, and then combining it with the estimated channel for frequency domain equalization, we obtain... ; （12） in, This is the frequency domain expression of the signal after frequency domain equalization. The frequency domain expression for the output signal of the matched filter; These are the equalization coefficients of the frequency domain equalizer; For whitening noise filter, denoted as ; ; in, （13） in, To estimate the frequency domain response of the channel; To estimate the frequency domain response of the channel Conjugate; Noise power spectrum; Again Perform a discrete inverse Fourier transform to obtain the soft information after frequency domain equalization. ; complex baseband signal The input is fed into an adaptive decision feedback equalizer to obtain the time-domain equalized soft information. ; （14） in, and K B These are the order of the feedforward filter and the order of the feedback filter, respectively. r n-j For sequence { r n The elements of} are the inputs to the feedforward filter. For phase offset estimation; Equalizer coefficients; For sequence The elements are used as inputs to the feedback filter; （15） （16） in, , For different phase-locked loop coefficients; For updated phase offset estimation; For intermediate quantities in the calculation; （17） in, This is the output symbol of the feedforward filter; This represents the prior estimation error; It is an imaginary number; in, ; ; in, For the input of the feedback filter; For soft information after time-domain equalization Information obtained through hard judgment; Combined with the obtained frequency domain equalization soft information Soft information after time-domain equalization Symbol estimation is performed based on maximum likelihood estimation to obtain the estimated symbol. ; （18） in, For estimation symbols The log-likelihood estimate; The symbol following the judgment; To define the conditional probability distribution function; , Represented as （19） （20） in, The symbols following the judgment The information obtained through mapping; For variance; for and In function F The unified representation in parentheses; The symbol number in the sequence represents the nth estimated symbol; Using estimation symbols Perform demapping and decision-making to obtain the decided symbol. To achieve joint time-frequency equalization; （21） in, ; For the first n One estimated symbol The symbol after demapping; For the first n -1 estimation symbol The symbol after demapping.

2. The time-frequency joint equalization method for GMSK underwater acoustic communication according to claim 1, characterized in that, After converting and mapping the transmitted signal sequence, the signal is modulated according to the GMSK signal modulation method based on Laurent decomposition to obtain the GMSK complex baseband signal, which is then modulated onto the carrier as the final transmitted signal and transmitted into the underwater acoustic channel. Its specific process includes: Transmitted signal sequence Add a cyclic prefix and tail symbol to convert it into a bipolar non-return-to-zero code signal sequence. ; This bipolar non-return-to-zero code signal sequence As a signal block, this signal block has a signal frame structure with multiple parameters concatenated; these multiple parameters include: data block length. Information sequence length, cyclic prefix length The length of the tail symbol sequence is Among these, the length of the cyclic prefix sequence must be greater than the maximum channel delay; the tail symbol in this signal block must ensure that the phase state of the information sequence returns to zero; And this bipolar non-return-to-zero code signal sequence Information-symbol mapping is performed to obtain the GMSK complex baseband signal sequence. ; （1） in, GMSK complex baseband signal sequence Elements in; A bipolar non-return-to-zero code signal sequence Elements in; It is an imaginary number; The GMSK signal modulation method based on Laurent decomposition employs a phase shaping function to modulate the GMSK signal sequence. Modulation was performed to obtain the GMSK complex baseband signal. , （2） And modulate it onto a carrier wave as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel; in, This represents the partial impulse response, where j is an imaginary number. The center frequency of the carrier wave; make ;but ; （3） （4） （5） in, q ( t () is a frequency-shaped pulse g ( τ The integral function of ). （6） in, T For symbol intervals, B For bandwidth, L The pulse memory length; （7） in, or ; This is a complementary error function.

3. The time-frequency joint equalization method for GMSK underwater acoustic communication according to claim 1, characterized in that, The method further includes: employing an adaptive algorithm, and based on the obtained decision symbol Update the equalizer coefficients to obtain the updated equalizer coefficients. ; （22） in, It is the gain vector; The equalizer coefficients from the last update; This is the error from the previous reading; .

4. A time-frequency joint equalization system for GMSK underwater acoustic communication, characterized in that, The system includes: The mapping and modulation module is used to convert and map the transmitted signal sequence, then modulate it according to the GMSK signal modulation method based on Laurent decomposition to obtain a GMSK complex baseband signal, which is then modulated onto a carrier wave as the final transmitted signal and transmitted into the underwater acoustic channel; and The filtering and equalization processing module is used to receive the final transmitted signal in the underwater acoustic channel, treat it as the received signal, and perform bandpass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and decision processing on the received signal to obtain the decided symbol and complete the time-frequency joint equalization. The filtering and equalization processing module includes a filtering unit and an equalization processing unit. The filtering unit is used to receive the final transmitted signal in the underwater acoustic channel. , denoted as the received signal ; （8） in, Channel response; To receive noise; This represents the length of the data block. T The symbol interval; Regarding the received signal Bandpass filtering is performed, and time-frequency two-dimensional synchronization is achieved using a synchronization sequence to obtain the synchronized signal; The synchronized signal is subjected to matched filtering using a low-pass filter and a coherent receiver to obtain the complex baseband signal. ; （9） in, After passing through a low-pass filter, the signal is obtained. ; It is a partial impulse response; in, The signal output by the matched filter; The noise output of the matched filter; The subscript used to represent the integral; ; （10） （11） The equalization processing unit is used to utilize complex baseband signals Channel estimation is performed using the cyclic prefix in the data to obtain the estimated channel; After performing a Discrete Fourier Transform on the complex baseband signal with the cyclic prefix removed, and then combining it with the estimated channel for frequency domain equalization, we obtain... ; （12） in, This is the frequency domain expression of the signal after frequency domain equalization. The frequency domain expression for the output signal of the matched filter; These are the equalization coefficients of the frequency domain equalizer; For whitening noise filter, denoted as ; ; in, （13） in, To estimate the frequency domain response of the channel; To estimate the frequency domain response of the channel Conjugate; Noise power spectrum; Again Perform a discrete inverse Fourier transform to obtain the soft information after frequency domain equalization. ; complex baseband signal The input is fed into an adaptive decision feedback equalizer to obtain the time-domain equalized soft information. ; （14） in, and K B These are the order of the feedforward filter and the order of the feedback filter, respectively. r n-j For sequence { r n The elements of} are the inputs to the feedforward filter. For phase offset estimation; Equalizer coefficients; For sequence The elements are used as inputs to the feedback filter; （15） （16） in, , For different phase-locked loop coefficients; For updated phase offset estimation; For intermediate quantities in the calculation; （17） in, This is the output symbol of the feedforward filter; This represents the prior estimation error; It is an imaginary number; in, ; ; in, For the input of the feedback filter; For soft information after time-domain equalization Information obtained through hard judgment; Combined with the obtained frequency domain equalization soft information Soft information after time-domain equalization Symbol estimation is performed based on maximum likelihood estimation to obtain the estimated symbol. ; （18） in, For estimation symbols The log-likelihood estimate; The symbol following the judgment; To define the conditional probability distribution function; , Represented as （19） （20） in, The symbols following the judgment The information obtained through mapping; For variance; for and In function F The unified representation in parentheses; The symbol number in the sequence represents the nth estimated symbol; Using estimation symbols Perform demapping and decision-making to obtain the decided symbol. To achieve joint time-frequency equalization; （21） in, ; For the first n One estimated symbol The symbol after demapping; For the first n -1 estimation symbol The symbol after demapping.

5. The time-frequency joint equalization system for GMSK underwater acoustic communication according to claim 1, characterized in that, The mapping modulation module includes: a mapping unit and a modulation unit; The mapping unit is used to map the transmitted signal sequence Add a cyclic prefix and tail symbol to convert it into a bipolar non-return-to-zero code signal sequence. ; Among them, the bipolar non-return-to-zero code signal sequence As a signal block, this signal block has a signal frame structure with multiple parameters concatenated; these multiple parameters include: data block length. Information sequence length, cyclic prefix length The length of the tail symbol sequence is Among these, the length of the cyclic prefix sequence must be greater than the maximum channel delay; the tail symbol in this signal block must ensure that the phase state of the information sequence returns to zero; And this bipolar non-return-to-zero code signal sequence Information-symbol mapping is performed to obtain the GMSK complex baseband signal sequence. ; （1） in, GMSK complex baseband signal sequence Elements in; A bipolar non-return-to-zero code signal sequence Elements in; It is an imaginary number; The modulation unit is used for GMSK signal modulation based on Laurent decomposition, employing a phase shaping function to modulate the GMSK signal sequence. Modulation was performed to obtain the GMSK complex baseband signal. And modulate it onto a carrier wave as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel; （2） And modulate it onto a carrier wave as the final transmitted signal. s f ( t ), transmitted into the underwater acoustic channel; in, This represents the partial impulse response, where j is an imaginary number. The center frequency of the carrier wave; make ;but ; （3） （4） （5） in, q ( t () is a frequency-shaped pulse g ( τ The integral function of ). （6） in, T For symbol intervals, B For bandwidth, L The pulse memory length; （7） in, or ; This is a complementary error function.

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