CN116827729A - Time-frequency joint equalization method and equalization system for GMSK underwater acoustic communication - Google Patents
Time-frequency joint equalization method and equalization system for GMSK underwater acoustic communication Download PDFInfo
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Abstract
The invention belongs to the technical field of underwater acoustic communication, and particularly relates to a time-frequency joint equalization method for GMSK underwater acoustic communication, which comprises the following steps: after the transmitting signal sequence is converted and mapped with information and symbols, the transmitting signal sequence is modulated according to a GMSK signal modulation mode based on Laurent decomposition, a GMSK complex baseband signal is obtained, and the GMSK complex baseband signal is modulated on a carrier wave to be used as a final transmitting signal and transmitted into an underwater sound channel; the underwater acoustic channel receives the final transmitting signal, takes the final transmitting signal as a receiving signal, and carries out band-pass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and judgment processing on the receiving signal to obtain a judged symbol, thereby completing time-frequency joint equalization.
Description
Technical Field
The invention belongs to the technical field of underwater acoustic communication, and particularly relates to a time-frequency joint equalization method and an equalization system for GMSK underwater acoustic communication.
Background
The underwater acoustic communication channel is quite complex and has the characteristics of frequency selective fading, time varying, limited bandwidth and the like. Gaussian minimum shift keying modulation (GMSK) has good power utilization rate and spectrum utilization rate due to the characteristics of continuous phase and constant envelope, and can effectively improve the effectiveness and reliability of a communication system. However, the channel structure in underwater acoustic communication is very complex and has a strong time-variability, and thus, it is necessary to process the received signal using an appropriate equalization technique.
At present, the traditional frequency domain equalization technology can effectively solve the interference of a complex multipath channel, but because the equalization coefficient cannot be updated in the duration of an information block, the communication performance can be obviously reduced under a time-varying channel. However, the complexity of the conventional time domain equalization increases exponentially with the signal length due to the symbol detection using the Viterbi decoder, and there is also an error propagation phenomenon.
Disclosure of Invention
In order to solve the problem of interference of a complex time-varying underwater acoustic channel to GMSK underwater acoustic communication in the prior art, the invention provides a time-frequency joint equalization method for GMSK underwater acoustic communication, which comprises the following steps:
after the transmitting signal sequence is converted and mapped with information and symbols, the transmitting signal sequence is modulated according to a GMSK signal modulation mode based on Laurent decomposition, a GMSK complex baseband signal is obtained, and the GMSK complex baseband signal is modulated on a carrier wave to be used as a final transmitting signal and transmitted into an underwater sound channel;
the underwater acoustic channel receives the final transmitting signal, takes the final transmitting signal as a receiving signal, and carries out band-pass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and judgment processing on the receiving signal to obtain a judged symbol, thereby completing time-frequency joint equalization.
As one of the improvements of the above technical scheme, the method comprises converting the transmission signal sequence and mapping the information to the symbols, modulating according to the modulation mode of the GMSK signal based on Laurent decomposition to obtain a GMSK complex baseband signal, and modulating the GMSK complex baseband signal onto a carrier wave as the final transmission signal s f (t) transmitting into the underwater acoustic channel; the specific process comprises the following steps:
will transmit a signal sequence { a } m Adding cyclic prefix and tail symbol, converting into bipolar non-return-to-zero code signal sequence { x }, and k }；
the bipolar non-return-to-zero code signal sequence { x }, is k As a signal block having a signal frame structure with a plurality of parameters connected in series; the plurality of parameters includes: the data block length N, the information sequence length L, the cyclic prefix length G and the tail symbol sequence length S; the length of the cyclic prefix sequence is required to be larger than the maximum time delay of the channel; tail symbols in the signal block need to ensure that the phase state of the information sequence returns to zero;
and for the bipolar non-return-to-zero code signal sequence { x } k Information-symbol mapping to obtain GMSK complex baseband signal sequence { b }, and n }；
wherein ,bn For GMSK complex baseband signal sequence { b } n Elements in }; x is x k For bipolar non-return-to-zero code signal sequence { x } k Elements in }; j is an imaginary number;
GMSK signal modulation mode based on Laurent decomposition adopts phase shaping function to make the GMSK signal sequence { b } n Modulating to obtain GMSK complex baseband signal s (t),
and modulates it onto a carrier wave as a final transmitted signal s f (t) transmitting into the underwater acoustic channel;
s f (t)＝s(t)×exp(j×2π×fc×t)
wherein c (t-nT) is a partial impulse response, j is an imaginary number, and fc is a center frequency of the carrier;
let t 1 =t-nT; then c (t) 1 )＝c(t-nT)；
Wherein q (t) is the integral function of the frequency shaping pulse g (τ);
wherein, T is symbol interval, B is bandwidth, L pulse memory length;
wherein ,or->Q(x 1 ) As a complementary error function.
As one of the improvements of the above technical scheme, the underwater acoustic channel receives the final transmitting signal, takes the final transmitting signal as a receiving signal, and performs bandpass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and decision processing on the receiving signal to obtain a decided symbol, so as to complete time-frequency joint equalization; the specific process comprises the following steps:
the underwater acoustic channel receives the final transmitted signal s f (t) denoted as received signal r f (t)；
wherein ,channel response; z (t) is the reception noise;
for the received signal r f (t) band-pass filtering and time-frequency two-dimensional synchronization by utilizing a synchronization sequence to obtain a synchronized signal;
the synchronized signal is matched and filtered by a low-pass filter and a coherent receiver to obtain a complex baseband signal r n ；
wherein ,rf (t) after passing through a low pass filter, obtaining a signal r (t);
wherein ,sn A signal output by the matched filter; z n Noise output by the matched filter; η is used to denote the index of the integral; η = 0,1,2,..;
using complex baseband signals r n Performing channel estimation on the cyclic prefix in the channel to obtain an estimated channel;
performing discrete Fourier transform on the complex baseband signal with the head cyclic prefix removed, and performing frequency domain equalization by combining with the estimated channel to obtain
wherein ,is of the pass frequencyA frequency domain expression of the domain equalized signal; r is R k Outputting a frequency domain representation of the signal for the matched filter; />Equalizing coefficients for a frequency domain equalizer; w (W) k For whitening noise filter, is noted +.>
wherein ,
wherein ,Hk To estimate the frequency domain response of the channel;to estimate the frequency domain response H of the channel k Conjugation of (2); n (N) 0 Is a noise power spectrum;
re-pairingPerforming discrete Fourier transform to obtain soft information after frequency domain equalization>
Will complex baseband signal r n Input to adaptive decision feedback equalizer to obtain soft information after time domain equalization
wherein ,KF and KB The feedforward filter order and the feedback filter order, r, respectively n-j For the sequence { r } n Elements of }, feedforward filter input, θ n Estimating for phase offset; lambda (lambda) j Equalizer coefficients; v n-j For the sequence { v n -an element, a feedback filter input;
wherein ,K1 、K 2 Different phase-locked loop coefficients;estimating for the updated phase offset; phi m Is the calculated intermediate quantity;
wherein ,ρn Outputting a symbol for the feedforward filter; e, e n Estimating error for a priori; j is an imaginary number;
wherein ,en ＝v n -d n ；
wherein ,vn Is a feedback filter input; d, d n For soft information after equalization by time domainInformation obtained by hard decision;
combining the obtained soft information after frequency domain equalizationSoft message after time domain equalizationRest->Symbol estimation is performed based on maximum likelihood estimation, and estimated symbol +.>
wherein ,for estimating sign->Log-likelihood estimates of (2); />Is the symbol after the judgment; p () is a defined conditional probability distribution function;
f (kappa) is represented by
wherein ,bn Is made of decided symbolsMapping the obtained information; sigma is variance; kappa is-> and />Unified representation in function F (); n is the number of the symbol in the sequence, representing the nth estimated symbol;
using estimated symbolsDemapping and deciding to obtain decided symbol +.>Completing time-frequency joint equalization;
wherein ,y n estimated symbol for n->Demapped symbols; y is n-1 Estimated symbol +.1 for n-1->Demapped symbols.
As an improvement of the foregoing technical solution, the method further includes: an adaptive algorithm is adopted and based on the obtained symbol after judgmentUpdating equalizer coefficients to obtain updated equalizer coefficients lambda n ；
λ n ＝λ n-1 +ψ n e n-1 (22)
wherein ,ψn Is a gain vector; lambda (lambda) n-1 Equalizer coefficients that were last updated; e, e n-1 Is the last error;
the invention also provides a time-frequency joint equalization system for GMSK underwater acoustic communication, which comprises:
the mapping modulation module is used for converting the transmitting signal sequence and mapping information and symbols, modulating according to a GMSK signal modulation mode based on Laurent decomposition to obtain a GMSK complex baseband signal, modulating the GMSK complex baseband signal onto a carrier wave to serve as a final transmitting signal, and transmitting the final transmitting signal into an underwater sound channel; and
the filtering equalization processing module is used for receiving the final transmitting signal by the underwater acoustic channel, taking the final transmitting signal as a receiving signal, and carrying out band-pass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and judgment processing on the receiving signal to obtain a judged symbol, thereby completing time-frequency joint equalization.
As one of the improvements of the above technical solution, the mapping modulation module includes: a mapping unit and a modulation unit;
the mapping unit is used for mapping the transmission signal sequence { a } m Adding cyclic prefix and tail symbol, converting into bipolar non-return-to-zero code signal sequence { x }, and k }；
wherein the bipolar non-return-to-zero code signal sequence { x }, is k As a signal block having a signal frame structure with a plurality of parameters connected in series; the plurality of parameters includes: the data block length N, the information sequence length L, the cyclic prefix length G and the tail symbol sequence length S; the length of the cyclic prefix sequence is required to be larger than the maximum time delay of the channel; tail symbols in the signal block need to ensure that the phase state of the information sequence returns to zero;
for the bipolar non-return-to-zero code signal sequence { x } k Information-symbol mapping to obtain GMSK complex baseband signal sequence { b }, and n }；
wherein ,bn For GMSK complex baseband signal sequence { b } n Elements in }; x is x k For bipolar non-return-to-zero code signal sequence { x } k Elements in }; j is an imaginary number;
the modulation unit is used for modulating the GMSK signal based on Laurent decomposition by adopting a phase shaping function to the GMSK signal sequence { b } n Modulating to obtain GMSK complex baseband signal s (t),
and modulates it onto a carrier wave as a final transmitted signal s f (t) transmitting into the underwater acoustic channel;
s f (t)＝s(t)×exp(j×2π×fc×t)
wherein c (t-nT) is a partial impulse response, j is an imaginary number, and fc is a center frequency of the carrier;
let t 1 =t-nT; then c (t) 1 )＝c(t-nT)；
Wherein q (t) is the integral function of the frequency shaping pulse g (τ);
wherein, T is symbol interval, B is bandwidth, L pulse memory length;
wherein ,or->Q(x 1 ) As a complementary error function.
As one of the improvements of the above technical solution, the filter equalization processing module includes: a filtering unit and an equalization processing unit;
the filtering unit is used for receiving the final transmitting signal s by the underwater sound channel f (t) denoted as received signal r f (t)；
wherein ,channel response; z (t) is the reception noise;
for the received signal r f (t) band-pass filtering and time-frequency two-dimensional synchronization by utilizing a synchronization sequence to obtain a synchronized signal;
the synchronized signal is matched and filtered by a low-pass filter and a coherent receiver to obtain a complex baseband signal r n ；
wherein ,rf (t) after passing through a low pass filter, obtaining a signal r (t);
wherein ,sn A signal output by the matched filter; z n Noise output by the matched filter; η is used to denote the index of the integral; η = 0,1,2,..;
the equalization processing unit is used for utilizing the complex baseband signal r n Performing channel estimation on the cyclic prefix in the channel to obtain an estimated channel;
performing discrete Fourier transform on the complex baseband signal with the head cyclic prefix removed, and performing frequency domain equalization by combining with the estimated channel to obtain
wherein ,is a frequency domain expression of the signal after frequency domain equalization; r is R k Outputting a frequency domain representation of the signal for the matched filter; />Equalizing coefficients for a frequency domain equalizer; w (W) k For whitening noise filter, is noted +.>
wherein ,
wherein ,Hk To estimate the frequency domain response of the channel;to estimate the frequency domain response H of the channel k Conjugation of (2); n (N) 0 Is a noise power spectrum;
re-pairingPerforming discrete Fourier transform to obtain soft information after frequency domain equalization>
Will complex baseband signal r n Input to adaptive decision feedback equalizer to obtain soft information after time domain equalization
wherein ,KF and KB The feedforward filter order and the feedback filter order, r, respectively n-j For the sequence { r } n Elements of }, feedforward filter input, θ n Estimating for phase offset; lambda (lambda) j Equalizer coefficients; v n-j For the sequence { v n -an element, a feedback filter input;
wherein ,K1 、K 2 Different phase-locked loop coefficients;estimating for the updated phase offset; phi m Is the calculated intermediate quantity;
wherein ,ρn Outputting a symbol for the feedforward filter; e, e n Estimating error for a priori; j is an imaginary number;
wherein ,en ＝v n -d n ；
wherein ,vn Is a feedback filter input; d, d n For soft information after equalization by time domainInformation obtained by hard decision;
combining the obtained soft information after frequency domain equalizationSoft information after time domain equalization>Symbol estimation is performed based on maximum likelihood estimation, and estimated symbol +.>
wherein ,for estimating sign->Log-likelihood estimates of (2); />Is the symbol after the judgment; p () is a defined conditional probability distribution function;
f (kappa) is represented by
wherein ,bn Is made of decided symbolsMapping the obtained information; sigma is variance; kappa is-> and />Unified representation in function F (); n is the number of the symbol in the sequence, representing the nth estimated symbol;
using estimated symbolsDemapping and deciding to obtain decided symbol +.>Completing time-frequency joint equalization;
wherein ,y n estimated symbol for n->Demapped symbols; y is n-1 Estimated symbol +.1 for n-1->Demapped symbols.
Compared with the prior art, the invention has the beneficial effects that:
1. the equalizer designed based on Laurent decomposition can replace Viterbi decoding by a simple detector, so that the complexity of a conventional self-adaptive decision feedback equalizer is greatly reduced;
2. in the equalizer, the method of the invention adopts a self-adaptive algorithm, can carry out symbol-by-symbol iterative updating on equalizer coefficients, can effectively track a time-varying underwater acoustic channel, and greatly improves the performance and environmental adaptability of GMSK communication under the time-varying underwater acoustic channel;
3. the input soft information of the feedback filter is corrected by the frequency domain equalization based on the signal block, so that error propagation of the self-adaptive decision feedback equalizer is reduced, and communication performance is improved.
Drawings
Fig. 1 is a block structure of a final transmission signal in an embodiment of a method for transmitting an underwater acoustic signal in a time-frequency joint equalization method for GMSK underwater acoustic communication according to the present invention;
fig. 2 is a method flow diagram of a method for transmitting an underwater acoustic signal in a time-frequency joint equalization method for GMSK underwater acoustic communication according to the present invention;
fig. 3 is a signal equalization flow in an embodiment of a time-frequency joint equalization method for GMSK underwater acoustic communications in accordance with the present invention;
fig. 4a is a time domain waveform diagram of an underwater sound GMSK signal according to the method of the present invention;
fig. 4b is a time-frequency diagram of an underwater sound GMSK signal according to the method of the present invention;
FIG. 5 is a schematic representation of measured channel delay-normalized amplitude in an offshore underwater acoustic communications test in one embodiment of the method of the present invention;
FIG. 6a is a time domain waveform diagram of an exemplary marine underwater acoustic communication test after receiving a signal bandpass filter;
FIG. 6b is a time-frequency plot of the received signal after bandpass filtering in an example marine underwater acoustic communications experiment;
FIG. 7 is a schematic diagram of matching the time domain signal delay-normalized amplitude after filtering in an offshore underwater acoustic communications experiment in an embodiment of the method of the present invention;
fig. 8 is a schematic diagram of equalizer output soft information symbol number-normalized amplitude in an offshore underwater acoustic communications test in an embodiment of the method of the present invention.
Detailed Description
The invention will now be further described with reference to the accompanying drawings.
As shown in fig. 1, the invention provides a time-frequency joint equalization method for GMSK underwater acoustic communication, which combines a traditional frequency domain equalization technology based on Laurent decomposition and a self-adaptive decision feedback equalization technology, tracks the change of a channel by updating equalization coefficients symbol by symbol, reduces error propagation, greatly improves the transmission performance of GMSK signals under an underwater acoustic time-varying channel, and has lower complexity compared with the traditional time domain equalization technology.
The method comprises the following steps:
after converting the transmitting signal sequence and mapping the information to the symbol, modulating according to the GMSK signal modulation mode based on Laurent decomposition to obtain a GMSK complex baseband signal, and modulating the GMSK complex baseband signal onto a carrier wave to obtain a final transmitting signal s f (t) transmitting into the underwater acoustic channel;
specifically, the signal sequence { a } will be transmitted m Adding cyclic prefix and tail symbol, converting into bipolar non-return-to-zero code signal sequence { x }, and k }；
the bipolar non-return-to-zero code signal sequence { x }, is k As a signal block having a signal frame structure with a plurality of parameters connected in series; the plurality of parameters includes: the data block length N, the information sequence length L, the cyclic prefix length G and the tail symbol sequence length S; the length of the cyclic prefix sequence is required to be larger than the maximum time delay of the channel; tail symbols in the signal block need to ensure that the phase state of the information sequence returns to zero; the cyclic prefix is any sequence which is not related to the information sequence, and the phase state of the cyclic prefix needs to be satisfied from the zero state to the zero state;
and for the bipolar non-return-to-zero code signal sequence { x } k Information-symbol mapping to obtain GMSK complex baseband signal sequence { b }, and n }；
wherein ,bn For GMSK complex baseband signal sequence { b } n Elements in }; x is x k For bipolar non-return-to-zero code signal sequence { x } k Elements in }; j is an imaginary number;
according to the GMSK signal modulation mode based on Laurent decomposition, a phase shaping function is adopted to make the GMSK signal sequence { b } n Modulating to obtain GMSK complex baseband signal s (t),
and modulates it onto a carrier wave as a final transmitted signal s f (t) transmitting into the underwater acoustic channel;
s f (t)＝s(t)×exp(j×2π×fc×t)
wherein c (t-nT) is the partial impulse response, i.e. the function c (t 1 ) Shifting the nT length in the x-axis; j isImaginary number, fc, is the center frequency of the carrier;
let t 1 =t-nT; then c (t) 1 ) =c (t-nT); partial impulse response c (t 1 ) Can be represented by c 0 (t) wherein t is 1 ＝t-nT；c 0 (t) can be obtained from the integral function q (t) of the frequency shaping pulse g (t):
wherein the partial impulse response c (t 1 ) Can be represented by c 0 (t) the process is carried out,
where q (t) is the integral function of the frequency shaping pulse g (τ).
/>
Wherein T is symbol interval, B is bandwidth, L pulse memory length,as a complementary error function;
wherein ,or->Q(x 1 ) As a complementary error function;
the underwater acoustic channel receives the final transmitted signal s f (t) denoted as received signal r f (t) and for the received signal r f And (t) carrying out bandpass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and judgment processing to obtain judged symbols, and completing time-frequency joint equalization.
Specifically, the final transmitted signal s f (t) after passing through the underwater acoustic channel, obtaining a receiving signal r after the receiving end is subjected to band-pass filtering and time-frequency two-dimensional synchronization f (t); the band-pass filtering can be processed by a band-pass filter designed by the signal bandwidth, and the time-frequency two-dimensional synchronization can be processed by using a synchronization sequence.
The underwater acoustic channel receives the final transmitted signal s f (t) denoted as received signal r f (t)，
wherein ,channel response; z (t) is the reception noise;
and for the received signal r f (t) band-pass filtering and time-frequency two-dimensional synchronization by utilizing a synchronization sequence to obtain a synchronized signal; wherein, band-pass filtering and synchronization belong to a conventional pretreatment method in underwater acoustic communication;
the synchronized signal is matched and filtered by a low-pass filter and a coherent receiver to obtain a complex baseband signal r n ；
wherein ,rf (t)After passing through a low-pass filter, obtaining a signal r (t);
wherein ,sn A signal output by the matched filter; z n Noise output by the matched filter; η is used to denote the index of the integral; η = 0,1,2,..;
/>
using complex baseband signals r n Performing channel estimation on the cyclic prefix in the channel to obtain an estimated channel;
for complex baseband signal r with head cyclic prefix removed n After discrete Fourier transform, combining with the estimated channel to perform frequency domain equalization to obtain
wherein ,is a frequency domain expression of the signal after frequency domain equalization; r is R k Outputting a frequency domain representation of the signal for the matched filter; />Equalizing coefficients for a frequency domain equalizer; w (W) k For whitening noise filter, is noted +.>
For GMSK signals s (t), c (0, 0; l) may be approximated as {0.996,0.513,0.0567,0.000654, …,0.000654,0.0567,0.513}.
wherein ,
wherein ,Hk To estimate the frequency domain response of the channel;to estimate the frequency domain response H of the channel k Conjugation of (2); n (N) 0 Is a noise power spectrum;
re-pairingPerforming discrete Fourier transform to obtain soft information after frequency domain equalization>
Will complex baseband signal r n Input to adaptive decision feedback equalizer to obtain soft information after time domain equalization
wherein ,KF and KB The feedforward filter order and the feedback filter order, r, respectively n-j For the sequence { r } n Elements of }, feedforward filter input, θ n Estimating for phase offset; lambda (lambda) j Equalizer coefficients; v n-j For the sequence { v n Element, feedback filteringAn input; wherein, the two items on the right of the equal sign are a feedforward filter and a feedback filter respectively;
wherein ,K1 、K 2 Different phase-locked loop coefficients;estimating for the updated phase offset; phi m Is the calculated intermediate quantity;
wherein ,ρn Outputting a symbol for the feedforward filter; e, e n Estimating error for a priori; j is an imaginary number;
wherein ,en ＝v n -d n ；
wherein ,vn Is a feedback filter input; d, d n For soft information after equalization by time domainInformation obtained by hard decision; />
Wherein, the hard decision refers to whenWhen the value is greater than 0, then the +.>1 is shown in the specification; when->When the value is less than 0, then the +.>Is-1;
combining the obtained soft information after frequency domain equalizationSoft information after time domain equalization>Symbol estimation is performed based on maximum likelihood estimation, and estimated symbol +.>
wherein ,for estimating sign->Log-likelihood estimates of (2); />Is the symbol after the judgment; p () is a defined conditional probability distribution function;
f (kappa) is represented by
wherein ,bn Is made of decided symbolsMapping the obtained information; sigma is variance; kappa is-> and />Unified representation in function F (); n is the number of the symbol in the sequence, representing the nth estimated symbol;
using estimated symbolsDemapping and deciding to obtain decided symbol +.>Completing time-frequency joint equalization;
wherein ,y n estimated symbol for n->Demapped symbols; y is n-1 Estimated symbol +.1 for n-1->Demapped symbols.
Y is found using equations (20) and (21) as equalizers n Thereby obtaining x n Due to equalizer requirementThe detector and equalizer cannot be completely independent because the symbol-by-symbol iteration is performed, i.e., after one symbol is found, it is returned to the equalizer for equalization and the next symbol is found.
The method further comprises the steps of: an adaptive algorithm is adopted and based on the obtained symbol after judgmentUpdating equalizer coefficients to obtain updated equalizer coefficients lambda n ；
λ n ＝λ n-1 +ψ n e n-1 (22)
wherein ,ψn Is a gain vector; lambda (lambda) n-1 Equalizer coefficients that were last updated; e, e n-1 Is the last error;
in an embodiment of the present invention, the use of the method of the present invention for GMSK signal underwater information transmission is discussed. The bandwidth of a signal transmitting system of the underwater acoustic transducer matched with the power amplifier is 4-8kHz, the center frequency is 6kHz, the code element period is set to be 0.5ms when GMSK modulation is carried out, and original information 1038bits is transmitted.
In the method of the present invention, referring to fig. 2, the flow of the transmitting end first performs frame structure design on the transmitting signal, and adds a cyclic prefix with a length of 256bits, where the cyclic prefix is formed by special words. The complete signal frame structure of the final transmitted signal is shown in fig. 1, and has a plurality of parameters, namely, a data block length N, an information sequence length L, a cyclic prefix length G, and a tail symbol sequence length S. Mapping and modulating according to Laurent decomposition of GMSK signal to obtain GMSK complex baseband signal s (t), and modulating it onto carrier wave as final transmission signal s f (t) transmitting into the underwater acoustic channel.
As shown in the time domain waveform of the transmit signal of fig. 4a, 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. The GMSK shown in fig. 4b emits a signal in the frequency spectrum, and it can be seen that the signal has low out-of-band energy and good frequency utilization.
The channel structure of the underwater acoustic communication in the example is shown in fig. 5, and the maximum delay of the channel is 100ms, so that the underwater acoustic communication has a relatively complex multipath structure.
The flow of the method at the receiving end refers to fig. 2, after time-frequency two-dimensional synchronization is performed by using the synchronization sequence, band-pass filtering is performed on the received signal, and the time-frequency diagram after the filtering is shown in fig. 6a and 6 b. As can be seen from the time domain waveform, the channel produces more severe multipath interference to the signal. The time-frequency diagram of the received signal can be seen that the GMSK signal has small out-of-band radiation and high bandwidth efficiency.
The band-pass filtered signal is matched and filtered through a filter (8), and a complex baseband signal r is obtained n As shown in fig. 7. Fig. 7 shows a signal that has not undergone equalization processing, and the information contained in the diagram cannot be restored to the transmitted binary sequence.
Reference is made to fig. 3 for complex baseband signal r n And (5) performing equalization and demodulation. First estimating a channel using cyclic prefixAnd for complex baseband signal r with cyclic prefix removed n Performing frequency domain equalization to obtain frequency domain equalization output soft information b n The equalization coefficient is shown in formula (11). Will complex baseband signal r n Output adaptive decision feedback filter using cyclic prefix to calculate filter tap coefficients, i.e., λ in equation (14) j 。
When the (n=1) th symbol passes through the equalizer, the adaptive decision feedback filter output soft information d1 and the frequency domain equalization output soft information b1 are subjected to joint symbol estimation based on maximum likelihood estimation, and the estimated symbols are utilizedThe filter tap coefficients are updated and then computed iteratively symbol by symbol. Estimated symbol +.>As shown in fig. 8, the complete output information is obtained after demapping and deciding>And 1038bits in total, and the whole communication process is completed. Each dot in fig. 8 represents a symbol; above 0, a decision can be made as 1; below 0 can be decided as-1; this allows access to the transmitted binary sequence.
The invention also provides a time-frequency joint equalization system for GMSK underwater acoustic communication, which comprises: the mapping modulation module and the filtering equalization processing module;
the mapping modulation module is used for converting the transmitting signal sequence and mapping the information to the symbol, modulating according to the GMSK signal modulation mode based on Laurent decomposition to obtain a GMSK complex baseband signal, and modulating the GMSK complex baseband signal onto a carrier wave to serve as a final transmitting signal s f (t) transmitting into the underwater acoustic channel;
specifically, the mapping modulation module includes: a mapping unit and a modulation unit;
the mapping unit is used for mapping the transmission signal sequence { a } m Adding cyclic prefix and tail symbol, converting into bipolar non-return-to-zero code signal sequence { x }, and k }；
the bipolar non-return-to-zero code signal sequence { x }, is k As a signal block having a signal frame structure with a plurality of parameters connected in series; the plurality of parameters includes: the data block length N, the information sequence length L, the cyclic prefix length G and the tail symbol sequence length S; the length of the cyclic prefix sequence is required to be larger than the maximum time delay of the channel; tail symbols in the signal block need to ensure that the phase state of the information sequence returns to zero;
for the bipolar non-return-to-zero code signal sequence { x } k Information-symbol mapping to obtain GMSK complex baseband signal sequence { b }, and n }；
wherein ,bn Is GMSK complex baseband signal sequence { b } n Elements in }; x is x k For bipolar non-return-to-zero code signal sequence { x } k Elements in }; j is an imaginary number;
the modulation unit is used for modulating the GMSK signal based on Laurent decomposition by adopting a phase shaping function to the GMSK signal sequence { b } n Modulating to obtain GMSK complex baseband signal s (t),
modulating the signal on a carrier wave to serve as a final transmitting signal, and transmitting the final transmitting signal into an underwater sound channel;
s f (t)＝s(t)×exp(j×2π×fc×t)
wherein c (t-nT) is a partial impulse response, j is an imaginary number, and fc is a center frequency of the carrier;
let t1=t-nT; then c (t) 1 )＝c(t-nT)；
Wherein q (t) is the integral function of the frequency shaping pulse g (τ);
wherein, T is symbol interval, B is bandwidth, L pulse memory length;
wherein ,or->Q(x 1 ) As a complementary error function.
The filtering equalization processing module is used for receiving a final transmitting signal through the underwater acoustic channel, taking the final transmitting signal as a receiving signal, carrying out band-pass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and judgment processing on the receiving signal to obtain a judged symbol, and completing time-frequency joint equalization.
Specifically, the filter equalization processing module includes: a filtering unit and an equalization processing unit;
the filtering unit is used for receiving the final transmitting signal s by the underwater sound channel f (t) denoted as received signal r f (t)；
wherein ,channel response; z (t) is the reception noise;
for the received signal r f (t) band-pass filtering and time-frequency two-dimensional synchronization by utilizing a synchronization sequence to obtain a synchronized signal;
the synchronized signal is matched and filtered by a low-pass filter and a coherent receiver to obtain a complex baseband signal r n ；
wherein ,rf (t) after passing through a low pass filter, obtaining a signal r (t);
wherein ,sn A signal output by the matched filter; z n Noise output by the matched filter; η is used to denote the index of the integral; η = 0,1,2,..;
the equalization processing unit is used for utilizing the complex baseband signal r n Performing channel estimation on the cyclic prefix in the channel to obtain an estimated channel;
performing discrete Fourier transform on the complex baseband signal with the head cyclic prefix removed, and performing frequency domain equalization by combining with the estimated channel to obtain
wherein ,is a frequency domain expression of the signal after frequency domain equalization; r is R k Outputting a frequency domain representation of the signal for the matched filter; />Equalizing coefficients for a frequency domain equalizer; w (W) k For whitening noise filter, is noted +.>
wherein ,
wherein ,Hk To estimate the frequency domain response of the channel;to estimate the frequency domain response H of the channel k Conjugation of (2); n (N) 0 Is a noise power spectrum;
re-pairingPerforming discrete Fourier transform to obtain soft information after frequency domain equalization>
Will complex baseband signal r n Input to adaptive decision feedback equalizer to obtain soft information after time domain equalization
wherein ,KF and KB The feedforward filter order and the feedback filter order, r, respectively n-j For the sequence { r } n Elements of }, feedforward filter input, θ n Estimating for phase offset; lambda (lambda) j Equalizer coefficients; v n-j For the sequence { v n -an element, a feedback filter input;
wherein ,K1 、K 2 Different phase-locked loop coefficients;estimating for the updated phase offset; phi m Is the calculated intermediate quantity;
wherein ,ρn Outputting a symbol for the feedforward filter; e, e n Estimating error for a priori; j is an imaginary number;
wherein ,en ＝v n -d n ；
wherein ,vn Is a feedback filter input; d, d n For soft information after equalization by time domainInformation obtained by hard decision;
combining the obtained soft information after frequency domain equalizationSoft information after time domain equalization>Symbol estimation is performed based on maximum likelihood estimation, and estimated symbol +.>
wherein ,for estimating sign->Log-likelihood estimates of (2); />Is the symbol after the judgment; p () is a defined conditional probability distribution function;
f (kappa) is represented by
/>
wherein ,bn Is made of decided symbolsMapping the obtained information; sigma is variance; kappa is-> and />Unified representation in function F (); n is the number of the symbol in the sequence, representing the nth estimated symbol;
using estimated symbolsDemapping and judging to obtain judgmentThe symbol of->Completing time-frequency joint equalization;
wherein ,y n estimated symbol for n->Demapped symbols; y is n-1 Estimated symbol +.1 for n-1->Demapped symbols.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.
Claims (7)
1. A time-frequency joint equalization method for GMSK underwater acoustic communication, the method comprising:
after the transmitting signal sequence is converted and mapped with information and symbols, the transmitting signal sequence is modulated according to a GMSK signal modulation mode based on Laurent decomposition, a GMSK complex baseband signal is obtained, and the GMSK complex baseband signal is modulated on a carrier wave to be used as a final transmitting signal and transmitted into an underwater sound channel;
the underwater acoustic channel receives the final transmitting signal, takes the final transmitting signal as a receiving signal, and carries out band-pass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and judgment processing on the receiving signal to obtain a judged symbol, thereby completing time-frequency joint equalization.
2. The time-frequency joint equalization method of GMSK underwater acoustic communication according to claim 1, wherein after the transmitting signal sequence is converted and mapped to information-symbol, the transmitting signal sequence is modulated according to a GMSK signal modulation method based on Laurent decomposition, so as to obtain a GMSK complex baseband signal, and the GMSK complex baseband signal is modulated onto a carrier wave as a final transmitting signal, and is transmitted into an underwater acoustic channel; the specific process comprises the following steps:
will transmit a signal sequence { a } m Adding cyclic prefix and tail symbol, converting into bipolar non-return-to-zero code signal sequence { x }, and k }；
the bipolar non-return-to-zero code signal sequence { x }, is k As a signal block having a signal frame structure with a plurality of parameters connected in series; the plurality of parameters includes: the data block length N, the information sequence length L, the cyclic prefix length G and the tail symbol sequence length S; the length of the cyclic prefix sequence is required to be larger than the maximum time delay of the channel; tail symbols in the signal block need to ensure that the phase state of the information sequence returns to zero;
and for the bipolar non-return-to-zero code signal sequence { x } k Information-symbol mapping to obtain GMSK complex baseband signal sequence { b }, and n }；
wherein ,bn For GMSK complex baseband signal sequence { b } n Elements in }; x is x k For bipolar non-return-to-zero code signal sequence { x } k Elements in }; j is an imaginary number;
GMSK signal modulation mode based on Laurent decomposition adopts phase shaping function to make the GMSK signal sequence { b } n Modulating to obtain GMSK complex baseband signal s (t),
and modulates it onto a carrier wave as a final transmitted signal s f (t) transmitting into the underwater acoustic channel;
s f (t)＝s(t)×exp(j×2π×fc×t)
wherein c (t-nT) is a partial impulse response, j is an imaginary number, and fc is a center frequency of the carrier;
let t1=t-nT; then c (t) 1 )＝c(t-n T )；
Wherein q (t) is the integral function of the frequency shaping pulse g (τ);
wherein, T is symbol interval, B is bandwidth, L pulse memory length;
wherein ,or->Q(x 1 ) As a complementary error function.
3. The method for time-frequency joint equalization of GMSK underwater acoustic communication according to claim 1, wherein the final transmission signal is received by the underwater acoustic channel and is used as a reception signal, and the reception signal is subjected to bandpass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and decision processing to obtain a decided symbol, thereby completing time-frequency joint equalization; the specific process comprises the following steps:
the underwater acoustic channel receives the final transmitted signal s f (t) denoted as received signal r f (t)；
wherein ,channel response; z (t) is the reception noise;
for the received signal r f (t) band-pass filtering and time-frequency two-dimensional synchronization by utilizing a synchronization sequence to obtain a synchronized signal;
the synchronized signal is matched and filtered by a low-pass filter and a coherent receiver to obtain a complex baseband signal r n ；
wherein ,rf (t) after passing through a low pass filter, obtaining a signal r (t);
wherein ,sn A signal output by the matched filter; z n Noise output by the matched filter; η is used to denote the index of the integral; η = 0,1,2,..;
using complex baseband signals r n Performing channel estimation on the cyclic prefix in the channel to obtain an estimated channel;
performing discrete Fourier transform on the complex baseband signal with the head cyclic prefix removed, and performing frequency domain equalization by combining with the estimated channel to obtain
wherein ,is a frequency domain expression of the signal after frequency domain equalization; r is R k Outputting a frequency domain representation of the signal for the matched filter; />Equalizing coefficients for a frequency domain equalizer; w (W) k For whitening noise filter, is noted +.>
wherein ,
wherein ,Hk To estimate the frequency domain response of the channel;to estimate the frequency domain response H of the channel k Conjugation of (2); n (N) 0 Is a noise power spectrum;
re-pairingPerforming discrete Fourier transform to obtain soft information after frequency domain equalization>
Will complex baseband signal r n Input to adaptive decision feedback equalizer to obtain soft information after time domain equalization
wherein ,KF and KB The feedforward filter order and the feedback filter order, r, respectively n-j For the sequence { r } n Elements of }, feedforward filter input, θ n Estimating for phase offset; lambda (lambda) j Equalizer coefficients; v n-j For the sequence { v n -an element, a feedback filter input;
wherein ,K1 、K 2 Different phase-locked loop coefficients;estimating for the updated phase offset; phi m Is the calculated intermediate quantity;
wherein ,ρn Outputting a symbol for the feedforward filter; e, e n Estimating error for a priori; j is an imaginary number;
wherein ,en ＝v n -d n ；
wherein ,vn Is a feedback filter input; d, d n For soft information after equalization by time domainInformation obtained by hard decision;
combining the obtained soft information after frequency domain equalizationSoft information after time domain equalization>Symbol estimation is performed based on maximum likelihood estimation, and estimated symbol +.>
wherein ,for estimating sign->Log-likelihood estimates of (2); />Is the symbol after the judgment; p () is a defined conditional probability distribution function;
f (kappa) is represented by
wherein ,bn Is made of decided symbolsMapping the obtained information; sigma is variance; kappa is-> and />Unified representation in function F (); n is the number of the symbol in the sequence, representing the nth estimated symbol;
using estimated symbolsDemapping and deciding to obtain decided symbolNumber->Completing time-frequency joint equalization;
wherein ,y n estimated symbol for n->Demapped symbols; y is n-1 Estimated symbol +.1 for n-1->Demapped symbols.
4. The time-frequency joint equalization method for GMSK underwater acoustic communication of claim 1, further comprising: an adaptive algorithm is adopted and based on the obtained symbol after judgmentUpdating equalizer coefficients to obtain updated equalizer coefficients lambda n ；
λ n ＝λ n-1 +ψ n e n-1 (22)
wherein ,ψnIs that A gain vector; lambda (lambda) n-1 Equalizer coefficients that were last updated; e, e n-1 Is the last error;
5. a time-frequency joint equalization system for GMSK underwater acoustic communications, the system comprising:
the mapping modulation module is used for converting the transmitting signal sequence and mapping information and symbols, modulating according to a GMSK signal modulation mode based on Laurent decomposition to obtain a GMSK complex baseband signal, modulating the GMSK complex baseband signal onto a carrier wave to serve as a final transmitting signal, and transmitting the final transmitting signal into an underwater sound channel; and
the filtering equalization processing module is used for receiving the final transmitting signal by the underwater acoustic channel, taking the final transmitting signal as a receiving signal, and carrying out band-pass filtering, time-frequency two-dimensional synchronization, matched filtering, time-frequency equalization, demapping and judgment processing on the receiving signal to obtain a judged symbol, thereby completing time-frequency joint equalization.
6. The time-frequency joint equalization system of GMSK underwater acoustic communication of claim 1 wherein the map modulation module comprises: a mapping unit and a modulation unit;
the mapping unit is used for mapping the transmission signal sequence { a } m Adding cyclic prefix and tail symbol, converting into bipolar non-return-to-zero code signal sequence { x }, and k }；
wherein, bipolar non-return-to-zero code signal sequence { x }, is provided k As a signal block having a signal frame structure with a plurality of parameters connected in series; the plurality of parameters includes: the data block length N, the information sequence length L, the cyclic prefix length G and the tail symbol sequence length S; the length of the cyclic prefix sequence is required to be larger than the maximum time delay of the channel; tail symbols in the signal block need to ensure that the phase state of the information sequence returns to zero;
and for the bipolar non-return-to-zero code signal sequence { x } k Information-symbol mapping to obtain GMSK complex baseband signal sequence { b }, and n }；
wherein ,bn For GMSK complex baseband signal sequence { b } n Elements in }; x is x k For bipolar non-return-to-zero code signal sequence { x } k In }An element; j is an imaginary number;
the modulation unit is used for modulating the GMSK signal based on Laurent decomposition by adopting a phase shaping function to the GMSK signal sequence { b } n Modulated to obtain GMSK complex baseband signal s (t) and modulated onto carrier wave as final transmission signal s f (t) transmitting into the underwater acoustic channel;
and modulates it onto a carrier wave as a final transmitted signal s f (t) transmitting into the underwater acoustic channel;
s f (t)＝s(t)×exp(j×2π×fc×t)
wherein c (t-nT) is a partial impulse response, j is an imaginary number, and fc is a center frequency of the carrier;
let t 1 =t-nT; then c (t) 1 )＝c(t-nT)；
Wherein q (t) is the integral function of the frequency shaping pulse g (τ);
wherein, T is symbol interval, B is bandwidth, L pulse memory length;
wherein ,or->Q(x 1 ) As a complementary error function.
7. The time-frequency joint equalization system of GMSK underwater acoustic communication of claim 1 wherein the filter equalization processing module comprises: a filtering unit and an equalization processing unit;
the filtering unit is used for receiving the final transmitting signal s by the underwater sound channel f (t) denoted as received signal r f (t)；
wherein ,channel response; z (t) is the reception noise;
for the received signal r f (t) band-pass filtering and time-frequency two-dimensional synchronization by utilizing a synchronization sequence to obtain a synchronized signal;
the synchronized signal is matched and filtered by a low-pass filter and a coherent receiver to obtain a complex baseband signal r n ；
wherein ,rf (t) after passing through a low pass filter, obtaining a signal r (t);
wherein ,sn A signal output by the matched filter; z n Noise output by the matched filter; η is used to denote the index of the integral; η = 0,1,2,..;
the equalization processing unit is used for utilizing the complex baseband signal r n Performing channel estimation on the cyclic prefix in the channel to obtain an estimated channel;
performing discrete Fourier transform on the complex baseband signal with the head cyclic prefix removed, and performing frequency domain equalization by combining with the estimated channel to obtain
wherein ,is a frequency domain expression of the signal after frequency domain equalization; r is R k Outputting a frequency domain representation of the signal for the matched filter; />Equalizing coefficients for a frequency domain equalizer; w (W) k For whitening noise filter, is noted +.>
wherein ,
wherein ,Hk To estimate the frequency domain response of the channel;to estimate the frequency domain response H of the channel k Conjugation of (2); n (N) 0 Is a noise power spectrum;
re-pairingPerforming discrete Fourier transform to obtain soft information after frequency domain equalization>
Will complex baseband signal r n Input to adaptive decision feedback equalizer to obtain soft information after time domain equalization
wherein ,KF and KB The feedforward filter order and the feedback filter order, r, respectively n-j For the sequence { r } n Elements of }, feedforward filter input, θ n Estimating for phase offset; lambda (lambda) j Equalizer coefficients; v n-j For the sequence { v n -an element, a feedback filter input;
wherein ,K1 、K 2 Different phase-locked loop coefficients;estimating for the updated phase offset; phi m Is the calculated intermediate quantity;
wherein ,ρn Outputting a symbol for the feedforward filter; e, e n Estimating error for a priori; j is an imaginary number;
wherein ,en ＝v n -d n ；
wherein ,vn Is a feedback filter input; d, d n For soft information after equalization by time domainInformation obtained by hard decision;
combining the obtained soft information after frequency domain equalizationSoft information after time domain equalization>Symbol based on maximum likelihood estimationEstimating to obtain estimated symbol->
wherein ,for estimating sign->Log-likelihood estimates of (2); />Is the symbol after the judgment; p () is a defined conditional probability distribution function;
f (kappa) is represented by
wherein ,bn Is made of decided symbolsMapping the obtained information; sigma is variance; kappa is-> and />Unified representation in function F (); n is the number of the symbol in the sequence, representing the nth estimated symbol;
using estimated symbolsDemapping and deciding to obtain decided symbol +.>Completing time-frequency joint equalization;
wherein ,y n estimated symbol for n->Demapped symbols; y is n-1 Estimated symbol +.1 for n-1->Demapped symbols.
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