CN109802911A - A kind of Fast Channel estimation and signal synchronizing method suitable for underwater acoustic modem - Google Patents
A kind of Fast Channel estimation and signal synchronizing method suitable for underwater acoustic modem Download PDFInfo
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Abstract
The invention discloses a kind of Fast Channel estimation suitable for underwater acoustic modem and signal synchronizing methods, are suitable for underwater acoustic modem real-time online and demodulate field.The present invention passes through design underwater sound communication modem physical layer data chain blocks pilot signal, utilize Fast Fourier Transform (FFT) and subspace projection, realize the quick estimation and online decoded process of underwater acoustic channel, at the same time, utilize the period autocorrelation performance of pseudo-random sequence, it realizes quick decorrelation process, realizes that physical layer signal is synchronous.Relative to the estimation of general time domain underwater acoustic channel and signal synchronizing method, the algorithm advantage is, can fast implementing with the systems such as digital signal processor (DSP) and field programmable gate array (FPGA) reduce computational complexity while guaranteeing channel estimation.It is particularly suitable for sparse underwater acoustic channel estimation.
Description
Technical field
The present invention relates to a kind of Fast Channel estimation suitable for underwater acoustic modem and signal synchronizing methods, are suitable for the underwater sound
The Fast Channel estimation of the communications field is synchronous with the signal of physical layer data block.
Technical background
Real-time water sound communication model machine or underwater acoustic modem high speed low error rate performance relatively difficult to achieve, reason are water
Acoustic channel has the double extended attributes of dynamic, and existing channel estimation method is typically derived from wireless channel.It is related to reverse temperature intensity,
Classical channel estimation methods include least-squares estimation, Minimum Mean Squared Error estimation, compressed sensing estimation etc..But unlike that
Wireless channel has Rayleigh fading characteristic and compared with short channel shock response.Underwater acoustic channel has long delay characteristics, reverse temperature intensity
Computational complexity it is very high, be not able to satisfy the demand of real-time water sound communication system.Based on the considerations of system real time and reliability.
The method synchronous with signal is estimated the invention proposes a kind of Fast Channel.
Summary of the invention
The present invention relates to a kind of quick underwater acoustic channel estimation and signal synchronizing methods, mainly include two aspect summary of the invention:
(1) pass through the pilot signal of design physical layer data block: two identical pseudo-random sequences with period autocorrelation performance are pressed
It is arranged successively according to time sequencing, signal matrix can be become to complete cyclic shift matrices, be suitble to Fast Fourier Transform (FFT), pass through Fu
In leaf transformation, realize channel according to a preliminary estimate, at the same time, pass through the perfect period autocorrelation performance of pseudo-random sequence, Neng Goushi
The synchronization of existing signal;(2) update is iterated to channel according to a preliminary estimate by iterative algorithm and space projection algorithm, with tradition
Method compares, and improves estimated accuracy, reduces computational complexity.
The present invention is achieved through the following technical solutions:
A kind of Fast Channel suitable for underwater acoustic modem is estimated with signal synchronizing method
1) it is designed for underwater acoustic modem physical layer data chain blocks frequency pilot sign;Pilot signal is identical using two groups
Pseudo-random sequence;
2) cyclic shift related operation is carried out according to the locally known pilot signal of step 1) and reception signal, carries out signal
Precise synchronization;
3) step 2) is obtained into the signal of precise synchronization, extracts pilot portion, carried out with local pilot frequency pseudo-random signal fast
Fast Fourier transformation and inverse Fourier transform obtain preliminary channel estimation results;
4) subspace projection for being iterated the preliminary channel estimated result that step 3) obtains carries out fine channel and estimates
Meter;The algorithm iteration based on Fast Fourier Transform (FFT) is carried out, after update reaches convergence, stops iteration;
5) it is utilized the underwater acoustic channel estimated for decoding online according to step 4), Expectation equilibrium decoding effect is such as not achieved
Balanced device output result is re-started channel estimation by fruit;And step 3) and step 5) are repeated until reaching Expectation equilibrium decoding
Effect.
Preferably, the step 1), specifically:
Step 1.1: the frequency pilot sign using two groups of identical pseudo-random sequences as physical layer data chain blocks sends letter
Breath symbol sebolic addressing is expressed as formula (1):
In formula (1), c indicates pseudo-random sequence vector, skIndicate that k-th of transmission set of symbols vector, T are transposition symbol;
Step 1.2: pseudo-random sequence has cyclic shift characteristic, and property can be expressed as formula (2):
In formula (2), M indicates that the order of pseudo-random sequence, m indicate the subscript of element in pseudo-random sequence, also illustrate that signal
Time delay, T are the matrix operators with cyclic shift property, can be expressed as formula (3),
Matrix operator in formula (3) has property below, TjC operation can be by j code of pseudo-random sequence cyclic shift
Leaf length.
Preferably, the step 2), specifically:
Step 2.1: carrying out cyclic shift related operation with locally known pilot signal and reception signal sequence y, wherein this
Ground known pilot signal, that is, pseudo-random sequence;Input/output model can be expressed as formula (4):
V (j)=[Tjc]Ty (4)
In formula (4), v (j) is that the matching of receiving end circulative shift operation exports;
Step 2.2: the peak value after autocorrelation matching output is found, if with two identical pseudo-random sequences, it can
There are 2 peak-to-peak values, at this time by sorting operation, can determine the position of two peak-to-peak values, is synchronized to realize and receive signal.
Preferably, the step 3), specifically:
Step 3.1: using the frequency pilot sign with cyclic shift characteristic, receiving signal and emit the input and output mould of signal
Type can be expressed as
In formula (5), * indicates conjugate operation,For maximum Doppler component corresponding to every independent pathway of channel;z
[i] is discrete Gaussian noise;Indicated using matrix, using the cyclic identities of two groups of same pilot symbols, formula (5) it is discrete
Convolution can be expressed as Matrix Multiplication French (6)
Step 3.2: eigen value decomposition, the form of available Fast Fourier Transform (FFT), such as formula are carried out to circular matrix X
(7)
X=FHΛXF (7)
In formula (7), ()HIndicating conjugate transposition operation, F is the fourier matrix of M × M rank,ΛXIt is diagonal matrix, the elements in a main diagonal is the Fourier transformation shape for sending information symbol sequence x
Formula Fx;
Step 3.3: Fast Fourier Transform (FFT) is done to symbolic vector y is received in formula (6), that is, is had:
In formula (8), fast Fourier matrix is multiplied for unit battle array with its own conjugate transposition: FFH=I;Channel h can lead to
Fast Fourier Transform (FFT) estimation is crossed, such as formula (9)
Formula (9) illustrates, can be become by doing Fast Fourier Transform (FFT) respectively to designed frequency pilot sign and reception signal
Frequency domain characterization is changed to, then frequency domain characterization vector inner element is done a little except operation, then the frequency-region signal put after removing is carried out inverse
Fourier transformation, the channel estimated, formula (9) also may indicate that are as follows:
In formula (10) ,/representative element point division operation.
Preferably, the step 4), specifically:
Step 4.1: the channel estimation obtained using step 3) Fourier transformationAs initial value, the steepest of channel is constructed
Gradient decreasing function, such as formula (11)
In formula (11), | | | |1For the l of vector1Norm, sign are sign function, it may be assumed that the element in h greater than 0 is set as 1, small
Element in 0 is set as -1, and iteration updates steepest gradient direction, such as formula (12)
In formula (12), μkFor step factor, region of search can be passed through?
It arrives;
Step 4.2: being obtained by formula (12)It also include due in quick Fu except true channel region is contained
Leaf transformation bring redundant area,Other spaces are projected to, eliminate redundant area, and noise gate is set, using two
Re-projection, wherein the first re-projection, such as formula (13)
Formula (13) can ensure that channel information constrains in the region that energy is mainly distributed;Wherein P1For the sky of channel main energetic
Between projection matrix, Elower, EupperThe respectively lower limit and the upper limit in preset channel energy section.
Second re-projection establishes objective function and constraint using convex optimum theory, and projector space is expressed as formula (14)
Wherein P2, ε is respectively the least commitment of subspace projection matrix and majorized function, by introducing Lagrangian
λ solves the restricted problem of formula (14), such as formula (15)
Formula (15) can ensure that the channel that iteration updates controls in restriction range, improve estimated accuracy;
Step 4.3: whenOr the maximum number of iterations of setting is reached, it updates and stops;WhenOr the maximum number of iterations without reaching setting, it is recoverable (12), continue to update iteration, wherein δ
To preset residual error thresholding.
Preferably, the formula (15) can also be realized with Fast Fourier Transform (FFT), such as formula (16):
In formula (16), FFT, IFFT respectively represent Fast Fourier Transform (FFT) and inverse fast fourier transform .* representation vector
Inner element is corresponding to be multiplied.
Compared with prior art, of the invention to there is gain effect to be:
(1) it by tactic same pseudo-random sequence, realizes the perfect period auto-correlation of signal, it is same to improve signal
The precision of step.
(2) cyclic shift matrices for utilizing periodic signal, realize Fast Fourier Transform (FFT), reduce the complexity of channel estimation
Degree.
(3) channel estimated by Fourier transformation promotes channel using space projection iterative algorithm as original state
While estimated accuracy, compared with traditional reverse temperature intensity, computational complexity is reduced.
(4) it can be applied to the underwater sound communications real-time system such as digital signal processor and field programmable gate array.
Detailed description of the invention
Fig. 1 is quick underwater acoustic channel estimation and signal synchronizing method flow chart.
Fig. 2 is the pseudo-random sequence synchronous effect figure with period autocorrelation performance.
Fig. 3 is that the channel estimating performance of space projection algorithm and matched filtering algorithm based on Fast Fourier Transform (FFT) compares
Figure.
Specific embodiment
The present invention is described in detail with reference to the accompanying drawing, but implementation and protection scope of the invention is without being limited thereto.
As shown in Figure 1, a kind of quick underwater acoustic channel estimation and signal synchronizing method supplement are as follows:
Step 1:
Step 1.1: the frequency pilot sign using two groups of identical pseudo-random sequences as physical layer data chain blocks sends letter
Breath symbol sebolic addressing is expressed as formula (1):
Step 1.2: there is cyclic shift characteristic using pseudo-random sequence, property can be expressed as formula (2):
In formula (2), M indicates that the order of pseudo-random sequence, m indicate the subscript of element in pseudo-random sequence, also illustrate that signal
Time delay.T is the matrix operator with cyclic shift property, can be expressed as formula (3),
Step 2:
Step 2.1: with locally known pilot signal, i.e. pseudo-random sequence carries out cyclic shift phase with signal sequence y is received
Operation is closed, input/output model can be expressed as being represented by formula (4):
V (j)=[Tjc]Ty (4)
In formula (4), v (j) is that the matching of receiving end circulative shift operation exports.
Step 2.2: the peak value after autocorrelation matching output is found, if with two identical pseudo-random sequences, it can
There are 2 peak-to-peak values, at this time by sorting operation, can determine the position of two peak-to-peak values, is synchronized to realize and receive signal.
As a result as shown in Figure 2.
Step 3:
Step 3.1: using the frequency pilot sign of cyclic shift characteristic, the input/output model for receiving signal and transmitting signal can
To be expressed as
In formula (5), * indicates conjugate operation,For maximum Doppler component corresponding to every independent pathway of channel.
It is indicated using matrix, using the cyclic identities of two groups of same pilot symbols, the discrete convolution of formula (5) can be expressed as square
Battle array multiplication formula (6)
Step 3.2: eigen value decomposition, the form of available Fast Fourier Transform (FFT), such as formula are carried out to circular matrix X
(7)
X=FHΛXF (7)
In formula (7), ()HIndicating conjugate transposition operation, F is the fourier matrix of M × M rank,ΛXIt is diagonal matrix, the elements in a main diagonal is the Fourier transformation form for sending symbolic vector x
Fx。
Step 3.3: Fast Fourier Transform (FFT) is done to symbolic vector y is received in formula (6), that is, is had:
In formula (8), fast Fourier matrix is multiplied for unit battle array with its own conjugate transposition: FFH=I.Channel h can lead to
Fast Fourier Transform (FFT) estimation is crossed, such as formula (9)
Formula (9) illustrates, can be become by doing Fast Fourier Transform (FFT) respectively to designed frequency pilot sign and reception signal
Frequency domain characterization is changed to, then frequency domain characterization vector inner element is done a little except operation, then the frequency-region signal put after removing is carried out inverse
Fourier transformation, the channel estimated, formula (9) also may indicate that are as follows:
In formula (10) ,/representative element point division operation.FFT, IFFT respectively represent Fast Fourier Transform (FFT) and against quickly
Fourier transformation.
Step 4:
Step 4.1: the channel estimation obtained using Fourier transformationAs initial value, under the steepest gradient for constructing channel
Decreasing function, such as formula (11)
In formula (11), | | | |1For the l of vector1Norm, sign are sign function, it may be assumed that the element in h greater than 0 is set as 1, small
Element in 0 is set as -1, and iteration updates steepest gradient direction, such as formula (12)
In formula (12), μkFor step factor, region of search can be passed through?
It arrives.
Step 4.2:Other spaces are projected to, eliminate redundant area, also, noise gate should be set, this patent
Using two re-projections, the first re-projection, such as formula (13)
Second re-projection establishes objective function and constraint using convex optimum theory, and projector space is expressed as
By introducing Lagrangian λ, the restricted problem of formula (14) is solved, such as formula (15)
Formula (15) can ensure that the channel that iteration updates controls in restriction range, improve estimated accuracy.This method can be with
It is realized with faster Fast Fourier Transform (FFT), such as formula (16)
In formula (16), FFT, IFFT respectively represent Fast Fourier Transform (FFT) and inverse fast fourier transform .* representation vector
Inner element is corresponding to be multiplied.
Step 4.3: whenOr the maximum number of iterations of setting is reached, it updates and stops;WhenOr to without up to setting maximum number of iterations, it is recoverable (12), continue update iteration.
Step 5:
Using the underwater acoustic channel estimated for decoding online, if Expectation equilibrium decoding effect is not achieved in effect, by balanced device
Output result re-starts channel estimation.Repeat step 3 and step 4.Fig. 3 is the performance of proposed method and traditional matched filtering
Comparison.Under sparse underwater acoustic channel, the subspace projection algorithm based on Fast Fourier Transform (FFT) can be mentioned than matched filtering algorithm
For higher time sense, more accurate channel estimation is obtained.
Claims (6)
1. a kind of Fast Channel estimation and signal synchronizing method suitable for underwater acoustic modem, it is characterised in that include the following:
1) it is designed for underwater acoustic modem physical layer data chain blocks frequency pilot sign;Pilot signal uses two groups of identical puppets
Random sequence;
2) cyclic shift related operation is carried out according to the locally known pilot signal of step 1) and reception signal, it is accurate carries out signal
It is synchronous;
3) step 2) is obtained into the signal of precise synchronization, extracts pilot portion, carry out quick Fu with local pilot frequency pseudo-random signal
In leaf transformation and inverse Fourier transform, obtain preliminary channel estimation results;
4) subspace projection for being iterated the preliminary channel estimated result that step 3) obtains carries out fine channel estimation;
The algorithm iteration based on Fast Fourier Transform (FFT) is carried out, after update reaches convergence, stops iteration;
5) it is utilized the underwater acoustic channel estimated for decoding online according to step 4), Expectation equilibrium decoding effect is such as not achieved, it will
Balanced device output result re-starts channel estimation;And step 3) and step 5) are repeated until reaching Expectation equilibrium decoding effect.
2. the Fast Channel estimation suitable for underwater acoustic modem physical layer and signal synchronizing method according to claim 1, special
Sign is the step 1), specifically:
Step 1.1: the frequency pilot sign using two groups of identical pseudo-random sequences as physical layer data chain blocks sends information symbol
Number sequence is expressed as formula (1):
In formula (1), c indicates pseudo-random sequence vector, skIndicate that k-th of transmission set of symbols vector, T are transposition symbol;
Step 1.2: pseudo-random sequence has cyclic shift characteristic, and property can be expressed as formula (2):
In formula (2), M indicates that the order of pseudo-random sequence, m indicate the subscript of element in pseudo-random sequence, also illustrate that signal time delay,
T is the matrix operator with cyclic shift property, can be expressed as formula (3),
Matrix operator in formula (3) has property below, TjC operation can be long by j chip of pseudo-random sequence cyclic shift
Degree.
3. the Fast Channel estimation suitable for underwater acoustic modem physical layer and signal synchronizing method according to claim 2, special
Sign is the step 2), specifically:
Step 2.1: carrying out cyclic shift related operation with locally known pilot signal and reception signal sequence y, wherein locally
Know pilot signal i.e. pseudo-random sequence;Input/output model can be expressed as formula (4):
V (j)=[Tjc]Ty (4)
In formula (4), v (j) is that the matching of receiving end circulative shift operation exports;
Step 2.2: the peak value after autocorrelation matching output is found, if will appear 2 with two identical pseudo-random sequences
A peak-to-peak value can determine the position of two peak-to-peak values at this time by sorting operation, synchronize to realize and receive signal.
4. the Fast Channel estimation suitable for underwater acoustic modem physical layer and signal synchronizing method according to claim 1, special
Sign is the step 3), specifically:
Step 3.1: using the frequency pilot sign with cyclic shift characteristic, the input/output model for receiving signal and transmitting signal can
To be expressed as
In formula (5), * indicates conjugate operation,For maximum Doppler component corresponding to every independent pathway of channel;z[i]
For discrete Gaussian noise;It is indicated using matrix, using the cyclic identities of two groups of same pilot symbols, the discrete volume of formula (5)
Product, can be expressed as Matrix Multiplication French (6)
Step 3.2: eigen value decomposition, the form of available Fast Fourier Transform (FFT), such as formula (7) are carried out to circular matrix X
X=FHΛXF (7)
In formula (7), ()HIndicating conjugate transposition operation, F is the fourier matrix of M × M rank,ΛX
It is diagonal matrix, the elements in a main diagonal is the Fourier transformation form Fx for sending information symbol sequence x;
Step 3.3: Fast Fourier Transform (FFT) is done to symbolic vector y is received in formula (6), that is, is had:
In formula (8), fast Fourier matrix is multiplied for unit battle array with its own conjugate transposition: FFH=I;Channel h can be by fast
Fast Fourier transformation estimation, such as formula (9)
Formula (9) illustrates, can be transformed to by doing Fast Fourier Transform (FFT) respectively to designed frequency pilot sign and reception signal
Frequency domain characterization, then frequency domain characterization vector inner element is done a little except operation, then the frequency-region signal put after removing is carried out in inverse Fu
Leaf transformation, the channel estimated, formula (9) also may indicate that are as follows:
In formula (10) ,/representative element point division operation.
5. the Fast Channel estimation suitable for underwater acoustic modem physical layer and signal synchronizing method according to claim 1, special
Sign is the step 4), specifically:
Step 4.1: the channel estimation obtained using step 3) Fourier transformationAs initial value, the steepest gradient of channel is constructed
Decreasing function, such as formula (11)
In formula (11), | | | |1For the l of vector1Norm, sign are sign function, it may be assumed that the element in h greater than 0 is set as 1, less than 0
Element be set as -1, iteration updates steepest gradient direction, such as formula (12)
In formula (12), μkFor step factor, region of search can be passed throughIt obtains;
Step 4.2: being obtained by formula (12)It also include since fast Fourier becomes except true channel region is contained
Bring redundant area is changed,Other spaces are projected to, eliminate redundant area, and noise gate is set, using double throwing
Shadow, wherein the first re-projection, such as formula (13)
Formula (13) can ensure that channel information constrains in the region that energy is mainly distributed;Wherein P1It is thrown for the space of channel main energetic
Shadow matrix, Elower, EupperThe respectively lower limit and the upper limit in preset channel energy section.
Second re-projection establishes objective function and constraint using convex optimum theory, and projector space is expressed as formula (14)
Wherein P2, ε is respectively the least commitment of subspace projection matrix and majorized function, by introducing Lagrangian λ, solution
The restricted problem of formula (14), such as formula (15)
Formula (15) can ensure that the channel that iteration updates controls in restriction range, improve estimated accuracy;
Step 4.3: whenOr the maximum number of iterations of setting is reached, it updates and stops;WhenOr the maximum number of iterations without reaching setting, it is recoverable (12), continue to update iteration, wherein δ
To preset residual error thresholding.
6. the Fast Channel estimation suitable for underwater acoustic modem physical layer and signal synchronizing method according to claim 5, special
Sign is that the formula (15) can also be realized with Fast Fourier Transform (FFT), such as formula (16):
In formula (16), FFT, IFFT respectively represent Fast Fourier Transform (FFT) and inverse fast fourier transform, inside .* representation vector
Element is corresponding to be multiplied.
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