CN108833312B - Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain - Google Patents

Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain Download PDF

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CN108833312B
CN108833312B CN201810586326.5A CN201810586326A CN108833312B CN 108833312 B CN108833312 B CN 108833312B CN 201810586326 A CN201810586326 A CN 201810586326A CN 108833312 B CN108833312 B CN 108833312B
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伍飞云
杨坤德
田天
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Northwestern Polytechnical University
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Abstract

The invention relates to a time-varying sparse underwater acoustic channel estimation method based on a time-varying Doppler domain. And adopting a block-by-block training mode, combining with a Schmidt orthogonal matching pursuit algorithm to iterate and optimize to obtain a sparse underwater acoustic channel impulse response function of a delay Doppler domain, and constructing a minimum mean square error equalizer based on channel information at a receiving end for recovering the transmitted signal according to the estimated underwater acoustic channel information of the delay Doppler domain. The method is suitable for time-varying underwater acoustic channel estimation and underwater acoustic communication. The invention has the beneficial effects that: the method selects the matching atoms based on Schmidt orthogonalization, effectively avoids redundant calculation, and enables the time delay Doppler underwater acoustic channel estimation result generated by the method to have higher precision.

Description

Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain
Technical Field
The invention belongs to the fields of underwater acoustic communication, underwater acoustic signal processing and the like, and relates to a time-varying sparse underwater acoustic channel estimation method based on a delay-Doppler domain.
Background
The problems of underwater acoustic channel estimation, underwater acoustic communication and the like can be summarized into an estimation optimization problem of an impulse response function, and the sparse expression estimation is carried out on the time-varying underwater acoustic channel based on a training sequence and a received signal. Currently, the estimation method for the underwater acoustic channel includes a finite impulse response framework and a block-by-block estimation framework of a delay-doppler domain. For the details of the finite impulse response framework, see "New spark adaptive basic on the natural gradient and the L0-norm", published in 2013 at the No. 38 of IEEE Journal of scientific Engineering, with a start page 323. The block-by-block Estimation framework of the delay-Doppler domain is disclosed in the "Estimation of delay time-varying spark channels" published in 2007 at the 32 nd stage of IEEE Journal of scientific Engineering, and the starting page number is 927.
Due to the multipath expansion and time-varying characteristics of the underwater acoustic channel, the impulse response function of the underwater acoustic channel is extremely difficult to estimate, and therefore, the algorithm effect under the finite impulse response framework is poor. The time-varying characteristics and multipath spreading of the underwater acoustic channel are taken into account and can be characterized by the delay-doppler domain of the underwater acoustic channel. The invention is based on the model and estimates the time-varying underwater acoustic channel. However, the parameters to be estimated are many, the matrix calculation amount is large, and fortunately, the compressed sensing method can provide an effective estimation strategy. However, the underwater acoustic channel impulse response function of the actual offshore data is not a strict sparse signal, so that the current compressed sensing algorithm is difficult to directly apply. The invention provides that on the basis of a matching tracking algorithm, Schmidt orthogonalization processing is carried out on the atoms selected and updated so as to avoid redundant iteration of the atoms in the selection process. After underwater acoustic channel estimation of a delay Doppler domain is obtained, a minimum mean square error local balancer of a two-dimensional domain is established, and therefore signal sending information is recovered.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a time-varying sparse underwater acoustic channel estimation method based on a delay Doppler domain, which is used for effectively estimating the time-varying multipath underwater acoustic channel impulse response function.
Technical scheme
A time-varying sparse underwater acoustic channel estimation method based on a delay-Doppler domain is characterized by comprising the following steps:
step 1, establishing a delay Doppler domain model:
1. let the parameters Δ t, Δ τ and Δ f be the sampling intervals of observation time, time delay and doppler shift, respectively, and the discretized observation time is denoted as tnN, N is the maximum sampling point number of observation time, and the discretized time delay is expressed as:
τm＝τ0+(m-1)Δτ,m＝1,...,M (1)
wherein the parameter τ0Is the reference delay, M is the maximum delay sampling dimension, called the underwater acoustic channel order；
2. Discretized time-varying channel response is h [ t ]n,τm]The sampled doppler is defined as:
fl＝f0+(l-1)Δf,l＝1,...,L (2)
wherein f is0Is the smallest doppler frequency shift value, L is the largest doppler sampling dimension, therefore, the two-dimensional delay-doppler dimension size is denoted as LM;
is provided with
Figure GDA0002731820570000021
Wherein f issIf the signal frequency sampling rate is higher than the predetermined sampling rate, the discretized input-output relation is as follows:
Figure GDA0002731820570000022
w is noise;
definition u ═ u1,1,…,u1,M,u2,1,…,u2,M,…,uL,1,…,uL,M]TAnd the dimension is (L · M) × 1, the input-output relationship of the delay-doppler domain is expressed as:
Figure GDA0002731820570000023
wherein
Figure GDA0002731820570000024
The dimension of (a) is L x 1,
Figure GDA0002731820570000025
denotes the Kronecker product, x [ t ]n]＝[xn+M-1,…,xn+1,xn]THas a dimension of M × 1;
definition y ═ { y [ t ]1],y[t2],…,y[tN]}T,
Figure GDA0002731820570000031
A＝{a[t1],a[t2],…,a[tN]}HThe following input-output relationships are obtained:
y＝Au+w (5)
wherein y and w have dimensions of N × 1, and A and u have dimensions of N × (L · M), (L · M) × 1, respectively;
the specific method for estimating the channel impulse response function u comprises the following steps:
input parameter information setting: matrix A and received signal y, setting algorithm termination conditions
Figure GDA0002731820570000032
Setting output parameter information: a channel impulse response function estimated value u;
initializing: the initial estimated value is a zero vector u{0}When the ratio is 0: initial residual r{0}Y; the initial iteration number i is 0; the initial channel impulse response function supporting set is an empty set
Figure GDA0002731820570000033
Judging whether the algorithm termination condition is satisfied, namely whether | | | < r | | |thIf so, stopping iteration, otherwise, iterating according to the following iteration formula:
Figure GDA0002731820570000034
P{1}＝v{1}(v{1}Tv{1})-1v{1}T (7)
r{1}＝r{0}-P{1}y (8)
for the ith selected atom
Figure GDA0002731820570000035
Should be orthogonal to the previous choice, so the i-th orthogonal vector is:
Figure GDA0002731820570000036
the projection matrix obtained for the ith time is:
P{i}＝v{i}(v{i}Tv{i})-1v{i}T (10)
the i-th residual update is:
r{i}＝r{i-1}-P{i}y (11)
updating a support set:
S{i}＝S{i-1}∪s{i} (12)
the pseudo-inverse operation is then performed:
Figure GDA0002731820570000041
the estimated underwater acoustic channel impulse response function is:
Figure GDA0002731820570000042
step 2: the estimation value of the MMSE equalizer output to the transmission signal is expressed as follows:
Figure GDA0002731820570000043
wherein I represents an identity matrix of the cell,
Figure GDA0002731820570000044
a parameter representing noise energy, y represents a signal vector at the receiving end, and
Figure GDA0002731820570000045
represents an estimated value of the equalizer on the signal of the transmitting end, and
Figure GDA0002731820570000046
wherein
Figure GDA0002731820570000047
Is an N by N diagonal matrix, and the matrix UlDimension of NxNsFrom a vector ul＝[U(0,l),...,U(M-1,l)]TIs constructed in a specific arrangement mode that:
Figure GDA0002731820570000048
advantageous effects
The invention provides a time-varying sparse underwater acoustic channel estimation method based on a time-varying Doppler domain. And adopting a block-by-block training mode, combining with a Schmidt orthogonal matching pursuit algorithm to iterate and optimize to obtain a sparse underwater acoustic channel impulse response function of a delay Doppler domain, and constructing a minimum mean square error equalizer based on channel information at a receiving end for recovering the transmitted signal according to the estimated underwater acoustic channel information of the delay Doppler domain. The method is suitable for time-varying underwater acoustic channel estimation and underwater acoustic communication.
The invention utilizes the iterative framework of matching pursuit and adopts the Schmidt orthogonal method to update the atom selection process, thereby realizing the minimization of the iterative sequence error and avoiding redundant iteration. Finally, the required atoms are accurately selected to form the basis matrix. And finally, recovering the transmitted signal by combining the underwater acoustic channel estimation value of the two-dimensional domain and constructing a minimum mean square error equalizer.
The invention uses the matching pursuit method based on Schmidt orthogonalization to estimate the underwater sound channel impulse response function of the delay Doppler domain, and has the advantages that: the method selects the matching atoms based on Schmidt orthogonalization, effectively avoids redundant calculation, and enables the time delay Doppler underwater acoustic channel estimation result generated by the method to have higher precision.
Drawings
Fig. 1 is a comparison graph of time domain channel estimation results of a group of sea test data by a conventional Least mean Square error (LS), a Matching Pursuit Method (MP), and a method of the present invention (Schmidt Matching Pursuit, SMP).
Fig. 2 is a comparison graph of the time delay doppler domain channel estimation results of the group of sea test data by the conventional Least mean Square error (LS), the Matching Pursuit Method (MP), and the method of the present invention (Schmidt Matching Pursuit, SMP).
Fig. 3 is a comparison of equalizer constellation output results based on three channel estimation results.
Fig. 4 is a sequence error comparison diagram based on three channel estimation results.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
referring to fig. 1, a QPSK coding method is adopted, carrier frequency modulation is combined, data is processed offline, a symbol sampling frequency is 4kHz, in an input-output relational expression of a two-dimensional domain, a row number of a matrix is set to be 50, a column number is 400, a doppler domain dimension is 19, and a frequency search range is-4 to 4 Hz. The number of MP and SMP iterations is set to 25. The obtained result is shown in fig. 1, and it can be seen from fig. 1 that the LS algorithm has no sparse constraint term, so that the estimated underwater acoustic channel has false multipath, while the MP and SMP algorithms are improved compared with the LS algorithm, and the SMP algorithm adopts the schmitt orthogonalization strategy, so that redundant iteration is avoided in iteration, and thus a more accurate estimation result is obtained.
1. The time delay Doppler domain underwater acoustic channel estimation model is specifically realized by the following steps:
(1) setting parameters delta t, delta tau and delta f as sampling intervals of observation time, time delay and Doppler frequency shift respectively, and discretizing observation time tableShown as tnN Δ t, N1, N, the discretized time delay is expressed as:
τm＝τ0+(m-1)Δτ,m＝1,...,M (1)
wherein the parameter τ0Is the reference delay, and M is the largest delay sampling dimension, called the underwater acoustic channel order.
(2) Discretized time-varying channel response is h [ t ]n,τm]. The doppler of the sample is defined as:
fl＝f0+(l-1)Δf,l＝1,...,L (2)
wherein f is0Is the smallest doppler frequency shift value that can occur and L is the largest doppler sample dimension. Thus, the two-dimensional delay-doppler dimension size is denoted as LM. Is provided with
Figure GDA0002731820570000061
Wherein f issFor a signal frequency sampling rate, the discretized input-output relationship can be written as:
Figure GDA0002731820570000062
(3) definition u ═ u1,1,…,u1,M,u2,1,…,u2,M,…,uL,1,…,uL,M]TAnd the dimension is (L · M) × 1, the input-output relationship of the delay-doppler domain can be expressed as:
Figure GDA0002731820570000063
wherein
Figure GDA0002731820570000064
The dimension of (a) is L x 1,
Figure GDA0002731820570000065
denotes the Kronecker product, x [ t ]n]＝[xn+M-1,…,xn+1,xn]THas dimension of M × 1. Definition y ═ { y [ t ]1],y[t2],…,y[tN]}T,
Figure GDA0002731820570000066
A＝{a[t1],a[t2],…,a[tN]}HThe following input-output relationships can be obtained:
y＝Au+w (5)
wherein y and w have dimensions of N × 1, and A and u have dimensions of N × (L · M), (L · M) × 1, respectively.
2. The specific method for estimating the channel impulse response function u comprises the following steps:
input parameter information setting: matrix A and received signal y, setting algorithm termination conditions
Figure GDA0002731820570000071
Setting output parameter information: channel impulse response function estimate u
Initializing: the initial estimated value is a zero vector u{0}When the ratio is 0: initial residual r{0}Y; the initial iteration number i is 0; the initial channel impulse response function supporting set is an empty set
Figure GDA0002731820570000072
Judging whether the algorithm termination condition is satisfied, namely whether | | | < r | | |thIf so, stopping iteration, otherwise, iterating according to the following iteration formula:
Figure GDA0002731820570000073
P{1}＝v{1}(v{1}Tv{1})-1v{1}T (7)
r{1}＝r{0}-P{1}y (8)
for the ith selected atom
Figure GDA0002731820570000074
Should be orthogonal to the previous choice, so the i-th orthogonal vector is:
Figure GDA0002731820570000075
the projection matrix for the ith pass is thus obtained as:
P{i}＝v{i}(v{i}Tv{i})-1v{i}T (10)
the i-th residual update is:
r{i}＝r{i-1}-P{i}y (11)
updating a support set:
S{i}＝S{i-1}∪s{i} (12)
the pseudo-inverse operation is then performed:
Figure GDA0002731820570000081
the finally estimated underwater sound channel impulse response function is as follows:
Figure GDA0002731820570000082
the algorithm provided by the invention can obtain kappa nonzero components after iteration for kappa times, and because of Schmidt orthogonalization operation, redundant calculation and redundant selection of atoms can be effectively avoided.
3. The estimated value of the final MMSE equalizer output for the transmitted signal is expressed as:
Figure GDA0002731820570000083
wherein I represents an identity matrix of the cell,
Figure GDA0002731820570000084
a parameter representing the noise energy. y denotes a signal vector at the receiving end, and
Figure GDA0002731820570000085
representing the equalizer's estimated value for the transmit-side signal. And is
Figure GDA0002731820570000086
Wherein
Figure GDA0002731820570000087
Is an N by N diagonal matrix, and the matrix UlDimension of NxNsIn which N issFor transmitting the sequence length, by vector ul＝[U(0,l),...,U(M-1,l)]TIs constructed. The specific arrangement mode is
Figure GDA0002731820570000088
The underwater acoustic channel estimation result based on the delay-doppler domain is shown in fig. 2, the underwater acoustic channel estimation problem in the two-dimensional domain can also be regarded as an underdetermined problem, the estimation result is relatively rough due to the fact that the LS algorithm does not have a sparse constraint item on the underwater acoustic channel in the two-dimensional domain optimization process, while the MP and SMP algorithms adopt sparse constraint, and the SMP algorithm adopts schmidt orthogonal to avoid redundant iteration in the optimization process, so that a more accurate estimation result is obtained.
To further examine the effect of the estimation results produced by the present invention on the recovery of the transmitted signal. And respectively performing two-dimensional equalizer calculation with minimum mean square error criterion according to the estimation result in fig. 2 to obtain a constellation diagram of the equalizer output result. Since the more accurate the channel estimation result is, the more compact the constellation diagram is the equalizer output based on the channel estimation, the more accurate the estimation result can be judged from the result of the constellation diagram. As can be seen from fig. 3, the SMP algorithm obtains an accurate estimate of the underwater acoustic channel that is beneficial to the equalizer output.
To further illustrate the estimation performance of the three methods, sequence errors are used for comparison, and the energy of the received signal is provided as a reference. The result is shown in fig. 4, and it can be seen that the sequence error estimated by the LS algorithm is the largest, which indicates that the estimation accuracy is not high, while the SMP algorithm obtains accurate estimation and benefits from avoiding redundancy calculation by the schmitt orthogonal iteration, thereby obtaining better performance than the MP algorithm.
The method has obvious implementation effect in sea test data of sparse underwater acoustic channel estimation, and compared with the classic LS and MP algorithms, the precision of the estimation result of the method is improved in both time domain and delay Doppler domain.

Claims (1)

1. A time-varying sparse underwater acoustic channel estimation method based on a delay-Doppler domain is characterized by comprising the following steps:
step 1, establishing a delay Doppler domain model:
1. let the parameters Δ t, Δ τ and Δ f be the sampling intervals of observation time, time delay and doppler shift, respectively, and the discretized observation time is denoted as tnN, N is the maximum sampling point number of observation time, and the discretized time delay is expressed as:
τm＝τ0+(m-1)Δτ,m＝1,...,M (1)
wherein the parameter τ0Is a reference delay, and M is the largest delay sampling dimension, called the underwater acoustic channel order;
2. discretized time-varying channel response is h [ t ]n,τm]The sampled doppler is defined as:
fl＝f0+(l-1)Δf,l＝1,...,L (2)
wherein f is0Is the minimum Doppler shiftThe value, L, is the largest Doppler sampling dimension, and thus the two-dimensional delay-Doppler dimension size is denoted as LM;
is provided with
Figure FDA0002731820560000011
Wherein f issIf the signal frequency sampling rate is higher than the predetermined sampling rate, the discretized input-output relation is as follows:
Figure FDA0002731820560000012
w is noise;
definition u ═ u1,1,…,u1,M,u2,1,…,u2,M,…,uL,1,…,uL,M]TAnd the dimension is (L · M) × 1, the input-output relationship of the delay-doppler domain is expressed as:
Figure FDA0002731820560000013
wherein
Figure FDA0002731820560000014
The dimension of (a) is L x 1,
Figure FDA0002731820560000015
denotes the Kronecker product, x [ t ]n]＝[xn+M-1,…,xn+1,xn]THas a dimension of M × 1;
definition y ═ { y [ t ]1],y[t2],…,y[tN]}T,
Figure FDA0002731820560000016
A＝{a[t1],a[t2],…,a[tN]}HThe following input-output relationships are obtained:
y＝Au+w (5)
wherein y and w have dimensions of N × 1, and A and u have dimensions of N × (L · M), (L · M) × 1, respectively;
the specific method for estimating the channel impulse response function u comprises the following steps:
input parameter information setting: matrix A and received signal y, setting algorithm termination conditions
Figure FDA0002731820560000021
Setting output parameter information: a channel impulse response function estimated value u;
initializing: the initial estimated value is a zero vector u{0}When the ratio is 0: initial residual r{0}Y; the initial iteration number i is 0; the initial channel impulse response function supporting set is an empty set
Figure FDA0002731820560000022
Judging whether the algorithm termination condition is satisfied, namely whether | | | < r | | |thIf so, stopping iteration, otherwise, iterating according to the following iteration formula:
Figure FDA0002731820560000023
P{1}＝v{1}(v{1}Tv{1})-1v{1}T (7)
r{1}＝r{0}-P{1}y (8)
for the ith selected atom
Figure FDA0002731820560000024
Should be orthogonal to the previous choice, so the i-th orthogonal vector is:
Figure FDA0002731820560000025
the projection matrix obtained for the ith time is:
P{i}＝v{i}(v{i}Tv{i})-1v{i}T (10)
the i-th residual update is:
r{i}＝r{i-1}-P{i}y (11)
updating a support set:
S{i}＝S{i-1}∪s{i} (12)
the pseudo-inverse operation is then performed:
Figure FDA0002731820560000026
the estimated underwater acoustic channel impulse response function is:
Figure FDA0002731820560000031
step 2: the estimation value of the MMSE equalizer output to the transmission signal is expressed as follows:
Figure FDA0002731820560000032
wherein I represents an identity matrix of the cell,
Figure FDA0002731820560000033
a parameter representing noise energy, y represents a signal vector at the receiving end, and
Figure FDA0002731820560000034
represents an estimated value of the equalizer on the signal of the transmitting end, and
Figure FDA0002731820560000035
wherein
Figure FDA0002731820560000036
Is an N by N diagonal matrix, and the matrix UlDimension of NxNsIn which N issFor transmitting the sequence length, by vector ul＝[U(0,l),...,U(M-1,l)]TIs constructed in a specific arrangement mode that:
Figure FDA0002731820560000037
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