CN109462427B - MIMO underwater acoustic channel estimation method - Google Patents

MIMO underwater acoustic channel estimation method Download PDF

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CN109462427B
CN109462427B CN201811186760.0A CN201811186760A CN109462427B CN 109462427 B CN109462427 B CN 109462427B CN 201811186760 A CN201811186760 A CN 201811186760A CN 109462427 B CN109462427 B CN 109462427B
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张秀再
赵慧
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Nanjing University of Information Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
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Abstract

The invention discloses a MIMO underwater acoustic channel estimation method based on an improved self-adaptive hybrid optimization smoothing L0 norm, which adopts an improved algorithm (MAReSL0) approximating a better target function of an L0 norm to self-adaptively generate a reliable regularization factor and balance errors based on the sparsity and residual error of a solution in a target function in an iterative process; in order to ensure that iteration accurately converges to an optimal point, the initial value of a Nesterov gradient acceleration method (NAG) after inner loop iteration is used as the initial value of a Newton method for mixed optimization channel estimation. Numerical simulation shows that compared with other classical algorithms, the method has better noise robustness and effectively improves the channel estimation performance.

Description

MIMO underwater acoustic channel estimation method
Technical Field
The invention relates to the technical field of signal communication, in particular to a MIMO underwater acoustic channel estimation method based on an improved self-adaptive hybrid optimization smoothing L0 norm.
Background
With the development of ocean research and the need of national defense construction, people have more and more demands on underwater communication. The complexity of the marine environment, resulting in time-varying, multipath effects and limited bandwidth characteristics of the underwater acoustic channel, makes underwater acoustic communications very challenging. In order to improve the quality of underwater acoustic communication, a multiple-input multiple-output (MIMO) technology is adopted, so that the channel capacity is improved and the power consumption of a receiving end is reduced on the premise of not additionally increasing the frequency bandwidth.
In order to realize reconstruction of sparse signals, H.Mohimani, M.Babaie-Zadeh and the like propose a smoothing L0(SL0) algorithm, higher precision is obtained by searching a solution of a sparsity problem, and underwater acoustic channel estimation can be converted into a sparsity solving problem, namely a minimum L0 norm solving problem. SL0 solves the optimization problem using sparsity constraints, maxFσ(x) s.t.y ═ Ax, definition
Figure GDA0002938133160000011
Wherein f isσFor a suitable set of smooth continuous functions, the L0 norm can be approximated and the optimal solution found using gradient descent. The threshold smoothing L0(T-SL0) algorithm avoids the SL0 inefficient iterative process and accelerates the iterative process by a preset threshold. Both SL0 and T-SL0 use the y-Ax equality constraint in the optimization problem. In practical situations, the observations are often contaminated with noise, i.e. there is an error between y and Ax. Therefore, under the noise environment, the reconstruction performance of the SL0 and the T-SL0 is obviously reduced. H.x.bu, r.tao proposed an improved algorithm regularizing SL0(ReSL0), effectively improving the anti-noise performance. The ReSL0 transforms the equality constraint into an inequality constraint, allows for some error, and uses a regularization factor to balance the relationship between its sparse solution and the residual error left by the objective function in the iteration. However, the selection of the regularization factor is the key to deal with noise, the regularization parameter in the ReSL0 algorithm is fixed during the iteration process, and the sparse solution does not change in proportion to the residual error. The ratio imbalance may destroy the sparsity of the solution, reducing the reconstruction performance. Chen J, Zhou Y, Jin L proposes an adaptive regularization factor selection method (AReSL0 algorithm) that balances the residual error and sparse solutions in the iterative process by generating appropriate regularization factors. The method is applied to the actual underwater acoustic channel, and the anti-noise performance is insufficient.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a MIMO underwater acoustic channel estimation method based on an improved adaptive hybrid optimization smoothing L0 norm, which effectively improves the noise robustness and the channel estimation performance.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a MIMO underwater acoustic channel estimation method based on an improved adaptive hybrid optimization smoothing L0 norm, which comprises the following steps:
step 1, establishing a network with NtA transmitting terminal and NrMIMO system of each receiving end, forming an Nt×NrEach subchannel corresponds to an underwater acoustic channel model, and the mth transmission time t of the subchannel is obtainedChannel frequency domain response D of the terminal and the nth receiving terminal in time delay of taumn(t, τ) to obtain N for the entire MIMO systemt×NrA channel frequency domain response matrix D (t, tau) of the underwater acoustic channel under the time delay of t time tau;
step 2, vectorizing the obtained channel frequency domain response matrix D (t, tau) into a vector h of Nx 1
h＝vec(D(t,τ))
Wherein vec (.) represents a vectorization function, and N is the number of elements of the vector h;
step 3, establishing an underwater acoustic channel compressed sensing equation y ═ Ax + r, wherein x represents an underwater acoustic channel vector to be estimated, y represents a one-dimensional observation vector, the dimension of the one-dimensional observation vector is Mx 1, M represents the number of elements of the observation vector y, A is a known random Gaussian matrix measurement matrix, the dimension of the A is Mx N, r represents independent and identically distributed Gaussian white noise, the mean value of the R is 0, and the variance is w2；
Step 4, performing hybrid optimization by adopting an iterative algorithm combining a Nesterov gradient acceleration method and a Newton method to obtain a final iterated underwater acoustic channel vector estimation value x; the method comprises the following specific steps:
step 4a, initialization:
step A, solving an initial value x of an underwater sound channel by using a least square method(0)Presetting the first cycle number as L and the second cycle number as K;
step B, selecting a sequence [ sigma ]1,σ2,σ3,....,σJ.]And σ1>σ2>σ3>,...,>σJWherein σ isjJ represents the value of the jth control parameter σ, J represents the sequence number of the control parameter σ, and J is 1;
step (1) of setting the control parameter σ of the objective function in the SL0 algorithm to σjCalculating L times by using Nesterov gradient acceleration method, and solving fσ(x) Minimum value x of (1)L (j)Wherein x isL (j)Representing the minimum value after L cycles in the j iteration;
selection of an objective function f in the SL0 algorithmσ(x) As a function of the norm of approximate L0SL0 algorithm, fσ(x) Is expressed as
Figure GDA0002938133160000021
Wherein e represents a natural base number, and sigma represents a control parameter of the objective function;
step (2), initializing a Newton method: x ═ xL (j)；
Computing K times by using Newton method, and solving fσ(x) Minimum value x of (1)K (j)Wherein x isK (j)Representing the minimum value after K cycles in the j iteration;
calculating a regularization factor lambda and projecting it onto the feasible set:
Figure GDA0002938133160000031
x(j)＝xK (j)-AH(AAH+λ-1Im)-1(AxK (j)-y)
wherein, ()HDenotes a conjugate transpose, ImRepresenting an identity matrix of order M x M, Q being a constant, x(j)Is the optimal value of the underwater acoustic channel after the jth iteration;
and (3) outputting x ═ x(j)；
Step 4b, when sigmaj>σJWhen j is equal to j +1, σj＝βσj-1Turning to step (1), β is the attenuation factor, 0<β<1。
As a further optimization scheme of the MIMO underwater acoustic channel estimation method based on the improved self-adaptive hybrid optimization smoothing L0 norm, sigma1＝1。
As a further optimization scheme of the MIMO underwater acoustic channel estimation method based on the improved adaptive hybrid optimization smoothing L0 norm, in step 1, the channel frequency domain response D of a subchannel is obtainedmn(t, τ) is
Figure GDA0002938133160000032
Wherein p is the number of paths of each sub-channel, m, n respectively represent the mth transmitting end and the nth receiving end, Dmn(t, tau) represents the frequency domain response of the mth transmitting end and the nth receiving end in the time of tau time delay at the time of t, taui,mnRepresenting the delay, h, of the ith path between the mth transmitting end and the nth receiving endi,mn(t) represents the impulse response of the ith path between the mth transmitting end and the nth receiving end at the time t, delta (t-tau)i,mn) Is expressed at taui,mnA unit impulse function of the time delay;
n of the whole MIMO systemt×NrThe channel frequency domain response matrix D (t, tau) of the underwater acoustic channel at the time t time tau is expressed as
Figure GDA0002938133160000033
As a further optimization scheme of the MIMO underwater acoustic channel estimation method based on the improved adaptive hybrid optimization smoothing L0 norm, K is 3, and L is 2.
As a further optimization scheme of the MIMO underwater acoustic channel estimation method based on the improved adaptive hybrid optimization smoothing L0 norm, β is 0.5.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
(1) on the basis of a regularization SL0(ReSL0) algorithm, a target function with a better L0 norm is approximated, and a reliable regularization factor is generated in a self-adaptive mode to balance errors based on the sparsity and residual error of a solution in the target function in an iteration process; in order to ensure that iteration accurately converges to an optimal point, the initial value after inner loop iteration of a Nesterov gradient acceleration method (NAG) is adopted as the initial value of a Newton method to carry out mixed optimization channel estimation, and the noise robustness and the channel estimation performance are effectively improved;
(2) in the actual underwater acoustic channel, because the sparsity characteristic of the channel cannot be exactly known, the method can better estimate the channel information without acquiring the prior information of the sparsity of the channel on the basis of the compressive sensing theory; the MAReSL0 algorithm performs mixed optimization of the Neisseliverv gradient acceleration method and the Newton method based on a new objective function, adaptively generates a proper regularization factor for estimation of a sparse underwater acoustic channel, and compares estimation performance of the MAReSL0 algorithm with that of SL0, improved SL0, ReSL0, improved ReSL0 and AReSL0 algorithms; the comparison result shows that the method is obviously superior to other 5 algorithms in MSE and SER performance indexes, the channel estimation performance is better, and the robustness to noise is better.
Drawings
Fig. 1 is an underwater acoustic MIMO communication system model.
Fig. 2 is a distribution diagram of each objective function, where σ is 0.1.
FIG. 3 is a 4-channel impulse response for a simulated MIMO channel; wherein, (a), (b), (c) and (d) are channels 1, 2, 3 and 4 respectively.
Fig. 4 is a channel mean square error curve of 6 estimation algorithms.
Fig. 5 is a bit error rate curve for 6 estimation algorithms.
Fig. 6 is a flow chart of MIMO underwater acoustic channel estimation based on an improved adaptive hybrid optimization smoothing L0 norm.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
Fig. 6 is a flow chart of MIMO underwater acoustic channel estimation based on an improved adaptive hybrid optimization smoothing L0 norm. The method specifically comprises the following steps:
1): as shown in FIG. 1, establish a channel with NtMIMO system of transmitting end and Nr receiving ends, forming one NtA sub-channel model of x Nr, each sub-channel corresponding to an underwater acoustic channel model, and obtaining the channel frequency domain response D of the sub-channelmn(t, τ) is
Figure GDA0002938133160000041
Wherein p is the number of paths of each sub-channel, m, n respectively represent the mth transmitting end and the nth receiving end, Dmn(t, tau) represents the frequency domain response of the mth transmitting end and the nth receiving end in the time of tau time delay at the time of t, taui,mnRepresenting the delay, h, of the ith path between the mth transmitting end and the nth receiving endi,mn(t) represents the impulse response of the ith path of the mth transmitting end and the nth receiving end at the time t, Dmn(t, τ) channel frequency domain responses of the mth transmitting end and the nth receiving terminal channels;
the channel frequency domain response matrix D (t, tau) of the Nt multiplied by Nr underwater acoustic channel of the whole MIMO system under the time delay of t time tau is expressed as
Figure GDA0002938133160000051
2) Vectorizing the obtained channel frequency domain response matrix D (t, tau) into an Nx 1 vector h
h＝vec(D(t,τ))
Wherein vec (.) represents a vectorization function, and N is the number of elements of the vector h;
3) establishing an underwater acoustic channel compressed sensing equation y as Ax + r, wherein x represents an underwater acoustic channel vector to be estimated, y represents a one-dimensional observation vector with dimension of M × 1, M represents the number of elements of the observation vector y, A is a known random Gaussian matrix measurement matrix with dimension of M × N, r represents independent and uniformly distributed white Gaussian noise with mean value of 0 and variance of w2；
4) Performing hybrid optimization by adopting an iterative algorithm combining a Nesterov gradient acceleration method and a Newton method to obtain a final iterated underwater acoustic channel vector estimation value x; the method comprises the following specific steps:
4a, initialization:
A. method for solving initial value x of underwater acoustic channel by least square method(0)Presetting the first cycle number as L and the second cycle number as K;
B. selecting a sequence [ sigma ]1,σ2,σ3,....,σJ.]And σ1>σ2>σ3>,...,>σJWherein j is 1, σjRepresents the value of the jth control parameter sigma, and J represents the sequence number of the control parameter sigma;
(1) let the control parameter sigma of the objective function in the SL0 algorithm be sigmajCalculating L times by using Nesterov gradient acceleration method, and solving fσ(x) Minimum value x of (1)L (j)Wherein x isL (j)Representing the minimum value after L cycles in the j iteration;
target function selection in the SL0 algorithm approximates the better performing target function as shown in FIG. 2, target function selection f in the SL0 algorithmσ(x) SL0 algorithm was performed as a function of an approximate L0 norm, fσ(x) Is expressed as
Figure GDA0002938133160000052
Wherein e represents a natural base number, and sigma represents a control parameter of the objective function;
(2) initializing Newton method: x ═ xL (j)；
Computing K times by using Newton method, and solving fσ(x) Minimum value x of (1)K (j)Wherein x isK (j)Representing the minimum value after K cycles in the j iteration;
calculating a regularization factor lambda and projecting it onto the feasible set:
Figure GDA0002938133160000061
x(j)＝xK (j)-AH(AAH+λ-1Im)-1(AxK (j)-y)
wherein, ()HDenotes a conjugate transpose, ImRepresenting an identity matrix of order M x M, Q being a constant, x(j)Is the optimal value of the underwater acoustic channel after the jth iteration;
(3) x is output(j)；
4b, when σj>σJWhen j is equal to j +1, σj＝βσj-1Turning to (1), β is the attenuation factor, 0<β<1。。
Simulation experiment
1 underwater acoustic channel sparsity simulation
In order to verify the performance of the MAReSL0 algorithm, a bellhop underwater acoustic channel simulation model is adopted to model a sparse underwater acoustic channel, and N is sett2 emitting sources and Nr 2 receiving ends, the depth is 10m and 20m respectively, the distance is 1000m, the water depth is 150m, the uniform sound velocity is 1500m/s, and 4 channels are formed from the emitting sources to the receiving ends.
Fig. 3 shows the simulated channel normalized impulse response absolute values of 4 channels respectively. In FIG. 3, (a), (b), (c), (d) are channels 1, 2, 3, 4, respectively. As can be seen from fig. 3, the underwater acoustic channel has a significant sparsity. The number of the paths of the 4 channels in the simulation is 44, 43, 44 and 43 respectively, namely the sparsity of each channel.
2MAReSL0 algorithm performance simulation
In the simulation experiment, simulation parameters include: the length N of the vectorized channel h is 800, and M is 64; the signal to noise ratio varies from 0dB to 20dB against a background of gaussian white noise in the experiment. The simulation was run 100 times and averaged for comparison. The marcsl 0 algorithm of the present invention has two iterations K-3, L-2, and β -0.5, all of which are empirical values.
The performance indexes of the algorithm adopted by the invention are channel estimation Mean Square Error (MSE) and error rate (SER), which are respectively expressed as
Figure GDA0002938133160000062
Figure GDA0002938133160000063
In terms of performance, the smaller the values of MSE and SER, the better the algorithm estimates performance.
The MAReSL0 algorithm carries out channel estimation by using the sparse characteristic of a channel, and is compared with SL0[3], MSL0, ReSL0[6], MReSL0 and AReSL0[7] algorithms in simulation experiments, wherein the MSL0 and MReSL0 algorithms are obtained by replacing original objective functions in SL0 and ReSL0 algorithms with the objective functions. In the simulation experiment, different random gaussian matrices are taken to operate for 100 times and then an average value is taken to calculate, and the mean square error and the error rate curves of the channels of the 6 estimation algorithms are respectively shown in fig. 4 and fig. 5.
As can be seen from fig. 4 and 5, the new objective function of the present invention is adopted, so the channel estimation performance of the improved SL0 and the improved rel 0 algorithms is slightly better than that of the SL0 and the rel 0 algorithms, respectively.
As can be seen from fig. 4 and 5, in a noise environment, both MSE and SER performance of the SL0 algorithm are inferior to those of other algorithms, and the noise immunity performance of the SL0 algorithm is the worst; the ReSL0 algorithm introduces a regularization factor that estimates better performance than the SL0, modified SL0 algorithm. In a noise environment, because the regularization parameter of the ReSL0 algorithm is fixed in the iteration process, the sparse solution of the channel does not change proportionally with the residual error, and the estimation performance of the channel is greatly reduced; the AReSL0 algorithm can adaptively generate regularization factors in iterations that estimate performance superior to the SL0, the modified SL0, the ReSL0, and the modified ReSL0 algorithms.
As can be seen from fig. 4 and 5, the improved adaptive regularization SL0 (marisl 0) algorithm of the present invention adopts an adaptive regularization iterative algorithm that is a mixture of a nertiov gradient acceleration method and a newton method, which can not only obtain an optimal value accurately, but also generate a regularization error factor adaptively, maintain channel sparsity and balance of residual errors in an iterative process, and have better estimation performance, and noise robustness is better than that of SL0, improved SL0, renl 0, improved renl 0, and AReSL0 algorithms.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (5)

1. A MIMO underwater acoustic channel estimation method based on improved adaptive hybrid optimization smoothing L0 norm is characterized by comprising the following steps:
step 1, establishing a network with NtA transmitting terminal and NrMIMO system of each receiving end, forming an Nt×NrEach subchannel corresponds to an underwater acoustic channel model, and channel frequency domain response D of the mth transmitting end and the nth receiving end of the subchannel at the time t in tau time delay is obtainedmn(t, τ) to obtain N for the entire MIMO systemt×NrA channel frequency domain response matrix D (t, tau) of the underwater acoustic channel under the time delay of t time tau;
step 2, vectorizing the obtained channel frequency domain response matrix D (t, tau) into an Nx 1 vector h which is equal to vec (D (t, tau))
Wherein vec (.) represents a vectorization function, and N is the number of elements of the vector h;
step 3, establishing an underwater acoustic channel compressed sensing equation y ═ Ax + r, wherein x represents an underwater acoustic channel vector to be estimated, y represents a one-dimensional observation vector, the dimension of the one-dimensional observation vector is Mx 1, M represents the number of elements of the observation vector y, A is a known random Gaussian matrix measurement matrix, the dimension of the A is Mx N, r represents independent and identically distributed Gaussian white noise, the mean value of the R is 0, and the variance is w2；
Step 4, performing hybrid optimization by adopting an iterative algorithm combining a Nesterov gradient acceleration method and a Newton method to obtain a final iterated underwater acoustic channel vector estimation value x; the method comprises the following specific steps:
step (1), initialization:
step (1-1) of determining an initial value x of an underwater acoustic channel by using a least square method(0)Presetting the first cycle number as L and the second cycle number as K;
step (1-2), selecting a sequence [ sigma ]1,σ2,σ3,....,σJ]And σ1>σ2>σ3>,...,>σJWherein σ isjJ represents the value of the jth control parameter σ, J represents the sequence number of the control parameter σ, and J is 1;
step (1-2-1) of setting control parameter σ of objective function in SL0 algorithm to σ ═ σ -jBy using Nesterov gradient acceleration methodCalculating L times and solving fσ(x) Minimum value x of (1)L (j)Wherein x isL (j)Representing the minimum value after L cycles in the j iteration;
selection of an objective function f in the SL0 algorithmσ(x) SL0 algorithm was performed as a function of an approximate L0 norm, fσ(x) Is expressed as
Figure FDA0002938133150000011
Wherein e represents a natural base number, and sigma represents a control parameter of the objective function;
step (1-2-2), Newton method initialization: x ═ xL (j)；
Computing K times by using Newton method, and solving fσ(x) Minimum value x of (1)K (j)Wherein x isK (j)Representing the minimum value after K cycles in the j iteration;
calculating a regularization factor lambda and projecting it onto the feasible set:
Figure FDA0002938133150000021
x(j)＝xK (j)-AH(AAH+λ-1Im)-1(AxK (j)-y)
wherein, ()HDenotes a conjugate transpose, IMRepresenting an identity matrix of order M x M, Q being a constant, x(j)Is the optimal value of the underwater acoustic channel after the jth iteration;
step (1-2-3) of outputting x ═ x(j)；
Step (2) when sigma isj>σJWhen j is equal to j +1, σj＝βσj-1Turning to step (1-2-1), β is the attenuation factor, 0<β<1。
2. Adaptive mixing based on improvement according to claim 1The MIMO underwater sound channel estimation method for synthesizing and optimizing the smooth L0 norm is characterized in that sigma1＝1。
3. The MIMO underwater acoustic channel estimation method based on the improved L0 norm of the adaptive hybrid-optimized smoothing as claimed in claim 1, wherein in step 1, the channel frequency domain response D of the sub-channel is obtainedmn(t, τ) is
Figure FDA0002938133150000022
Wherein p is the number of paths of each sub-channel, m, n respectively represent the mth transmitting end and the nth receiving end, Dmn(t, tau) represents the frequency domain response of the mth transmitting end and the nth receiving end in the time of tau time delay at the time of t, taui,mnRepresenting the delay, h, of the ith path between the mth transmitting end and the nth receiving endi,mn(t) represents the impulse response of the ith path between the mth transmitting end and the nth receiving end at the time t, delta (t-tau)i,mn) Is expressed at taui,mnA unit impulse function of the time delay;
n of the whole MIMO systemt×NrThe channel frequency domain response matrix D (t, tau) of the underwater acoustic channel at the time t time tau is expressed as
Figure FDA0002938133150000023
4. The MIMO underwater acoustic channel estimation method based on the improved adaptive hybrid-optimized smoothed L0 norm of claim 1, wherein K is 3 and L is 2.
5. The MIMO underwater acoustic channel estimation method based on the improved adaptive hybrid-optimized smoothed L0 norm of claim 1, wherein β is 0.5.
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