CN113691473A - Underwater channel estimation method based on convex optimization - Google Patents

Underwater channel estimation method based on convex optimization Download PDF

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CN113691473A
CN113691473A CN202111230581.4A CN202111230581A CN113691473A CN 113691473 A CN113691473 A CN 113691473A CN 202111230581 A CN202111230581 A CN 202111230581A CN 113691473 A CN113691473 A CN 113691473A
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季浩然
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
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Abstract

The invention discloses an underwater channel estimation method based on convex optimization, which minimizes the convolution error of received data and signals with a channel, and solves the convolution error of the received data and signals with the channel by adopting a Lagrange method to obtain the estimated value of the channel; a channel with the minimum error is found in the trust domain, a regularization coefficient which changes along with time is introduced, and the estimated value of the channel is updated when each frame signal arrives. Compared with the prior art, the method can realize the self-adaptive adjustment of the channel estimation algorithm under the unknown underwater acoustic environment, realize the accurate estimation of the underwater acoustic channel with higher calculation efficiency, and meet the requirements of the accurate channel estimation and communication application under the unknown underwater acoustic channel environment; and the transmitted signal passing through the underwater acoustic channel can be estimated, so that the influence of the self-transmitting transducer on the system can be reduced in a channel estimation mode.

Description

Underwater channel estimation method based on convex optimization
Technical Field
The invention relates to the field of underwater acoustic communication, in particular to an underwater channel estimation method based on convex optimization.
Background
Currently, underwater channel estimation usually adopts a pilot training insertion mode. The conventional channel estimation method generally employs a least square algorithm (LMS), since the least square algorithm is easily interfered by noise, and the performance of the LMS algorithm is also degraded by inter-subcarrier interference. ZHAO Y et al proposes a pilot noise reduction method using transform domain filter, zhaoli et al proposes a compressed sensing-based adaptive sparse underwater acoustic channel estimation algorithm, combines the compressed sensing algorithm OMP/CoSaMP with the hard threshold LMS algorithm to estimate the underwater acoustic channel impulse response; wangnong et al proposed pilot-based OFDM underwater communication channel estimation, improved training pilots, considered the underwater acoustic channel as a comb filter, and improved transform domain filter pilot noise reduction method to improve the inter-subcarrier interference problem. However, these algorithms require the sparse nature of the known channel, and in practical underwater environments, sparse algorithms are not easily adopted because complex underwater space-time propagation channels do not usually satisfy sparsity.
In addition, the underwater duplex communication system performs receiving and transmitting operations simultaneously. The received data becomes very weak after being attenuated for a long distance; the self transmitting signal generally needs a high-power amplifier to drive the transducer to transmit the signal in order to be capable of propagating to a longer distance. Therefore, the received data is affected by the self-transmitted signal.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides an underwater channel estimation method based on convex optimization.
In order to achieve the purpose, the invention is implemented according to the following technical scheme:
an underwater channel estimation method based on convex optimization comprises the following steps:
s1, assuming that the MIMO system has J receiving transducers and P transmitting transducers, assuming that the receiving transducers receive data
Figure 972058DEST_PATH_IMAGE001
P transmitting transducers transmit data as
Figure 889198DEST_PATH_IMAGE002
The channel from the pth transmitting transducer to the jth receiving transducer is
Figure 105153DEST_PATH_IMAGE003
And M is the channel length, the data of the jth receiving array element is as follows:
Figure 500363DEST_PATH_IMAGE004
；
wherein the content of the first and second substances,
Figure 252418DEST_PATH_IMAGE005
is a noise, and the noise is,
Figure 74880DEST_PATH_IMAGE006
is a matrix generated from the transmit data as follows:
Figure 279597DEST_PATH_IMAGE007
；
s2, minimizing convolution error of the received data and signal with the channel:
Figure 478497DEST_PATH_IMAGE008
；
wherein the content of the first and second substances,
Figure 147376DEST_PATH_IMAGE009
is composed of
Figure 78423DEST_PATH_IMAGE010
The matrix of the composition is formed by the following components,
Figure 832752DEST_PATH_IMAGE011
；
and solving convolution error of the received data and signal with the channel by Lagrange method to obtain estimated value of the channel
Figure 3052DEST_PATH_IMAGE012
；
S3, searching a channel with the minimum error in the trust domain, introducing a regularization coefficient which changes along with time, and updating the estimated value of the channel when each frame signal arrives.
Further, in step S2, the specific step of solving the convolution error between the received data and the signal and the channel by using the Lagrange method includes:
order:
Figure 526438DEST_PATH_IMAGE014
；
to pair
Figure 893965DEST_PATH_IMAGE015
And (5) solving a gradient to obtain:
Figure 135591DEST_PATH_IMAGE016
；
let the gradient equal to 0 to obtain the estimated value of the channel
Figure 410714DEST_PATH_IMAGE017
：
Figure 991868DEST_PATH_IMAGE018
。
Further, the step S3 specifically includes:
find a channel with the smallest error in the trust domain:
Figure 327035DEST_PATH_IMAGE019
；
wherein the superscript is
Figure 993639DEST_PATH_IMAGE020
The data representing the i-th frame is,
Figure 72454DEST_PATH_IMAGE021
is the error coefficient;
its equivalent, and introduces regularization coefficients that vary with time
Figure 6649DEST_PATH_IMAGE022
Obtaining:
Figure 778296DEST_PATH_IMAGE023
；
when each frame signal comes, an updating formula is obtained for updating the estimated value of the channel:
Figure 666618DEST_PATH_IMAGE024
。
compared with the prior art, the method can realize the self-adaptive adjustment of the channel estimation algorithm under the unknown underwater acoustic environment, realize the accurate estimation of the underwater acoustic channel with higher calculation efficiency, and meet the requirements of the accurate channel estimation and communication application under the unknown underwater acoustic channel environment; and the transmitted signal passing through the underwater acoustic channel can be estimated, so that the influence of the self-transmitting transducer on the system can be reduced in a channel estimation mode.
Drawings
Fig. 1 shows the channel simulation estimation result estimated by the simulation example 1 ucembo and LMS method.
Fig. 2 shows the channel error estimated by the coembco method and the LMS method in the simulation example 2.
Fig. 3 shows the channel error estimated by the simulation example 3ucembco method and the LMS method.
Fig. 4 shows the channel error estimated by the simulation example 4ucembco method and the LMS method.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. The specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The embodiment provides an underwater channel estimation method based on convex optimization, which comprises the following steps:
assuming that the MIMO system has J receiving transducers and P transmitting transducers, the receiving transducers receive data
Figure 549123DEST_PATH_IMAGE025
P transmitting transducers transmit data as
Figure 901607DEST_PATH_IMAGE026
P th hairThe channel from the transmitting transducer to the jth receiving transducer is
Figure 781839DEST_PATH_IMAGE027
And M is the channel length, the data of the jth receiving array element is as follows:
Figure 219773DEST_PATH_IMAGE028
Figure 578073DEST_PATH_IMAGE029
（1）
wherein the content of the first and second substances,
Figure 50643DEST_PATH_IMAGE030
is a noise, and the noise is,
Figure 603240DEST_PATH_IMAGE031
is a matrix generated from the transmit data as follows:
Figure 528471DEST_PATH_IMAGE032
（2）
s2, minimizing convolution error of the received data and signal with the channel:
Figure 752779DEST_PATH_IMAGE033
（3）
wherein the content of the first and second substances,
Figure 689642DEST_PATH_IMAGE034
is composed of
Figure 973993DEST_PATH_IMAGE035
The matrix of the composition is formed by the following components,
Figure 324203DEST_PATH_IMAGE036
；
formula 3) shows that it is an unconstrained convex problem, apparently satisfying a strong dual. Then, solving convolution errors of the received data and the signal and the channel by adopting a Lagrange method:
order:
Figure 352202DEST_PATH_IMAGE037
（4）
to pair
Figure 970003DEST_PATH_IMAGE038
And (5) solving a gradient to obtain:
Figure 159675DEST_PATH_IMAGE039
（5）
let the gradient equal to 0 to obtain the estimated value of the channel
Figure 997181DEST_PATH_IMAGE040
：
Figure 563292DEST_PATH_IMAGE041
（7）；
S3, searching a channel with the minimum error in the trust domain, introducing a regularization coefficient which changes along with time, and updating the estimated value of the channel when each frame signal arrives.
Further, in step S2, the specific step of solving the convolution error between the received data and the signal and the channel by using the Lagrange method includes:
order:
Figure 864960DEST_PATH_IMAGE042
（8）；
to pair
Figure 163218DEST_PATH_IMAGE038
And (5) solving a gradient to obtain:
Figure 550337DEST_PATH_IMAGE043
（9）；
let the gradient equal to 0 to obtain the estimated value of the channel
Figure 857821DEST_PATH_IMAGE044
：
Figure 748417DEST_PATH_IMAGE045
（10）。
The specific algorithm flow in multiple input multiple output is as follows:
1. transmitting data giving P transmitting array elements
Figure 545472DEST_PATH_IMAGE046
And received data of J receiving array elements
Figure 587596DEST_PATH_IMAGE047
. If there is a pre-estimated channel
Figure 761088DEST_PATH_IMAGE048
Then, this result is used for subsequent calculations; otherwise initialize
Figure 709453DEST_PATH_IMAGE049
；
2. Cycle l = 0 to P-1;
3. looping, and jumping out of the loop until a convergence condition is met (for example, the channel change is smaller than a preset value before and after updating) or the loop time exceeds a preset time;
4. cycle J = 0 to J-1;
5、
Figure 677409DEST_PATH_IMAGE050
；
6. outputting channel estimation results
Figure 711224DEST_PATH_IMAGE051
。
Verifying convergence of the algorithm:
Figure 422828DEST_PATH_IMAGE052
（11）
when the data transmitted by different transmitting array elements are uncorrelated and the noise is uncorrelated with the transmitted signal
Figure 288016DEST_PATH_IMAGE053
（12）
The algorithm converges unbiased.
When considering channel estimation in the form of a signal stream (the signal is obtained by the receiving system in the form of frames), a channel with the smallest error is sought in the trust domain:
Figure 364556DEST_PATH_IMAGE054
（13）；
wherein the superscript is
Figure 947984DEST_PATH_IMAGE055
The data representing the i-th frame is,
Figure 633918DEST_PATH_IMAGE056
is the error coefficient;
its equivalent, and introduces regularization coefficients that vary with time
Figure 619192DEST_PATH_IMAGE057
Obtaining:
Figure 866634DEST_PATH_IMAGE058
（14）；
when each frame signal comes, an updating formula is obtained for updating the estimated value of the channel:
Figure 937358DEST_PATH_IMAGE059
（15）。
when faced with complex environments, the regularization coefficients may be selected according to the transformation of the environment. If the environment changes rapidly over time, then less should be set
Figure 928447DEST_PATH_IMAGE060
Enabling the estimation result to follow the environmental change; when the environmental change speed is slow, a larger one can be selected
Figure 768228DEST_PATH_IMAGE061
And the updating stability is ensured.
The specific algorithm flow in multiple input multiple output is as follows:
1. in the processing of the ith frame, transmission data is given
Figure 248887DEST_PATH_IMAGE062
And receiving data
Figure 479012DEST_PATH_IMAGE063
Giving the estimation result of the previous frame
Figure 336109DEST_PATH_IMAGE064
And, if in the case of the first frame,
Figure 344910DEST_PATH_IMAGE065
；
2. cycle l = 0 to P-1;
3. is circulated until
Figure 996471DEST_PATH_IMAGE066
Or reaching the upper limit of the cycle times;
4. cycle J = 0 to J-1;
5、
Figure 979471DEST_PATH_IMAGE067
；
6. outputting channel estimation results
Figure 374680DEST_PATH_IMAGE068
。
Further, in order to verify that the present invention can realize higher accuracy channel estimation, the following simulation experiment was performed:
simulation example 1
A single-input single-output model is set, the transmitted signal is a random signal, the signal length is 1024, and Gaussian white noise with 5dB signal-to-noise ratio is added. The channel length is set to 200. The LMS algorithm was used for comparison and the simulation results are shown in fig. 1. As can be seen from fig. 1, the channel estimated by using the method of the present invention, ucembo, is more accurate than LMS.
Simulation example 2
Assuming a 1-input-1-output signal model in which the length of the channel is set to 200, the length of the transmitted signal per frame is 1024, the transmitted signal is a random signal, and 0dB of white gaussian noise is added. And transmitting 50 frames of signals in total, and observing the error condition of the channel estimation result.
Both algorithms have converged in the calculation of the first frame due to the long length of one frame. The absolute error of Lms method is about 9 and the absolute error of diucembco is less than 1. The simulation result is shown in fig. 2, and as can be seen from fig. 2, the error of the method ucembo is far lower than that of the lms method, and a more accurate channel estimation result is obtained.
Simulation example 3
Assuming a 1-input-1-output signal model in which the length of the channel is set to 200, the length of the transmitted signal is 512 per frame, and the transmitted signal is a random signal. The signal-to-noise ratio was set to-20 dB to 20dB, with calculations being made every 1 dB. Under each signal-to-noise ratio setting, 50 times of simulation is carried out, and the average value of errors is taken.
The simulation result is shown in FIG. 3, and it can be known from FIG. 3 that the estimation error of the method of the present invention, ucembco, is always smaller than lms in the [ -20,20] dB signal-to-noise ratio interval. The method of the invention is always superior to the lms method, the estimation error of the method of the invention is rapidly reduced along with the increase of the signal to noise ratio, and the method of the invention is adopted in the actual environment to obtain better results.
Simulation example 4
Assume a 2-in 2-out signal model in which the length of the channel is set to 20, the length of the transmit signal is 1024, the transmit signal is a random signal, and 0dB of white gaussian noise is added. The observation simulation results are shown in fig. 4. The results of fig. 4 show that the present invention, ucembo, gives very accurate estimates for all channels.
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.

Claims (3)

1. An underwater channel estimation method based on convex optimization is characterized by comprising the following steps:
s1, assuming that the MIMO system has J receiving transducers and P transmitting transducers, assuming that the receiving transducers receive data
Figure 578334DEST_PATH_IMAGE001
P transmitting transducers transmit data as
Figure 188045DEST_PATH_IMAGE002
The channel from the pth transmitting transducer to the jth receiving transducer is
Figure 198726DEST_PATH_IMAGE003
And M is the channel length, the data of the jth receiving array element is as follows:
Figure 104365DEST_PATH_IMAGE004
；
wherein the content of the first and second substances,
Figure 200497DEST_PATH_IMAGE005
is a noise, and the noise is,
Figure 849784DEST_PATH_IMAGE006
is a matrix generated from the transmit data as follows:
Figure 714972DEST_PATH_IMAGE007
；
s2, minimizing convolution error of the received data and signal with the channel:
Figure 791512DEST_PATH_IMAGE008
；
wherein the content of the first and second substances,
Figure 374940DEST_PATH_IMAGE009
is composed of
Figure 624656DEST_PATH_IMAGE010
The matrix of the composition is formed by the following components,
Figure 49078DEST_PATH_IMAGE011
；
and solving convolution error of the received data and signal with the channel by Lagrange method to obtain estimated value of the channel
Figure 358836DEST_PATH_IMAGE012
；
S3, searching a channel with the minimum error in the trust domain, introducing a regularization coefficient which changes along with time, and updating the estimated value of the channel when each frame signal arrives.
2. The convex optimization-based underwater channel estimation method according to claim 1, wherein in the step S2, the specific step of solving the convolution error between the received data and the signal and the channel by using the Lagrange method includes:
order:
Figure 367244DEST_PATH_IMAGE013
；
to pair
Figure 420650DEST_PATH_IMAGE014
And (5) solving a gradient to obtain:
Figure 198113DEST_PATH_IMAGE015
；
let the gradient equal to 0 to obtain the estimated value of the channel
Figure 678773DEST_PATH_IMAGE016
：
Figure 971214DEST_PATH_IMAGE017
。
3. The convex optimization-based underwater channel estimation method according to claim 1, wherein the step S3 specifically includes:
find a channel with the smallest error in the trust domain:
Figure 765995DEST_PATH_IMAGE018
；
wherein the superscript is
Figure 460282DEST_PATH_IMAGE019
The data representing the i-th frame is,
Figure 548061DEST_PATH_IMAGE020
is the error coefficient;
its equivalent, and introduces regularization coefficients that vary with time
Figure 593377DEST_PATH_IMAGE021
Obtaining:
Figure 926270DEST_PATH_IMAGE022
；
when each frame signal comes, an updating formula is obtained for updating the estimated value of the channel:
Figure 475063DEST_PATH_IMAGE023
。
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