[go: up one dir, main page]
More Web Proxy on the site http://driver.im/

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

Info

Publication number
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
Authority
CN
China
Prior art keywords
time
underwater acoustic
delay
acoustic channel
doppler
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810586326.5A
Other languages
Chinese (zh)
Other versions
CN108833312A (en
Inventor
伍飞云
杨坤德
田天
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Northwestern Polytechnical University
Original Assignee
Northwestern Polytechnical University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Northwestern Polytechnical University filed Critical Northwestern Polytechnical University
Priority to CN201810586326.5A priority Critical patent/CN108833312B/en
Publication of CN108833312A publication Critical patent/CN108833312A/en
Application granted granted Critical
Publication of CN108833312B publication Critical patent/CN108833312B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B13/00—Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Power Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Mathematical Physics (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
  • Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)

Abstract

本发明涉及一种基于时延多普勒域的时变稀疏水声信道估计方法，首先，针对时变水声信道进行时延多普勒域建模，以期获得稀疏的二维域表达方式，在时延多普勒域表达的基础上。采用逐块训练模式，并结合施密特正交匹配追踪算法迭代寻优得到时延多普勒域的稀疏水声信道冲激响应函数，将所估计得到的时延多普勒域水声信道信息，在接收端，构造基于信道信息的最小均方误差均衡器对发送信号进行恢复。该项发明适用于时变水声信道估计、水声通信。本发明有益效果体现在：本发明基于施密特正交化选择匹配原子，有效避免了冗余计算，使得本发明产生的时延多普勒水声信道估计结果具有更高的精度。

Figure 201810586326

The invention relates to a time-varying sparse underwater acoustic channel estimation method based on the time-delayed Doppler domain. First, the time-varying underwater acoustic channel is modeled in the time-delayed Doppler domain, in order to obtain a sparse two-dimensional domain representation, On the basis of the expression in the time-delay Doppler domain. The block-by-block training mode is used, combined with the iterative optimization of the Schmitt orthogonal matching pursuit algorithm to obtain the sparse underwater acoustic channel impulse response function in the delay Doppler domain, and the estimated delay Doppler domain underwater acoustic channel is At the receiving end, a minimum mean square error equalizer based on channel information is constructed to restore the transmitted signal. The invention is suitable for time-varying underwater acoustic channel estimation and underwater acoustic communication. The beneficial effects of the present invention are as follows: the present invention selects matching atoms based on Schmidt orthogonalization, which effectively avoids redundant calculation, so that the time delay Doppler underwater acoustic channel estimation result generated by the present invention has higher precision.

Figure 201810586326

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)

1.一种基于时延多普勒域的时变稀疏水声信道估计方法，其特征在于步骤如下：1. a time-varying sparse underwater acoustic channel estimation method based on time-delay Doppler domain, is characterized in that the steps are as follows: 步骤1、建立时延多普勒域模型：Step 1. Establish a time-delay Doppler domain model: 1、设参数Δt,Δτ和Δf分别为观测时间、时延、以及多普勒频移的采样间隔,离散化的观测时间表示为tn＝nΔt,n＝1,...,N,N为观测时间最大采样点数，离散化的时延表示为：1. Let the parameters Δt, Δτ and Δf be the observation time, time delay, and sampling interval of Doppler frequency shift, respectively, and the discretized observation time is expressed as t n =nΔt,n=1,...,N,N is the maximum number of sampling points in the observation time, and the discretized delay is expressed as: τm＝τ0+(m-1)Δτ,m＝1,...,M (1)τ m =τ 0 +(m-1)Δτ,m=1,...,M (1) 其中参数τ0是参考时延,M是最大的时延采样维度,称为水声信道阶数；The parameter τ 0 is the reference delay, and M is the maximum delay sampling dimension, which is called the underwater acoustic channel order; 2、离散化时变信道响应为h[tn,τm]，定义采样的多普勒为：2. The discrete time-varying channel response is h[t n ,τ m ], and the sampled Doppler is defined as: fl＝f0+(l-1)Δf,l＝1,...,L (2)f l =f 0 +(l-1)Δf,l=1,...,L (2) 其中f0是最小的多普勒频移值,L是最大的多普勒采样维度，因此,二维的时延-多普勒维度大小表示为LM；Where f 0 is the smallest Doppler frequency shift value, L is the largest Doppler sampling dimension, therefore, the two-dimensional delay-Doppler dimension size is expressed as LM; 设
Figure FDA0002731820560000011
其中fs是信号频率采样率,则离散化的输入输出关系式为：Assume
Figure FDA0002731820560000011
Where f s is the signal frequency sampling rate, the discretized input and output relationship is:
Figure FDA0002731820560000012
Figure FDA0002731820560000012
 w为噪声；w is noise; 定义u＝[u1,1,…,u1,M,u2,1,…,u2,M,…,uL,1,…,uL,M]T,其维数为(L·M)×1,则时延多普勒域的输入输出关系表达为：Define u=[u 1,1 ,…,u 1,M ,u 2,1 ,…,u 2,M ,…,u L,1 ,…,u L,M ] T , whose dimension is (L M)×1, then the input-output relationship in the delay Doppler domain is expressed as:
Figure FDA0002731820560000013
Figure FDA0002731820560000013
 其中
Figure FDA0002731820560000014
的维数是L×1,
Figure FDA0002731820560000015
表示Kronecker乘积,x[tn]＝[xn+M-1,…,xn+1,xn]T的维数为M×1；in
Figure FDA0002731820560000014
The dimension of is L×1,
Figure FDA0002731820560000015
Representing the Kronecker product, x[t n ]=[x n+M-1 ,...,x n+1 ,x n ] The dimension of T is M×1; 定义y＝{y[t1],y[t2],…,y[tN]}T,
Figure FDA0002731820560000016
A＝{a[t1],a[t2],…,a[tN]}H,得到以下输入输出关系：Define y={y[t 1 ],y[t 2 ],...,y[t N ]} T ,
Figure FDA0002731820560000016
A={a[t 1 ],a[t 2 ],...,a[t N ]} H , the following input-output relationship is obtained: y＝Au+w (5)y=Au+w (5) 其中y和w的维数都为N×1,A和u的维数分别为N×(L·M),(L·M)×1；The dimensions of y and w are both N×1, and the dimensions of A and u are N×(L·M) and (L·M)×1, respectively; 信道冲激响应函数u估计的具体方法为：The specific method for estimating the channel impulse response function u is as follows: ①输入参数信息设置：矩阵A和接收信号y，设置算法终止条件
Figure FDA0002731820560000021
①Input parameter information setting: matrix A and received signal y, set the algorithm termination condition
Figure FDA0002731820560000021
 ②输出参数信息设置：信道冲激响应函数估计值u；②Output parameter information setting: channel impulse response function estimated value u; ③初始化：初始估计值为零向量u{0}＝0：初始残差r{0}＝y；初始迭代次数i＝0；初始信道冲激响应函数支撑集为空集
Figure FDA0002731820560000022
③Initialization: The initial estimated value is zero, the vector u {0} = 0: the initial residual r {0} = y; the initial number of iterations i = 0; the initial channel impulse response function support set is an empty set
Figure FDA0002731820560000022
 ④判断算法终止条件是否满足，即是否||r||＜rth，若是，则停止迭代，若否，则按照如下迭代式迭代：④ Determine whether the termination condition of the algorithm is satisfied, that is, whether ||r||<r th , if so, stop the iteration, if not, iterate according to the following iterative formula:
Figure FDA0002731820560000023
Figure FDA0002731820560000023
 P{1}＝v{1}(v{1}Tv{1})-1v{1}T (7)P {1} = v {1} (v {1}T v {1} ) -1 v {1}T (7) r{1}＝r{0}-P{1}y (8)r {1} =r {0} -P {1} y(8) 对于第i次选择的原子
Figure FDA0002731820560000024
应该与之前所选择的正交，因此第i次的正交向量为：For the i-th chosen atom
Figure FDA0002731820560000024
It should be orthogonal to the one chosen before, so the ith orthogonal vector is:
Figure FDA0002731820560000025
Figure FDA0002731820560000025
 得到第i次的投影矩阵为：The i-th projection matrix is obtained as: P{i}＝v{i}(v{i}Tv{i})-1v{i}T (10)P {i} = v {i} (v {i}T v {i} ) -1 v {i}T (10) 第i次的残差更新为：The i-th residual is updated as: r{i}＝r{i-1}-P{i}y (11)r {i} =r {i-1} -P {i} y (11) 支撑集更新：Support set update: S{i}＝S{i-1}∪s{i} (12)S {i} = S {i-1} ∪s {i} (12) 接下来求伪逆运算：Next, find the pseudo-inverse operation:
Figure FDA0002731820560000026
Figure FDA0002731820560000026
 估计的水声信道冲激响应函数为：The estimated impulse response function of the underwater acoustic channel is:
Figure FDA0002731820560000031
Figure FDA0002731820560000031
 步骤2：本MMSE均衡器输出的对发送信号的估计值表示为：Step 2: The estimated value of the transmitted signal output by the MMSE equalizer is expressed as:
Figure FDA0002731820560000032
Figure FDA0002731820560000032
 其中I表示单位矩阵，
Figure FDA0002731820560000033
表示噪声能量的参数，y表示接收端的信号向量，而
Figure FDA0002731820560000034
表示均衡器对发送端信号的估计值，且where I represents the identity matrix,
Figure FDA0002731820560000033
is the parameter representing the noise energy, y represents the signal vector at the receiver, and
Figure FDA0002731820560000034
represents the equalizer's estimate of the signal at the transmitter, and
Figure FDA0002731820560000035
Figure FDA0002731820560000035
 其中in
Figure FDA0002731820560000036
Figure FDA0002731820560000036
 是一个N×N的对角矩阵，而矩阵Ul维数为N×Ns，其中Ns为发送序列长度，由向量ul＝[U(0,l),...,U(M-1,l)]T构造而成，具体排列方式为：is an N×N diagonal matrix, and the dimension of the matrix U l is N×N s , where N s is the length of the transmission sequence, which is defined by the vector u l =[U(0,l),...,U(M -1,l)] T is constructed, and the specific arrangement is:
Figure FDA0002731820560000037
Figure FDA0002731820560000037
CN201810586326.5A 2018-06-08 2018-06-08 Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain Active CN108833312B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810586326.5A CN108833312B (en) 2018-06-08 2018-06-08 Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810586326.5A CN108833312B (en) 2018-06-08 2018-06-08 Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain

Publications (2)

Publication Number Publication Date
CN108833312A CN108833312A (en) 2018-11-16
CN108833312B true CN108833312B (en) 2021-01-05

Family

ID=64143491

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810586326.5A Active CN108833312B (en) 2018-06-08 2018-06-08 Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain

Country Status (1)

Country Link
CN (1) CN108833312B (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109743269A (en) * 2019-02-19 2019-05-10 哈尔滨工程大学 A Method of Underwater Acoustic OFDM Channel Reconstruction Based on Data Fitting
CN111711584B (en) * 2020-05-22 2022-06-07 西北工业大学 Sparse underwater acoustic channel estimation method based on proportional normalization minimum mean square error
CN112054973B (en) * 2020-08-28 2021-07-06 西北工业大学 A minimum mean square error sparse underwater acoustic channel estimation method
CN112054974B (en) * 2020-08-28 2021-07-16 西北工业大学 Underwater acoustic channel identification method based on regularized minimum mean square error variable step size algorithm
CN112906632B (en) * 2021-03-18 2022-11-11 中北大学 Automatic extraction method of highly adaptive time delay target signal
CN114124245B (en) * 2021-11-05 2024-05-03 北京长城电子装备有限责任公司 Underwater sound high-speed communication method under time-varying channel
CN115236648B (en) * 2022-06-30 2023-03-17 哈尔滨工程大学 Polar region under-ice target acoustic echo signal time delay and Doppler joint estimation method

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107395536A (en) * 2017-07-20 2017-11-24 西北工业大学 The method estimated the underwater acoustic channel impulse response function under more way environment

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR102364688B1 (en) * 2015-11-13 2022-02-21 한국전자통신연구원 Apparatus and method for estimating parameter of multi path signal

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107395536A (en) * 2017-07-20 2017-11-24 西北工业大学 The method estimated the underwater acoustic channel impulse response function under more way environment

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
基于稀疏采样的水声OFDM通信信道估计技术研究;陈艳;《中国优秀硕士学位论文》;20140815;全文 *
采用时域联合稀疏恢复的多输入多输出水声信道压缩感知估计;童峰;《通信学报》;20160612;全文 *
长时延扩展水声信道的联合稀疏恢复估计;周跃海;《通信学报》;20160225;全文 *

Also Published As

Publication number Publication date
CN108833312A (en) 2018-11-16

Similar Documents

Publication Publication Date Title
CN108833312B (en) Time-varying sparse underwater acoustic channel estimation method based on delay-Doppler domain
CN104283825B (en) A kind of channel estimation methods perceived based on dynamic compression
JP5484682B2 (en) WIRELESS COMMUNICATION DEVICE, EQUALIZER, EQUALIZER WEIGHT COEFFICIENT PROGRAM AND Equalizer Weight Coefficient Calculation Method
CN106130939B (en) An iterative method for fast time-varying channel estimation in MIMO-OFDM systems
CN103905355B (en) A kind of virtual time reversal underwater sound OFDM channel equalization methods
CN109802911B (en) A Fast Channel Estimation and Signal Synchronization Method for Underwater Acoustic Modem
US8737460B2 (en) Equalizer and detector arrangement employing joint entropy-based calibration
CN110311872B (en) A method, system, device and storage medium for underwater acoustic sparse channel estimation
CN113242191B (en) Improved time sequence multiple sparse Bayesian learning underwater acoustic channel estimation method
US7203257B2 (en) Best linear unbiased channel estimation for frequency selective multipath channels with long delay spreads
WO2001050695A1 (en) Method for equalizing data received
CN109088835A (en) Underwater sound time-varying channel estimation method based on time multiple management loading
CN107395536B (en) Method for Estimating Impulse Response Function of Underwater Acoustic Channel in Multipath Environment
CN108965186B (en) Downlink time-frequency synchronization method for low-earth-orbit satellite mobile communication system
CN102664841A (en) Method for SC-FDE (single carrier-frequency domain equalization) system low complexity RLS self-adaption channel estimation
CN110380994B (en) Fast Bayesian Matching Pursuit for Maritime Sparse Channel Estimation
WO2007149630A2 (en) An efficient doppler compensation method and receiver for orthogonal-frequency-division-multiplexing (ofdm) systems
CN111291511B (en) Soft Kalman filtering iteration time-varying channel estimation method based on historical information
US20040240587A1 (en) Channel estimation for frequency selective multipath channels with long delay spreads based on an assumed physical channel
CN110971546B (en) Channel tracking method for large-scale MIMO system
CN110753011A (en) Single carrier equalization method for GMSK signal
CN111555994B (en) A Cluster Sparse Channel Estimation Method Based on the Maximum Skip Line Criterion Algorithm
CN110233808B (en) A kind of FTN system signal detection method
CN116915555B (en) An underwater acoustic channel estimation method and device based on self-supervised learning
CN113472704B (en) HPLC channel estimation method and device based on weighted iterative global least squares

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant