CN111224704A - Distributed self-adaptive reduced rank beam forming method - Google Patents

Distributed self-adaptive reduced rank beam forming method Download PDF

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CN111224704A
CN111224704A CN201911099146.5A CN201911099146A CN111224704A CN 111224704 A CN111224704 A CN 111224704A CN 201911099146 A CN201911099146 A CN 201911099146A CN 111224704 A CN111224704 A CN 111224704A
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CN111224704B (en
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夏威
李菁华
方惠
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • 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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming

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Abstract

The invention belongs to the technical field of distributed self-adaptation, and mainly relates to a distributed self-adaptation strategy and a space-domain rank-reduction beam forming method, in particular to a distributed self-adaptation rank-reduction beam forming method; the method aims to solve the problems that when the number of array elements is large, the complexity of a distributed array anti-interference adaptive algorithm is increased, and the convergence speed is reduced. The invention effectively combines the distributed adaptive strategy, the rank reduction technology and the beam forming method, adopts the ATC thought, ensures that the nodes can effectively communicate with other nodes in the adaptive and combining processes, and can reduce the complexity of the algorithm by utilizing the rank reduction joint iterative optimization thought under the condition of more array elements, thereby avoiding unnecessary calculation cost.

Description

Distributed self-adaptive reduced rank beam forming method
Technical Field
The invention belongs to the technical field of distributed self-adaptation, mainly relates to a distributed self-adaptation strategy and a space-domain rank-reduction beam forming method, and particularly relates to a distributed self-adaptation rank-reduction beam forming method.
Background
Distributed or cooperative network-based processing is widely applied to the fields of environmental monitoring, disaster relief management, source location, etc. as an efficient network application processing technology, compared with a traditional centralized processing technology, the distributed processing technology utilizes local computation of each node and communication between adjacent nodes to solve the problem of the whole network, and the cooperative manner enables each node to utilize the spatial diversity and temporal diversity obtained by the geographical distribution of the node, thereby expanding the scalability and flexibility of the network.
Since 2006, Ali h. In 2009, Ali h.sayed et al applied the L MS adaptive algorithm to the distributed network in the document Diffusion LMS strategies for distributed determination, and proposed that parameter estimation be performed using the idea of adaptive and combined (ATC) and the idea of combined and adaptive (CTA), and that nodes can effectively communicate with other nodes during the combination and adaptation process; in 2012, in all h.sayed et al, in the document "Beam correlation estimation adaptation over beamforming" in the document, an optimal weight vector is solved by using the ATC idea, and a received signal of any array is filtered by using the weight vector to achieve the purposes of retaining a desired signal and suppressing interference. However, when the parameter vector to be estimated has a large number of parameters, the network needs a large communication bandwidth to enable the adjacent nodes to transmit their local estimates, which limits the practicability of the algorithm, and therefore, dimension reduction becomes an important means for solving the large data set distribution problem; ribeiro et al propose several distributed quantization Kalman filtering algorithms, Scaglione et al propose distributed main subspace estimation in document D existing structured basic estimation in wireless sensor networks in 2011, K.Slavakis et al propose Krylov subspace optimization technology in document tracking off complex communication costs in distributed adaptive estimation via for dimensional reduction in 2013; however, the Distributed dimension reduction algorithm still has the disadvantages of high computational complexity and unsatisfactory performance, in this case, the rank reduction technology is a powerful tool for performing dimension reduction, in 2017, Songcen Xu, Rodrigo c.de Lamare provided with a rank reduction joint iterative optimization method in the document "Distributed low-random adaptive estimation algorithm based on adaptive optimization", and two adaptive joint iterative methods are provided in the document for parameter estimation. Based on this, the invention provides a distributed adaptive rank reduction beam forming method.
Disclosure of Invention
The invention aims to provide a distributed self-adaptive rank-reduction beam forming method, and aims to solve the problems that the complexity of a distributed array anti-interference self-adaptive algorithm is increased and the convergence speed is reduced when the number of array elements is large. The invention effectively combines the distributed adaptive strategy, the rank reduction technology and the beam forming method, and still adopts the thought of ATC, so that the nodes can effectively communicate with other nodes in the adaptive and combining processes, and the thought of rank reduction combined iterative optimization can be utilized to reduce the complexity of the algorithm and avoid unnecessary calculation cost under the condition of more array elements.
In order to achieve the purpose, the invention adopts the technical scheme that:
a distributed adaptive rank reduction beam forming method comprises the following steps:
step 1, obtaining array receiving signals of node k
Setting a desired far-field complex narrowband signal
Figure BDA0002269282650000021
Incident on the uniform linear array network and simultaneously subjected to P-1 complex narrow-band signals
Figure BDA0002269282650000022
Then the discrete complex baseband received signal vector of the kth node array is represented as:
Figure BDA0002269282650000023
wherein i represents the ith time, sp(i) Is a narrow band signal
Figure BDA0002269282650000024
Discrete baseband form of (a); n isk(i) Is a zero mean additive white gaussian noise vector; a (theta)p) As a guide vector, a (θ)1) As a guide vector of the desired signal, thetapAngle of arrival for the p-th incident signal;
step 2, initializing the reduced rank weight vector, the reduced rank matrix and the related parameters
Initializing rank-reduced weight vector initial values for all node arrays
Figure BDA0002269282650000025
With initial values of the reduced rank matrix Sk(0) The condition constraint is satisfied:
Figure BDA0002269282650000026
and obtaining a switching matrix C and a combining matrix F, G according to the calculation rule:
Figure BDA0002269282650000027
wherein, cl,kFor the (l, k) th element, f, of the switching matrix Cl,kFor the (l, k) -th element, g, of the combined matrix Fl,kIs the (l, k) th element of the combining matrix G;
Figure BDA00022692826500000317
a set of neighborhood nodes, r, representing the kth node array including itselfkIs composed of
Figure BDA00022692826500000318
The total number of nodes contained;
step 3, diffusing the received signals of each node array, and enabling the received signals of the node arrays to pass through a reduced rank beam former;
1) for array received signal xl(i) And a desired signal steering vector a (theta)1) Performing rank reduction processing to obtain the array receiving signal after rank reduction
Figure BDA0002269282650000031
Sum rank reduced desired signal steering vector
Figure BDA0002269282650000032
Figure BDA0002269282650000033
Figure BDA0002269282650000034
Wherein S isk(i-1) is a reduced rank matrix of the kth node array at the ith-1 moment;
2) obtained after rank reduction treatment
Figure BDA0002269282650000035
Obtaining an array output signal through a reduced rank filter:
Figure BDA0002269282650000036
wherein,
Figure BDA0002269282650000037
a rank reduction weight vector of the kth node array at the ith-1 moment;
and 4, diffusing the output signals of the node arrays and the array receiving signals after the rank reduction, and iteratively updating the rank reduction matrix Q of the kth node arrayk(i) Intermediate estimation of sum rank reduced weight vector
Figure BDA0002269282650000038
Figure BDA0002269282650000039
Figure BDA00022692826500000310
Wherein,
Figure BDA00022692826500000311
and
Figure BDA00022692826500000312
are projection matrices;
Figure BDA00022692826500000313
and
Figure BDA00022692826500000314
respectively carrying out iteration step length of intermediate estimation of the reduced rank matrix and the reduced rank weight vector;
and 5, diffusing the intermediate estimation of the reduced rank weight vector of each node array, and randomly arranging the intermediate estimation of the reduced rank weight vector of the adjacent node including the node array of the kth node array to obtain:
Figure BDA00022692826500000315
and calculating a combination matrix of the reduced rank matrix estimation of the kth node array:
Figure BDA00022692826500000316
and 6, diffusing the combined matrix of the reduced rank matrix and the reduced rank matrix estimation of each node array, and updating to obtain the estimation of the reduced rank matrix of the kth node array:
Figure BDA0002269282650000041
and 7, calculating a combination matrix of the reduced rank weight vector estimation of the kth node array:
Figure BDA0002269282650000042
Figure BDA0002269282650000043
therein, unwecm,n{. is a matrixing function;
and 8, calculating the reduced rank weight vector estimation of the kth node array:
Figure BDA0002269282650000044
obtaining the optimal weight of the kth node array, and calculating a beam function:
Figure BDA0002269282650000045
Figure BDA0002269282650000046
wherein, wkFull rank weight vector for kth node array, Ek(θ) is the beam function, θ ∈ (-90 °,90 °).
A distributed adaptive rank reduction beam forming method comprises the following steps:
step 1, obtaining array receiving signals of node k
Setting a desired far-field complex narrowband signal
Figure BDA0002269282650000047
Incident on the uniform linear array network and simultaneously subjected to P-1 complex narrow-band signals
Figure BDA0002269282650000048
Then the discrete complex baseband received signal vector of the kth node array is represented as:
Figure BDA0002269282650000049
wherein i represents the ith time, sp(i) Is a narrow band signal
Figure BDA00022692826500000410
Discrete baseband form of (a); n isk(i) Is a zero mean additive white gaussian noise vector; a (theta)p) As a guide vector, a (θ)1) As a guide vector of the desired signal, thetapAngle of arrival for the p-th incident signal;
step 2, initializing the reduced rank weight vector, the reduced rank matrix and the related parameters
Initializing rank-reduced weight vector initial values for all node arrays
Figure BDA00022692826500000411
With initial values of the reduced rank matrix Sk(0) The condition constraint is satisfied:
Figure BDA00022692826500000412
and obtaining a switching matrix C and a combining matrix F, G according to the calculation rule:
Figure BDA00022692826500000515
wherein, cl,kFor the (l, k) th element, f, of the switching matrix Cl,kFor the (l, k) -th element, g, of the combined matrix Fl,kIs the (l, k) th element of the combining matrix G;
Figure BDA00022692826500000516
a set of neighborhood nodes, r, representing the kth node array including itselfkIs composed of
Figure BDA00022692826500000517
The total number of nodes contained;
step 3, diffusing the received signals of each node array, and enabling the received signals of the node arrays to pass through a reduced rank beam former;
1) for array received signal xl(i) And a desired signal steering vector a (theta)1) Performing rank reduction processing to obtain the array receiving signal after rank reduction
Figure BDA0002269282650000051
Sum rank reduced desired signal steering vector
Figure BDA0002269282650000052
Figure BDA0002269282650000053
Figure BDA0002269282650000054
Wherein S isk(i-1) is a reduced rank matrix of the kth node array at the ith-1 moment;
2) obtained after rank reduction treatment
Figure BDA0002269282650000055
Obtaining an array output signal through a reduced rank filter:
Figure BDA0002269282650000056
wherein,
Figure BDA0002269282650000057
a rank reduction weight vector of the kth node array at the ith-1 moment;
and 4, diffusing the output signals of the node arrays and the array receiving signals after the rank reduction, and iteratively updating the rank reduction matrix Q of the kth node arrayk(i) Intermediate estimation of sum rank reduced weight vector
Figure BDA0002269282650000058
Figure BDA0002269282650000059
Figure BDA00022692826500000510
Wherein,
Figure BDA00022692826500000511
and
Figure BDA00022692826500000512
are projection matrices;
Figure BDA00022692826500000513
and
Figure BDA00022692826500000514
respectively carrying out iteration step length of intermediate estimation of the reduced rank matrix and the reduced rank weight vector;
step 5, diffusing the reduced rank matrix Q of each node arrayk(i) And randomly arranging the intermediate estimation of the reduced rank matrix of the adjacent nodes of the kth node array including the kth node array to obtain:
Σk(i)＝[Ql(i),l∈Nk]T
and calculating a combination matrix of the reduced rank weight vector estimation of the kth node array:
Figure BDA0002269282650000061
and 6, diffusing the combined matrix of the intermediate estimation and the reduced rank weight vector estimation of each node array, and updating to obtain the reduced rank weight vector estimation of the kth node array:
Figure BDA0002269282650000062
and 7, calculating a combination matrix of the reduced rank matrix estimation of the kth node array:
Figure BDA0002269282650000063
Figure BDA0002269282650000064
therein, unwecm,n{. is a matrixing function;
and 8, calculating the reduced rank matrix estimation of the kth node array:
Sk(i)＝Σk(i)Λk(i)
obtaining the optimal weight of the kth node array, and calculating a beam function:
Figure BDA0002269282650000065
Figure BDA0002269282650000066
wherein, wkFull rank weight vector for kth node array, Ek(θ) is the beam function, θ ∈ (-90 °,90 °).
The invention has the beneficial effects that:
the invention provides a distributed self-adaptive reduced rank beam forming method, which has the following advantages:
1) the invention combines the distributed adaptive strategy, the adaptive rank reduction technology and the beam forming method, and provides a basic framework of the distributed adaptive rank reduction beam former; in the framework, the rank reduction technology and the beam forming algorithm can be replaced or adjusted according to the requirements of users; has better flexibility.
2) Compared with a centralized algorithm, the distributed adaptive rank-reduction beamforming method can effectively utilize the difference of received signals caused by different geographic positions and mutual cooperation and information exchange among nodes, and avoids the situation that the anti-interference capability is weakened or even fails caused by the occurrence of problems in a fusion center.
3) The invention provides a self-adaptive distributed reduced rank beam forming method, wherein the reduced rank technology, the combination of node information and the beam forming are self-adaptive; when the arrival angle of the desired signal or the interference signal changes, the method provided by the invention can also adjust in a self-adaptive manner, and effectively suppresses the interference signal while ensuring the undistorted output of the desired signal.
4) The self-adaptive rank reduction method provided by the invention allows a user to set a proper rank reduction dimension according to requirements so as to obtain a better interference suppression effect; the information sharing method based on the adaptive combined matrix can utilize the differentiated information of the neighbor nodes, and is beneficial to improving the estimation performance of the reduced rank matrix and the reduced rank weight vector; after the distributed reduced rank matrix calculation is completed, the reduced rank beam forming method can obtain the interference suppression effect equivalent to that of the full rank beam forming method under the conditions of low calculation complexity and smaller communication bandwidth; has good practicability.
5) Compared with the existing distributed adaptive algorithm utilizing the adaptive combination coefficient, the invention provides the distributed adaptive algorithm based on the adaptive combination matrix; the method is not only related to the network topology, but also related to the reduced rank weight vector or the reduced rank matrix; by effectively utilizing the information of the neighbor nodes, the self-adaptive capacity and robustness of the distributed beam forming method can be further enhanced.
Drawings
FIG. 1 is a diagram of a distributed array network architecture of the present invention;
FIG. 2 is a block diagram of a reduced rank beamformer on node k according to the present invention;
fig. 3 is a schematic diagram of an implementation process on a node k in embodiment 1 of the present invention;
fig. 4 is a schematic diagram of an implementation process of embodiment 2 on a node k;
FIG. 5 is a diagram of a distributed network topology of the present invention;
fig. 6, 7, and 8 are comparison diagrams of directional diagrams, output SINR, and MSE learning curves of the dramm-1 algorithm proposed in embodiment 1 and the dramm-2 algorithm proposed in embodiment 2 and the Beam coding algorithm of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific examples.
The invention provides a distributed reduced rank beam forming method, which solves a reduced rank matrix and a reduced rank weight vector by using the thought of alternative iterative optimization, namely, one of the reduced rank matrix and the reduced rank weight vector is fixed to solve the other, so that two strategies are adopted to obtain the reduced rank matrix and the reduced rank weight vector in the invention; in embodiment 1, the method for fixing the combination matrix of the reduced rank matrix and then solving the combination matrix of the reduced rank weight vector is shown in fig. 3; in embodiment 2, a method for fixing a combination matrix of a reduced rank weight vector and then solving the combination matrix of the reduced rank matrix is shown in a flow diagram 4; specifically speaking:
example 1
The embodiment provides a distributed rank-reduction beamforming method, as shown in fig. 3, on an arbitrary node k, the specific process is as follows:
step 1, obtaining array receiving signals of node k
Considering a network comprising N nodes, each node comprising an identical antenna array, wherein the number of array elements is M; the antenna array here may be any array, and for simplicity, the present embodiment is described by using a uniform linear array, as shown in fig. 1;
setting a desired far-field complex narrow-band signal
Figure BDA0002269282650000081
Incident on the uniform linear array network and simultaneously subjected to P-1 complex narrow-band signals
Figure BDA0002269282650000082
Then the discrete complex baseband received signal vector of the kth node array is represented as:
Figure BDA0002269282650000083
wherein i represents the ith time, sp(i) Is a narrow band signal
Figure BDA0002269282650000084
Discrete baseband form of (a); n isk(i) Is a variance of
Figure BDA0002269282650000085
Zero mean additive white Gaussian noise vector of (1) with n at different nodes or different timesl(i1) Receiving signals x independently of each other and of the arrayk(i) (ii) a The guide vector is
Figure BDA0002269282650000086
In particular, a (θ)1) As a guide vector of the desired signal, thetapThe arrival angle of the p-th incident signal is expressed as follows:
Figure BDA0002269282650000087
wherein phi isp＝2πdsinθpλ, d denotes the spacing between adjacent array elements, λ is the carrier wavelength ·TRepresenting a transpose;
step 2, initializing the reduced rank weight vector, the reduced rank matrix and the related parameters
For an array of all nodes k 1,2
Figure BDA0002269282650000088
And initial values of the reduced rank matrix Sk(0) And for the subsequent iteration update, the initial value of the reduced rank weight vector and the initial value of the reduced rank matrix need to satisfy the following condition constraint:
Figure BDA0002269282650000089
wherein the reduced rank matrix SkThe dimension of the signal is M multiplied by D, the dimension of the reduced rank weight vector is D multiplied by 1, D represents the dimension after the reduced rank processing, and the physical meaning of the condition constraint is to enable the undistorted output of the expected signal; in addition, an array of all nodesAll of which are the same, and a switching matrix C and a combining matrix F, G need to be obtained according to the corresponding calculation rules,
Figure BDA00022692826500000810
a set of neighborhood nodes, r, including itself, representing node kkThe specific calculation rule of the total number of nodes contained in the neighborhood node set representing the kth node is as follows:
Figure BDA00022692826500000811
step 3, the node receiving signal passes through the rank-reducing beam former
When the array element number or the sampling data of the array is many, the convergence speed of the self-adaptive method is greatly reduced, so that the rank reduction theory is introduced into the method, the complexity of the method can be effectively reduced through the rank reduction treatment, and the convergence speed of the method is improved; fig. 2 shows a schematic flow chart of spreading array receiving signals and performing rank reduction processing on node received signals, which includes the following specific steps:
1) for array received signal xl(i) And a desired signal steering vector a (theta)1) Performing rank reduction processing to obtain the array receiving signal after rank reduction
Figure BDA0002269282650000091
Sum rank reduced desired signal steering vector
Figure BDA0002269282650000092
The rank reduction is performed by multiplying by a rank reduction matrix SkConjugate transpose (. cndot.) of (i-1)H) The implementation is as follows:
Figure BDA0002269282650000093
Figure BDA0002269282650000094
2) obtained after rank reduction treatment
Figure BDA0002269282650000095
Obtaining an array output signal through a reduced rank filter:
Figure BDA0002269282650000096
and 4, diffusing the output signals of each node array and the array receiving signals after the rank reduction, and iteratively updating the rank reduction matrix Q of the node array kk(i) Intermediate estimation of sum rank reduced weight vector
Figure BDA0002269282650000097
Figure BDA0002269282650000098
Figure BDA0002269282650000099
Wherein,
Figure BDA00022692826500000910
and
Figure BDA00022692826500000911
are all projection matrices;
Figure BDA00022692826500000912
and
Figure BDA00022692826500000913
respectively controlling the speed and the steady state of iterative convergence by using the intermediate estimated iterative step length of the reduced rank matrix and the reduced rank weight vector; coefficient cl,kIs the (l, k) th element of the switching matrix C, which satisfies the constraint:
Figure BDA00022692826500000914
cn,k＝0,1TC＝1Tc1 is 1, i.e. the sum of the column elements of the switching matrix C is 1, the sum of the row elements is also 1Is 1; i isMAn identity matrix representing dimensions M x M; i isDAn identity matrix representing dimensions D × D; x is the number ofl(i) Receiving signals for the array of the node l at the moment i;
and 5, diffusing the intermediate estimation of the rank-reduced weight vector of each node, and randomly arranging the intermediate estimation of the rank-reduced weight vector of the neighborhood nodes including the node k to obtain:
Figure BDA00022692826500000915
and calculating a combination matrix of the reduced rank matrix estimates for node k:
Figure BDA00022692826500000916
wherein the coefficient fl,kIs the (l, k) th element of the combined matrix F, and the combined matrix F satisfies the constraint:
Figure BDA0002269282650000101
fl,k＝0,1TF＝1Tthe sum of column elements of the combination matrix F is 1;
and 6, diffusing the combined matrix of the reduced rank matrix and the reduced rank matrix estimation of each node array, and updating to obtain the estimation of the reduced rank matrix of the node k array:
Figure BDA0002269282650000102
and 7, calculating a combination matrix of the reduced rank weight vector estimation of the node k:
Figure BDA0002269282650000103
Figure BDA0002269282650000104
wherein z isk(i) Is a combination matrix Tk(i) The vectorized expression of (a) is,
Figure BDA0002269282650000105
representing the Kronecker product, a matrixing function unwecm,n{. is an operator that converts a column vector of mn elements into an m × n matrix;
and 8, calculating the rank reduction weight vector estimation of the node k:
Figure BDA0002269282650000106
obtaining the optimal weight of the node array k, and calculating a beam function:
Figure BDA0002269282650000107
Figure BDA0002269282650000108
wherein, wkTo complete a sufficiently sufficient number of iterations of the full rank weight vector, E, of node kk(θ) is the beam function, θ ∈ (-90 °,90 °).
Example 2
The embodiment provides a distributed rank-reduction beamforming method, as shown in fig. 4, on an arbitrary node k, the specific process is as follows: the first 4 steps of this embodiment are the same as those of embodiment 1, and therefore are not described again, and will be started from step 5:
step 5, diffusing the reduced rank matrix Q of each node arrayk(i) Randomly arranging the reduced rank matrix of the neighborhood nodes including the node k to obtain:
Σk(i)＝[Ql(i),l∈Nk]T
and calculating a combination matrix of the reduced rank weight vector estimates of the node k:
Figure BDA0002269282650000109
wherein the coefficient gl,kIs a combined matrix GThe (l, k) th element, and the combination matrix G satisfies the following constraint:
Figure BDA0002269282650000111
gl,k＝0,1TG＝1T；
and 6, diffusing the combined matrix of the intermediate estimation of the reduced rank weight vector and the reduced rank weight vector estimation of each node array, and updating to obtain the reduced rank weight vector estimation of the node k:
Figure BDA0002269282650000112
and 7, calculating a combined matrix of the reduced rank matrix estimation of the node array k:
Figure BDA0002269282650000113
Figure BDA0002269282650000114
wherein v isk(i) Is a combined matrix Λk(i) The vectorized expression of (a) is,
Figure BDA0002269282650000115
representing the Kronecker product, a matrixing function unwecm,n{. is an operator that converts a column vector of mn elements into an m × n matrix;
and 8, calculating the reduced rank matrix estimation of the node array k:
Sk(i)＝Σk(i)Λk(i)
obtaining the optimal weight of the node array k, and calculating a beam function:
Figure BDA0002269282650000116
Figure BDA0002269282650000117
wherein, wkTo complete a sufficiently sufficient number of iterations of the full rank weight vector, E, of node kk(θ) is the beam function, θ ∈ (-90 °,90 °).
The feasibility and superiority of the invention will be described by comparing the anti-interference effects of the algorithm DRACM-1 proposed in embodiment 1 and the algorithm proposed in embodiment 2 with the anti-interference effects of the D RACM-2 and the Beam coding algorithm through simulation experiments:
simulation experiment
Simulation 1: a network topology structure with 10 nodes interconnected, as shown in fig. 5, each node is a uniform linear array with an array element number M of 40, the spacing between adjacent array elements is half-wavelength, considering a desired single-tone signal, the arrival angle is 20 degrees, the power is 0dB, the frequency is 1kHz, three single-tone interference signals, the arrival angles are-60 degrees, 0 degrees, 60 degrees, the powers are all 10dB, the frequencies are 1.5kHz, 2kHz, 0.5kHz, the sampling rate is 8kHz, the iteration step sizes of the reduced-rank matrix and the reduced-rank weight vector in the algorithms of dramm-1 and dramm-2 are μsk＝0.0002,k＝1,2,..,N，μwk0.0003, k 1,2, N, and the initial values of the reduced rank matrix and the reduced rank weight vector are I, respectivelyM,D，
Figure BDA0002269282650000118
Iteration step size of BeamCoordination algorithm is muk0.0001, k 1,2, N, the initial value of the weight vector is
Figure BDA0002269282650000121
The number of rapid beats was 50000, and the experimental results are shown in fig. 6, 7 and 8 after 100 independent repeated experiments.
As shown in fig. 6, the DRACM-1 and DRACM-2 algorithms proposed by the present invention can effectively suppress interference and enable undistorted output of a desired signal; as shown in fig. 7, compared with the Beam coding algorithm without information exchange, the dramm-1 and dramm-2 algorithms can improve the output signal to interference plus noise ratio, and compared with the distributed Beam coding algorithm, the dramm-1 and dramm-2 algorithms perform rank reduction, but the output signal to interference plus noise ratio thereof is basically consistent with the output signal to interference plus noise ratio of the Beam coding algorithm, that is, the rank reduction does not greatly reduce the performance of the algorithm, which can also be verified from the MSE learning curve shown in fig. 8.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.

Claims (2)

1. A distributed adaptive rank reduction beam forming method comprises the following steps:
step 1, obtaining array receiving signals of node k
Setting a desired far-field complex narrowband signal
Figure FDA0002269282640000011
Incident on the uniform linear array network and simultaneously subjected to P-1 complex narrow-band signals
Figure FDA0002269282640000012
Then the discrete complex baseband received signal vector of the kth node array is represented as:
Figure FDA0002269282640000013
wherein i represents the ith time, sp(i) Is a narrow band signal
Figure FDA0002269282640000014
Discrete baseband form of (a); n isk(i) Is a zero mean additive white gaussian noise vector; a (theta)p) As a guide vector, a (θ)1) As a guide vector of the desired signal, thetapAngle of arrival for the p-th incident signal;
step 2, initializing the reduced rank weight vector, the reduced rank matrix and the related parameters
Initializing rank-reduced weight vector initial values for all node arrays
Figure FDA0002269282640000015
With initial values of the reduced rank matrix Sk(0) The condition constraint is satisfied:
Figure FDA0002269282640000016
and obtaining a switching matrix C and a combining matrix F, G according to the calculation rule:
Figure FDA0002269282640000017
wherein, cl,kFor the (l, k) th element, f, of the switching matrix Cl,kFor the (l, k) -th element, g, of the combined matrix Fl,kIs the (l, k) th element of the combining matrix G;
Figure FDA0002269282640000018
a set of neighborhood nodes, r, representing the kth node array including itselfkIs composed of
Figure FDA0002269282640000019
The total number of nodes contained;
step 3, diffusing the received signals of each node array, and enabling the received signals of the node arrays to pass through a reduced rank beam former;
1) for array received signal xl(i) And a desired signal steering vector a (theta)1) Performing rank reduction processing to obtain the array receiving signal after rank reduction
Figure FDA00022692826400000110
Sum rank reduced desired signal steering vector
Figure FDA00022692826400000111
Figure FDA00022692826400000112
Figure FDA00022692826400000113
Wherein S isk(i-1) is a reduced rank matrix of the kth node array at the ith-1 moment;
2) obtained after rank reduction treatment
Figure FDA00022692826400000114
Obtaining an array output signal through a reduced rank filter:
Figure FDA0002269282640000021
wherein,
Figure FDA0002269282640000022
a rank reduction weight vector of the kth node array at the ith-1 moment;
and 4, diffusing the output signals of the node arrays and the array receiving signals after the rank reduction, and iteratively updating the rank reduction matrix Q of the kth node arrayk(i) Intermediate estimation of sum rank reduced weight vector
Figure FDA0002269282640000023
Figure FDA0002269282640000024
Figure FDA0002269282640000025
Wherein,
Figure FDA0002269282640000026
and
Figure FDA0002269282640000027
are projection matrices;
Figure FDA0002269282640000028
and
Figure FDA0002269282640000029
respectively carrying out iteration step length of intermediate estimation of the reduced rank matrix and the reduced rank weight vector;
and 5, diffusing the intermediate estimation of the reduced rank weight vector of each node array, and randomly arranging the intermediate estimation of the reduced rank weight vector of the adjacent node including the node array of the kth node array to obtain:
Figure FDA00022692826400000210
and calculating a combination matrix of the reduced rank matrix estimation of the kth node array:
Figure FDA00022692826400000211
and 6, diffusing the combined matrix of the reduced rank matrix and the reduced rank matrix estimation of each node array, and updating to obtain the estimation of the reduced rank matrix of the kth node array:
Figure FDA00022692826400000212
and 7, calculating a combination matrix of the reduced rank weight vector estimation of the kth node array:
Figure FDA00022692826400000213
Figure FDA00022692826400000214
therein, unwecm,n{. is a matrixing function;
and 8, calculating the reduced rank weight vector estimation of the kth node array:
Figure FDA00022692826400000215
obtaining the optimal weight of the kth node array, and calculating a beam function:
Figure FDA00022692826400000216
Figure FDA0002269282640000031
wherein, wkFull rank weight vector for kth node array, Ek(θ) is the beam function, θ ∈ (-90 °,90 °).
2. A distributed adaptive rank reduction beam forming method comprises the following steps:
step 1, obtaining array receiving signals of node k
Setting a desired far-field complex narrowband signal
Figure FDA0002269282640000032
Incident on the uniform linear array network and simultaneously subjected to P-1 complex narrow-band signals
Figure FDA0002269282640000033
Then the discrete complex baseband received signal vector of the kth node array is represented as:
Figure FDA0002269282640000034
wherein i represents the ith time, sp(i) Is a narrow band signal
Figure FDA0002269282640000035
FromA scattered baseband form; n isk(i) Is a zero mean additive white gaussian noise vector; a (theta)p) As a guide vector, a (θ)1) As a guide vector of the desired signal, thetapAngle of arrival for the p-th incident signal;
step 2, initializing the reduced rank weight vector, the reduced rank matrix and the related parameters
Initializing rank-reduced weight vector initial values for all node arrays
Figure FDA0002269282640000036
With initial values of the reduced rank matrix Sk(0) The condition constraint is satisfied:
Figure FDA0002269282640000037
and obtaining a switching matrix C and a combining matrix F, G according to the calculation rule:
Figure FDA0002269282640000038
wherein, cl,kFor the (l, k) th element, f, of the switching matrix Cl,kFor the (l, k) -th element, g, of the combined matrix Fl,kIs the (l, k) th element of the combining matrix G;
Figure FDA0002269282640000039
a set of neighborhood nodes, r, representing the kth node array including itselfkIs composed of
Figure FDA00022692826400000310
The total number of nodes contained;
step 3, diffusing the received signals of each node array, and enabling the received signals of the node arrays to pass through a reduced rank beam former;
1) for array received signal xl(i) And a desired signal steering vector a (theta)1) Performing rank reduction processing to obtain the array receiving signal after rank reduction
Figure FDA00022692826400000311
Sum rank reduced desired signal steering vector
Figure FDA00022692826400000312
Figure FDA00022692826400000313
Figure FDA00022692826400000314
Wherein S isk(i-1) is a reduced rank matrix of the kth node array at the ith-1 moment;
2) obtained after rank reduction treatment
Figure FDA0002269282640000041
Obtaining an array output signal through a reduced rank filter:
Figure FDA0002269282640000042
wherein,
Figure FDA0002269282640000043
a rank reduction weight vector of the kth node array at the ith-1 moment;
and 4, diffusing the output signals of the node arrays and the array receiving signals after the rank reduction, and iteratively updating the rank reduction matrix Q of the kth node arrayk(i) Intermediate estimation of sum rank reduced weight vector
Figure FDA0002269282640000044
Figure FDA0002269282640000045
Figure FDA0002269282640000046
Wherein,
Figure FDA0002269282640000047
and
Figure FDA0002269282640000048
are projection matrices;
Figure FDA0002269282640000049
and
Figure FDA00022692826400000410
respectively carrying out iteration step length of intermediate estimation of the reduced rank matrix and the reduced rank weight vector;
step 5, diffusing the reduced rank matrix Q of each node arrayk(i) Randomly arranging the reduced rank matrix of the k node array including the neighbor nodes thereof to obtain:
Σk(i)＝[Ql(i),l∈Nk]T
and calculating a combination matrix of the reduced rank weight vector estimation of the kth node array:
Figure FDA00022692826400000411
and 6, diffusing the combined matrix of the intermediate estimation and the reduced rank weight vector estimation of each node array, and updating to obtain the reduced rank weight vector estimation of the kth node array:
Figure FDA00022692826400000412
and 7, calculating a combination matrix of the reduced rank matrix estimation of the kth node array:
Figure FDA00022692826400000413
Figure FDA00022692826400000414
therein, unwecm,n{. is a matrixing function;
and 8, calculating the reduced rank matrix estimation of the kth node array:
Sk(i)＝Σk(i)Λk(i)
obtaining the optimal weight of the kth node array, and calculating a beam function:
Figure FDA0002269282640000051
Figure FDA0002269282640000052
wherein, wkFull rank weight vector for kth node array, Ek(θ) is the beam function, θ ∈ (-90 °,90 °).
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