CN111224704B - Distributed self-adaptive reduced rank beam forming method - Google Patents

Distributed self-adaptive reduced rank beam forming method Download PDF

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CN111224704B
CN111224704B CN201911099146.5A CN201911099146A CN111224704B CN 111224704 B CN111224704 B CN 111224704B CN 201911099146 A CN201911099146 A CN 201911099146A CN 111224704 B CN111224704 B CN 111224704B
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CN111224704A (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 adaptation algorithm to a distributed network in the document Diffusion LMS formations for distributed evaluation, and proposed that parameter estimation be performed using the idea of adaptation and combination (ATC) and the idea of combination and adaptation (CTA), and that nodes can effectively communicate with other nodes during both combination and adaptation; in 2012, in a document "Beam correlation vision dispersion adaptation over array network", ali h.sayed et al applies a distributed adaptive strategy to Beam forming, and proposes to solve an optimal weight vector by using an ATC idea, and filter a received signal of any array by using the weight vector to achieve the purposes of retaining a desired signal and suppressing interference in order to expand the application of a distributed processing method in other fields. 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 approximation 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, and 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 iterative 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 array element number 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, s p (i) Is a narrow band signal
Figure BDA0002269282650000024
Discrete baseband form of (a); n is k (i) Is a zero mean additive white gaussian noise vector; a (theta) p ) As a guide vector, a (θ) 1 ) Is a steering vector, θ, of the desired signal p Angle of arrival for the p-th incident signal;
step 2, initialization of reduced rank weight vector, reduced rank matrix and related parameters
Initializing rank-reduced weight vector initial values for all node arrays
Figure BDA0002269282650000025
And initial value of reduced rank matrix S k (0) The condition constraint is satisfied:
Figure BDA0002269282650000026
and obtaining a switching matrix C and a combination matrix F, G according to the calculation rule:
Figure BDA0002269282650000027
wherein, c l,k For the (l, k) th element, f, of the switching matrix C l,k For the (l, k) -th element, g, of the combined matrix F l,k Is the (l, k) th element of the combining matrix G;
Figure BDA00022692826500000317
a set of neighborhood nodes, r, representing the kth node array including itself k Is 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 x l (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 is k (i-1) a reduced rank matrix of the kth node array at the time of the i-1;
2) Obtained after rank reduction
Figure BDA0002269282650000035
Obtaining an array output signal through a reduced rank filter:
Figure BDA0002269282650000036
wherein the content of the first and second substances,
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 array k (i) Intermediate estimation of sum rank reduced weight vector
Figure BDA0002269282650000038
Figure BDA0002269282650000039
Figure BDA00022692826500000310
Wherein the content of the first and second substances,
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 estimate for 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, unwec m,n {. Is a matrixing function;
step 8, calculating the rank reduction 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 w k Full rank weight vector for kth node array, E k (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, s p (i) Is a narrow band signal
Figure BDA00022692826500000410
Discrete baseband form of (a); n is k (i) Is a zero mean additive white gaussian noise vector; a (theta) p ) As a steering vector, a (θ) 1 ) As a guide vector of the desired signal, theta p Angle 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
And initial value of reduced rank matrix S k (0) The condition constraint is satisfied:
Figure BDA00022692826500000412
and obtaining a switching matrix C and a combination matrix F, G according to the calculation rule:
Figure BDA00022692826500000515
wherein, c l,k For the (l, k) th element, f, of the switching matrix C l,k For the (l, k) -th element, g, of the combined matrix F l,k Is the (l, k) th element of the combining matrix G;
Figure BDA00022692826500000516
a set of neighborhood nodes representing the kth node array including itself, r k Is 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 x l (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 is k (i-1) a reduced rank matrix of the kth node array at the time of the i-1;
2) Obtained after rank reduction treatment
Figure BDA0002269282650000055
Obtaining an array output signal through a reduced rank filter:
Figure BDA0002269282650000056
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002269282650000057
a rank reduction weight vector of the kth node array at the (i-1) th 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 array k (i) Intermediate estimation of sum rank reduced weight vector
Figure BDA0002269282650000058
Figure BDA0002269282650000059
Figure BDA00022692826500000510
Wherein the content of the first and second substances,
Figure BDA00022692826500000511
and
Figure BDA00022692826500000512
are projection matrices;
Figure BDA00022692826500000513
and
Figure BDA00022692826500000514
respectively is the iteration step length of the intermediate estimation of the reduced rank matrix and the reduced rank weight vector;
step 5, diffusing the reduced rank matrix Q of each node array k (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:
Σ k (i)＝[Q l (i),l∈N k ] 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
step 7, calculating a combination matrix of the reduced rank matrix estimation of the kth node array:
Figure BDA0002269282650000063
Figure BDA0002269282650000064
therein, unwec m,n {. Is a matrixing function;
and 8, calculating the reduced rank matrix estimation of the kth node array:
S k (i)＝Σ k (i)Λ k (i)
obtaining the optimal weight of the kth node array, and calculating a beam function:
Figure BDA0002269282650000065
Figure BDA0002269282650000066
wherein, w k Full rank weight vector for kth node array, E k (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 self-adaptive rank-reduction beam forming 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 the anti-interference capability is invalid caused by the problem of 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 combination matrix can utilize differentiated information of neighbor nodes, and is favorable for improving the estimation performance of a reduced rank matrix and a 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 combination matrix of the reduced rank matrix is fixed first, and then the method for solving the combination matrix of the reduced rank weight vector is provided, and the schematic flow diagram 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, s p (i) Is a narrow band signal
Figure BDA0002269282650000084
Discrete baseband form of (a); n is k (i) Is a variance of
Figure BDA0002269282650000085
Zero mean additive white Gaussian noise vector of (1) with n at different nodes or different times l (i 1 ) Receiving signals x independently of each other and of the array k (i) (ii) a The guide vector is
Figure BDA0002269282650000086
In particular, a (θ) 1 ) As a guide vector of the desired signal, theta p The arrival angle of the p-th incident signal is expressed as follows:
Figure BDA0002269282650000087
wherein phi is p ＝2πdsinθ p λ, d denotes the spacing between adjacent array elements, λ is the carrier wavelength · T Representing 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 S k (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 S k The 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, the step length of the arrays of all the nodes is the same, and the switching matrix C and the combining matrix F, G need to be obtained according to the corresponding calculation rule,
Figure BDA00022692826500000810
a set of neighborhood nodes, r, including itself, representing node k k The 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 x l (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 S k Conjugate transposition 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 k k (i) Intermediate estimation of sum rank reduced weight vector
Figure BDA0002269282650000097
Figure BDA0002269282650000098
Figure BDA0002269282650000099
Wherein the content of the first and second substances,
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 c l,k Is the (l, k) th element of the switching matrix C, which satisfies the constraint:
Figure BDA00022692826500000914
c n,k ＝0,1 T C＝1 T c1=1, i.e. the sum of the column elements of the switching matrix C is 1, the sum of the row elements is also 1; i is M An identity matrix representing dimensions M x M; i is D An identity matrix representing dimensions D × D; x is the number of l (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 f l,k Is the (l, k) th element of the combined matrix F, and the combined matrix F satisfies the constraint:
Figure BDA0002269282650000101
f l,k ＝0,1 T F＝1 T the 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 is k (i) Is a combination matrix T k (i) The vectorized expression of (a) is,
Figure BDA0002269282650000105
representing the Kronecker product, a matrixing function unwec m,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, w k To complete a sufficiently sufficient number of iterations of the full rank weight vector, E, of node k k (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 array k (i) Randomly arranging the reduced rank matrix of the neighborhood nodes including the node k to obtain:
Σ k (i)＝[Q l (i),l∈N k ] T
and calculating a combination matrix of the reduced rank weight vector estimates of the node k:
Figure BDA0002269282650000109
wherein the coefficient g l,k Is the (l, k) th element of the combined matrix G, and the combined matrix G satisfies the following constraints:
Figure BDA0002269282650000111
g l,k ＝0,1 T G＝1 T ；
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 is k (i) Is a combined matrix Λ k (i) The vectorized expression of (a) is,
Figure BDA0002269282650000115
representing the Kronecker product, a matrixing function unwec m,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:
S k (i)＝Σ k (i)Λ k (i)
obtaining the optimal weight of the node array k, and calculating a beam function:
Figure BDA0002269282650000116
Figure BDA0002269282650000117
wherein, w k To complete a sufficiently sufficient number of iterations of the full rank weight vector, E, of node k k (θ) is the beam function, θ ∈ (-90 °,90 °).
The feasibility and superiority of the invention are illustrated by comparing the anti-interference effects of the algorithm DRACM-1 and the algorithm provided in the embodiments 1 and 2, and the D RACM-2 and the Beam Coordination algorithm, which are provided in the embodiment 1, 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 M =40 array elements, the spacing between adjacent array elements is half-wavelength, a desired single-tone signal is considered, the arrival angle is 20 degrees, the power is 0dB, the frequency is 1kHz, three single-tone interference signals are considered, the arrival angles are-60 degrees, 0 degrees, 60 degrees, the powers are 10dB, the frequencies are 1.5khz,2khz,0.5khz, the sampling rate is 8khz, the iteration step lengths of the rank reduction matrix and the iteration step lengths of the rank reduction weight vector in the algorithms of dramcm-1 and dramcm-2 are respectively μ sk ＝0.0002,k＝1,2,..,N，μ wk K =0.0003, k =1, 2., N, and the initial values of the reduced rank matrix and the reduced rank weight vector are I M,D ，
Figure BDA0002269282650000118
The iteration step size of the Beam coding algorithm is mu k K =0.0001, 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 correlation 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 correlation 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 correlation 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 FDA0003697582780000011
Incident on the uniform linear array network and simultaneously subjected to P-1 complex narrow-band signals
Figure FDA0003697582780000012
Then the discrete complex baseband received signal vector of the kth node array is represented as:
Figure FDA0003697582780000013
wherein i represents the ith time, s p (i) Is a narrow band signal
Figure FDA0003697582780000014
Discrete baseband form of (a); n is k (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, theta p Angle 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 FDA0003697582780000015
With initial values of the reduced rank matrix S k (0) The condition constraint is satisfied:
Figure FDA0003697582780000016
and obtaining a switching matrix C and a combination matrix F, G according to a calculation rule:
Figure FDA0003697582780000017
wherein, c l,k For the (l, k) th element of the switching matrix C, f l,k For the (l, k) -th element, g, of the combined matrix F l,k Is the (l, k) th element of the combined matrix G;
Figure FDA0003697582780000018
a set of neighborhood nodes, r, representing the kth node array including itself k Is composed of
Figure FDA0003697582780000019
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 x l (i) And a desired signal steering vector a (theta) 1 ) Performing rank reduction processing to obtain the array receiving signal after rank reduction
Figure FDA00036975827800000110
Sum rank reduced desired signal steering vector
Figure FDA00036975827800000111
Figure FDA00036975827800000112
Figure FDA00036975827800000113
Wherein S is k (i-1) is a reduced rank matrix of the kth node array at the ith-1 moment;
2) Obtained after rank reduction
Figure FDA00036975827800000114
Obtaining an array output signal through a reduced rank filter:
Figure FDA0003697582780000021
wherein the content of the first and second substances,
Figure FDA0003697582780000022
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 array k (i) Intermediate estimation of sum rank reduced weight vector
Figure FDA0003697582780000023
Figure FDA0003697582780000024
Figure FDA0003697582780000025
Wherein the content of the first and second substances,
Figure FDA0003697582780000026
and
Figure FDA0003697582780000027
are projection matrices;
Figure FDA0003697582780000028
and
Figure FDA0003697582780000029
respectively carrying out iteration step length of intermediate estimation of the reduced rank matrix and the reduced rank weight vector; i is M Representing an identity matrix of dimension M x M, I D Representing a unit matrix with dimension of D multiplied by D, and M, D is the dimension of the reduced rank matrix;
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 FDA00036975827800000210
and calculating a combination matrix of the reduced rank matrix estimation of the kth node array:
Figure FDA00036975827800000211
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 FDA00036975827800000212
and 7, calculating a combination matrix of the reduced rank weight vector estimation of the kth node array:
Figure FDA00036975827800000213
Figure FDA00036975827800000214
therein, unwec m,n {. Is a matrixing function;
and 8, calculating the reduced rank weight vector estimation of the kth node array:
Figure FDA00036975827800000215
obtaining the optimal weight of the kth node array, and calculating a beam function:
Figure FDA0003697582780000031
Figure FDA0003697582780000032
wherein w k Full rank weight vector for kth node array, E k (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 FDA0003697582780000033
Incident on the uniform linear array network and simultaneously subjected to P-1 complex narrow-band signals
Figure FDA0003697582780000034
The discrete complex baseband received signal vector of the kth node array is represented as:
Figure FDA0003697582780000035
wherein i represents the ith time, s p (i) Is a narrow band signal
Figure FDA0003697582780000036
Discrete baseband form of (a); n is k (i) Is a zero mean additive white gaussian noise vector; a (theta) p ) As a steering vector, a (θ) 1 ) As a guide vector of the desired signal, theta p Angle of arrival for the p-th incident signal;
step 2, initialization of reduced rank weight vector, reduced rank matrix and related parameters
Initializing rank-reduced weight vector initial values for all node arrays
Figure FDA0003697582780000037
With initial values of the reduced rank matrix S k (0) The condition constraint is satisfied:
Figure FDA0003697582780000038
and obtaining a switching matrix C and a combination matrix F, G according to the calculation rule:
Figure FDA0003697582780000039
wherein, c l,k For the (l, k) th element, f, of the switching matrix C l,k For the (l, k) -th element, g, of the combined matrix F l,k Is the (l, k) th element of the combining matrix G;
Figure FDA00036975827800000310
a set of neighborhood nodes, r, representing the kth node array including itself k Is composed of
Figure FDA00036975827800000311
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 x l (i) And a desired signal steering vector a (theta) 1 ) Performing rank reduction processing to obtain the array receiving signal after rank reduction
Figure FDA00036975827800000312
Sum rank reduced desired signal steering vector
Figure FDA00036975827800000313
Figure FDA00036975827800000314
Figure FDA00036975827800000315
Wherein S is k (i-1) is a reduced rank matrix of the kth node array at the ith-1 moment;
2) Obtained after rank reduction treatment
Figure FDA0003697582780000041
Obtaining an array output signal through a reduced rank filter:
Figure FDA0003697582780000042
wherein the content of the first and second substances,
Figure FDA0003697582780000043
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 array k (i) Intermediate estimation of sum rank reduced weight vector
Figure FDA0003697582780000044
Figure FDA0003697582780000045
Figure FDA0003697582780000046
Wherein the content of the first and second substances,
Figure FDA0003697582780000047
and
Figure FDA0003697582780000048
are projection matrices;
Figure FDA0003697582780000049
and
Figure FDA00036975827800000410
respectively carrying out iteration step length of intermediate estimation of the reduced rank matrix and the reduced rank weight vector; i is M Representing an identity matrix of dimension M x M, I D Representing a unit matrix with dimension of D multiplied by D, and M, D is the dimension of the reduced rank matrix;
step 5, diffusing the reduced rank matrix Q of each node array k (i) Randomly arranging the reduced rank matrix of the k node array including the neighbor nodes thereof to obtain:
Σ k (i)＝[Q l (i),l∈N k ] T
and calculating a combination matrix of the reduced rank weight vector estimation of the kth node array:
Figure FDA00036975827800000411
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 FDA00036975827800000412
and 7, calculating a combination matrix of the reduced rank matrix estimation of the kth node array:
Figure FDA00036975827800000413
Figure FDA00036975827800000414
therein, unwec m,n {. Is a matrixing function;
and 8, calculating the reduced rank matrix estimation of the kth node array:
S k (i)＝Σ k (i)Λ k (i)
obtaining the optimal weight of the kth node array, and calculating a beam function:
Figure FDA0003697582780000051
Figure FDA0003697582780000052
wherein, w k Full rank weight vector for kth node array, E k (θ) is the beam function, θ ∈ (-90 °,90 °).
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