CN107733490B - Joint beam forming and optimal power distribution method in bidirectional untrusted relay network - Google Patents

Joint beam forming and optimal power distribution method in bidirectional untrusted relay network Download PDF

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CN107733490B
CN107733490B CN201710957051.7A CN201710957051A CN107733490B CN 107733490 B CN107733490 B CN 107733490B CN 201710957051 A CN201710957051 A CN 201710957051A CN 107733490 B CN107733490 B CN 107733490B
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matrix
precoding matrix
useful signal
user
power distribution
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CN107733490A (en
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姚如贵
姚鲁坤
陆亚南
徐菲
徐娟
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Northwestern Polytechnical University
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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
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H04B7/043—Power distribution using best eigenmode, e.g. beam forming or beam steering
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/155—Ground-based stations
    • H04B7/15564—Relay station antennae loop interference reduction
    • H04B7/15571—Relay station antennae loop interference reduction by signal isolation, e.g. isolation by frequency or by antenna pattern, or by polarization
    • 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
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03891—Spatial equalizers
    • H04L25/03898—Spatial equalizers codebook-based design
    • H04L25/0391—Spatial equalizers codebook-based design construction details of matrices
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/38—TPC being performed in particular situations
    • H04W52/46—TPC being performed in particular situations in multi hop networks, e.g. wireless relay networks

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Abstract

The invention provides a method for combining beam forming and optimal power distribution in a bidirectional untrusted relay network, which designs an interference signal precoding matrix Q at a source node and a destination nodeAAnd QBMaximizing the power of the cooperative interference signal reaching the relay node; jointly optimized useful signal precoding matrix FAAnd FBAnd each user sends a power distribution scheme of a useful signal and a cooperative interference signal, so that the achievable safety rate of the network is further improved. The invention aligns the useful signal to the equivalent signal space and forces the interference signal to be orthogonal, and simultaneously generates the optimal power distribution of each user, thereby improving the safety rate to the maximum extent.

Description

Joint beam forming and optimal power distribution method in bidirectional untrusted relay network
Technical Field
The invention relates to a beam forming and power distribution method.
Background
In recent years, security issues of wireless networks have received more and more attention, and unlike conventional encryption mechanisms, physical layer security has the advantages of lower computational complexity and saving time and spectrum resources. As the security of wireless communication is more and more improved, physical layer security has gained wide attention in both theoretical research and practical applications.
With the shortage of communication resources and the development of multi-antenna technology, multi-antenna based physical layer security research has attracted much attention. In an actual application system, a plurality of antennas are generally configured for a signal source, a signal sink and a relay, so that greater Freedom (DoF) and flexibility are provided for system optimization. However, the complexity of the optimization of the system increases dramatically. In addition, for a Destination-Assisted-Jamming (DAJ) technology capable of improving the physical layer security, optimizing the power allocation of the useful signal and the cooperative Jamming signal of each user can further improve the security rate. Therefore, the research on the beam forming technology of the bidirectional untrusted relay network and the design of an efficient optimization algorithm to seek the optimal power allocation have important significance for improving the total safe rate of the system.
Document 1, "Spectral efficiency protocols for half-duplex decoding relays [ IEEE Journal on Selected Areas in Communications, vol.25, No.2,2007 ]" obtains a conclusion that cooperative relaying can improve the achievable security rate of the system, and proposes a bidirectional relay transmission scheme, which can complete information exchange between two source nodes in two time slots, thereby effectively improving the spectrum efficiency.
Document 2 "Cooperation with an undirected relay a secret experience [ ieee transactions on Information Theory, vol.56, No.8, pp.3807-3827,2009 ]" proves that the adoption of the DAJ scheme for the communication of an untrusted relay node is higher than the security rate achievable by simply regarding the untrusted relay node as an eavesdropping node.
Document 3 "Joint secure beamforming design at the source and the relay for an amplified and a forwarded MIMO undirected relay system [ IEEE Transactions on signal Processing, vol.60, No.1, pp.310-325,2012 ]" indicates that an untrusted relay has a greater effect in cooperative transmission with Amplify-and-Forward (AF) or Compress-and-Forward (CF), which can improve the security rate of the system, and proves that beamforming combining an untrusted relay and an untrusted relay can maximize the achievable security rate.
Document 4, "Destination-based coordinated amplitude-and-forward relay networks: resource allocation and performance determination [ ietc communications, vol.10, No.1, pp.17-23,2016 ]" provides a closed expression for optimal power distribution under a large-scale antenna array at a high Signal-to-Noise Ratio (SNR) condition for a multi-antenna unidirectional untrusted relay network.
Document 5, "Destination-assisted cooperative mapping for dual-hop amplification-and-forward MIMO unregulated relay systems [ IEEE Transactions on vehicular technology, vol.65, No.9, pp.7274-7284,2016 ]" maximizes the security rate by jointly designing precoding matrices of a source node, a relay node, and a Destination node for a multi-antenna unidirectional untrusted relay network, and proposes an iterative optimization algorithm to solve the non-convex problem.
Currently, in the research on the physical layer security technology, optimization design is mainly performed on eavesdropping nodes, and the relay network itself is trusted (as in document 1), secondly, the existing research is mainly performed on the case that the information source and the information sink are single antennas (as in document 2), and furthermore, the existing research on the beam forming technology and power distribution in the multi-antenna untrusted relay network is mainly performed on the optimization design for unidirectional transmission (as in documents 3 to 5).
In the Chinese invention patent 'a beam forming method in a multi-antenna untrusted relay network' (patent acceptance number: 201710299458.5), aiming at a unidirectional untrusted relay transmission network, a beam forming technology with channel selection is provided, and a pre-programmed matrix F is optimally designedSAnd FDTo improve the system security rate. The patent does not consider the bi-directional transmission case and the power allocation problem.
For a system comprising two users: (
Figure GDA0002439933230000021
And
Figure GDA0002439933230000022
) And untrusted relay nodes
Figure GDA0002439933230000023
The channel model of the bidirectional AF network has no direct transmission link between two users due to long-distance transmission or shadow effect, so that the users
Figure GDA0002439933230000024
And
Figure GDA0002439933230000025
is communicated through the non-trusted relay node
Figure GDA0002439933230000026
And (4) establishing. Suppose a user
Figure GDA0002439933230000027
And
Figure GDA0002439933230000028
are respectively provided with NtThe number of the antenna elements is the same as the number of the antenna elements,
Figure GDA0002439933230000029
with NrRoot antenna of Nr＞NtTo ensure sufficient multiplexing gain. The transmission of each user information needs to go through two phases (broadcast phase and relay phase). The wireless link between any two nodes is subject to flat quasi-static rayleigh block fading, which means that the channel gain remains unchanged for two consecutive frames and has independent fading. To avoid user information quilt
Figure GDA00024399332300000210
And (4) cracking, adopting a cooperative interference scheme as shown in figure 1.
Consecutive transmission slots are divided into odd and even slots.
1) In odd time slots, i.e.
Figure GDA00024399332300000211
A broadcasting stage of (
Figure GDA00024399332300000212
The relay phase of (a),
Figure GDA00024399332300000213
transmitting a useful signal xA，
Figure GDA00024399332300000214
Transmitting a cooperative interference signal (artificial noise) xJBSimultaneous relay node
Figure GDA00024399332300000215
Forwarding the signal received by the previous even time slot
Figure GDA00024399332300000216
Wherein
Figure GDA0002439933230000031
And
Figure GDA0002439933230000032
are respectively from
Figure GDA0002439933230000033
Of the broadcast phase of the system, wherein
Figure GDA0002439933230000034
Is that
Figure GDA0002439933230000035
The useful symbol vector to be transmitted is,
Figure GDA0002439933230000036
to represent
Figure GDA0002439933230000037
The transmit pre-coding matrix of (2),
Figure GDA0002439933230000038
is that
Figure GDA0002439933230000039
The vector of the transmitted interfering symbols is then transmitted,
Figure GDA00024399332300000310
to represent
Figure GDA00024399332300000311
The cooperative interference precoding matrix of (2).
In the odd time slot
Figure GDA00024399332300000312
The received data rate:
Figure GDA00024399332300000313
wherein
Figure GDA00024399332300000314
H and
Figure GDA00024399332300000315
are respectively from
Figure GDA00024399332300000316
To
Figure GDA00024399332300000317
And from
Figure GDA00024399332300000318
To
Figure GDA00024399332300000319
Is obtained from reciprocity of channels
Figure GDA00024399332300000320
To
Figure GDA00024399332300000321
And
Figure GDA00024399332300000322
can be respectively represented as HHAnd GH。PAAnd PBAre respectively
Figure GDA00024399332300000323
And
Figure GDA00024399332300000324
total transmit power in two consecutive time slots α∈ [0, 1 ]]And β∈ [0, 1 ]]Are respectively users
Figure GDA00024399332300000325
And the user
Figure GDA00024399332300000326
So that for two consecutive time slots, the user is allocated a power factor
Figure GDA00024399332300000327
The power for transmitting the useful signal and the cooperative interference signal is α PAAnd (1- α) PA(ii) a For the user
Figure GDA00024399332300000328
Then β P respectivelyBAnd (1- β) PB. User' s
Figure GDA00024399332300000329
The received data rate:
Figure GDA00024399332300000330
wherein
Figure GDA00024399332300000331
To represent
Figure GDA00024399332300000332
The additive noise vector of (a) is,
Figure GDA00024399332300000333
to represent
Figure GDA00024399332300000334
An additive noise vector.
2) In the case of an even time slot,
Figure GDA00024399332300000335
transmitting a cooperative interference signal xJA，
Figure GDA00024399332300000336
Transmitting a useful signal xBSimultaneous relay node
Figure GDA00024399332300000337
Forwarding the signal received from the previous odd time slot
Figure GDA00024399332300000338
Wherein
Figure GDA00024399332300000339
And
Figure GDA00024399332300000340
from
Figure GDA00024399332300000341
The desired signal and the interfering signal of the broadcast phase of (a),
Figure GDA00024399332300000342
is that
Figure GDA00024399332300000343
The useful symbol vector to be transmitted is,
Figure GDA00024399332300000344
to represent
Figure GDA00024399332300000345
The transmit pre-coding matrix of (2),
Figure GDA00024399332300000346
is that
Figure GDA00024399332300000347
The vector of the transmitted interfering symbols is then transmitted,
Figure GDA00024399332300000348
to represent
Figure GDA00024399332300000349
The cooperative interference precoding matrix of (2).
In even time slot
Figure GDA00024399332300000350
The received data rate:
Figure GDA00024399332300000351
wherein
Figure GDA00024399332300000352
User' s
Figure GDA00024399332300000353
The received data rate:
Figure GDA00024399332300000354
wherein
Figure GDA00024399332300000355
To represent
Figure GDA00024399332300000356
An additive noise vector.
The total safe rate of the bidirectional untrusted relay network is then
Figure GDA00024399332300000357
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for searching the beam forming and the optimal power distribution scheme of each user, aiming at a bidirectional untrusted relay network, and maximizing the system safety rate.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step one, including the user
Figure GDA00024399332300000358
User' s
Figure GDA00024399332300000359
And untrusted relay nodes
Figure GDA00024399332300000360
In the bidirectional AF network of
Figure GDA00024399332300000361
And
Figure GDA00024399332300000362
are respectively provided with NtThe number of the antenna elements is the same as the number of the antenna elements,
Figure GDA00024399332300000363
with NrA root antenna; setting user
Figure GDA00024399332300000364
User' s
Figure GDA00024399332300000365
Power distribution coefficient of (2) is set to an initial value α - α*＝0.5，β＝β*0.5; the power distribution coefficient refers to that for two continuous time slots, users
Figure GDA0002439933230000041
The power for transmitting the useful signal and the cooperative interference signal is α PAAnd (1- α) PAFor the user
Figure GDA0002439933230000042
Then β P respectivelyBAnd (1- β) PB；
Step two, adjusting the user
Figure GDA0002439933230000043
User' s
Figure GDA0002439933230000044
Interference signal precoding matrix QAAnd QBMaking it orthogonal to H and G, H and
Figure GDA0002439933230000045
are respectively from
Figure GDA0002439933230000046
To
Figure GDA0002439933230000047
And from
Figure GDA0002439933230000048
To
Figure GDA0002439933230000049
Of the multi-antenna channel matrix, QA＝λAHH， QB＝λBGHWherein
Figure GDA00024399332300000410
So that QAAnd QBThe power constraint condition is satisfied;
step three, optimizing
Figure GDA00024399332300000411
Useful signal precoding matrix FAFirst, a matrix is constructed
Figure GDA00024399332300000412
GSVD joint decomposition is carried out on the two matrixes to obtain phiB＝UB∑BKH，
Figure GDA00024399332300000413
Wherein the content of the first and second substances,
Figure GDA00024399332300000414
and
Figure GDA00024399332300000415
is a unitary matrix of the matrix,
Figure GDA00024399332300000416
is phiBAnd
Figure GDA00024399332300000445
is determined by the common non-singular matrix of (a),
Figure GDA00024399332300000417
and
Figure GDA00024399332300000418
is a diagonal matrix, 0 ≦ ηB，1≤…≤ηB，N t1 or less and
Figure GDA00024399332300000419
are respectively phiBAnd
Figure GDA00024399332300000444
the singular value of (a);
when in use
Figure GDA00024399332300000420
And is
Figure GDA00024399332300000421
When 1 is more than ma≤NtAnd is
Figure GDA00024399332300000422
By (K)H)-1Finally LA＝Nt-ma+1 column vectors
Figure GDA00024399332300000423
The useful signal precoding matrix is
Figure GDA00024399332300000424
Wherein the content of the first and second substances,
Figure GDA00024399332300000425
is (K)H)-1J ∈ { 1., Nt}；
When in use
Figure GDA00024399332300000426
Time, structure
Figure GDA00024399332300000427
The useful signal precoding matrix is FA＝(KH)-1；
When in use
Figure GDA00024399332300000428
When the channel capacity is negative, the actual transmission is meaningless;
step four, optimizing
Figure GDA00024399332300000429
Useful signal precoding matrix FBFirst, a matrix is constructed
Figure GDA00024399332300000430
GSVD joint decomposition is carried out on the two matrixes to obtain phiA＝UA∑AWH，
Figure GDA00024399332300000431
Wherein
Figure GDA00024399332300000432
And
Figure GDA00024399332300000433
is a unitary matrix of the matrix,
Figure GDA00024399332300000434
is phiAAnd
Figure GDA00024399332300000447
of the common matrix of (a) and (b),
Figure GDA00024399332300000435
and
Figure GDA00024399332300000436
is a diagonal matrix, 0 ≦ ηA，1≤…≤η A，Nt1 or less and
Figure GDA00024399332300000437
are respectively phiAAnd
Figure GDA00024399332300000446
the singular value of (a);
when in use
Figure GDA00024399332300000438
And is
Figure GDA00024399332300000439
When 1 is more than mb≤NtAnd is
Figure GDA00024399332300000440
By (W)H)-1Last LB＝Nt-mb+1 column vectors
Figure GDA00024399332300000441
The useful signal precoding matrix is
Figure GDA00024399332300000442
Wherein the content of the first and second substances,
Figure GDA00024399332300000443
is (W)H)-1J ∈ { 1., Nt}；
When in use
Figure GDA0002439933230000051
Time, structure
Figure GDA0002439933230000052
The useful signal precoding matrix is FB＝(WH)-1；
When in use
Figure GDA0002439933230000053
When the channel capacity is negative, the actual transmission is meaningless;
step five, optimizing the user
Figure GDA0002439933230000054
And
Figure GDA0002439933230000055
power distribution coefficients α and β, and total safe speed of the system is improved
Figure GDA0002439933230000056
Wherein the content of the first and second substances,
Figure GDA0002439933230000057
Figure GDA0002439933230000058
the specific implementation method comprises the following steps:
handle α ═ α*Substitution into
Figure GDA0002439933230000059
Solving the root according to the constraint of 0- β -1, and making β*Equal to the valid root to update β, change β to β*Bringing in
Figure GDA00024399332300000510
Solving the root according to the constraint of 0- α -1, and making α*Equal to the valid root to update α;
and step six, replacing the α and β values obtained in the last step back to the step three, optimizing the useful signal precoding matrix and power distribution in the next round, and ending after 10 times of circulation to obtain the optimal useful signal precoding matrix FAAnd FAAnd power distribution coefficients α and β, where the total safe rate of the system is maximized.
The invention has the beneficial effects that: DAJ technology is introduced, joint beam forming and optimal power distribution schemes in the bidirectional untrusted relay network are researched, useful signals are aligned to an equivalent signal space, interference signals are forced to be orthogonal, optimal power distribution of each user is generated at the same time, and safety rate is improved to the maximum extent.
Drawings
Fig. 1 is a schematic diagram of DAJ scheme in a bidirectional relay transmission network, wherein (a) is odd time slot and (b) is even time slot;
FIG. 2 is a graph at N t6 and NrWhen the network is 8, the two-way untrusted relay network can reach the safe speed diagram;
FIG. 3 is a diagram illustrating a comparison of proposed beam-forming achievable security rates for different antenna configurations;
FIG. 4 is a graph at N t6 and NrWhen the SNR is 8, the convergence of the optimal power allocation in the first outer loop in algorithm 1 under different SNRs is shown;
FIG. 5 is a graph at N t6 and NrWhen the SNR is 8, the convergence of the optimal power allocation in the second outer loop in algorithm 1 under different SNRs is shown;
FIGS. 6(a) and 6(b) are at N t6 and NrWhen it is 8, the convergence of the useful signal precoding matrix (outer loop of algorithm 1) under different SNRs is schematically shown, where fig. 6(a) shows the user
Figure GDA00024399332300000511
6(b) represents the user
Figure GDA00024399332300000512
Convergence of the useful signal precoding matrix of (a);
FIG. 7 is a graph at NrGiven by 8, the two-way untrusted relay network can achieve a safe rate schematic diagram;
FIG. 8 is at NrGiven by 8, the optimal power distribution diagram of the bidirectional untrusted relay network;
FIG. 9 is at NtGiven by 6, the two-way untrusted relay network can achieve a safe rate schematic diagram;
FIG. 10 is at NtGiven 6, the optimal power allocation of the bidirectional untrusted relay network is shown.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
The present invention provides a two-way untrusted systemBeam forming and optimal power distribution in relay network, and design interference signal precoding matrix Q at source node and destination nodeAAnd QBTo reach the relay node
Figure GDA0002439933230000061
The cooperative interference signal power of (a) is maximized; a new method is proposed for jointly optimizing a useful signal precoding matrix FAAnd FBAnd each user sends a power distribution scheme of a useful signal and a cooperative interference signal, so that the achievable safety rate of the network is further improved.
At present, the research on the physical layer security technology is mainly to develop an optimization design aiming at an eavesdropping node, and a relay network is credible (as in document 1). Secondly, the existing research mainly aims at the situation that the information source and the information sink are single antennas (as in document 2), and the single antenna is expanded to the multi-antenna research in the invention. In addition, most of the existing research on beamforming technology and power allocation in the multi-antenna untrusted relay network is optimized for unidirectional transmission (see documents 3 to 5), and the present invention provides beamforming and power allocation optimized design for bidirectional transmission.
The invention comprises the following steps:
step one, setting an initial value α of the power distribution coefficient to α*＝0.5，β＝β*＝0.5。
Step two, precoding matrix Q by adjusting interference signalAAnd QBSo that they are orthogonal to H and G, respectively, then
Figure GDA0002439933230000062
The received SNR at (a) will increase. Since the matched filtering precoding matrix can maximize the received SNR, an interference precoding matrix is constructed based on the matched filtering precoding matrix, and Q is setA＝λAHH，QB＝λBGH. Wherein
Figure GDA0002439933230000063
Figure GDA0002439933230000064
So that QAAnd QBThe power constraint is satisfied.
Step three, optimizing
Figure GDA0002439933230000065
Useful signal precoding matrix FAFirst, a matrix is constructed
Figure GDA0002439933230000066
GSVD joint decomposition is carried out on the two matrixes to obtain phiB＝UB∑BKH，
Figure GDA0002439933230000067
Wherein the content of the first and second substances,
Figure GDA0002439933230000068
and
Figure GDA0002439933230000069
is a unitary matrix of the matrix,
Figure GDA00024399332300000610
is phiBAnd
Figure GDA00024399332300000615
is determined by the common non-singular matrix of (a),
Figure GDA00024399332300000611
and
Figure GDA00024399332300000612
is a diagonal matrix of the angles,
Figure GDA00024399332300000616
and
Figure GDA00024399332300000613
are respectively phiBAnd
Figure GDA00024399332300000614
the singular value of (a).
When in use
Figure GDA0002439933230000071
And is
Figure GDA0002439933230000072
(1＜ma≤NtAnd is
Figure GDA0002439933230000073
) When using (K)H)-1Finally LA＝Nt-ma+1 column vectors
Figure GDA0002439933230000074
The useful signal precoding matrix is
Figure GDA0002439933230000075
Wherein the content of the first and second substances,
Figure GDA0002439933230000076
is (K)H)-1J ∈ { 1., Nt}。
When in use
Figure GDA0002439933230000077
Time, structure
Figure GDA00024399332300000740
The useful signal precoding matrix is FA＝(KH)-1。
When in use
Figure GDA0002439933230000078
When the channel capacity is negative, the actual transmission is meaningless.
Step four, optimizing
Figure GDA0002439933230000079
Useful signal precoding matrix FBFirst, a matrix is constructed
Figure GDA00024399332300000710
GSVD joint decomposition is carried out on the two matrixes to obtain phiA＝UA∑AWH，
Figure GDA00024399332300000711
Wherein
Figure GDA00024399332300000712
And
Figure GDA00024399332300000713
is a unitary matrix of the matrix,
Figure GDA00024399332300000714
is phiAAnd
Figure GDA00024399332300000736
of the first matrix.
Figure GDA00024399332300000715
And
Figure GDA00024399332300000716
is a diagonal matrix of the angles,
Figure GDA00024399332300000739
and
Figure GDA00024399332300000717
are respectively phiAAnd
Figure GDA00024399332300000737
the singular value of (a).
When in use
Figure GDA00024399332300000738
And is
Figure GDA00024399332300000719
(1＜mb≤NtAnd is
Figure GDA00024399332300000720
) When using (W)H)-1Last LB＝Nt-mb+1 column vectors
Figure GDA00024399332300000721
The useful signal precoding matrix is
Figure GDA00024399332300000722
Wherein the content of the first and second substances,
Figure GDA00024399332300000723
is (W)H)-1J ∈ { 1., Nt}。
When in use
Figure GDA00024399332300000724
Time, structure
Figure GDA00024399332300000725
The useful signal precoding matrix is FB＝(WH)-1。
When in use
Figure GDA00024399332300000726
When the channel capacity is negative, the actual transmission is meaningless.
Step five, optimizing the user
Figure GDA00024399332300000727
And
Figure GDA00024399332300000728
(power distribution coefficients α and β) further improve the overall safe rate of the system
Figure GDA00024399332300000729
Wherein the content of the first and second substances,
Figure GDA00024399332300000730
Figure GDA00024399332300000731
the specific implementation method comprises the following steps:
handle α ═ α*Substitution into
Figure GDA00024399332300000732
Solving the root according to the constraint of 0- β -1, and making β*Equal to the valid root to update β, change β to β*Bringing in
Figure GDA00024399332300000733
Solving the root according to the constraint of 0- α -1, and making α*Equal to the valid root to update α loop iteration 5 ends.
And step six, replacing the α and β values obtained in the last step back to the step three, optimizing the useful signal precoding matrix and power distribution in the next round, and ending the cycle after 10 times to obtain the optimal useful signal precoding matrix FAAnd FBAnd power distribution coefficients α and β, where the total safe rate of the system is maximized.
The channel model studied in the embodiment of the present invention is a channel model comprising two users: (
Figure GDA00024399332300000734
And
Figure GDA00024399332300000735
) And untrusted relay nodes
Figure GDA0002439933230000081
The bidirectional AF network of (1). Due to long-distance transmission or shadow effect, no direct transmission link exists between two users, so that the users
Figure GDA0002439933230000082
And
Figure GDA0002439933230000083
is communicated through the non-trusted relay node
Figure GDA0002439933230000084
And (4) establishing. Suppose a user
Figure GDA0002439933230000085
And
Figure GDA0002439933230000086
are respectively provided with NtThe number of the antenna elements is the same as the number of the antenna elements,
Figure GDA0002439933230000087
with NrRoot antenna of Nr＞NtTo ensure sufficient multiplexing gain. The transmission for each user needs to go through two phases (broadcast phase and relay phase). The wireless link between any two nodes is subject to flat quasi-static rayleigh block fading, which means that the channel gain remains unchanged for two consecutive frames and has independent fading. To avoid user information quilt
Figure GDA0002439933230000088
For cracking, we adopt a cooperative interference scheme, as shown in fig. 1.
The embodiments of the present invention are described in two parts: communication schemes, joint beamforming and optimized power allocation in a bidirectional untrusted relay network.
I communication scheme
The communication process used by the present invention is described in detail as follows:
in any transmission process, two users simultaneously send signals to the relay node, one sends a useful signal, and the other sends a cooperative interference signal. The relay node forwards the received signal to a destination node user of the next time slot. The above is a flow of unidirectional transmission, and the present invention studies the transmission of bidirectional information.
In the present invention, we divide consecutive transmission slots into odd and even slots. In the case of the odd time slots,
Figure GDA0002439933230000089
transmitting a useful signal xA，
Figure GDA00024399332300000810
Transmitting a cooperative interference signal (artificial noise) xJBSimultaneous relay node
Figure GDA00024399332300000811
Forwarding the signal received by the previous even time slot
Figure GDA00024399332300000812
On the contrary, in the even time slot,
Figure GDA00024399332300000813
transmitting a cooperative interference signal xJA，
Figure GDA00024399332300000814
Transmitting a useful signal xBSimultaneous relay node
Figure GDA00024399332300000815
Forwarding the signal received from the previous odd time slot
Figure GDA00024399332300000816
Suppose that
Figure GDA00024399332300000817
And
Figure GDA00024399332300000818
are respectively from
Figure GDA00024399332300000819
Of the broadcast phase of the system, wherein
Figure GDA00024399332300000820
Is that
Figure GDA00024399332300000821
The useful symbol vector to be transmitted is,
Figure GDA00024399332300000822
to represent
Figure GDA00024399332300000823
The transmit pre-coding matrix of (2),
Figure GDA00024399332300000824
is that
Figure GDA00024399332300000825
The vector of the transmitted interfering symbols is then transmitted,
Figure GDA00024399332300000826
to represent
Figure GDA00024399332300000827
The cooperative interference precoding matrix of (2). Also, the same applies to
Figure GDA00024399332300000828
And
Figure GDA00024399332300000829
from
Figure GDA00024399332300000830
The desired signal and the interfering signal of the broadcast phase of (a),
Figure GDA00024399332300000831
is that
Figure GDA00024399332300000832
The useful symbol vector to be transmitted is,
Figure GDA00024399332300000833
to represent
Figure GDA00024399332300000834
The transmit pre-coding matrix of (2),
Figure GDA00024399332300000835
is that
Figure GDA00024399332300000836
The vector of the transmitted interfering symbols is then transmitted,
Figure GDA00024399332300000837
to represent
Figure GDA00024399332300000838
The cooperative interference precoding matrix of (2). For both the useful and interfering signal vectors it is assumed that their powers are normalized, i.e.
Figure GDA00024399332300000839
PAAnd PBAre respectively
Figure GDA00024399332300000840
And
Figure GDA00024399332300000841
total transmit power in two consecutive time slots α∈ [0, 1 ]]And β∈ [0, 1 ]]Are respectively users
Figure GDA00024399332300000842
And the user
Figure GDA00024399332300000843
So that for two consecutive time slots, the user is allocated a power factor
Figure GDA00024399332300000844
The power for transmitting the useful signal and the cooperative interference signal is α PAAnd (1- α) PA(ii) a For the user
Figure GDA00024399332300000845
Then β P respectivelyBAnd (1- β) PB。
1) In odd time slots, i.e.
Figure GDA0002439933230000091
A broadcasting stage of (
Figure GDA0002439933230000092
Relay phase) of the relay node
Figure GDA0002439933230000093
A received signal vector of
Figure GDA0002439933230000094
Can be expressed as
Figure GDA0002439933230000095
Wherein H and
Figure GDA0002439933230000096
are respectively from
Figure GDA0002439933230000097
To
Figure GDA0002439933230000098
And from
Figure GDA0002439933230000099
To
Figure GDA00024399332300000910
The multi-antenna channel matrix of (a),
Figure GDA00024399332300000911
to represent
Figure GDA00024399332300000912
An additive noise vector.
Order to
Figure GDA00024399332300000913
Odd time slot
Figure GDA00024399332300000914
The rate of (A) can be expressed as
Figure GDA00024399332300000915
Since the channel has reciprocity, then
Figure GDA00024399332300000916
To
Figure GDA00024399332300000917
May be represented as HH. It is assumed that the transmit and receive channels are completely separated, so in odd slots, the users
Figure GDA00024399332300000918
To the received signal vector
Figure GDA00024399332300000919
Can be expressed as
Figure GDA00024399332300000920
Wherein the content of the first and second substances,
Figure GDA00024399332300000921
to represent
Figure GDA00024399332300000922
The received vector at the previous even time slot,
Figure GDA00024399332300000923
to represent
Figure GDA00024399332300000924
An additive noise vector. Also, the second term in the equation (3) represents a self-interference term, i.e., xJAIs that
Figure GDA00024399332300000925
A cooperative interference signal transmitted in a previous even time slot. Suppose that
Figure GDA00024399332300000926
Has the advantages ofAnd the self-interference item can be completely eliminated due to the channel state information of the channel. The received signal vector in equation (3) can be converted into
Figure GDA00024399332300000927
Order to
Figure GDA00024399332300000928
In the case of the odd time slots,
Figure GDA00024399332300000929
velocity of (2)
Figure GDA00024399332300000930
Can be expressed as
Figure GDA00024399332300000931
2) In even time slots, i.e.
Figure GDA00024399332300000932
In the relay stage (b)
Figure GDA00024399332300000933
Broadcast phase) of the relay node
Figure GDA00024399332300000934
A received signal vector of
Figure GDA00024399332300000935
Can be expressed as
Figure GDA00024399332300000936
Order to
Figure GDA00024399332300000937
Even time slot
Figure GDA00024399332300000938
The rate of (A) can be expressed as
Figure GDA00024399332300000939
In the same way, from
Figure GDA00024399332300000940
To
Figure GDA00024399332300000941
May be denoted as GHThus in even time slots, users
Figure GDA00024399332300000942
To the received signal vector
Figure GDA00024399332300000943
Can be expressed as
Figure GDA00024399332300000944
Wherein the content of the first and second substances,
Figure GDA0002439933230000101
to represent
Figure GDA0002439933230000102
The received signal vector at the previous odd slot,
Figure GDA0002439933230000103
to represent
Figure GDA0002439933230000104
An additive noise vector.
Order to
Figure GDA0002439933230000105
Then
Figure GDA0002439933230000106
The rate of (A) can be expressed as：
Figure GDA0002439933230000107
II Joint beamforming and optimized power allocation
1. Optimization problem design
In the DAJ technique, optimizing the beam forming and power allocation for each user to transmit the useful signal and the cooperative interference signal is an important issue. The present invention aims to maximize the overall safe rate of a bidirectional untrusted relay network by optimizing power consumption by adjusting power distribution and focusing interfering signals. From this point of view, using equations (2), (5), (7) and (9), the total safe rate for two slots can be defined as:
Figure GDA0002439933230000108
based on the safety rate of equation (10), the optimization problem can be defined as:
Figure GDA0002439933230000109
s.t.：α∈[0，1](11b)
β∈[0，1](11c)
Figure GDA00024399332300001010
Figure GDA00024399332300001011
Figure GDA00024399332300001012
Figure GDA00024399332300001013
in the above formula, (11b) and (11c) respectively represent
Figure GDA00024399332300001014
And
Figure GDA00024399332300001015
the transmit precoding matrix constraints of the desired signal are (11d) and (11e), respectively, and the transmit precoding matrix constraints of the interfering signal are (11f) and (11g), respectively. By dividing a target problem into two different subproblems, a local optimal solution approaching the optimal solution is found through an iterative algorithm. First, a new beamforming scheme for focusing interfering signals at a given power allocation is used to transmit a desired signal. An iterative algorithm is then used to obtain the optimal power allocation.
2. Joint beamforming
The invention first considers the design of each transmit precoding matrix for constant power allocation (α and β) only during the communication process, each user transmits a useful signal in the broadcast phase and an interfering signal in the relay phase
Figure GDA00024399332300001016
Or
Figure GDA00024399332300001017
In the link, the transmission of the interfering signal requires a sufficiently high interference power to reach the relay node in order to maximize the safe rate per transmission path.
1) Cooperative interference precoding matrix
As can be seen from equations (4) and (8), the design of each transmit precoding matrix for the interfering signal has a direct relationship with the safe rate, since the received signal of each user completely eliminates the self-interference term. Thus, the pair of interference precoding matrices
Figure GDA0002439933230000111
And
Figure GDA0002439933230000112
it has no influence. However, they are in contact with
Figure GDA0002439933230000113
There is a direct relationship to the achievable rate. Based on this, we will adjust the cooperative interference signal transmission precoding matrix to focus the interference signal and improve the safe rate. From formula (10), we have found that
Figure GDA0002439933230000114
The rate minimization may help to maximize the safe rate. Therefore, it can be further seen from equation (7) that the received cooperative interference signal should be maximized.
We precode the matrix Q by adjusting the interfering signalAAnd QBSo that they are orthogonal to H and G, respectively, then
Figure GDA0002439933230000115
The received SNR at (a) will increase. Since the matched filter precoding matrix can maximize the received SNR, let
Figure GDA0002439933230000116
Wherein λ isAAnd λBRespectively make QAAnd phiBThe coefficients that satisfy the power constraints of equations (11f) and (11g) can be calculated as
Figure GDA0002439933230000117
And
Figure GDA0002439933230000118
thereby ensuring that the even time slot and the odd time slot are respectively accessed
Figure GDA0002439933230000119
And
Figure GDA00024399332300001110
arrive at
Figure GDA00024399332300001111
The interference power is the largest. Thus, equations (2) and (7)) As defined in
Figure GDA00024399332300001112
The reception rate of (d) can be expressed as:
Figure GDA00024399332300001113
wherein the content of the first and second substances,
Figure GDA00024399332300001114
substituting equations (5), (9) and (13) into (11), the optimization problem in equation (11) is simplified to:
Figure GDA00024399332300001115
2) useful signal precoding matrix
Analysis of the objective function in equation (14) reveals that the first term of the equation is only associated with FAIs related to the optimization of (1), the second term is related to F onlyBIs relevant to the optimization of (2). To maximize the safe rate, we need to maximize each term separately (since the safe rate is the sum of the two terms).
(1) User' s
Figure GDA0002439933230000121
Transmitting a useful signal precoding matrix FAIs optimized
As can be seen from the above-described analysis,
Figure GDA0002439933230000122
transmitting a useful signal precoding matrix FAThe optimization problem of (a) can be summarized as:
Figure GDA0002439933230000123
we pass the maximization of TATo find the optimum F under constant power allocationA. From equation (15), maximizing the safe rate can be explained from a physical point of view: we have found thatThe useful signal transmission precoding matrix must be optimized such that
Figure GDA0002439933230000124
Is aligned to phiBThe expanded subspace, and
Figure GDA00024399332300001228
the unfolded subspaces are orthogonal. From a mathematical point of view, by choosing the sum ofBLarger singular value sum of
Figure GDA00024399332300001229
Corresponding to the common column of smaller singular values to construct FATo achieve the optimization. Based on this, we jointly decompose Φ using GSVDBAnd
Figure GDA00024399332300001230
obtaining:
Figure GDA0002439933230000125
wherein the content of the first and second substances,
Figure GDA0002439933230000126
and
Figure GDA0002439933230000127
is a unitary matrix of the matrix,
Figure GDA0002439933230000128
is phiBAnd
Figure GDA0002439933230000129
is determined by the common non-singular matrix of (a),
Figure GDA00024399332300001210
and
Figure GDA00024399332300001211
is a diagonal matrix, based on one of the most important properties of GSVD:
Figure GDA00024399332300001212
is provided with
Figure GDA00024399332300001231
Figure GDA00024399332300001213
Are respectively phiBAnd
Figure GDA00024399332300001214
the singular value of (a).
By making FA＝(KH)-1By derivation, TACan directly calculate
Figure GDA00024399332300001215
Consider ∑BAnd
Figure GDA00024399332300001216
the characteristics of the medium singular value, we adopt the following FAThe structural scheme of (1). To achieve the maximum safe rate we need to adjust FATo select to satisfy
Figure GDA00024399332300001217
The channel of (2). Suppose that
Figure GDA00024399332300001218
Wherein
Figure GDA00024399332300001219
Is (K)H)-1J ∈ { 1., Nt}。
When in use
Figure GDA00024399332300001220
And is
Figure GDA00024399332300001221
(1＜ma≤NtAnd is
Figure GDA00024399332300001222
) Then use (K)H)-1Finally LA＝Nt-ma+1 column vectors to construct FAI.e. by
Figure GDA00024399332300001223
Useful signal precoding matrix of
Figure GDA00024399332300001224
Is composed of
Figure GDA00024399332300001225
When in use
Figure GDA00024399332300001226
Time, structure
Figure GDA00024399332300001227
The useful signal precoding matrix is FA＝(KH)-1。
When in use
Figure GDA0002439933230000131
When the channel capacity is negative, the actual transmission is meaningless.
(2) User' s
Figure GDA0002439933230000132
Transmitting a useful signal precoding matrix FBIs optimized
In the same way, the method for preparing the composite material,
Figure GDA0002439933230000133
transmitting a useful signal precoding matrix FBThe optimization problem of (a) can be summarized as:
Figure GDA0002439933230000134
using the same algorithm, iCan obtain FB. By joint decomposition of phi by (19)AAnd
Figure GDA0002439933230000135
to design
Figure GDA0002439933230000136
Transmit a useful signal precoding matrix
Figure GDA0002439933230000137
Wherein the content of the first and second substances,
Figure GDA0002439933230000138
and
Figure GDA0002439933230000139
is a unitary matrix of the matrix,
Figure GDA00024399332300001310
is phiAAnd
Figure GDA00024399332300001311
of the first matrix.
Figure GDA00024399332300001312
And
Figure GDA00024399332300001313
is a diagonal matrix. One of the most important properties based on GSVD is
Figure GDA00024399332300001329
And
Figure GDA00024399332300001314
are respectively phiAAnd
Figure GDA00024399332300001315
the singular value of (a).
By making FB＝(WH)-1，TBCan be calculated as
Figure GDA00024399332300001316
Then we adjust F in order to achieve the maximum safe rateBTo select to satisfy
Figure GDA00024399332300001317
The channel of (2). Order to
Figure GDA00024399332300001318
Wherein
Figure GDA00024399332300001319
Is (W)H)-1Column j.
When in use
Figure GDA00024399332300001320
And is
Figure GDA00024399332300001321
(1＜mb≤NtAnd is
Figure GDA00024399332300001322
) When using (W)H)-1Last LB＝Nt-mb+1 column vector construction FBI.e. by
Figure GDA00024399332300001323
Useful signal precoding matrix of
Figure GDA00024399332300001324
Is composed of
Figure GDA00024399332300001325
When in use
Figure GDA00024399332300001326
Time, structure
Figure GDA00024399332300001327
The useful signal precoding matrix is FB＝(WH)-1。
When in use
Figure GDA00024399332300001328
When the channel capacity is negative, the actual transmission is meaningless.
Since the useful signal precoding matrix ignores all channels with equivalent gain less than 1 and aligns the useful signal to the effective space. Therefore, the safe rate will increase.
3. Optimizing power allocation
By optimizing the precoding matrix for both phases (broadcast and relay) of the user, i.e. the precoding matrix F for transmitting the useful signalAAnd FBAnd a matched filtering precoding matrix theta for transmitting the interference signalAAnd ΘBThe overall safe rate can be maximized. The invention next aims at optimizing the user
Figure GDA0002439933230000141
And
Figure GDA0002439933230000142
(α and β) further improve the overall safe rate of the system then, the problem in equation (14) translates directly into
Figure GDA0002439933230000143
s.t.：α∈[0，1](23b)
β∈[0，1](23c)
Wherein the content of the first and second substances,
Figure GDA0002439933230000144
Figure GDA0002439933230000145
at the fixed FAAnd FB、QAAnd QBUnder the conditions of (3), power distribution coefficients α and β are optimized by substituting the initial value α into the partial derivative of the objective function (23a) with respect to β (assuming pairs of
Figure GDA0002439933230000146
Constant power allocation) is performed, the roots are solved and checked for validity according to constraints, the valid roots are set to an approximately optimal value of β. the approximately optimal value of β is substituted into the partial derivative of the objective function (23a) with respect to α, the roots are solved and checked for validity according to constraints, the valid roots are set to an approximately optimal value of α. the approximately optimal value of β is updated again with updated α, and the optimal values of α and β are obtained after 5 times of cyclic updating.
Since it is difficult to prove that the optimization function is a convex function and find a global solution for the general optimization method of equation (23), and its complexity will also follow NtIs increased. Therefore, we use the iterative algorithm described above to optimize the problem.
4. Summary of the Algorithm
Algorithm 1 summarizes the overall steps of the present invention to design joint beamforming and optimized power allocation for bi-directional relay transmission using the DAJ approach. Internal circulation for optimizing FAAnd FBGiven the power allocation, the outer loop is used to update the transmit useful signal precoding matrix based on the new power allocation (α and β).
Algorithm 1 flow:
1) setting initial conditions of power distribution coefficients α*0.5 and β*Adjusting the maximum number of iterations of the outer loop to be N (0.5)BF5, inner loop is NOPA＝10；
2) Constructing an interference precoding matrix based on the matched filtering precoding matrix so that Q isA＝HH，QB＝GH；
3) Combined decomposition of Φ in equation (16) using GSVDBAnd
Figure GDA0002439933230000147
finding K, joint decomposition in formula (20)ΦAAnd
Figure GDA0002439933230000148
finding out W;
external circulation:
4) construction with K, W, α and β according to the methods described previously
Figure GDA0002439933230000151
And
Figure GDA0002439933230000152
5) internal circulation:
a) handle α ═ α*Substitution into
Figure GDA0002439933230000153
Solving the root according to the constraint of 0- β -1, and making β*Equal to the valid root to update β.
b) Handle β ═ β*Bringing in
Figure GDA0002439933230000154
Solving the root according to the constraint of 0- α -1, and making α*Equal to the valid root to update α.
Performing an inner loop step NOPAAnd then the next step is carried out.
Recycling N in the steps 4) and 5)BFNext, the process is carried out.
The invention carries out numerical simulation and comparison on the safety rate performance of the proposed pre-coding matrix. The elements of H and G are assumed to be independently identically distributed complex gaussian random variables with a mean of 0 and a variance of 1. All simulations were run 10000 times independently using a fading channel model. To avoid loss of generality, we assume
Figure GDA0002439933230000155
User' s
Figure GDA0002439933230000156
And
Figure GDA0002439933230000157
the total power transmitted being the same, i.e. PA＝PBP. Furthermore, the SNR can be adjusted by the transmit power P, we further define the equivalent signal-to-noise ratio as
Figure GDA0002439933230000158
To evaluate system performance. In order to show the performance improvement of the beamforming scheme of the optimal power allocation proposed by the present invention, we introduce other four beamforming schemes of equal power allocation for comparison. Equal beamforming, which is (1) equal power allocation, respectively, transmitting useful and interfering signals in all directions; (2) the method comprises the steps of equal-power distributed equal-beam forming and matched pre-coding, sending a cooperative interference signal through a matched filtering pre-coding matrix, and sending useful signals to all directions; (3) random beam forming with equal power distribution and non-directional transmission of useful and interference signals; (4) the method comprises the steps of equal-power distributed random beam forming and matched precoding, and transmits a cooperative interference signal through a matched filtering precoding matrix, and transmits a useful signal without directivity.
FIG. 2 shows N t6 and NrBeamforming for the optimal power allocation proposed herein and the other four equal power allocations (i.e., the
Figure GDA0002439933230000159
And
Figure GDA00024399332300001510
) The beamforming schemes of (a) are compared to achieve a safe rate. From fig. 2, we conclude that random beamforming is the lowest safe rate, since its beamforming is randomly directed and the useful signal may not pass through the relay. Equal beamforming is safer than random beamforming because it ensures that at least some of the signals can reach the relay. By using the matching precoding matrix to focus the cooperative interference signals of the two users to the untrusted relay, the security performance is improved when the matching precoding matrix is used to transmit the interference signals under the equal beamforming and random beamforming schemes. Beamforming for optimal power allocation proposedShape safety is highest because it aligns the wanted signal to the effective signal space, which focuses the wanted signal and optimizes the power allocation over all SNRs according to the channel gain.
We find that the beamforming using the optimal power allocation proposed by the present invention is better than the safety performance of the equal power allocation in the bidirectional relay transmission through the DAJ technique, we provide a comparison of the optimal power allocation results calculated by the Mat L ab toolbox to verify the correctness of the optimal power allocation achieved using the algorithm 1, the results show that the safety rate obtained by the algorithm 1 is consistent with the safety rate obtained by the Mat L ab toolbox.
FIG. 4 shows the values at 0dB, 5dB, 10dB and 30dB, N t6 and NrAt 8, the convergence of the inner loop of the optimal power allocation in the first outer loop in algorithm 1.
FIG. 5 shows the values at 0dB, 5dB, 10dB and 30dB, N t6 and NrFrom fig. 4 and 5, we find that the values of α and β at each SNR converge in the third or fourth iteration in each outer loop, the optimal values converge faster as the SNR increases, at smaller SNRs, the effect of large noise on α and β requires more iterations to smooth, although at the second outer loop (update F)AAnd FB) Within this, the modification of each optimal power allocation is very small, with little change in the third cycle.
Fig. 6(a) and 6(b) verify the convergence of the outer loop. Here, we introduce a differential norm between two successive external iterations to show convergence, which can be defined as
Figure GDA0002439933230000161
Wherein the content of the first and second substances,
Figure GDA0002439933230000162
and
Figure GDA0002439933230000163
is the user in the second iteration of the outer loop of algorithm 1
Figure GDA0002439933230000164
And
Figure GDA0002439933230000165
beamforming of the transmitted useful signal. From fig. 6(a) and 6(b) we find that the two precoding matrices converge rapidly at different SNRs.
FIG. 7 shows a user
Figure GDA0002439933230000166
And
Figure GDA0002439933230000167
difference of upper antenna configuration (N)t4, 5, 6) pairs of constant number of relay antennas NrImpact of achievable safe rate at 8. It can be seen that the safe rate increases with the number of antennas for the user, since the DoF is larger and more favorable for beamforming focusing.
FIG. 8 shows a user
Figure GDA0002439933230000168
And
Figure GDA0002439933230000169
difference of upper antenna configuration (N)t4, 5, 6) pairs of constant number of relay antennas NrGiven the average of α and β at different SNRs, we conclude that the optimal values of α and β are approximately the same, since from the user the impact of the optimal power allocation at 8 is given
Figure GDA00024399332300001610
And
Figure GDA00024399332300001611
to
Figure GDA00024399332300001612
Have the same statistical properties. And by increasing the SNR, more power will be allocated to a given NtTo a user
Figure GDA00024399332300001613
And
Figure GDA00024399332300001614
to transmit a useful signal. In addition, more power will be allocated to NtLarger users transmit useful signals. These results all contribute to cooperative interference signals at high SNR or large NtEasy focusing.
FIG. 9 shows the difference NrAnd fixing NtThe system can reach a safe rate. From fig. 9 we find that a larger DoF relay improves its ability to decode the wanted signal as the number of relay antennas increases, thereby reducing the safe rate performance.
FIG. 10 shows the difference NrAnd fixing NtAnd (4) allocating the optimal work power. From fig. 10 we conclude that: when the number of relay antennas increases, the decoding capability of the relay increases, and therefore, more power needs to be allocated to the cooperative interference signal to reduce the decoding capability of the relay on the useful signal.
And (4) conclusion: the present invention uses DAJ technology to increase the security rate of a bi-directional untrusted relay network. According to the DAJ technique, each user transmits a useful and interfering signal in two consecutive time slots. A novel beam forming scheme is adopted to align the useful signal to the effective space of the useful signal, the useful signal is focused on a link of a source node, a relay node and a destination node, and a matched filter is used for precoding to focus an interference signal; and an iterative algorithm is provided to optimize the transmission power distribution, so that the network can reach the safe rate to the maximum. Simulation results show the correctness and effectiveness of the proposed joint beamforming and optimal power allocation scheme.

Claims (1)

1. A method for combining beam forming and optimal power distribution in a bidirectional untrusted relay network is characterized by comprising the following steps:
step one, including the user
Figure FDA0002439933220000011
User' s
Figure FDA0002439933220000012
And untrusted relay nodes
Figure FDA0002439933220000013
In the bidirectional AF network of
Figure FDA0002439933220000014
And
Figure FDA0002439933220000015
are respectively provided with NtThe number of the antenna elements is the same as the number of the antenna elements,
Figure FDA0002439933220000016
with NrA root antenna; setting user
Figure FDA0002439933220000017
User' s
Figure FDA0002439933220000018
Power distribution coefficient of (2) is set to an initial value α - α*＝0.5，β＝β*0.5; the power distribution coefficient refers to P for two continuous time slotsAAnd PBAre respectively
Figure FDA0002439933220000019
And
Figure FDA00024399332200000110
total transmission power in two consecutive time slots, user
Figure FDA00024399332200000111
The power for transmitting the useful signal and the cooperative interference signal is α PAAnd (1- α) PAFor the user
Figure FDA00024399332200000155
Then β P respectivelyBAnd (1- β) PB；
Step two, adjusting the user
Figure FDA00024399332200000112
User' s
Figure FDA00024399332200000113
Interference signal precoding matrix QAAnd QBMaking it orthogonal to H and G, H and
Figure FDA00024399332200000114
are respectively from
Figure FDA00024399332200000115
To
Figure FDA00024399332200000116
And from
Figure FDA00024399332200000117
To
Figure FDA00024399332200000118
Of the multi-antenna channel matrix, QA＝λAHH，QB＝λBGHWherein
Figure FDA00024399332200000119
So that QAAnd QBThe power constraint condition is satisfied;
step three, optimizing
Figure FDA00024399332200000120
Useful signal precoding matrix FAFirst, a matrix is constructed
Figure FDA00024399332200000121
GSVD joint decomposition is carried out on the two matrixes to obtain phiB＝UB∑BKH，
Figure FDA00024399332200000122
Wherein the content of the first and second substances,
Figure FDA00024399332200000123
is composed of
Figure FDA00024399332200000124
Where the variance of the additive noise is received,
Figure FDA00024399332200000125
is composed of
Figure FDA00024399332200000126
Where the variance of the additive noise is received,
Figure FDA00024399332200000127
and
Figure FDA00024399332200000128
is a unitary matrix of the matrix,
Figure FDA00024399332200000129
is phiBAnd
Figure FDA00024399332200000130
is determined by the common non-singular matrix of (a),
Figure FDA00024399332200000131
and
Figure FDA00024399332200000132
is a diagonal matrix of the angles,
Figure FDA00024399332200000133
and
Figure FDA00024399332200000134
are respectively phiBAnd
Figure FDA00024399332200000135
the singular value of (a);
when in use
Figure FDA00024399332200000136
And is
Figure FDA00024399332200000137
When 1 is more than ma≤NtAnd is
Figure FDA00024399332200000138
By (K)H)-1Finally LA＝Nt-ma+1 column vectors
Figure FDA00024399332200000139
The useful signal precoding matrix is
Figure FDA00024399332200000140
Wherein the content of the first and second substances,
Figure FDA00024399332200000141
Figure FDA00024399332200000142
is (K)H)-1J ∈ { 1.,. Nt}；
When in use
Figure FDA00024399332200000143
Time, structure
Figure FDA00024399332200000144
The useful signal precoding matrix is FA＝(KH)-1；
When in use
Figure FDA00024399332200000145
When the channel capacity is negative, the actual transmission is meaningless;
step four, optimizing
Figure FDA00024399332200000146
Useful signal precoding matrix FBFirst, a matrix is constructed
Figure FDA00024399332200000147
GSVD joint decomposition is carried out on the two matrixes to obtain phiA＝UA∑AWH，
Figure FDA00024399332200000148
Wherein the content of the first and second substances,
Figure FDA00024399332200000149
is composed of
Figure FDA00024399332200000150
Where the variance of the additive noise is received,
Figure FDA00024399332200000151
and
Figure FDA00024399332200000152
is a unitary matrix of the matrix,
Figure FDA00024399332200000153
is phiAAnd
Figure FDA00024399332200000154
of the common matrix of (a) and (b),
Figure FDA0002439933220000021
and
Figure FDA0002439933220000022
is a diagonal matrix of the angles,
Figure FDA0002439933220000023
and
Figure FDA0002439933220000024
are respectively phiAAnd
Figure FDA00024399332200000222
the singular value of (a);
when in use
Figure FDA0002439933220000025
And is
Figure FDA0002439933220000026
When 1 is more than mb≤NtAnd is
Figure FDA0002439933220000027
By (W)H)-1Last LB＝Nt-mb+1 column vectors
Figure FDA00024399332200000221
The useful signal precoding matrix is
Figure FDA0002439933220000028
Wherein the content of the first and second substances,
Figure FDA0002439933220000029
Figure FDA00024399332200000210
is (W)H)-1J ∈ { 1.,. Nt}；
When in use
Figure FDA00024399332200000211
Time, structure
Figure FDA00024399332200000212
The useful signal precoding matrix is FB＝(WH)-1；
When in use
Figure FDA00024399332200000213
When the channel capacity is negative, the actual transmission is meaningless;
step five, optimizing the user
Figure FDA00024399332200000214
And
Figure FDA00024399332200000215
power distribution coefficients α and β, and total safe speed of the system is improved
Figure FDA00024399332200000216
Wherein the content of the first and second substances,
Figure FDA00024399332200000217
Figure FDA00024399332200000218
the specific implementation method comprises the following steps:
handle α ═ α*Substitution into
Figure FDA00024399332200000219
Solving the root according to the constraint of 0- β -1, and making β*Equal to the valid root to update β, change β to β*Bringing in
Figure FDA00024399332200000220
Solving the root according to the constraint of 0- α -1, and making α*Equal to the valid root to update α;
and step six, replacing the α and β values obtained in the last step back to the step three, optimizing the useful signal precoding matrix and power distribution in the next round, and ending after 10 times of circulation to obtain the optimal useful signal precoding matrix FAAnd FBAnd power distribution coefficients α and β, where the total safe rate of the system is maximized.
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