CN108173575A - multiple-input and multiple-output relay antenna design method - Google Patents
multiple-input and multiple-output relay antenna design method Download PDFInfo
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- CN108173575A CN108173575A CN201711308483.1A CN201711308483A CN108173575A CN 108173575 A CN108173575 A CN 108173575A CN 201711308483 A CN201711308483 A CN 201711308483A CN 108173575 A CN108173575 A CN 108173575A
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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
- H04B7/022—Site diversity; Macro-diversity
- H04B7/026—Co-operative diversity, e.g. using fixed or mobile stations as relays
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B17/00—Monitoring; Testing
- H04B17/30—Monitoring; Testing of propagation channels
- H04B17/309—Measuring or estimating channel quality parameters
- H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B17/00—Monitoring; Testing
- H04B17/30—Monitoring; Testing of propagation channels
- H04B17/391—Modelling the propagation channel
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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
- H04B7/0456—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
- H04B7/02—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
- H04B7/046—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account
- H04B7/0469—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account taking special antenna structures, e.g. cross polarized antennas into account
Abstract
Multiple-input and multiple-output relay antenna design method.The present invention relates to a kind of relay antenna design method for considering the imperfect signal noise distortion with power constraint of hardware and optimizing than SNDR, including two kinds of scenes of relay antenna total power constraint and individual antenna power constraint.Information sends out channel from source node and is transferred to relay node, relay node expands forwarding channel by antenna again and is transferred to destination node, and wherein information can be influenced by the imperfect factor of hardware when source node and relay node are sent out and cause to damage distortion accordingly.Antenna array vector type closed solutions when under total power constraint scene, multiple-input and multiple-output MIMO relay system signal noise is distorted based on matrix-vector and than SNDR optimization problem equivalences is converted to general Rayleigh entropy form, and be obtained SNDR maximums；Under individual antenna power constraint scene, decomposed based on order and randomization gives a kind of optimization problem numerical solution algorithm using SNDR as object function, realize the promotion of network system performance to a certain extent.
Description
Technical field
The present invention relates to wireless communication field, more particularly, to a kind of consideration hardware is imperfect and power constraint, based on letter
Number noise distortion is than the relay antenna design method of optimization.
Background technology
With the development of cordless communication network technology and the extensive development of wireless traffic, the performance of network system transmission is always
It is one of key problem of academia and industry concern.Double jump relay transmission technology in being transmitted as cooperation, because it is easily real
It applies and helps to transmit signal message, and be deeply applied to the effective drop for going the promotion and cost for obtaining system performance in practice
It is low.
In actual wireless transmission, correlative study has shown that transceiver hardware often by such as high power amplifier width
The influence of the imperfect factor such as non-linear, phase noise and I/Q imbalances is spent, this causes to generate when transmitting and receiving signal
Some are inevitably distorted.This problem will be more obvious in following high rate communication systems it.Lead to relative to single-hop
The hardware of letter system is imperfect to have had many relevant researchs in academia, it is notable that existing research work is big
All it is the transmission for considering no relay node.Minority considers that the research model of relay transmission is all based on relay system configuration
Single antenna it is assumed that and having achievement to show that the imperfect performance to network communicating system of node transceiver hardware can generate negative
Face acts on.
Invention content
MIMO technology is applied to due to it can improve the dimension of transmission in modern communications practice.The present invention is in double jump
After other than considering the imperfect factor of hardware, inquiring into fusion MIMO technology in Transmission system, that is, consider relay node antenna configuration
Multiple antennas, to realize the performance boost of wireless network transmission system.Antenna simultaneously based on MIMO technology analysis relay system
Optimization design is also meaningful.Because the transmission of trunk channel is mostly assumed that in existing MIMO technology related work
Matrix is certain fixed structure, amplification factor or simple numbers matrix such as constant.In fact, the wave of relay system
Beam transmission matrix can carry out corresponding optimization design based on different object functions and constraints.In addition to relay antenna total work
Outside the constraint scene of rate, the relay antenna considered present invention is alternatively directed to property under practical single-antenna power limited case is set
Meter, corresponding Antenna Design and corresponding network when Optimal Signals noise distortion ratio SNDR is calculated by convextiry analysis and optimization
Performance evaluation.
The purpose of the present invention be exactly in order to overcome defect of the existing technology and provide a kind of consideration hardware it is imperfect and
Power constraint, the MIMO relay antenna design methods based on signal noise distortion than optimization, including relay antenna total power constraint
With two kinds of scenes of individual antenna power constraint, compared with prior art, the present invention fully considered that hardware is imperfect and power about
The optimization design of MIMO relay antennas in the case of beam, and the promotion of network system performance is realized to a certain extent.
The purpose of the present invention can be achieved through the following technical solutions：
Under total power constraint scene, signal noise is distorted based on matrix-vector and is converted to one than optimization problem equivalence
As Rayleigh entropy form, and antenna array vector type closed solutions when being obtained SNDR maximums；In individual antenna power constraint scene
Under, it is decomposed based on order and randomization gives a kind of optimization problem numerical solution algorithm using SNDR as object function.It includes
Step in detail below：
1. in relay antenna total power constraint scene signals transmission process, establish based on the maximized Optimized models of SNDR
And it solves the method for obtaining relay antenna matrix and is：
1) objective optimization model is established under relay antenna total power constraint, meets the following formula：
In formula, h1And h2System source node respectively to relay node, relay node to destination node the dimension channel of N × 1 to
Amount, W are relay antenna beamforming matrixs, κ1And κ2Hardware damage level ginseng when being source node and relay node transmitting signal respectively
Number, power of the P for source information, PrFor the general power of MIMO relay antennas, N0It is channel white noise parameter,Represent plural number
Domain,Represent channel vector h2Transposition operation, | |2For the square operation of several absolute values, | | | |2It is vectorial or matrix
The square operation of norm.
2) the general of above-mentioned optimization problem is obtained by matrix-vector and substitution of variable under relay antenna total power constraint
Rayleigh entropy situation, meet the following formula：
In formula, f=vec (W),(·)*()HRepresent vectorial or matrix respectively
Conjugation and conjugate transposition operation, I represents N rank unit matrixs, I2Represent N2Rank unit square
Battle array.Specifically, f is the vectorization of relay antenna beamforming matrix W,For channel vector h1And h2All ask after conjugation
Amount product operation,For channel vector h1The tensor product operation after conjugation is all asked with unit matrix I,For unit matrix I and
Channel vector h2All ask the tensor product operation after conjugation.
Its optimal solution isIn formulaIt substitutes into optimization problem
Object function up to SNDR maximum values, and can construct to obtain MIMO relay system beamforming matrix.
2. in individual antenna power constraint scene signals transmission process, establish based on the maximized Optimized models of SNDR simultaneously
Solve relay node antenna array method be：
1) objective optimization model is established under individual antenna power constraint, meets the following formula：
s.t.E|ydi|2≤Pri, i=1,2 ..., N
In formula Pri(i=1,2 ..., N) represent relaying
Power constraint value of the system on i-th of antenna.Specifically, eiThe unit column vector for being 1 for i-th point of vector, Tr ()
For the mark operation of matrix,For channel vector h1The tensor product operation after conjugation is all asked with unit matrix I.
2) based on matrix-vector and substitution of variable method under individual antenna power constraint, we are converted to Optimized model
Following equivalent form：
In formulaF=ffH, f=vec (W), I represents N rank unit matrixs, I2Represent N2Rank unit matrix and
Representing matrixOrder.
Since the constraint that order is 1 has nonconvex property, we remove the constraint and obtain a semi definite programming problem that can be solved,
And the solution of former problem is discussed：
It is total for the Xie that the semi definite programming problem of 1 constraint obtains based on no order when relaying system antenna number no more than 2
It can obtain the solution that an order is 1；
When relaying system antenna number equal to or more than 3, we have used a kind of method of randomization to be obtained from following problem
To a non-convex quadratically constrained quadratic programming approximate solution
Specific algorithm is：Consider that an obedience mean value is 0 and variance isGaussian Profile n n-dimensional random variable n ξ, and structure
Make new variableObtain the positive semidefinite optimization problem of a stochastic approximation
The solution of the problem and corresponding target function value are the optimal antenna when relaying system antenna number and be equal to or more than 3
The maximum value of SNDR under design scenario.
Compared with prior art, the present invention has the following advantages：
1) the double jump MIMO that the present invention is analyzed when being maximized based on end-to-end SNDR expands the optimal of forward relay network
Antenna Design.Original optimization problem equivalence is converted into, and ask by general Rayleigh entropy problem scenario by matrix-vector method
Obtain closed solutions when SNDR is optimal under total power constraint.Simulation result shows optimal antenna designing scheme proposed by the invention
It can realize apparent performance boost.
2) Antenna Design under total power constraint is further expanded to the application scenarios of single-antenna power constraint by the present invention,
And propose a kind of antenna optimization design algorithm based on relaying single-antenna power constraint.The result shows that when relay system day
When line number is no more than 2, (SDR) method that can always be relaxed by positive semidefinite acquires optimal solution；When relaying system antenna number is more than 2
When, it can obtain an approximate optimal solution with the randomized algorithm of proposition.Simulation result shows that increase relay antenna number can
To improve the performance for expanding forward relay network based on the imperfect double jump MIMO with single-antenna power constraint of hardware.
Description of the drawings
Fig. 1 is considers that the faulty double jump MIMO of hardware expands forward relay transport frame schematic diagram；
Fig. 2 is works as threshold gammathThe interruption performance of the imperfect antenna optimization design with total power constraint of hardware is considered when=3
Analyze comparison schematic diagram；
Fig. 3 is works as threshold gammathThe interruptibility of the imperfect antenna optimization design with total power constraint of hardware is considered when=31
Comparison schematic diagram can be analyzed；
Fig. 4 is to consider that hardware is imperfect excellent at random with the antenna of single-antenna power constraint when relay system antenna number N=2
Change the interruption performance analysis schematic diagram of design；
Fig. 5 is to consider that hardware is imperfect excellent at random with the antenna of single-antenna power constraint when relay system antenna number N=4
Change the interruption performance analysis schematic diagram of design.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention
Premised on implemented, give detailed embodiment and specific operating process, but protection scope of the present invention is not limited to
Following embodiments.
Consider that hardware is imperfect the present invention relates to a kind of and power constraint, optimized than (SNDR) based on signal noise distortion
Multiple-input and multiple-output (MIMO) expands forwarding (AF) relay system antenna design method, including relay antenna total power constraint and list
A antenna power constrains two kinds of scenes.Information sends out channel from source node and is transferred to relay node, and relay node passes through day again
Line expands forwarding channel and is transferred to destination node, and wherein information can be endless by hardware when source node and relay node are sent out
U.S. factor influences and causes to damage distortion accordingly.
Under total power constraint scene, SNDR optimization problem equivalences are converted to general auspicious by we based on matrix-vector
Sharp entropy form, and the antenna array vector type closed solutions being obtained under maximum S/N DR；Under individual antenna power constraint scene, we
It is decomposed and is randomized based on order and give a kind of optimization problem numerical solution algorithm using SNDR as object function.
(1)
As shown in Figure 1, information x expands forward relay transmission mode from source node to destination node using double jump MIMO, together
When we consider the faulty distortion noises of hardware to influence.Under relay antenna total power constraint scene, establish based on SNDR
Maximized Optimized model simultaneously solves the method for obtaining relay antenna matrix and includes the following steps：
1) objective optimization model is established under relay antenna total power constraint, meets the following formula：
In formula, h1And h2System source node respectively to relay node, relay node to destination node the dimension channel of N × 1 to
Amount, W are relay antenna beamforming matrixs, κ1And κ2Hardware damage level ginseng when being source node and relay node transmitting signal respectively
Number, power of the P for source information, PrFor the general power of MIMO relay antennas, N0It is channel white noise parameter,Represent plural number
Domain,Represent channel vector h2Transposition operation, | |2For the square operation of several absolute values, | | | |2It is vectorial or matrix
The square operation of norm.
2) based on matrix-vector method under relay antenna total power constraint, Optimized model is converted to following equivalence by we
Form：
s.t.fHD3F=Pr
In formula, f=vec (W),(·)*()HRepresent vectorial or matrix respectively
Conjugation and conjugate transposition operation,I2Represent N2Rank unit matrix,I represents N rank unit matrixs.Specifically, f is relaying day
The vectorization of line beamforming matrix W,For channel vector h1And h2The tensor product operation after conjugation is all asked,For channel to
Measure h1The tensor product operation after conjugation is all asked with unit matrix I,For unit matrix I and channel vector h2After all seeking conjugation
Tensor product operation.
3) the general Rayleigh entropy situation of above-mentioned optimization problem is obtained by substitution of variable under relay antenna total power constraint,
Meet the following formula：
In formula,
Its optimal solution isIn formulaIt substitutes into optimization problem
Target letter up to SNDR maximum values, and can construct to obtain MIMO relay system beamforming matrix.It substitutes into outage probability and calculates public affairs
Performance charts of the Shi Ke get when relay antenna total power constraint and corresponding SNDR can obtain maximum value.Fig. 2 and Fig. 3 difference
To work as threshold gammath=3 and γthThe interruption performance of the imperfect antenna optimization design with total power constraint of hardware is considered when=31
Traditional fixed income before analyzing comparison schematic diagram, with optimization relays and variable income repeater mode is comparatively, to MIMO
Relay transmission pattern after antenna optimizes can obtain corresponding performance boost (the corresponding outage probabilities of identical SNR
Smaller).
(2)
As shown in Figure 1, information x expands forward relay transmission mode from source node to destination node using double jump MIMO, together
When we consider the faulty distortion noises of hardware to influence.Under individual antenna power constraint scene, establish based on SNDR most
The Optimized model changed greatly and the method for solving relay antenna beamforming matrix, include the following steps：
1) objective optimization model is established under individual antenna power constraint, meets the following formula：
s.t.E|ydi|2≤Pri, i=1,2 ..., N
In formula Pri(i=1,2 ..., N) represent relaying
Power constraint value of the system on i-th of antenna.Specifically, eiThe unit column vector for being 1 for i-th point of vector, Tr ()
For the mark operation of matrix,For channel vector h1The tensor product operation after conjugation is all asked with unit matrix I.
2) the plan convex problem of above-mentioned optimization problem is obtained by substitution of variable under individual antenna power constraint, met following public
Formula：
s.t.Tr[QiF]+N0≤Pri, i=1,2 ..., N
Rank (F)=1
In formula, F=ffH,
The order of rank (F) representing matrixes F.
3) it converts to obtain equivalence problem form with Charnes-Cooper, meets the following formula：
In formula
Since the constraint that order is 1 has nonconvex property, we remove the constraint and obtain a semi definite programming problem that can be solved,
And the solution of former problem is discussed：
It is total for the Xie that the semi definite programming problem of 1 constraint obtains based on no order when relaying system antenna number no more than 2
It can obtain the solution that an order is 1.Specific algorithm is
I. assume that removing the semi definite programming Optimum Solution that order is 1 constraint isOrder is rF。
II. by optimal solutionIt resolves intoIn formula
III. the r of a non-zero is foundF×rFHermitian matrixes MFMeet linear equation
IV. calculating matrix MFFeature vectorAnd it takes
V. structural matrixAnd remember
VI. previous step II-V is repeated, untilUntil order is 1.
When relaying system antenna number equal to or more than 3, we have used a kind of method of randomization to be obtained from following problem
To a non-convex quadratically constrained quadratic programming approximate solution
Specific algorithm is：Consider that an obedience mean value is 0 and variance isGaussian Profile n n-dimensional random variable n ξ, and structure
Make new variableObtain the positive semidefinite optimization problem of a stochastic approximation
s.t.Tr(DX)+zN0=1
Tr[QiX]+zN0≤zPri, i=1,2 ..., N.
The solution of the problem and corresponding target function value are the optimal antenna when relaying system antenna number and be equal to or more than 3
The maximum value of SNDR under design scenario.Substituting into outage probability calculation formula can obtain in individual antenna power constraint and corresponding SNDR
Can obtain performance chart during maximum value, Fig. 4 and Fig. 5 be respectively consider as antenna number N=2 and N=4 hardware it is imperfect and
The interruption performance analysis schematic diagram of the antenna random optimization design of single-antenna power constraint, compares two figures and can be seen that in MIMO
Increase after system antenna number can be substantially reduced the outage probability (during in identical SNR) of system, show the use of multiple antenna
The transmission performance that relay system can be obtained is promoted.
Claims (3)
1. a kind of multiple-input and multiple-output relay antenna design method, including relay antenna total power constraint and individual antenna power about
Two kinds of scenes of beam；Under total power constraint scene, SNDR optimization problem equivalences are converted to based on matrix-vector general auspicious
Sharp entropy form, and the antenna array vector type closed solutions being obtained under SNDR maximal conditions；Under individual antenna power constraint scene,
It is decomposed based on order and method of randomization gives a kind of optimization problem numerical solution algorithm using SNDR as object function.
2. multiple-input and multiple-output relay antenna design method according to claim 1, which is characterized in that the relay antenna
In total power constraint scene signals transmission process, establish based on the maximized Optimized models of SNDR and solve relay antenna matrix
Method includes the following steps：
1) objective optimization model is established under relay antenna total power constraint, meets the following formula：
In formula, h1And h2It is system source node respectively to relay node, the dimension channel vector of N × 1 of relay node to destination node, W
It is relay antenna beamforming matrix, κ1And κ2Hardware damage horizontal parameters when being source node and relay node transmitting signal respectively, P
For the power of source information, PrFor the general power of MIMO relay antennas, N0It is channel white noise parameter,Represent complex field,
Represent channel vector h2Transposition operation, | |2For the square operation of several absolute values, | | | |2It is vectorial or norm of matrix
Square operation.
2) the general auspicious of above-mentioned optimization problem is obtained by matrix-vector and substitution of variable under relay antenna total power constraint
Sharp entropy situation, meets the following formula：
In formula, f=vec (W),() * and ()HThe conjugation of vector or matrix is represented respectively
With conjugate transposition operation, I represents N rank unit matrixs, I2Represent N2Rank unit square
Battle array.Specifically, f is the vectorization of relay antenna beamforming matrix W,For channel vector h1And h2All ask after conjugation
Amount product operation,For channel vector h1The tensor product operation after conjugation is all asked with unit matrix I,For unit matrix I and
Channel vector h2All ask the tensor product operation after conjugation.
Its optimal solution isIn formulaSubstitute into the mesh in optimization problem
Scalar functions can construct to obtain MIMO relay system beamforming matrix up to SNDR maximum values.
3. multiple-input and multiple-output relay antenna design method according to claim 1, which is characterized in that the individual antenna
In power constraint scene signals transmission process, the side of relay antenna matrix is established based on the maximized Optimized models of SNDR and solved
Method includes the following steps：
1) objective optimization model is established under individual antenna power constraint, meets the following formula：
s.t.E|ydi|2≤Pri, i=1,2 ..., N
In formula Pri(i=1,2 ..., N) represent relaying
Power constraint value of the system on i-th of antenna.Specifically, eiThe unit column vector for being 1 for i-th point of vector, Tr ()
For the mark operation of matrix,For channel vector h1The tensor product operation after conjugation is all asked with unit matrix I.
2) based on matrix-vector and substitution of variable method under individual antenna power constraint, Optimized model is simplified to as follows by we
Equivalence formula：
In formulaF=ffH, f=vec (W), I represents N rank unit matrixs, I2Represent N2Rank unit matrix and
Representing matrixOrder.
Since the constraint that order is 1 has nonconvex property, remove the constraint and obtain a semi definite programming problem that can be solved, and original is discussed
The solution of problem：
It, always can be with for the obtained Xie of semi definite programming problem of 1 constraint based on no order when relaying system antenna number and being no more than 2
Obtain the solution that an order is 1；
When relaying system antenna number and being equal to or more than 3, obtained from following problem with method of randomization one it is non-convex secondary
Constrain quadratic programming approximate solution
Specific algorithm is：Consider that an obedience mean value is 0 and variance isGaussian Profile n n-dimensional random variable n ξ, and construct new
VariableObtain the positive semidefinite optimization problem of a stochastic approximation
s.t.Tr(DX)+zN0=1
Tr[QiX]+zN0≤zPri, i=1,2 ..., N.
The solution of the problem and corresponding target function value are the optimal antenna design when relaying system antenna number and be equal to or more than 3
The maximum value of SNDR under scene.
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