CN110213185A - A kind of three dimensional channel method for parameter estimation based on atom norm minimum - Google Patents
A kind of three dimensional channel method for parameter estimation based on atom norm minimum Download PDFInfo
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Abstract
The invention belongs to fields of communication technology, and in particular to a kind of three dimensional channel method for parameter estimation based on atom norm minimum.The pilot signal that the pilot signal and known mobile station that the method is received according to base station are sent carries out the estimation of channel parameter；Three parameters for possessing vandermonde structure: angle of setting out AoA, angle of arrival AoD and time delay are contained in known channel matrix H [k], according to the sparse scattering properties of millimeter wave channel, the channel estimation problems of system can be seen as to three-dimensional linear spectral estimation problem, high-precision recovers the above parameter in the way of mesh free by the method for ANM；And using the independence between parameter, three-dimensional ANM channel estimation problems are decomposed into the estimation problem of two-dimentional ANM and one-dimensional ANM, to reduce the algorithm complexity of three-dimensional ANM channel estimation.
Description
Technical field
The invention belongs to fields of communication technology, and in particular to a kind of three dimensional channel parameter based on atom norm minimum is estimated
Meter method.
Background technique
Millimetre-wave attenuator is the research hotspot of 5G in the related technology, and millimetre-wave attenuator works in 30-300GHz wave band, possesses
The message transmission rate of bandwidth resources and high speed abundant.Millimetre-wave attenuator also brings lot of challenges, first high band simultaneously
Millimetre-wave attenuator path loss in an atmosphere it is very big, secondly the millimetre-wave attenuator of ultra high bandwidth also results in frequency selectivity
Decline.In order to solve this problem, can by millimeter wave and extensive MIMO (multiple inputmultiple output,
MIMO) technology combines, and compensates path loss using the beam forming gain of large-scale antenna array.And the size of antenna with
Carrier wavelength is proportional, so the short wavelength of millimeter wave is conducive to transmitting terminal and large-scale antenna array is arranged in receiving end.In order to gram
Frequency selective fading is taken, OFDM (orthogonal frequency selective fading, OFDM) technology can be used
Broad-band channel is divided into multiple parallel flat subchannels.So the extensive MIMO-OFDM system of millimeter wave is 5G wireless communication
Research hotspot.
Beam forming technique can bring huge directive gain for the extensive MIMO-OFDM system of millimeter wave, however wave
Beam shaping technology needs design launching beam forming vector according to channel state information and receive combined vector.Therefore, how
Accurately estimate that the channel state information in the extensive MIMO-OFDM system of millimeter wave becomes the new challenge for being worth research.
In the prior art, the method based on tensor resolution is used for the channel estimation of the extensive MIMO-OFDM system of millimeter wave,
This method needs just can be carried out channel estimation under the premise of known channel order, and channel exponent number needs to be obtained with other algorithms
, increase calculation amount.Also, there is two-dimentional ANM method to be applied to the millimeter wave MIMO-OFDM system of narrowband at present, actually
Millimeter wave bandwidth is very wide, and wherein time delay is cannot ignore the problem of.
To sum up, the channel estimation of the extensive MIMO-OFDM system of millimeter wave is significant, is worth research.
Summary of the invention
In view of the above technical problems, the present invention provides a kind of three dimensional channel parameter Estimation side based on atom norm minimum
Method solves the problems, such as three-dimensional channel estimation and channel parameter estimation with decomposable three-dimensional ANM method, can be accurately
It obtains channel parameter and reduces computation complexity.
Wherein, atom norm minimum (atomic norm minimization, ANM) is a kind of optimization method, base
This thought is that the simple linear combination of several atoms of the signal to be estimated on known atom collection indicates, and utilizes atom
Structure extraction estimation signal in angle information.Millimeter wave channel has multipath sparse characteristic, the extensive MIMO- of millimeter wave
The channel estimation of ofdm system can be considered the linear spectral estimation problem of three-dimensional (angle of setting out, angle of arrival, time delay), this is asked
Topic can use ANM method and recover sparse signal --- channel state information.
The present invention is achieved by the following technical solutions:
A kind of three dimensional channel method for parameter estimation based on atom norm minimum, the method are extensive for millimeter wave
Channel parameter estimation in MIMO-OFDM system between base station and single mobile station；The extensive MIMO-OFDM system of millimeter wave
System sends data flow using subcarrier；
The channel matrix of the corresponding frequency domain of subcarrier includes three channel parameters with vandermonde structure: angle of setting out
AoA, angle of arrival AoD and time delay；It is according to the sparse scattering properties of millimeter wave channel, the millimeter wave is extensive
The channel parameter estimation of MIMO-OFDM system regards three-dimensional linear Power estimation as, using the method for atom norm minimum ANM with
The mode high-precision of mesh free recovers the parameter of the channel matrix and channel matrix；Wherein, three-dimensional ANM channel estimation packet
It includes and set out angle, angle of arrival and channel matrix is estimated using two dimension ANM；Using the estimation time delay and multiple increasing of one-dimensional ANM
Benefit, angle of setting out, angle of arrival, time delay and the complex gain finally obtained according to estimation, obtains complete channel matrix.
Further, the extensive MIMO-OFDM system of the millimeter wave includes a base station and multiple mobile stations, the base
It stands and the antenna of the multiple mobile station is all made of uniform linear array；
The base station is configured with NBSRoot transmitting antenna andRadio frequency link, each mobile station are configured with NMSRoot antenna
WithRF link；
The base station and the multiple mobile station use hybrid modulus precoder.
Further, set out angle and angle of arrival are estimated using two-dimentional ANM, specifically:
The channel matrix of the corresponding frequency domain of k-th of subcarrier are as follows:
Wherein, the item number for the scattering path that L is possessed by the channel between base station and mobile station；βl,kFor channel complex gain,αlIt is corresponding complex gain on l paths, l≤l≤L；J is imaginary unit, τlFor l paths
On time delay parameter, fsIt is sampling rate；K is the sum of subcarrier,It indicates for sending instruction
Practice the number of sub carrier wave of sequence；φl∈ [0,2 π] and θl∈ [0,2 π] is set out angle and angle of arrival on l paths respectively
Degree, aMS(φl) and aBS(θl) respectively correspond the antenna-array response vector of mobile station and base station, ()HIndicate to matrix or to
Amount carries out conjugate transposition variation；To expression aMS(φl) vector carry out conjugate transposition after vector；Wherein, because of τl
With set out angle and angle of arrival is independent from each other, by τ in the estimation of set out angle and angle of arrivallIt is considered as constant；
Matrix form atom collection is established, channel matrix H [k] is expressed as the shape that atom concentrates several atom linear combinations
Formula；The atom collection of given matrix formAre as follows:
Wherein,The element that the atom of representing matrix form is concentrated；
Based on matrix form atom collectionChannel matrix H [k] atom norm is defined as:
Inf { } indicates that the atom norm of H [k] is minimized；It is atom collectionIn element, A () indicate one
Kind matrix form, the interior variable for matrix of bracket；
When matrix form atom collectionIn atom close to really set out angle and angle of arrival when, channel matrix H
The atom norm of [k]It is up to minimum value；
Assuming that the φ in channel matrix H [k]lWith θlIndependently of each other, and φl/θlCorresponding sine value sin (φl)/sin
(θl) meet the separable condition of sufficient frequency, it may be assumed that
In formula, p, q indicates serial number；NBSFor the number of transmission antennas configured in base station, NMSFor the configuration of each mobile station
Antenna amount；
Meet sufficient frequency and separates conditionDecomposition be it is unique and sparse, i.e.,
Pass through the atom norm to channel matrix H [k]It is solved, obtains the atom of composition H [k], i.e.,
Determine φl/θl。
Further, be in base station channel matrix H [k] it is unknown, base station according to the pilot signal Y [k] received and
The pilot signal s [k] that known mobile station is sent recovers channel matrix H [k] and φl/θl, specifically:
According to given pilot signal Y [k], by the atom norm of channel matrix H [k]It is re-written as removal noise
ANM form:
Wherein,It is noise control item, W is the reception combination square of base station receiving end BS
Battle array, F are the pre-coding matrixes of mobile station transmitting terminal MS, and S is the pilot frequency sequence of transmission；||·||FThe norm of representing matrix, μ are
Normalized parameter relevant to noise power,
Wherein N=NBS+NMS；
In order to avoid infinite programming problem, is solved, is obtained using Semidefinite Programming SDP:
Constraint condition:
Wherein, uφ,k, uθ,kRespectively indicate T (uφ,k) and T (uθ,k) toeplitz matrix the first row；Solution obtains T
(uφ,k) and T (uθ,k) matrix the first row；Tr () represents the mark of matrix,
T(uφ,k) it is the first row u by itφ,kDetermining toeplitz matrix；T(uθ,k) it is the first row u by itθ,kDetermining Top
Ritz matrix；
By T (uφ,k) and T (uθ,k) be expressed as generalized circular matrix, i.e., by antenna-array response vector aMS(φl) and aBS(θl)
The form of composition:
By to T (uφ,k) and T (uθ,k) decomposition of level-one vandermonde is done, obtain φl/θl。
Further, using the estimation time delay and complex gain of one-dimensional ANM, specifically:
φ is obtained by two-dimentional ANM channel estimationlWith θlEstimated value, and then obtain mobile station and base station aerial array
ResponseWithIn order to obtain the time delay parameter τ on l pathslWith complex gain αlEstimated value,
Millimeter wave channel at k-th of subcarrier is rewritten as OFDM channel form:
Wherein, OFDM is orthogonal frequency division multiplexi；Multiple carrier waves are contained in OFDM, h [k] is at k-th of carrier wave
Channel；H [k] is by formulaIt obtains, []*The pseudoinverse of representing matrix or vector；
Given OFDM channel vectorElement in h withMiddle element has similar Mapping is closed
System；Therefore OFDM channel vector h is indicated are as follows:
Wherein, DELAY RESPONSE vector aτ(fl) is defined as:
Wherein, frequencyAssuming that τlMeetWherein LcpIt is the length of cyclic prefix；Frequency
flValue range beSection；
The frequency f that when estimating channel state information, will include in channel vector using one-dimensional ANM methodlValue
Range should be fromSection becomes the section of [0,1]:
Assuming that pilot tone form is Comb Pilot,The position of a pilot sub-carrier be from etc.Interval
The position collection of distributionMiddle random selection, is indicated with k 'The position rope of a Comb Pilot subcarrier
Draw, sub-carrier positions index meets with subcarrier serial numberRelationship, then the OFDM channel at kth ' a subcarrier
It indicates are as follows:
At this point, the frequency in OFDM channel vector hANM method estimation time delay can be used；
Based on atom collectionOFDM channel vector h one dimensional atom norm is defined as:
Wherein,
Assuming that frequency flMeet sufficient frequency and separates condition, atom normIt is expressed as SDP planning:
Wherein, t indicates a constant；U indicates the first row of toeplitz matrix T (u)；hHIndicate OFDM channel vector h
Conjugate transposition；It is the PSD toeplitz matrix being made of its first row u；T (u) can be expressed as by model
Moral covers matrix Aτ(f) form formed:
Wherein, Aτ(f)=[aτ(f1),…,aτ(fL)], D is positive semi-definite diagonal matrix；
Frequency is extracted from T (u) using MUSIC method
When the time delay parameter for obtaining L propagation pathAfterwards, DELAY RESPONSE vector is constitutedPlural path
The corresponding diagonal matrix of gainCalculation formula are as follows:
Diagonal matrix
Complete channel matrixCan set out angle, angle of arrival according to estimated valueTime delayWith
Path gainIt recovers.
Advantageous effects of the invention:
(1) the channel state information estimation method based on ANM of three-dimensional provided by the invention utilizes three-dimensional ANM for the first time
Method is estimated to obtain the channel state information of the extensive MIMO-OFDM system of millimeter wave.ANM method is the channel estimation of mesh free
Method can accurately estimate the various parameter values of multiple channels, and not need precognition channel exponent number.
(2) based on the independence between parameter, three-dimensional ANM channel matrix decomposition is two dimension by the method for the invention
The channel estimation of ANM and one-dimensional ANM significantly reduce computation complexity while keeping accuracy comparable with three-dimensional ANM.
(3) the method for the invention solves ANM by SDP, obtains the support being made of the array response vector of estimation parameter
Puli's hereby matrix；And the channel parameter in toeplitz matrix can be extracted using MUSIC algorithm, it is determined using peak value searching
Estimate the value of parameter.
Detailed description of the invention
The MSE of different parameters under Fig. 1 difference SNR；
MSE performance under Fig. 2 difference SNR compares；
Application scenarios model Fig. 3 of the invention.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is explained in further detail.It should be appreciated that specific embodiment described herein is used only for explaining the present invention, and
It is not used in the restriction present invention.
On the contrary, the present invention covers any substitution done on the essence and scope of the present invention being defined by the claims, repairs
Change, equivalent method and scheme.Further, in order to make the public have a better understanding the present invention, below to of the invention thin
It is detailed to describe some specific detail sections in section description.Part without these details for a person skilled in the art
The present invention can also be understood completely in description.
The embodiment of the present invention provides a kind of three dimensional channel method for parameter estimation based on atom norm minimum.Channel ginseng
Number estimation method is suitable for the extensive MIMO-OFDM system of millimeter wave.It include one in the extensive MIMO-OFDM system of millimeter wave
The antenna of base station and multiple mobile stations, base station and mobile station using uniform linear array (uniform linear array,
ULA), base station is configured with NBSRoot transmitting antenna andRadio frequency (radio frequency, RF) link, mobile station are configured with
NMSRoot antenna andRF link.
The base station and the multiple mobile station use hybrid modulus precoder to use hybrid modulus in the present embodiment
The reason of precoder is: performance and the complexity for simulating precoder are lower, performance, complexity and the RF of digital precode device
The expense of chain is higher, and base station and mobile station are all made of hybrid modulus precoder in the present embodiment, can be improved precoder
Performance and reduce complexity and RF chain expense.
Wherein, the extensive MIMO-OFDM communication system of millimeter wave sends N using K subcarrierSData stream.Due to
Orthogonality between pilot signal, method provided by the present embodiment only estimate the channel between base station and single mobile station.
According to the limited scattering properties of millimeter wave channel, it is assumed that the channel between base station and mobile station possesses L item scattering road
Diameter, in the non-line-of-sight environment of dense city, the corresponding wideband frequency selective decline of the extensive MIMO-OFDM system of millimeter wave
Channel matrix is H (τ):
Wherein, the item number for the scattering path that L is possessed by the channel between base station and mobile station；αlIt is on l paths
Corresponding complex gain, l≤l≤L；J is imaginary unit；φl∈ [0,2 π] and θl∈ [0,2 π] is the angle of departure on l paths
(angle of departure, AoD) and angle of arrival (angle of arrival, AoA) are spent,And aBS(θl)
The antenna-array response vector of mobile station and base station is respectively corresponded, in addition, H (τ) indicates the channel matrix of time delay domain, δ () table
Show Dirac function；τ is variable, τlIt is time delay；τlFor the time delay parameter on l paths.All due to base station and mobile station
Using ULA antenna, therefore corresponding antenna-array response vector is embodied as:
Wherein, λ and d respectively indicate the distance between carrier wavelength and adjacent antenna.
According to the channel model of time delay domain above, the channel matrix of the corresponding frequency domain of k-th of subcarrier can be provided:
Wherein, fsIt is sampling rate, K is the sum of subcarrier,Indicate the number of sub carrier wave for sending training sequence.
Assuming that mobile station is in the continuous N frame frequency pilot sign that k-th of subcarrier is sentThen base station connects
The pilot signal receivedIt indicates are as follows:
Wherein, F [k] indicates the pre-coding matrix of the corresponding mobile station of k-th of subcarrier；W [k] indicates k-th of subcarrier
The reception combinatorial matrix of corresponding base station；N [k] indicates the corresponding expression white Gaussian noise of k-th of subcarrier；In order to facilitate channel
The solution of algorithm for estimating, it is assumed that the pre-coding matrix of different sub-carrier is identical, and frequency pilot sign is also identical, so [k] is omitted.It is the pre- of mobile station respectively
The reception combinatorial matrix of encoder matrix and base station.The two pre-coding matrixes are by simulation RF pre-coding matrix FRF/WRFAnd number
Base band pre-coding matrix FBB[k]/WBB[k] is constituted.In order to facilitate the solution of channel estimation method, it is assumed that different sub-carrier it is pre-
Encoder matrix is identical, and frequency pilot sign is also identical.
Channel is carried out according to the pilot signal Y [k] and known pilot signal transmitted s [k] received's
Estimation.Three parameters (AoA, AoD and time delay) for possessing vandermonde structure are contained in known channel matrix H [k], according to
The sparse scattering properties of millimeter wave channel, the channel estimation problems of the system can be seen as three-dimensional linear spectral estimation problem.
This three-dimensional linear spectral estimation problem, the method that can use ANM recover the above parameter in high precision in a manner of mesh free.
Using the independence between parameter, three-dimensional ANM channel estimation problems are decomposed into the estimation problem of two-dimentional ANM and one-dimensional ANM,
To reduce the algorithm complexity of three-dimensional ANM channel estimation.
Channel estimation methods of the invention are divided into two steps: two-dimentional ANM estimation AoA AoD and channel matrix, one-dimensional ANM
Estimate time delay and complex gain.
Two-dimentional ANM estimates AoA and AoD:
AoDs/AoAs is obtained using the mesh free channel estimation methods of two-dimentional ANM.Because of time delay parameter τlWith
AoDs/AoAsφl/θlIt is independent from each other, so in the estimation of AoDs/AoAs, by τlIt is considered as constant, ifTherefore (4) formula is separately written as:
Wherein, the item number for the scattering path that L is possessed by the channel between base station and mobile station；βl,kFor channel complex gain,αlIt is corresponding complex gain on l paths, l≤l≤L；J is imaginary unit, τlFor l paths
On time delay parameter, fsIt is sampling rate；K is the sum of subcarrier,It indicates for sending instruction
Practice the number of sub carrier wave of sequence；φl∈ [0,2 π] and θl∈ [0,2 π] is set out angle and angle of arrival on l paths respectively
Degree, aMS(φl) and aBS(θl) respectively correspond the antenna-array response vector of mobile station and base station, ()HIndicate to matrix or to
Amount carries out conjugate transposition variation；To expression aMS(φl) vector carry out conjugate transposition after vector；Wherein, because of τl
With set out angle and angle of arrival is independent from each other, by τ in the estimation of set out angle and angle of arrivallIt is considered as constant；
ANM method estimates that channel matrix H [k] and AoDs/AoAs are firstly the need of matrix form atom collection, atom collection is established
The basis of ANM method, channel matrix H [k] can be expressed as the form that atom concentrates several atom linear combinations.Given rectangular
The atom collection of formula are as follows:
Wherein,The element that the atom of representing matrix form is concentrated；
H [k] has the characteristic that can be indicated by the monoatomic linear combination of several letters that atom is concentrated, so selection matrix shape
Formula atom collectionIn suitable atom, can determine the parameter value (angle value) in H [k].Based on atom collectionChannel
The atom norm of matrix H [k] is defined as:
Inf { } indicates that the atom norm of H [k] is minimized；It is atom collectionIn element, A () indicate one
Kind matrix form, the interior variable for matrix of bracket；
When matrix form atom collectionIn atom close to really set out angle and angle of arrival when, channel matrix H
The atom norm of [k]It is up to minimum value；
Assuming that the φ in channel matrix H [k]lWith θlIndependently of each other, and φl/θlCorresponding sine value sin (φl)/sin
(θl) meet the separable condition of sufficient frequency, it may be assumed that
In formula, p, q indicates serial number；NBSFor the number of transmission antennas configured in base station, NMSFor the configuration of each mobile station
Antenna amount；
Meet sufficient frequency and separates conditionDecomposition be it is unique and sparse, i.e.,
Pass through the atom norm to channel matrix H [k]It is solved, obtains the atom of composition H [k], i.e.,
Determine φl/θl。
However, actually H [k] is unknown in base station.It base station will be according to the pilot signal Y [k] that receives and known
Pilot signal transmitted s [k] recover H [k] and φl/θl.According to given Y [k], (8) are re-written as to the ANM of removal noise
Form:
Wherein,It is noise control item, W is the reception combination square of base station receiving end BS
Battle array, F are the pre-coding matrixes of mobile station transmitting terminal MS, and S is the pilot frequency sequence of transmission；||·||FThe norm of representing matrix, μ are
Normalized parameter relevant to noise power,
Wherein N=NBS+NMS；
In order to avoid infinite programming problem, solved using Semidefinite Programming (semidefinite programming, SDP)
(10),
Wherein, tr () represents the mark of matrix, Point
It is not the first row by themWithPositive semidefinite (the positive of the level-one of definition
Semidefinite, PSD) toeplitz matrix.PSD matrix T (uφ,k) and T (uθ,k) it is also referred to as generalized circular matrix (antenna
Array response vector aMS(φl) and aBS(θl)) constitute form,
To sum up, by T (uφ,k) and T (uθ,k) decomposition of level-one vandermonde is done, φ can be obtainedl/θl。
Preferably, from T (uφ,k) and T (uθ,k) extract angle in matrix method it is very much, such as matrix tree method and based on revolving
Turn the Signal parameter estimation method etc. of constant technology.Using Multiple Signal Classification (multiple single classification,
MUSIC) method obtains φ in a manner of peak value searchingl/θl.Then, using pairing algorithm to obtained φl/θlIt is matched.
Using the estimation time delay and complex gain of one-dimensional ANM, specifically:
φ is obtained by two-dimentional ANM channel estimationlWith θlEstimated value, and then obtain mobile station and base station aerial array
ResponseWithIn order to obtain the time delay parameter τ on l pathslWith complex gain αlEstimated value,
Millimeter wave channel at k-th of subcarrier is rewritten as OFDM channel form:
Wherein, OFDM is orthogonal frequency division multiplexi；Multiple carrier waves are contained in OFDM, h [k] is at k-th of carrier wave
Channel；H [k] is by formulaIt obtains, []*The pseudoinverse of representing matrix or vector；
Given OFDM channel vectorElement in h withMiddle element has similar Mapping is closed
System；Therefore OFDM channel vector h is indicated are as follows:
Wherein, DELAY RESPONSE vector aτ(f) is defined as:
Wherein, frequencyAssuming that delay, τlMeetWherein LcpIt is the length of cyclic prefix.
Therefore, frequency flValue range beSection.
Channel state information is estimated using one-dimensional ANM method, the value range for the frequency f for including in channel vector is answered
FromSection becomes the section of [0,1].Assuming that the pilot tone form of system is Comb Pilot,The position of a pilot sub-carrier
Set be from etc.The position collection being spaced apartMiddle random selection, is indicated with k 'The location index of a Comb Pilot subcarrier, sub-carrier positions index meet with subcarrier serial numberRelationship.
Therefore the OFDM channel at kth ' a subcarrier is expressed as
Frequency in present OFDM channel vector hTherefore when can be using the estimation of ANM method
Prolong.Based on atom collectionOFDM channel vector h one dimensional atom norm is defined as:
Wherein
Assuming that frequency flMeet sufficient frequency and separates condition, subsequent atom normIt can be expressed as SDP rule
It draws:
Wherein, t indicates a constant；U indicates the first row of toeplitz matrix T (u)；hHIndicate OFDM channel vector h
Conjugate transposition；It is the PSD toeplitz matrix being made of its first row u；T (u) can be expressed as by model
Moral covers matrix Aτ(f) form formed,
Wherein, Aτ(f)=[aτ(f1),…,aτ(fL)], D is positive semi-definite diagonal matrix.It is similar in two dimension ANM, it uses
MUSIC method extracts frequency from T (u)
When the time delay for obtaining L propagation pathAfterwards, it may be constructed DELAY RESPONSE vectorThen plural path
The corresponding diagonal matrix of gainCalculating can be passed through
It obtains, diagonal matrix
Finally, complete channel matrixIt can be according to estimated value AoAs, AoDsTime delayThe road and
Diameter gainIt recovers.
Millimeter wave MIMO-OFDM system channel is estimated, it is proposed by the present invention decomposable to assess to carry out analog simulation
Three-dimensional ANM method performance.By the method for the invention with the ANM and compressed sensing of traditional vector quantization three-dimensional
(compressed sensing, CS) method compares.CS method solves estimation problem using orthogonal matching pursuit algorithm, and
It is solved on the grid of 40 × 40 × 40 (AoD-AoA- time delays).Mean square error (mean square error, MSE) is made
For the standard for assessing all method performances.Simulation result is the average value of 200 Monte Carlo experiment results.If without spy
It does not mentionlet alone bright, indicates decomposable three-dimensional ANM method with D-ANM, ANM indicates traditional vector quantization ANM method.Simulation parameter setting is shown in
Table 1.
1 system parameter setting of table
Compare the accuracy of channel parameter (AoD, AoA and time delay) estimation first.It is provided by the invention as shown in Fig. 1 (a)
Method can accurately estimate angle value.The MSE performance of D-ANM method and the MSE performance of ANM are very close.And CS performance
Poor, and with the increase of SNR, MSE performance is without substantially changeing.Fig. 1 (b) is the comparison about time delay estimation performance, ANM method
The performance of middle time delay estimation is identical with the performance of angle estimation, but the method for D-ANM is slightly below ANM to the estimation performance of time delay,
This is because two dimension ANM channel matrix obtained before the time delay estimation of one-dimensional ANM needs to utilize in D-ANM, channel matrix
The precision of estimation influences subsequent time delay estimation.
Next, comparing the performance of different channels estimation method.Figure it is seen that the methodical MSE of institute is with SNR
Increase and reduce.Wherein, the accuracy of estimation of D-ANM method is suitable with ANM, their MSE is above CS.D-ANM method
Performance it is suitable with ANM, and be higher than CS method, the computation complexity of D-ANM method is far smaller than ANM.
Method provided by the present invention carries out the three-dimensional of the extensive MIMO-OFDM system of millimeter wave using the method for ANM
Channel estimation, advantage is at 3 points: first, being suitable for broadband millimeter-wave communication system；Second, the estimates of parameters essence obtained
It spends high；Third, computation complexity is lower.
Claims (5)
1. a kind of three dimensional channel method for parameter estimation based on atom norm minimum, which is characterized in that the method is for milli
Channel parameter estimation in the extensive MIMO-OFDM system of metric wave between base station and single mobile station；The millimeter wave is extensive
MIMO-OFDM system sends data flow using subcarrier；
The channel matrix of the corresponding frequency domain of subcarrier includes three channel parameters with vandermonde structure: angle of setting out AoA,
Angle of arrival AoD and time delay；According to the sparse scattering properties of millimeter wave channel, by the extensive MIMO- of the millimeter wave
The channel parameter estimation of ofdm system regards three-dimensional linear Power estimation as, using the method for atom norm minimum ANM with no net
The mode high-precision of lattice recovers the parameter of the channel matrix and channel matrix；Wherein, three-dimensional ANM channel estimation includes adopting
Set out angle, angle of arrival and channel matrix are estimated with two-dimentional ANM；Using the estimation time delay and complex gain of one-dimensional ANM, most
Angle of setting out, angle of arrival, time delay and the complex gain obtained afterwards according to estimation, obtains complete channel matrix.
2. a kind of three dimensional channel method for parameter estimation based on atom norm minimum, feature exist according to claim 1
In the extensive MIMO-OFDM system of millimeter wave includes a base station and multiple mobile stations, the base station and the multiple shifting
The antenna of dynamic platform is all made of uniform linear array；
The base station is configured with NBSRoot transmitting antenna andRadio frequency link, each mobile station are configured with NMSRoot antenna and
RF link；
The base station and the multiple mobile station use hybrid modulus precoder.
3. a kind of three dimensional channel method for parameter estimation based on atom norm minimum, feature exist according to claim 2
In, set out angle and angle of arrival are estimated using two-dimentional ANM, specifically:
The channel matrix of the corresponding frequency domain of k-th of subcarrier are as follows:
Wherein, the item number for the scattering path that L is possessed by the channel between base station and mobile station；βl,kFor channel complex gain,αlIt is corresponding complex gain on l paths, l≤l≤L；J is imaginary unit, τlIt is the l articles
Time delay parameter on path, fsIt is sampling rate；K is the sum of subcarrier,It indicates for sending out
Send the number of sub carrier wave of training sequence；φl∈ [0,2 π] and θl∈ [0,2 π] is that setting out on l paths and is arrived angle respectively
Up to angle, aMS(φl) and aBS(θl) respectively correspond the antenna-array response vector of mobile station and base station, ()HIt indicates to matrix
Or vector carries out conjugate transposition variation；To expression aMS(φl) vector carry out conjugate transposition after vector；Wherein, because
For τlWith set out angle and angle of arrival is independent from each other, by τ in the estimation of set out angle and angle of arrivallIt is considered as constant；
Matrix form atom collection is established, channel matrix H [k] is expressed as the form that atom concentrates several atom linear combinations；It gives
The atom collection of set matrix formAre as follows:
Wherein,The element that the atom of representing matrix form is concentrated；
Based on matrix form atom collectionChannel matrix H [k] atom norm is defined as:
Inf { } indicates that the atom norm of H [k] is minimized；It is atom collectionIn element, A () indicates a kind of square
Formation formula, the interior variable for matrix of bracket；
When matrix form atom collectionIn atom close to really set out angle and angle of arrival when, channel matrix H [k]
Atom normIt is up to minimum value；
Assuming that the φ in channel matrix H [k]lWith θlIndependently of each other, and φl/θlCorresponding sine value sin (φl)/sin(θl) full
The sufficient frequency of foot separates condition, it may be assumed that
In formula, p, q indicates serial number；NBSFor the number of transmission antennas configured in base station, NMSFor the day of each mobile station configuration
Line number amount；
Meet sufficient frequency and separates conditionDecomposition be it is unique and sparse, i.e.,
Pass through the atom norm to channel matrix H [k]It is solved, obtains the atom of composition H [k], that is, determined
φl/θl。
4. a kind of three dimensional channel method for parameter estimation based on atom norm minimum, feature exist according to claim 3
In, be in base station channel matrix H [k] it is unknown, base station is sent out according to the pilot signal Y [k] received and known mobile station
The pilot signal s [k] sent recovers channel matrix H [k] and φl/θl, specifically:
According to given pilot signal Y [k], by the atom norm of channel matrix H [k]It is re-written as removal noise
ANM form:
Wherein,It is noise control item, W is the reception combinatorial matrix of base station receiving end BS, and F is
The pre-coding matrix of mobile station transmitting terminal MS, S are the pilot frequency sequences of transmission；||·||FThe norm of representing matrix, μ are and noise
The relevant normalized parameter of power,
Wherein N=NBS+NMS；
In order to avoid infinite programming problem, is solved, is obtained using Semidefinite Programming SDP:
Constraint condition:
Wherein, uφ,k, uθ,kRespectively indicate T (uφ,k) and T (uθ,k) toeplitz matrix the first row；Solution obtains T (uφ,k) and T
(uθ,k) matrix the first row；Tr () represents the mark of matrix,
T(uφ,k) it is the first row u by itφ,kDetermining toeplitz matrix；T(uθ,k) it is the first row u by itθ,kDetermining Top
Ritz matrix；
By T (uφ,k) and T (uθ,k) be expressed as generalized circular matrix, i.e., by antenna-array response vector aMS(φl) and aBS(θl) constitute
Form:
By to T (uφ,k) and T (uθ,k) decomposition of level-one vandermonde is done, obtain φl/θl。
5. a kind of three dimensional channel method for parameter estimation based on atom norm minimum, feature exist according to claim 3
In, using the estimation time delay and complex gain of one-dimensional ANM, specifically:
φ is obtained by two-dimentional ANM channel estimationlWith θlEstimated value, and then obtain mobile station and base station antenna-array responseWithIn order to obtain the time delay parameter τ on l pathslWith complex gain αlEstimated value, by kth
Millimeter wave channel at a subcarrier is rewritten as OFDM channel form:
Wherein, OFDM is orthogonal frequency division multiplexi；Multiple carrier waves are contained in OFDM, h [k] is the channel at k-th of carrier wave；
H [k] is by formulaIt obtains, []*The pseudoinverse of representing matrix or vector；
Given OFDM channel vectorElement in h withMiddle element has similar Mapping is closed
System；Therefore OFDM channel vector h is indicated are as follows:
Wherein, DELAY RESPONSE vector aτ(fl) is defined as:
Wherein, frequencyAssuming that τlMeetWherein LcpIt is the length of cyclic prefix；Frequency fl's
Value range isSection；
The frequency f that when estimating channel state information, will include in channel vector using one-dimensional ANM methodlValue range answer
FromSection becomes the section of [0,1]:
Assuming that pilot tone form is Comb Pilot,The position of a pilot sub-carrier be from etc.It is spaced apart
Position collectionMiddle random selection, is indicated with k 'The location index of a Comb Pilot subcarrier, sub- load
Wave location index and subcarrier serial number meetRelationship, then the OFDM channel at kth ' a subcarrier is expressed as:
At this point, the frequency in OFDM channel vector hANM method estimation time delay can be used；
Based on atom collectionOFDM channel vector h one dimensional atom norm is defined as:
Wherein,
Assuming that frequency flMeet sufficient frequency and separates condition, atom normIt is expressed as SDP planning:
Wherein, t indicates a constant；U indicates the first row of toeplitz matrix T (u)；hHIndicate the conjugation of OFDM channel vector h
Transposition；It is the PSD toeplitz matrix being made of its first row u；T (u) can be expressed as by vandermonde square
Battle array Aτ(f) form formed:
Wherein, Aτ(f)=[aτ(f1),…,aτ(fL)], D is positive semi-definite diagonal matrix；
Frequency is extracted from T (u) using MUSIC method
When the time delay parameter for obtaining L propagation pathAfterwards, DELAY RESPONSE vector is constitutedPlural path gain
Corresponding diagonal matrixCalculation formula are as follows:
Diagonal matrix
Complete channel matrixCan set out angle, angle of arrival according to estimated valueTime delayThe path and
GainIt recovers.
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