CN114143896A - Large-scale MIMO cross-frequency cooperation robust transmission method - Google Patents

Large-scale MIMO cross-frequency cooperation robust transmission method Download PDF

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CN114143896A
CN114143896A CN202111505864.5A CN202111505864A CN114143896A CN 114143896 A CN114143896 A CN 114143896A CN 202111505864 A CN202111505864 A CN 202111505864A CN 114143896 A CN114143896 A CN 114143896A
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channel
frequency
matrix
csi
precoding
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高西奇
汤金科
尤力
石雪远
吴昊旻
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Southeast University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/542—Allocation or scheduling criteria for wireless resources based on quality criteria using measured or perceived quality
    • 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

Abstract

The invention discloses a large-scale MIMO cross-frequency cooperation robust transmission method which is characterized in that a Lagrange multiplier method and an MM iteration method are used for deducing a precoding matrix expression with maximized speed aiming at accurate CSI on a high-frequency channel under ideal conditions. And then two types of error sources of uplink detection and channel outdating are analyzed under the non-ideal condition, and the second-order statistic of the errors is modeled and represented by the statistical CSI of the low-frequency channel based on the basic principle of LS and MMSE estimation and a first-order Markov process. And finally, reconstructing channel information by using the error statistics and the channel estimation value, substituting the channel information into an expression of a sum-rate maximization precoding matrix, and realizing downlink robust transmission of the high-frequency channel. Compared with the traditional downlink precoding transmission method, the method has obvious rate performance gain.

Description

Large-scale MIMO cross-frequency cooperation robust transmission method
Technical Field
The invention particularly relates to a method for modeling Channel errors under non-ideal conditions by means of statistical Channel State Information (CSI) of a low-frequency Channel in a cross-frequency band communication system, reconstructing the CSI by using an error modeling value and a Channel estimation value, realizing downlink robust transmission in a precoding process of substituting and maximizing the rate, belonging to the field of communication,
background
Large-scale Multiple-Input Multiple-Output (MIMO) communication technology is continuously developed, with the requirement of channel capacity continuously rising, spectrum scarcity is also a problem to be solved in future communication system design, and the application of a multi-frequency communication system enables resources with higher frequency to be explored. Typical multi-frequency communication systems include cooperative communication of millimeter wave and sub-6GHz channels, Wireless Local Area Networks (WLAN) (2.4GHz and 5GHz), and the like. In addition to solving the problem of scarce frequency spectrum, the multi-frequency communication system can transmit information through co-located channel arrays on different frequencies, the system capacity is improved by means of mutual cooperation among frequency points,
in a cross-frequency-band MIMO communication system, a base station side carries out precoding on an original data stream transmitted in a downlink mode based on detected CSI. The traditional linear precoding method designs a precoding matrix based on the channel instantaneous CSI, and is widely used in the downlink transmission process due to low complexity. Under most conditions, on the one hand, the mobility of the channel causes the instantaneous information to change rapidly; on the other hand, in the case of low signal-to-noise ratio, the channel sounding values are also subject to errors due to noise, which all result in a reduction in precoding performance. Compared with the instant CSI which is greatly influenced by time and noise, the statistical CSI is the reflection of the long-term characteristics of the channel and is slightly influenced by the mobility of the terminal. How to reasonably utilize the statistical CSI to make up for the performance error caused by the inaccuracy of the instantaneous CSI to a certain extent is also one of the important contents that need to be researched urgently in downlink channel transmission. In the same cross-frequency communication system, the statistical CSI corresponding to the high-frequency channel is difficult to obtain directly through measurement, and the statistical CSI of different frequency channels has similar properties in terms of angles, so that the statistical CSI of the low-frequency channel can be used for replacing the statistical CSI of the high-frequency channel, and further downlink robust precoding transmission of the high-frequency channel is completed. Therefore, the invention provides a large-scale MIMO cross-frequency cooperation robust transmission method, which is based on low-frequency statistical CSI to assist robust transmission on a high-frequency channel, thereby not only avoiding huge expenses of measuring and calculating the statistical CSI on the high-frequency channel, but also correcting the precision of a precoding matrix by taking channel errors into account, and improving the sum rate performance of a system.
Disclosure of Invention
The purpose of the invention is as follows: aiming at a cross-frequency-band MIMO system, the invention provides a large-scale multi-input multi-output cross-frequency cooperation robust transmission method, the downlink robust precoding with the maximum sum rate on a high-frequency channel is completed by utilizing the statistical CSI of a low-frequency channel, the sum rate performance is greatly improved compared with the traditional precoding method under the non-ideal condition, and the feasibility of cross-frequency cooperation is proved.
The technical scheme is as follows: the invention discloses a large-scale multi-input multi-output cross-frequency cooperation robust transmission method which comprises the following steps:
step 1, in a cross-frequency-band MIMO communication system, transmitting antenna arrays corresponding to different frequencies are co-located and arranged in parallel at a base station side, and the base station communicates with all users in a cell simultaneously; each frequency corresponding channel uses a Time Division Duplex (TDD) transmission mode, a user side is supposed to send pilot frequency to a base station, the base station can estimate an instantaneous value of an uplink channel according to received uplink detection information, and an uplink Channel State Information (CSI) estimation value obtained by uplink detection is directly used in a design process of downlink precoding based on the characteristic of reciprocity of uplink and downlink;
step 2, under an ideal condition, the base station side performs precoding by using the accurate channel state information CSI of each moment, the system and the rate maximization are used as optimization targets, a lagrange multiplier method is used for establishing a problem model, and a minimum-maximum (MM, Minorize-Maximize) iteration method is used for obtaining an expression of a precoding matrix with the rate maximization;
step 3, under a non-ideal condition, firstly, in the uplink detection process, due to the influence of channel additive noise, channel estimation has errors, and in the same cross-frequency-band MIMO system, aiming at different channel estimation methods on a high-frequency channel, second-order statistics of the estimation errors can be represented by means of noise power and statistical Channel State Information (CSI) modeling of a low-frequency channel;
step 4, under the non-ideal condition, the uplink detection of the channel on each time block needs time, so that the channel estimation value cannot be used for the base station to design precoding in real time; considering the scene that relative movement speed exists between a base station side and a user side, the channel changes along with time to cause an error between an uplink detection value and ideal channel state information CSI, and an outdated error on a high-frequency channel is represented by statistical channel state information CSI modeling of a low-frequency channel by establishing a first-order Markov model;
and 5, reconstructing Channel State Information (CSI) of the high-frequency channel based on the channel estimation value of uplink detection and the estimation error and outdated error of the CSI modeling by means of low-frequency channel statistics in the steps 3 and 4, substituting the reconstructed CSI into the high-frequency channel and the precoding process with the maximum rate, and taking error sources into consideration by using the low-frequency CSI to realize cross-frequency cooperative robust transmission under the non-ideal condition.
Wherein:
obtaining a rate maximization precoding matrix in the step 2, if the transmit power constraint of the whole system is PmaxLet the original data stream number be S, the number of antennas at the receiving and transmitting ends be N and M, respectively, and the channel matrix corresponding to user k is
Figure BDA0003404346090000031
A precoding matrix is
Figure BDA0003404346090000032
Wherein
Figure BDA0003404346090000033
A complex matrix representing a certain dimension, with user k transmitting information xkAnd satisfies the orthogonality condition, the noise vector is nkThen the inter-user interference and additive noise experienced by user k may be combined into an interference term
Figure BDA0003404346090000034
The covariance matrix of the interference term may be expressed as
Figure BDA0003404346090000035
In the formula
Figure BDA0003404346090000036
Represents the averaging, INRepresenting an identity matrix of dimension NxN, σ2Representing a noise vector nkPower of (1)HRepresents a conjugate transpose of the matrix; definition of RsumTo systematic sum rate, then according to Shannon's theorem, the desired rate of user k is
Figure BDA0003404346090000037
Where det (-) represents determinant, assuming total number of users in the system is K, the system and rate have
Figure BDA0003404346090000038
In summary, the precoding matrix solving problem that maximizes the system traversal and rate is represented as
Figure BDA0003404346090000039
Figure BDA00034043460900000310
Where tr (-) denotes the trace of the matrix,
Figure BDA00034043460900000311
and expressing the optimal solution with the maximum satisfying sum rate, converting the original objective function into an optimization problem which is easier to solve due to the complicated solution of the original optimization problem, and using the MM algorithm to perform iterative solution.
The iteration using MM algorithm is carried out, and in the nth iteration, the precoding matrixes corresponding to all users in the iteration are respectively
Figure BDA00034043460900000312
Then the covariance of the interference term corresponding to user k is
Figure BDA0003404346090000041
Then the rate value of user k at this time can be obtained according to shannon's formula and the nature of determinant as
Figure BDA0003404346090000042
Wherein ISThe unit matrix is an unit matrix having a dimension of S × S, and is hereinafter expressed in this way. To facilitate the presentation
Figure BDA0003404346090000043
Defining matrices in the nth iteration simultaneously
Figure BDA0003404346090000044
To represent
Figure BDA0003404346090000045
Then a constant is defined for user k in that iteration
Figure BDA0003404346090000046
As follows
Figure BDA0003404346090000047
And an operator
Figure BDA0003404346090000048
Figure BDA0003404346090000049
Figure BDA00034043460900000410
Further obtaining the optimal precoding matrix meeting the sum rate maximization condition in the (n + 1) th iteration
Figure BDA00034043460900000411
Is composed of
Figure BDA00034043460900000412
In the formula of(n)Is a precoding matrix
Figure BDA00034043460900000413
By adjusting mu(n)So that
Figure BDA00034043460900000414
The power constraint is satisfied.
The second-order statistic of the estimation error in the step 3 is represented by means of noise power and the CSI (channel State information) of the low-frequency channel, and for the LS (least square) channel estimation method, the covariance matrix of the estimation error is represented by Rk,LSExpressed and calculated by the method of
Rk,LS＝σ2IMN,
Wherein IMNIs a unit matrix with the dimension of MN multiplied by MN, and for the minimum mean square error MMSE channel estimation method, the covariance matrix of the estimation error uses Rk,MMSEExpressed and calculated by the method of
Rk,MMSE＝σ2Rk(Rk+σ2IMN)-1,
Wherein R iskFor co-party of channel between base station and user kDifference matrix based on correlation between different frequency points in cross-frequency communication system, R on high-frequency channelkCovariance matrix reconstruction of the low frequency channel may be used.
In the step 4, the outdated error on the high-frequency channel is represented by statistical channel state information CSI modeling of the low-frequency channel, and the error of the channel between the base station and the user k caused by outdating at the time t
Figure BDA0003404346090000051
Can be represented by statistical CSI as
Figure BDA0003404346090000052
Wherein VMAnd UNArray response matrixes of a receiving end and a transmitting end respectively, subscripts M and N respectively represent the number of antennas of the receiving end and the transmitting end, and omegakRepresenting a discrete power distribution, W, of the angular domaink,tRepresenting a phase matrix, beta, consisting of elements satisfying a standard Gaussian distribution at time tkIs the correlation coefficient of the channel matrix between the uplink sounding value at the time t and the uplink sounding value at the previous time.
The error reconstruction in the step 5 is to reconstruct the channel impulse response matrix H at the time tk,tUsing detected values of a previous time
Figure BDA0003404346090000053
Estimating error statistics
Figure BDA0003404346090000054
And angular power distribution omegakThe reconstruction is represented as
Figure BDA0003404346090000055
In the formula Wk,t-1And Wk,tThe angle domain phase matrixes are respectively time t-1 and time t; h to be reconstructedk,tSubstituting the robust precoding expression to calculate an operator required by the robust transmission design at the time t
Figure BDA0003404346090000056
And
Figure BDA0003404346090000057
then substituted into
Figure BDA0003404346090000058
I.e. passing through the first at time tnSecondary precoding vector
Figure BDA0003404346090000059
Obtaining a sum rate maximization pre-coding vector obtained by n +1 th iteration at the time t
Figure BDA00034043460900000510
And (5) iterating by using a similar method until convergence, obtaining a final value of the precoding matrix, and finishing the design of the downlink robust transmission precoding matrix.
The cross-frequency cooperative robust transmission in the step 5 is to calculate the parameter omega of the angle domain on the low-frequency and high-frequency channels of the cross-frequency communication systemkAnd
Figure BDA00034043460900000511
similarity exists, so that estimation errors and outdated errors on a high-frequency channel can be modeled by using statistical parameters on a low-frequency channel; in the design of the robust transmission method of the high-frequency channel, the higher the frequency is, the higher the noise is, so that the channel state information CSI is counted by means of the angle domain of the low-frequency channel to complete Hk,tFurther increase Hk,tThe accuracy of the method, and then cross-frequency cooperative transmission is realized.
Has the advantages that: compared with the prior art, the invention has the following advantages:
1. in a multi-user scene, the precoding method takes the maximum system and rate as optimization conditions, considers the interference between users and the interference between data streams, and has certain performance gain under a quasi-static channel condition compared with the traditional method.
2. The precoding method considers detection errors and outdated errors, and in a non-ideal scene, the errors are represented by statistical CSI modeling, so that the method has obvious gain compared with a traditional method based on instantaneous CSI.
3. In a cross-frequency communication system, aiming at the problem that the high-frequency channel statistical CSI is difficult to obtain, the statistical CSI of the low-frequency channel is fully utilized by the method, cross-frequency cooperative robust transmission is realized, and compared with a traditional precoding method based on instantaneous CSI on the high-frequency channel, the method has obvious gain.
Drawings
FIG. 1 is a flow chart of a method according to an embodiment of the present invention.
Fig. 2 shows the implementation steps of the robust precoding method for maximizing the neutralization rate in the present invention.
Detailed Description
In order to achieve the above object, the massive MIMO cross-frequency cooperative robust transmission method according to the present invention includes the following steps:
(1) in a cross-frequency-band MIMO communication system, transmitting antenna arrays corresponding to different frequencies are co-located and arranged in parallel at a base station side, and the base station communicates with all users in a cell simultaneously. Each frequency corresponding channel uses a Time Division Duplex (TDD) transmission mode, a user side is supposed to send pilot frequency to a base station, the base station can estimate an instantaneous value of an uplink channel according to received uplink detection information, and an uplink CSI estimation value obtained by uplink detection can be directly used in a design process of downlink precoding based on the characteristic of reciprocity of uplink and downlink.
(2) Under ideal conditions, the base station side performs precoding by using accurate CSI at each moment, maximizes the system sum rate as an optimization target, establishes a problem model by using a Lagrange multiplier method, and obtains an expression of a sum rate maximization precoding matrix by using an MM iteration method.
(3) Under non-ideal conditions, firstly, in the process of uplink detection, due to the influence of channel additive noise, channel estimation has errors, and for different channel estimation methods, the second-order statistic of the estimation error can be represented by means of noise power and statistical CSI of a low-frequency channel.
(4) Under the non-ideal condition, the uplink detection of the channel in each time block needs time, so the channel estimation value cannot be used for the base station to design the precoding in real time. Considering the scene that the base station side and the user side have relative moving speed, the channel changes along with time to cause errors between the uplink detection value and the ideal CSI, and the outdated errors can be expressed by the statistic CSI modeling of the low-frequency channel by establishing a first-order Markov model.
(5) And reconstructing channel CSI based on the channel estimation value, estimation error and outdated error of uplink detection, and substituting the reconstructed CSI into the process of maximizing the precoding rate, wherein compared with the traditional method, the robust transmission under the non-ideal condition is realized by taking error sources into consideration.
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The following describes specific steps of the embodiment of the present invention with reference to specific scenarios:
1) large-scale MIMO system model:
in the large-scale MIMO communication system, it is assumed that the number of transmitting-end antennas is M, the number of receiving-end antennas is N, and the total number of users in the system is K. For user k, assume a channel matrix of
Figure BDA0003404346090000071
A precoding matrix is
Figure BDA0003404346090000072
The number of data streams of the original signal transmitted from the base station side is S, and the vector for the original signal
Figure BDA0003404346090000073
To representThen theoretically the receive end signal vector can be expressed as
yk＝HkPkxk+nk,
In the formula nkRepresenting an additive noise vector.
Considering the interference between users under multi-user condition, the receiving end signal can be further expressed as
Figure BDA0003404346090000074
The above equation shows that in the multi-user MIMO system, the error of the receiving end signal comes from two parts of inter-user interference and additive noise. In the actual channel transmission process, before downlink channel precoding is performed, channel CSI referred to by precoding needs to be obtained through sounding. Considering the transmission mode of Time Division Duplex (TDD), assuming that a user side sends pilot frequency to a base station, the base station can estimate the instantaneous value of an uplink channel according to the received uplink detection information, and the uplink channel estimation value obtained by uplink detection can be directly used in the design process of downlink precoding based on the characteristic of reciprocity of uplink and downlink.
Since the uplink channel sounding needs time in each time block, the channel estimation value cannot be used for the base station to design precoding in real time. Therefore, the total time sampling length is divided into a plurality of time slots, each time slot comprises a plurality of sampling points, and the number of the sampling points in each time slot is assumed to be NBEach sampling point corresponds to a time block, the first time block is used for the uplink detection of the channel, and the last N isBAnd 1 sampling point carries out precoding design by referring to the channel estimation value detected by the first time block, thereby realizing downlink transmission.
2) Sum rate maximized downlink precoding
Suppose the transmit power constraint of the overall system is PmaxLet the original data stream be S, the number of antennas at the receiving and transmitting ends be N and M, respectively, and the channel matrix corresponding to user k is
Figure BDA0003404346090000081
A precoding matrix is
Figure BDA0003404346090000082
While assuming that the transmission information is xkAnd is sufficient for the orthogonality condition, the noise vector is nkThen the interference and additive noise between users can be combined into an interference term
Figure BDA0003404346090000083
The covariance matrix of the interference terms can be expressed as
Figure BDA0003404346090000084
Definition of RsumTo be the systematic sum rate, then according to Shannon's theorem, the sum rate of user k is
Figure BDA0003404346090000085
Where det (-) denotes determinant, system and rate have
Figure BDA0003404346090000086
The precoding matrix solving problem that results in the system traversal and maximum rate can be expressed as
Figure BDA0003404346090000087
Figure BDA0003404346090000088
Wherein tr (·) represents the trace of the matrix, (·)HRepresenting the conjugate transpose of the matrix. Because the original optimization problem is solved more complexly, the original objective function is converted into an optimization problem which is easier to solve, and the MM algorithm is used for iterative solution.
In the nth MM algorithm iteration, the precoding matrix corresponding to the iteration
Figure BDA0003404346090000091
When the corresponding interference term covariance is
Figure BDA0003404346090000092
Then the rate value of user k at this time can be obtained according to shannon's formula and the nature of determinant as
Figure BDA0003404346090000093
Wherein ISThe unit matrix is an unit matrix having a dimension of S × S, and is hereinafter expressed in this way. To facilitate the presentation
Figure BDA0003404346090000094
Defining matrices in the nth iteration simultaneously
Figure BDA0003404346090000095
To represent
Figure BDA0003404346090000096
Then a constant is defined for user k in that iteration
Figure BDA0003404346090000097
As follows
Figure BDA0003404346090000098
Defining the following operators at the same time
Figure BDA0003404346090000099
Figure BDA00034043460900000910
Figure BDA00034043460900000911
Figure BDA00034043460900000912
Then the definition relates to the precoding group P1,…,PKFunction of (2)
Figure BDA00034043460900000913
As follows
Figure BDA00034043460900000914
The function is a system and rate function in a precoding group
Figure BDA0003404346090000101
A MM function of (a). Given a MM function for which the Shannon and Rate equations apply, the function g constructed in the nth iteration*(P1,…,PK) Can construct an optimization problem
Figure BDA0003404346090000102
Figure BDA0003404346090000103
Then in each iteration, a function g can be constructed*(P1,…,PK) By virtue of the above formulaAnd solving the problem to obtain a precoding group which can reach the maximum traversal and rate in each iteration. By using the Lagrange multiplier method, the optimization problem can be converted into
Figure BDA0003404346090000104
Wherein mu(n)Representing the Lagrange multiplier, and applying the above formula to any K ∈ [1, K ]]Precoding matrix P in (1)kDerivation is due to
Figure BDA0003404346090000105
Then derivation of the Lagrangian function is
Figure BDA0003404346090000106
If the above expression is 0, the optimal precoding matrix satisfying the condition can be obtained
Figure BDA0003404346090000107
Is composed of
Figure BDA0003404346090000108
3) Large-scale MIMO robust transmission method
In the traversal and rate maximization method, the operator in each iteration is matched with the actual channel HkIn the actual massive MIMO system, in order to represent different sampling time blocks, the instantaneous CSI of the kth user on the t time block is set to Hk,tThen at the t time block, the covariance matrix of the channel interference in the n iteration is
Figure BDA0003404346090000109
The robust precoding matrix found can be expressed as
Figure BDA00034043460900001010
In the formula
Figure BDA00034043460900001011
Is calculated by
Figure BDA0003404346090000111
Figure BDA0003404346090000112
Figure BDA0003404346090000113
Figure BDA0003404346090000114
The calculation of the above operators depends on the instantaneous channel information H of the t time blockk,t. In an actual communication system, since the channel CSI to be referred to for precoding by the base station is obtained by uplink sounding, a channel estimation error exists in the channel sounding. Meanwhile, due to the time difference between the channel detection and the downlink transmission, when the relative moving speed exists between the base station and the user, the channels have differences at different sampling points, so that an error caused by channel aging also exists between the channel CSI detected at the uplink and the channel at the downlink transmission time block. Based on the above sources of error, the detected channel is assumed
Figure BDA0003404346090000115
The error between the actual channel and the probe channel is Δ Hk,tI.e. by
Figure BDA0003404346090000116
In the formula,. DELTA.Hk,tIncluding channel estimation errors and outdated errors due to channel aging, in the calculation of an operator
Figure BDA0003404346090000117
For example, as
Figure BDA0003404346090000118
The first term of the equation can be directly substituted into the channel detection value for calculation, and the second term relates to the estimation error on each downlink detection time block, because the estimation term Δ Hk,tIt is not directly available separately on each time block and therefore the error term can be calculated from the point of view of statistical CSI. For convenience of presentation, assume a conjugate pair matrix Φ for an arbitrary N × N dimension1And M × M dimensional conjugate matrix phi2Definition of
Figure BDA0003404346090000119
Figure BDA00034043460900001110
According to the sparsity of the channel in the angle domain, the operator can be converted into
Figure BDA00034043460900001111
Wherein VMAn angle domain sampling matrix of the transmitting end is formed by the dimension of MxBTAt the same time, defining the dimension at the receiving end as NxBROver-sampling matrix UN,BTAnd BRThe number of angle domain samples at the receiving end and the transmitting end respectively, the two oversampling matrixes are generally constructed based on the form of DFT matrix, and the Λ is BT×BTDiagonal matrix of (2), diagonal elements thereofElement can pass through B on the angular domainR×BTEnergy coupling matrix omegakThe sum of the elements in each column. For the same reason, operator η2,k,t(Φ2) An energy coupling matrix omega may also be usedkThe sum of the elements in each row is calculated. In summary, the operators used in the calculation of the precoding matrix can be further expressed as
Figure BDA0003404346090000121
Using the following approximation
Figure BDA0003404346090000122
Using the formula Dk,tRepresentation, then operator
Figure BDA0003404346090000123
Can be converted into
Figure BDA0003404346090000124
At this time, from the viewpoint of statistical analysis, it is possible to perform
Figure BDA0003404346090000125
Is thus approximated, thereby
Figure BDA0003404346090000126
Can be expressed as
Figure BDA0003404346090000127
In general, at a known channel estimate
Figure BDA0003404346090000128
And error Δ Hk,tUnder the condition of the angle domain statistics of CSI, the downlink robust precoding can be completed. The flow chart of the downlink robust transmission method is shown in fig. 2.
4) Cross-frequency cooperation robust transmission method
In Time Division Duplex (TDD) transmission mode, the channel impulse response matrix H at time tk,tCan use the detected value of the previous time
Figure BDA0003404346090000129
Estimating error statistics
Figure BDA00034043460900001210
And angular power distribution omegakThe reconstruction is represented as
Figure BDA00034043460900001211
Order to
Figure BDA00034043460900001212
Then is known
Figure BDA00034043460900001213
Estimating error energy distribution
Figure BDA00034043460900001214
And outdated error energy distribution ΩkRobust transmission can be accomplished. In the unified cross-frequency communication system, the energy distribution of the channels on different frequencies in the angular domain is approximately the same, and it is assumed that the low frequency and the high frequency are respectively f1And f2Indicating, the angular domain power distribution of the high frequency channel
Figure BDA0003404346090000131
Angle-domain power distribution using low-frequency channels
Figure BDA0003404346090000132
Approximation, approximate computation f without estimating high frequency statistical CSI2Channel matrix at time t
Figure BDA0003404346090000133
Is composed of
Figure BDA0003404346090000134
The sounding channel item can be expressed as
Figure BDA0003404346090000135
The error term can be expressed as
Figure BDA0003404346090000136
Due to f2On frequency point, the robust transmission algorithm design needs to detect channel items
Figure BDA0003404346090000137
And error term
Figure BDA0003404346090000138
As a known condition, according to the above two equations,
Figure BDA0003404346090000139
it can be obtained by channel sounding and,
Figure BDA00034043460900001310
the angle domain statistical CSI may use statistical parameters on the low frequency channel
Figure BDA00034043460900001311
And calculating, and then completing the robust precoding transmission method on the high-frequency channel by using the low-frequency statistical information.

Claims (7)

1. A large-scale multiple-input multiple-output cross-frequency cooperation robust transmission method is characterized by comprising the following steps: the transmission method comprises the following steps:
step 1, in a cross-frequency-band MIMO communication system, transmitting antenna arrays corresponding to different frequencies are co-located and arranged in parallel at a base station side, and the base station communicates with all users in a cell simultaneously; each channel corresponding to each frequency uses a Time Division Duplex (TDD) transmission mode, a user side is supposed to send pilot frequency to a base station, the base station can estimate an instantaneous value of an uplink channel according to received uplink detection information, and an uplink Channel State Information (CSI) estimation value obtained by uplink detection is directly used in a design process of downlink precoding based on the characteristic of reciprocity of uplink and downlink;
step 2, under an ideal condition, the base station side performs precoding by using accurate Channel State Information (CSI) at each moment, the system and the rate maximization are taken as optimization targets, a problem model is established by using a Lagrange multiplier method, and an expression of a sum rate maximization precoding matrix is obtained by using a minimum-maximum iteration method;
step 3, under a non-ideal condition, firstly, in the uplink detection process, due to the influence of channel additive noise, channel estimation has errors, and in the same cross-frequency-band MIMO system, aiming at different channel estimation methods on a high-frequency channel, second-order statistics of the estimation errors can be represented by means of noise power and statistical Channel State Information (CSI) modeling of a low-frequency channel;
step 4, under the non-ideal condition, the uplink detection of the channel on each time block needs time, so that the channel estimation value cannot be used for the base station to design precoding in real time; considering the scene that relative movement speed exists between a base station side and a user side, the channel changes along with time to cause an error between an uplink detection value and ideal channel state information CSI, and an outdated error on a high-frequency channel is represented by statistical channel state information CSI modeling of a low-frequency channel by establishing a first-order Markov model;
and 5, reconstructing Channel State Information (CSI) of the high-frequency channel based on the channel estimation value of uplink detection and the estimation error and outdated error modeled by the low-frequency statistical CSI in the steps 3 and 4, substituting the reconstructed CSI into the high-frequency channel and the process of rate maximization precoding, and taking error sources into consideration by using the low-frequency CSI to realize cross-frequency cooperative robust transmission under the non-ideal condition.
2. The massive MIMO cross-frequency cooperative robust transmission method according to claim 1, wherein: obtaining a rate maximization precoding matrix in the step 2, if the transmit power constraint of the whole system is PmaxLet the original data stream number be S, the number of antennas at the receiving and transmitting ends be N and M, respectively, and the channel matrix corresponding to user k is
Figure FDA0003404346080000011
A precoding matrix is
Figure FDA0003404346080000012
Wherein
Figure FDA0003404346080000013
A complex matrix representing a certain dimension, with user k transmitting information xkAnd satisfies the orthogonality condition, the noise vector is nkThen the inter-user interference and additive noise experienced by user k may be combined into an interference term
Figure FDA0003404346080000021
The covariance matrix of the interference term may be expressed as
Figure FDA0003404346080000022
In the formula
Figure FDA0003404346080000023
Represents the averaging, INRepresenting an identity matrix of dimension NxN, σ2Representing a noise vector nkPower of (1)HRepresents a conjugate transpose of the matrix; definition of RsumTo systematic sum rate, then according to Shannon's theorem, the desired rate of user k is
Figure FDA0003404346080000024
Where det (-) represents determinant, assuming total number of users in the system is K, the system and rate have
Figure FDA0003404346080000025
In summary, the precoding matrix solving problem that maximizes the system traversal and rate is represented as
Figure FDA0003404346080000026
Figure FDA0003404346080000027
Where tr (-) denotes the trace of the matrix,
Figure FDA0003404346080000028
and expressing the optimal solution with the maximum satisfying sum rate, converting the original objective function into an optimization problem which is easier to solve due to the complicated solution of the original optimization problem, and using the MM algorithm to perform iterative solution.
3. The massive MIMO cross-frequency cooperative robust transmission method according to claim 2, wherein: the iteration using MM algorithm is carried out, and in the nth iteration, the precoding matrixes corresponding to all users in the iteration are respectively
Figure FDA0003404346080000029
Then the covariance of the interference term corresponding to user k is
Figure FDA00034043460800000210
The value of the rate of user k in the nth iteration is then given by the shannon formula and the nature of the determinant as
Figure FDA00034043460800000211
Wherein ISThe dimension is an unit matrix of S multiplied by S, and the unit matrix is expressed by the method below; to facilitate the presentation
Figure FDA0003404346080000031
Defining matrices in the nth iteration simultaneously
Figure FDA0003404346080000032
To represent
Figure FDA0003404346080000033
Then a constant is defined for user k in that iteration
Figure FDA0003404346080000034
As follows
Figure FDA0003404346080000035
And an operator
Figure FDA0003404346080000036
Figure FDA0003404346080000037
Figure FDA0003404346080000038
Further obtaining the optimal precoding matrix meeting the sum rate maximization condition in the (n + 1) th iteration
Figure FDA0003404346080000039
Is composed of
Figure FDA00034043460800000310
In the formula of(n)Is a precoding matrix
Figure FDA00034043460800000311
By adjusting mu(n)So that
Figure FDA00034043460800000312
The power constraint is satisfied.
4. The massive MIMO cross-frequency cooperative robust transmission method according to claim 1, wherein: the second-order statistic of the estimation error in the step 3 is represented by means of noise power and the CSI (channel State information) of the low-frequency channel, and for the LS (least square) channel estimation method, the covariance matrix of the estimation error is represented by Rk,LSExpressed and calculated by the method of
Rk,LS＝σ2IMN,
Wherein IMNIs a unit matrix with the dimension of MN multiplied by MN, and for the minimum mean square error MMSE channel estimation method, the covariance matrix of the estimation error uses Rk,MMSEExpressed and calculated by the method of
Rk,MMSE＝σ2Rk(Rk+σ2IMN)-1,
Wherein R iskBased on cross-frequency communication system for covariance matrix of channel between base station and user kCorrelation between different frequency points in the system, R on high frequency channelkCovariance matrix reconstruction of the low frequency channel may be used.
5. The massive MIMO cross-frequency cooperative robust transmission method according to claim 1, wherein: in the step 4, the outdated error on the high-frequency channel is represented by statistical channel state information CSI modeling of the low-frequency channel, and the error of the channel between the base station and the user k caused by outdating at the time t
Figure FDA0003404346080000041
Can be represented by statistical CSI as
Figure FDA0003404346080000042
Wherein VMAnd UNArray response matrixes of a receiving end and a transmitting end respectively, subscripts M and N respectively represent the number of antennas of the receiving end and the transmitting end, and omegakRepresenting a discrete power distribution, W, of the angular domaink,tRepresenting a phase matrix, beta, consisting of elements satisfying a standard Gaussian distribution at time tkIs the correlation coefficient of the channel matrix between the uplink sounding value at the time t and the uplink sounding value at the previous time.
6. The massive MIMO cross-frequency cooperative robust transmission method according to claim 1, wherein: the error reconstruction in the step 5 is to reconstruct the channel impulse response matrix H at the time tk,tUsing detected values of a previous time
Figure FDA0003404346080000043
Estimating error statistics
Figure FDA0003404346080000044
And angular power distribution omegakThe reconstruction is represented as
Figure FDA0003404346080000045
In the formula Wk,t-1And Wk,tThe angle domain phase matrixes are respectively time t-1 and time t; h to be reconstructedk,tSubstituting the robust precoding expression to calculate an operator required by the robust transmission design at the time t
Figure FDA0003404346080000046
And
Figure FDA0003404346080000047
then substituted into
Figure FDA0003404346080000048
I.e. passing through the first at time tnSecondary precoding vector
Figure FDA0003404346080000049
Obtaining a sum rate maximization pre-coding vector obtained by n +1 th iteration at the time t
Figure FDA00034043460800000410
And (5) iterating by using a similar method until convergence, obtaining a final value of the precoding matrix, and finishing the design of the downlink robust transmission precoding matrix.
7. The massive MIMO cross-frequency cooperative robust transmission method according to claim 1, wherein: the cross-frequency cooperative robust transmission in the step 5 is to calculate the parameter omega of the angle domain on the low-frequency and high-frequency channels of the cross-frequency communication systemkAnd
Figure FDA00034043460800000411
similarity exists, so that estimation errors and outdated errors on a high-frequency channel can be modeled by using statistical parameters on a low-frequency channel; and in the design of robust transmission method of high-frequency channel, due to frequencyThe higher the frequency is, the higher the noise is, so the channel state information CSI is counted by the angle domain of the low-frequency channel to complete Hk,tFurther increase Hk,tThe accuracy of the method, and then cross-frequency cooperative transmission is realized.
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CN114650086A (en) * 2022-03-28 2022-06-21 东南大学 Cross-frequency-band communication beam prediction method assisted by deep learning
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Publication number Priority date Publication date Assignee Title
CN114650086A (en) * 2022-03-28 2022-06-21 东南大学 Cross-frequency-band communication beam prediction method assisted by deep learning
CN114900214A (en) * 2022-05-06 2022-08-12 东南大学 Low-complexity linear precoding algorithm based on OFDM system
CN114900214B (en) * 2022-05-06 2024-01-26 东南大学 Low-complexity linear precoding algorithm based on OFDM system

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