CN108173576B - Calibration method of MIMO system - Google Patents

Calibration method of MIMO system Download PDF

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CN108173576B
CN108173576B CN201611110873.3A CN201611110873A CN108173576B CN 108173576 B CN108173576 B CN 108173576B CN 201611110873 A CN201611110873 A CN 201611110873A CN 108173576 B CN108173576 B CN 108173576B
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frequency gain
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罗喜良
潘振岗
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Spreadtrum Communications Shanghai Co Ltd
ShanghaiTech University
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ShanghaiTech University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/10—Monitoring; Testing of transmitters
    • H04B17/11—Monitoring; Testing of transmitters for calibration
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/20—Monitoring; Testing of receivers
    • H04B17/21—Monitoring; Testing of receivers for calibration; for correcting measurements

Abstract

The invention provides a calibration method of a MIMO system, which comprises the following steps: firstly, a measuring signal matrix is constructed, then a radio frequency gain ratio matrix is estimated according to the measuring signal matrix, in addition to the main diagonal elements of the radio frequency gain ratio matrix, other elements of the radio frequency gain ratio matrix except the main diagonal are also estimated in the calibration process, and the interaction between the antennas of the large-scale MIMO system is fully considered. The invention can improve the calibration effect of a large-scale MIMO system.

Description

Calibration method of MIMO system
Technical Field
The invention relates to the technical field of wireless communication, in particular to a calibration method of a Multiple Input Multiple Output (MIMO) system.
Background
In a TDD (Time Division duplex) mode MIMO (Multiple-input Multiple-Output) system, uplink and downlink channels propagating in free space are symmetrical, but since each antenna uses a different rf unit, the equivalent propagation channel including the rf link is asymmetrical because the different rf units have different gains.
To correct for this asymmetry, the downlink channel is calculated from the uplink channel and a radio frequency gain ratio matrix needs to be estimated. The (u, v) th element of the rf gain ratio matrix is the ratio of the transmit rf unit gain of antenna u to the receive rf unit gain of antenna v.
The existing calibration method only estimates the main diagonal elements of the radio frequency gain ratio matrix, because there is no interaction between the antennas of the general MIMO system, only the ratio of the transmission radio frequency unit gain of each antenna to the self reception radio frequency unit gain needs to be estimated. Without considering the ratio of the gain of the transmitting RF unit of one antenna to the gain of the receiving RF unit of the other antenna, the off-diagonal elements default to zero.
As a key technology of next-generation wireless communication, a massive MIMO system has characteristics of high spectral efficiency and high energy efficiency, but in the massive MIMO system, antennas are distributed in an array form, and the antennas are closely spaced, and an interaction occurs. Therefore, in the process of implementing the present invention, the inventors found that at least the following technical problems exist in the prior art:
the existing calibration method only estimates main diagonal elements of a radio frequency gain ratio matrix, neglects the interaction between antennas and has poor calibration effect for a large-scale MIMO system.
Disclosure of Invention
The calibration method of the MIMO system provided by the invention can improve the calibration effect of a large-scale MIMO system.
The invention provides a calibration method of an MIMO system, wherein all antennas of the MIMO system are equidistantly placed, and the method comprises the following steps:
constructing a measurement signal matrix Y, wherein the expression of the (u, v) th element of the measurement signal matrix Y is as follows:
yu,v＝αuhβv+nu,v，u∈[1,M]，v∈[1,M]，
wherein, yu,vFor the (u, v) th element, α, of the measurement signal matrix YuGain of the transmitting radio unit, beta, for antenna uvGain of the receiving RF unit for antenna v, h channel gain, nu,vMeasuring noise between an antenna u and an antenna v, wherein the antenna u and the antenna v are adjacent, and M is the total number of antennas on the base station side of the MIMO system;
and estimating a radio frequency gain ratio matrix by using the measurement signal matrix Y.
Optionally, the estimating a radio frequency gain ratio matrix using the measurement signal matrix Y includes:
estimating elements on the main diagonal of the radio frequency gain ratio matrix by using an N-LS method;
determining any node u, u belongs to [1, M ], and estimating the element of the column of the node u.
Optionally, the estimating, by using an N-LS method, elements on a main diagonal of the radio frequency gain ratio matrix includes:
for cost function
Figure BDA0001172339610000021
Taking the derivative and making the derivative zero, where AuDenotes a set of antenna numbers adjacent to the antenna u, and v denotes an antenna number adjacent to the antenna u.
Optionally, the determining any node u, u e [1, M ], and the estimating the element in the column where the node u is located includes:
for node t on the first level of the node u1Neglect of measurement noise, radio frequency gain ratio
Figure BDA0001172339610000022
Determined according to the following expression:
Figure BDA0001172339610000031
wherein t is1' is that said node u differs from t on a first level1And with t1An adjacent node;
for the node t on the k (k ≧ 2) th layer of the node ukSelecting a piece from u to tkShortest path, radio frequency gain ratio of
Figure BDA0001172339610000032
Determined according to the following expression:
Figure BDA0001172339610000033
wherein t isk-1Is a node on level k-1 of the node u.
Alternatively, when said from u to tkShortest path ofRadio frequency gain ratio in the presence of L strips
Figure BDA0001172339610000034
Determined according to the following expression:
Figure BDA0001172339610000035
wherein
Figure BDA0001172339610000036
Respectively, radio frequency gain ratios estimated when selecting different shortest paths
Figure BDA0001172339610000037
Optionally, the estimating a radio frequency gain ratio matrix using the measurement signal matrix Y includes:
defining an error function f (X)t,Xr)＝||Y-XtAXr||2，
Wherein, the expression of the matrix A is:
Figure BDA0001172339610000038
solving two diagonal matrices X using a block cooperative descent methodtAnd XrLet the error function f (X)t,Xr) And minimum.
Optionally, the two diagonal matrices X are solved using a block cooperation descent methodtAnd XrThe method comprises the following steps:
1) obtaining X at randomtAnd XrIs initialized to
Figure BDA0001172339610000039
And
Figure BDA00011723396100000310
and initializing a loop variable j equal to 0;
2) calculating according to expression (1)
Figure BDA0001172339610000041
Figure BDA0001172339610000042
3) Calculating according to expression (2)
Figure BDA0001172339610000043
Figure BDA0001172339610000044
4) Accumulating the cyclic variable j, and repeating the steps 2) to 3) until a preset termination criterion is met;
in the expression, Diag { } represents that a diagonal matrix is generated, and diagonal elements of the diagonal matrix are given by vectors in brackets; diag { } denotes generating a vector whose elements are diagonal elements of the matrix in brackets; a/denotes the dot division between pairs of vector elements.
The calibration method of the MIMO system provided by the invention comprises the steps of firstly constructing a measurement signal matrix, estimating a radio frequency gain ratio matrix according to the measurement signal matrix, estimating other elements of the radio frequency gain ratio matrix except a main diagonal in the calibration process except a main diagonal, namely estimating the ratio of the gain of a transmitting radio frequency unit of one antenna to the gain of receiving radio frequency units of other antennas, fully considering the interaction between the antennas of the large-scale MIMO system and improving the calibration effect of the large-scale MIMO system.
Drawings
Fig. 1 is an antenna array of a MIMO system according to an embodiment of the present invention;
fig. 2 is a flowchart of a calibration method of a MIMO system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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.
Suppose a base station has M antennas and each user has only 1 antenna. Because the number of the user terminal antennas is small, and the calibration is relatively simple, the user terminal calibration is assumed to be completed in the invention, and only the base station terminal calibration is concerned.
Two rf gain matrices are first defined:
CBS,t＝Diag{α1,α2,…,αM}
CBS,r＝Diag{β1,β2,…,βM}
where α isu,u∈[1,M]Representing the gain, beta, of the transmitting radio unit of the antenna uv,v∈[1,M]Denotes the receive radio unit gain of antenna v, and Diag { } denotes the diagonal matrix.
The expression of the rf gain ratio matrix P can thus be obtained as follows:
Figure BDA0001172339610000051
obviously, the matrix P is an MxM matrix in which the (u, v) th element
Figure BDA0001172339610000052
Figure BDA0001172339610000053
Representing the ratio of the gain of the transmitting RF unit of antenna u to the gain of the receiving RF unit of antenna v, the element of the u-th column of the matrix P
Figure BDA0001172339610000054
Representing the gain of the transmitting radio unit of antenna u and the gain of the receiving radio unit of all other antennas (including itself)The calibration of the MIMO system is ultimately the determination of all elements of the rf gain ratio matrix P.
As shown in fig. 1, the antennas of a MIMO system are distributed in an array of regular hexagonal shapes, and the distance between all the antennas is a half wavelength. To estimate the matrix P, signals need to be exchanged between adjacent antennas, specifically, one antenna transmits signals and 6 (or less) adjacent antennas next to it receive signals. This is performed for each antenna in the antenna array in turn. Since all antennas are placed equidistantly, the channel gain when signals are passed between adjacent antennas can be considered to be the same.
An embodiment of the present invention provides a calibration method for a MIMO system, as shown in fig. 2, the method includes:
s11, constructing a measurement signal matrix Y, if the antenna u and the antenna v are adjacent, the (u, v) th element of Y is given by the following expression:
yu,v＝αuhβv+nu,v，u∈[1,M]，v∈[1,M]，
wherein, yu,vFor the (u, v) th element, α, of the measurement signal matrix YuGain of the transmitting radio unit, beta, for antenna uvGain of the receiving RF unit for antenna v, h channel gain, nu,vMeasuring noise between an antenna u and an antenna v, wherein the antenna u and the antenna v are adjacent, and M is the total number of antennas on the base station side of the MIMO system;
and S12, estimating a radio frequency gain ratio matrix P by using the measurement signal matrix Y.
Two different schemes of estimating the matrix P are given in the present invention.
The first method of estimating the matrix P is called diagonal first scheme. As the name implies, the diagonal first scheme first estimates the elements on the main diagonal of the matrix P, and then estimates the elements outside the main diagonal.
The main diagonal elements can be estimated directly using the N-LS method: defining M-dimensional vectors
Figure BDA0001172339610000061
Where gamma is an adjustable scalar. In practice, the influence of γ on the estimation result can be ignored. The way to estimate c is to find a c that minimizes the cost function j (c) below:
Figure BDA0001172339610000062
where A isuDenotes a set of antenna numbers adjacent to the antenna u, and v denotes an antenna number adjacent to the antenna u.
By deriving the cost function j (c) and making the derivative zero, the optimal expression for c can be obtained as:
Figure BDA0001172339610000063
wherein c is11 is ═ 1, i.e
Figure BDA0001172339610000064
Figure BDA0001172339610000065
Where A is (a)1,A1) The (u, v) th element of a is obtained by the following formula:
Figure BDA0001172339610000066
having obtained the vector c, the main diagonal elements of the matrix P are known.
For the estimation of elements other than the main diagonal, we estimate the elements of the matrix P column by column, subject to column. As shown in fig. 1, the antenna array of the MIMO system can be seen as a special graph, each antenna corresponds to a node in the graph, and each node is only connected to the node nearest to it.
Without loss of generality, firstly determining any node u, u epsilon [1, M)]Estimating the element of the column of the node u, i.e. the element of the u-th column of the radio frequency gain ratio matrix P
Figure BDA0001172339610000071
Is denoted as P(u)。
For the sake of clarity, we define the "distance" between the antennas as: assuming that the path length between adjacent antennas is 1, the distance between the antennas is the shortest path length between the two antennas. Further, we define "layers" as: with respect to a certain node u (i.e., antenna u), all nodes with distance k from the node u constitute the kth level node of relative u. In FIG. 1, v1To v6Level 1, w, constituting node u1,w2… all nodes connected to each other constitute level 2, x, of node u1,x2… all nodes connected to each other constitute level 3 of node u.
Estimate P(u)The method is realized in an iterative mode, and in the k-th iteration, the radio frequency unit gain ratio of a node u and a k-th layer node relative to the node u is estimated.
For node t on the first level of the node u1If the measurement noise is ignored, the radio frequency gain ratio
Figure BDA0001172339610000072
Determined according to the following expression:
Figure BDA0001172339610000073
wherein t is1' is that said node u differs from t on a first level1And with t1An adjacent node;
specifically, as shown in FIG. 1, there are 6 nodes v on the first level of node u1To v6For node v on level 1i，i∈[1,6]We calculate directly from the measurement signal. If the measurement noise is ignored
Figure BDA0001172339610000074
The following relationship can be obtained:
Figure BDA0001172339610000081
obviously, node u and node v can be determined from the measurement signal y and the diagonal element c already obtainediRadio frequency gain ratio of
Figure BDA0001172339610000082
And by selecting different neighbouring nodes vjWhere j ≠ i, vi，vjAre all the first layer nodes of u to reduce the influence of measurement noise on the estimation accuracy. It should be noted that this method is only suitable for estimating layer 1 nodes, since signals are only passed between neighboring nodes.
For the node t on the k (k ≧ 2) th layer of the node ukWe can always find a line from u to tkThe shortest path of (2): u → t1→t2→…→tk-1→tk. Then the following relationship can be obtained:
Figure BDA0001172339610000083
wherein
Figure BDA0001172339610000084
And
Figure BDA0001172339610000085
having been derived in the 1 st iteration,
Figure BDA0001172339610000086
and
Figure BDA0001172339610000087
having been derived in the (k-1) th iteration,
Figure BDA0001172339610000088
and
Figure BDA0001172339610000089
already at vector c.
Further, if from u to tkThere are L groups ofTaking the average value of L paths as the final estimation result to improve the estimation quality, i.e. the shortest path of energy
Figure BDA00011723396100000810
Wherein
Figure BDA00011723396100000811
Respectively, radio frequency gain ratios estimated when selecting different shortest paths
Figure BDA00011723396100000812
For each node u of the antenna array, u ∈ [1, M ], the above iterative method may be used to obtain the element of the column where the node u is located, and after all nodes calculate the corresponding column in the matrix P, the entire matrix P is completely estimated.
The second method of estimating the matrix P is called a batch scheme. As can be seen from the expression of the matrix P, the elements of P contain all combinations of M α and M β. Therefore, unlike all previous calibration schemes, the batch scheme proposed by the present invention uses the measurement signal matrix Y to directly estimate each α and β, rather than their ratio. The estimation process of α and β can be implemented by solving an optimization problem. Defining an error function f (X)t,Xr) The following were used:
f(Xt,Xr)＝||Y-XtAXr||2，
where A is the neighbor node matrix:
Figure BDA0001172339610000091
our goal is to solve two matrices XtAnd XrLet the error function f (X)t,Xr) At a minimum, and these two matrices must be diagonal matrices, i.e.:
Xt＝Diag{xt,1,xt,2,…,xt,M}
Xr＝Diag{xr,1,xr,2,…,xr,M}
to recover X from the measurement signal matrix YtAnd XrWe can use the block co-ordinated descent (BCD) method to solve the optimization problem described above.
Firstly, randomly obtaining the initialization value of the matrix
Figure BDA0001172339610000092
And
Figure BDA0001172339610000093
simultaneously initializing a cycle variable j equal to 0; and then performing iterative operation.
The iteration process is as follows:
it is known that
Figure BDA0001172339610000094
This can be found by the following expression:
Figure BDA0001172339610000095
it is known that
Figure BDA0001172339610000096
This can be found by the following expression:
Figure BDA0001172339610000097
adding the cyclic variables j, and repeatedly calculating Xr (j+1)And Xt (j+1)Until a predetermined termination criterion is met, e.g. the iteration process exceeds a certain number of times, at which point the iteration process terminates.
In the expression, Diag { } represents that a diagonal matrix is generated, and diagonal elements of the diagonal matrix are given by vectors in brackets; diag { } denotes generating a vector whose elements are diagonal elements of the matrix in brackets; a/denotes the dot division between pairs of vector elements.
If neglected to measureMeasuring noise, wherein the measurement signal matrix Y satisfies the following relation that Y ═ hCBS,tACBS,rWhere h is the channel gain. Due to the connectivity of the antenna diagram, it can be demonstrated that through the iterative process, the optimal solution of the above problem satisfies the following relationship:
Xt＝μhCBS,t
Xr＝ωCBS,r
wherein μ and ω are arbitrary constants, and μ · ω ═ 1 is satisfied.
According to the obtained XtAnd XrThen C can be obtainedBS,tAnd CBS,rTherefore, the algorithm can accurately estimate alpha and beta under ideal conditions.
Using X in consideration of measurement noisetAnd XrApproximately instead of CBS,tAnd CBS,rThus, all estimated values of alpha and beta are obtained, the estimated values have deviation from the actual values, and the deviation degree is related to the noise power ratio of the measurement signal.
When all α and β have been estimated, the entire matrix P is estimated by comparing two by two.
The calibration method of the MIMO system provided by the embodiment of the invention comprises the steps of firstly constructing a measurement signal matrix, estimating a radio frequency gain ratio matrix according to the measurement signal matrix, estimating other elements of the radio frequency gain ratio matrix except a main diagonal in the calibration process except a main diagonal, namely estimating the ratio of the gain of a transmitting radio frequency unit of one antenna to the gain of receiving radio frequency units of other antennas, fully considering the interaction between the antennas of the large-scale MIMO system and improving the calibration effect of the large-scale MIMO system.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (4)

1. A calibration method for a MIMO system, wherein all antennas of the MIMO system are equidistantly placed, the method comprising:
constructing a measurement signal matrix Y, wherein the expression of the (u, v) th element of the measurement signal matrix Y is as follows:
yu,v＝αuhβv+nu,v，u∈[1,M]，v∈[1,M]，
wherein, yu,vFor the (u, v) th element, α, of the measurement signal matrix YuGain of the transmitting radio unit, beta, for antenna uvGain of the receiving RF unit for antenna v, h channel gain, nu,vMeasuring noise between an antenna u and an antenna v, wherein the antenna u and the antenna v are adjacent, and M is the total number of antennas on the base station side of the MIMO system;
estimating a radio frequency gain ratio matrix by using the measurement signal matrix Y, wherein the expression of the (u, v) th element of the radio frequency gain ratio matrix is as follows:
Figure FDA0002662119990000011
u∈[1,M]，v∈[1,M]，
wherein estimating a radio frequency gain ratio matrix using the measurement signal matrix Y comprises:
estimating the elements on the main diagonal of the radio frequency gain ratio matrix according to the following method: defining an M-dimensional vector
Figure FDA0002662119990000012
Where gamma is an adjustable scalar quantity calculated to make the cost function
Figure FDA0002662119990000013
The smallest vector c to estimate the elements on the main diagonal of the RF gain ratio matrix, where AuDenotes a set of antenna numbers adjacent to antenna u, v denotes an antenna number adjacent to antenna u, cuThe u-th element of the vector c is represented,
Figure FDA0002662119990000014
cvthe v-th element of the vector c is represented,
Figure FDA0002662119990000015
and estimating the element outside the main diagonal line of the radio frequency gain ratio matrix and positioned in the u column by the following method: with the antenna u as a central antenna, the remaining antennas being distributed in layers around said central antenna, for an antenna t on a first layer of said antenna u1Neglect of measurement noise, radio frequency gain ratio
Figure FDA0002662119990000016
Determined according to the following expression:
Figure FDA0002662119990000021
wherein t is1' is that the antenna u differs from the antenna t on a first layer1And with t1The adjacent antennas are arranged in such a way that,
Figure FDA0002662119990000029
t-th of vector c1' the number of the elements,
Figure FDA0002662119990000022
for the antenna t on the k (k ≧ 2) th layer of the antenna ukSelecting a piece from u to tkShortest path, radio frequency gain ratio of
Figure FDA0002662119990000023
Determined according to the following expression:
Figure FDA0002662119990000024
wherein t isk-1Is the antenna on the (k-1) th layer of the antenna u.
2. The method of claim 1, wherein said u to t is measured fromkWhen there are L pieces in the shortest path of (2), the radio frequency gain ratio
Figure FDA0002662119990000025
Determined according to the following expression:
Figure FDA0002662119990000026
wherein
Figure FDA0002662119990000027
i∈[1,L]Respectively, radio frequency gain ratios estimated when selecting different shortest paths
Figure FDA0002662119990000028
3. A calibration method for a MIMO system, wherein all antennas of the MIMO system are equidistantly placed, the method comprising:
constructing a measurement signal matrix Y, wherein the expression of the (u, v) th element of the measurement signal matrix Y is as follows:
yu,v＝αuhβv+nu,v，u∈[1,M]，v∈[1,M]，
wherein, yu,vFor the (u, v) th element, α, of the measurement signal matrix YuGain of the transmitting radio unit, beta, for antenna uvGain of the receiving RF unit for antenna v, h channel gain, nu,vMeasuring noise between an antenna u and an antenna v, wherein the antenna u and the antenna v are adjacent, and M is the total number of antennas on the base station side of the MIMO system;
estimating a radio frequency gain ratio matrix by using the measurement signal matrix Y, wherein the expression of the (u, v) th element of the radio frequency gain ratio matrix is as follows:
Figure FDA0002662119990000031
u∈[1,M]，v∈[1,M]，
wherein estimating a radio frequency gain ratio matrix using the measurement signal matrix Y comprises:
defining an error function f (X)t,Xr)＝||Y-XtAXr||2，
Wherein, the expression of the matrix A is:
Figure FDA0002662119990000032
solving two diagonal matrices X using a block cooperative descent methodtAnd XrLet the error function f (X)t,Xr) Minimum;
obtained XtAnd XrThe following expression is satisfied:
Xt＝μhCBS,t
Xr＝ωCBS,r
wherein μ and ω are arbitrary constants and satisfy μ · ω ═ 1, CBS,t＝Diag{α1,α2,…,αM}，CBS,r＝Diag{β1,β2,…,βM}；
And calculating and obtaining the estimated values of alpha and beta of all the antennas according to the expression so as to obtain all the elements of the radio frequency gain ratio matrix.
4. Method according to claim 3, characterized in that said solving of two diagonal matrices X using a block cooperative descent methodtAnd XrThe method comprises the following steps:
1) obtaining X at randomtAnd XrIs initialized to
Figure FDA0002662119990000033
And
Figure FDA0002662119990000034
and initializing a loop variable j equal to 0;
2) calculating according to expression (1)
Figure FDA0002662119990000035
Figure FDA0002662119990000037
3) Calculating according to expression (2)
Figure FDA0002662119990000036
Figure FDA0002662119990000041
4) Accumulating the cyclic variable j, and repeating the steps 2) to 3) until a preset termination criterion is met;
in the expression, Diag { } represents that a diagonal matrix is generated, and diagonal elements of the diagonal matrix are given by vectors in brackets; diag { } denotes generating a vector whose elements are diagonal elements of the matrix in brackets; a/denotes the dot division between pairs of vector elements.
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"Reciprocity Calibration for Massive MIMO Systems by Mutual Coupling between Adjacent Antennas";Hao Wei;Dongming Wang;Jingyu Hua;Xiaohu You;《2016 IEEE 83rd Vehicular Technology Conference (VTC Spring)》;20160707;第三章 *
Hao Wei，Dongming Wang，Huiling Zhu，Jiangzhou Wang."Mutual Coupling Calibration for Multiuser Massive MIMO Systems".《IEEE Transactions on Wireless Communications》.2015, *

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