CN101150877A - Improved multi-user selection method for block diagonally multi-in and multi-out system based on model - Google Patents
Improved multi-user selection method for block diagonally multi-in and multi-out system based on model Download PDFInfo
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Abstract
An improved multi-user selecting method based on block diagonalization multiple-input multiple-output system of norm is provided, firstly selecting a maximum user of the channel Frobenius norm, then adding the maximum user of the equivalent channel Frobenius norm sum acquired by multiplying channels of all selected user with corresponding precoding matrix in a backup user collection in turn, until the maximum number of users can be supported by the system synchronously. The invention reduces the calculation complexity from two sides: adopting an heuristic Gram-Schmidt orthogonalization method to simplify the design flow of the precoding matrix; after selceting a user every time, updating the backup user collection to make users of the collelction and users of the selected user collection satisfy the orthogonality, thereby reducing the searching range selected by users at next time.
Description
Technical Field
The invention relates to the technical field of Multiple Input Multiple Output (MIMO) of wireless communication, in particular to an improved multi-user selection method of a block diagonalization MIMO system based on norm.
Background
Block diagonalization is a common linear precoding technology for eliminating common channel interference among users and realizing space division multiple access in a downlink multi-user MIMO system. When the number of users in a system is large, how to effectively select a set of users capable of communicating simultaneously to improve the system performance is one of the main research subjects in the space division multiple access system. Two low-complexity multi-user selection methods suitable for a block diagonalization system are proposed in the institute of electrical and electronics engineers Signal Processing (IEEE Transactions on Signal Processing, volume 54, issue.9, sept.2006, pp.3658-3663), and the proposed multi-user selection algorithm based on the Frobenius norm still has great complexity due to the need of frequent Gram-Schmidt (Gram-Schmidt) orthogonalization calculation, and is difficult to be used in an actual system especially when the number of users in the system is large.
A low-complexity semi-orthogonal multi-user selection algorithm is proposed in the International society of electronic and Electrical Engineers (IEEE Journal on Sel. Areas in Communications, vol.24, no.3, 2006, pp.528-541). It is only applicable to the Zero Forcing Beamforming (ZFBF) system, which is a special case of the block diagonalization system, and is not applicable to the general block diagonalization system when the user receiving antenna is larger than 1.
Disclosure of Invention
The technical problem of the invention is solved: the method greatly reduces the computational complexity on the basis of keeping the throughput performance of the original multi-user selection method based on the norm, and is suitable for being used in an actual system.
The technical solution of the invention is as follows: the improved multi-user selection method of the block diagonalization multiple-input multiple-output system based on the norm is characterized in that: firstly, selecting a user with the maximum Frobenius norm of a channel matrix, and then sequentially adding the user with the maximum Frobenius norm sum of equivalent channel matrixes obtained by multiplying the channel matrixes of all selected users by corresponding pre-coding matrixes from a user set to be selected until the maximum number of users which can be simultaneously supported by the system is reached. When a precoding matrix of each user is designed, a heuristic Gram-Schmidt orthogonalization process is adopted to simplify Gram-Schmidt orthogonalization calculation in the conventional multi-user selection method based on norm, and the idea of a multi-user selection algorithm of channel quasi-orthogonality among users in a beam forming system is expanded to a block diagonalization system, so that a set of users to be selected and selected users meet certain orthogonality, and the range of user search each time is reduced, and the specific steps are as follows:
(1) And (5) initializing.
Selecting a 1 st user to be selected omega 1 Set of all users, i.e. omega 1 = {1,2, k }; the selected user set gamma is empty. 1 st selected user s 1 A set omega of the users to be selected with the maximum channel matrix Frobenius norm 1 Users of (i), i.e.
For the selected user s 1 Of the channel matrix H s1 Obtaining an orthogonal base V by adopting Gram-Schmidt orthogonalization s1 . To select a user s 1 Adding the set of selected users gamma, i.e. gamma = { s = 1 }; and will be orthogonal base V s1 Joining the orthogonal bases V of all selected users γ I.e. by
Updating the user set to be selected by adopting a user set reduction strategy to obtain a user set omega to be selected of the 2 nd user 2 。
(2) The ith user is selected (i ≧ 2).
For the selected user set omega of the ith user i Each user k in (i.e., k ∈ Ω) i Calculating its equivalent channel matrixThen
Orthogonal basis V falling on all selected users γ For each selected user s in the set of selected users gamma j (s j E g y (j =1,2, l, i-1)), the equivalent channel matrix of each selected user added to user k is updated according to the following two steps.
a. Obtaining a channel matrix H of a user k by adopting a heuristic Gram-Schmidt orthogonalization method k Joining subscriber s j Orthogonal basis V of all other selected users γ-{sj} (j =1,2,L,i-1) introduction of a new orthogonal groupV k，γ-{sj} I.e. by
The HGSO is the heuristic Gram-Schmidt orthogonalization method of the invention.
b. Selected subscriber s j The equivalent channel matrix of (2) is updated as follows:
selecting an equivalent channel for user k
And updated selected user equivalent channelsThe user with the maximum Frobenius norm sum is the ith selected user s i I.e. by
(3) And (5) storing. Adding the ith selected user s according to the result of the step (2) i Updated equivalent channel of selected user
Obtaining an orthogonal base V of the hybrid strain by Gram-Schmidt orthogonalization γ-{sj}+{si} . And stores them for the next iteration.
(4) And (6) updating. If the number of the selected users is less than the maximum number of the users supported by the system, updating and selecting the to-be-selected user set omega of the (i + 1) th user by adopting a user set reduction strategy i+1 (ii) a If omega i+1 If not, increasing 1 for i, and turning to the step (2) to select the (i + 1) th user; otherwise, ending the selection.
In the invention, the heuristic Gram-Schmidt orthogonalization principle is as follows:
when the (i + 1) th user is selected, the set omega of the users to be selected needs to be calculated i+1 And the selected set of users γ = { s = each user k in (d) } 1 ，K，s i Any i-1 users in the Chinese character 'Gama's code j J =1,2,k, i-1). In fact, V γ-{sj} Having been calculated during the i-th user selection process, the complexity of Gram-Schmidt orthogonalization is greatly reduced if this information is saved and utilized. V γ Is the set of users γ = { s = { [ S ] 1 ，K，s i The orthogonal basis of the channel matrix space spanned by k，γ Indicating that user k joins the orthogonal basis introduced by set y. The process of solving the orthogonal space formed by stretching a user set gamma + { k } channel matrix by heuristic Gram-Schmidt orthogonalization is recorded as V k，γ ＝HGSO(V γ ，H k ) The method comprises the following two steps:
(1) Channel matrix H of user k to be selected k Mapping to orthogonal space V γ In the method, an equivalent channel matrix of the user k to be selected is obtained
(2) If the number of the receiving antennas of the user k to be selected is more than 1, the pair
Orthogonalization by Gram-Schmidt to obtain V k，γ 。
In the present invention, the principle of the User Selection Set Reduction (USSR) is as follows:
in zero-forcing beamforming, two channel vectors h i And h j Normalized quantity product | h i h j H |/‖h i ‖‖h j Is used to construct a semi-orthogonal set of users. In block diagonalization, when a user has more than one receiving antenna, a normalized Frobenius norm is introduced to estimate a channel matrix H of the user i, j accordingly i ，H j The correlation of (a):
in which Nm (H) m×n )＝diag{‖[H m×n ] l ‖ -1 ，K，‖[H m×n ] m ‖ -1 }，[·] i Representing the ith row, n, of the matrix r，i ，n r，j The number of receive antennas for each user i, j. The normalized Frobenius norm indirectly reflects the correlation between the user channel matrices only if the normalized Frobenius norm of the alternative users and the currently selected user is smaller thanWhen a certain preset threshold value alpha is met, namely certain orthogonality is met, the user is added to the next user set to be selected, and therefore the user searching range is shortened. The user set reduction method comprises the following steps:
(1) Initialization: let the i-th user selection result in the selection of user s i . The set omega of the users to be selected by the (i + 1) th user i+1 To select the candidate user set omega of the ith user i Removing user s i I.e. omega i+1 ＝Ω i -{s i }。
(2) And (3) set reduction: for omega i+1 Calculating user k and user s for each user k in the set i Is | Nm (H) of channel matrix correlation si )H si H k H Nm(H k )‖ F 2 /(n r，si ·n r，k ) If the correlation result is greater than the set threshold alpha, then the set omega of the users to be selected i+1 In deleting user k, i.e. omega i+1 ＝Ω i+1 -{k}。
Compared with the prior art, the advantage lies in: the method adopts a heuristic Gram-Schmidt (Gram-Schmidt) orthogonalization method, so that the design flow of a precoding matrix is simplified; after each user is selected, the alternative user set is updated, so that certain orthogonality is met between the users in the set and the users in the selected user set, and the search range selected by the next user is reduced. The invention can greatly reduce the calculation complexity of the algorithm on the basis of keeping the swallowing and spitting performance, is suitable for being used in an actual system and reduces the use cost.
Drawings
FIG. 1 is a graph of the relationship between the relative complexity and the number of users for a signal-to-noise ratio of 20dB according to the present invention;
FIG. 2 is a graph of the relationship between throughput performance of the system and a threshold a;
FIG. 3 is a graph of the relative complexity versus threshold a resulting from the USSR strategy of the present invention;
FIG. 4 is a graph showing the relationship between the total system throughput and the relative complexity of 12 transmitting antennas and 4 receiving antennas according to the present invention;
fig. 5 is a graph showing the relationship between the total throughput and the relative complexity of the system of 8 transmitting antennas and 2 receiving antennas according to the present invention.
Detailed Description
The system of the embodiment adopts a downlink multi-user MIMO system of K users. The base station has n t A number of transmit antennas, for simplicity, all users are assumed to have the same number n of receive antennas r The maximum number of users that the system can support simultaneously is
Wherein
Is the largest integer not greater than a. It is assumed that the base station is able to know the Channel State Information (CSI), H, of each user j Each element of the channel matrix from the base station to the user j is a complex Gaussian random variable which is subjected to independent equal distribution, has the mean value of 0 and has the variance of 1. The threshold for narrowing the user set is set as alpha.
Record omega i In order to select the set of users to be selected when the ith user is selected, gamma is the set of the selected users, gamma + { a } adds a to the new set after the set gamma, gamma- { a } is the new set after the element a in the set gamma is removed, and V γ The orthogonal base for all selected users, K being the total number of users in the system, | A | F Frobenius norm, H of matrix A k Is the channel matrix for user k. The improved norm-based block diagonalization MIMO system multiuser selection method of the embodiment specifically comprises the following steps:
step 1: and (5) initializing.
1. The candidate user set omega of the first user 1 =1,2,k, k, having selected user set γ =phi.
2. According to
Selecting the 1 st subscriber s 1 . For H s1 Obtaining an orthogonal base V by adopting Gram-Schmidt orthogonalization s1 . User s 1 Adding the set of selected users gamma, then gamma = { s = 1 }，
3. Updating the user set to be selected by adopting a user set reduction strategy to obtain a user set omega to be selected for selecting the 2 nd user 2 ：
a. Initialization: omega 2 ＝Ω 1 -{s 1 }。
b. And (3) set reduction: for each k ∈ Ω 2 Calculating
If it is used
Then the user k, i.e. omega, is deleted from the set of users to be selected 2 ＝Ω 2 -{k}。
Step 2: the ith user is selected (i ≧ 2).
1: for each user k ∈ Ω i The following calculations were performed:
(1) Calculating its equivalent channel matrix
Then
Falls on V γ The null space of (a).
(2) For each selected user s j E.g. gamma (j =1,2, L, i-1), and updating the equivalent channel matrix of each selected user after adding the user k by adopting a heuristic Gram-Schmidt orthogonalization method:
a. user channel matrix H k Mapping to orthogonal space V γ-{sj} In the method, an equivalent channel matrix of the user k is obtained
b. If n is r > 1, to
Orthogonalizing with Gram-Schmidt to obtain V k，γ-{sj} 。
c. Subscriber s j The equivalent channel matrix of (c) may be updated as follows:
2: selecting the ith user:
and step 3: and (5) storing.
To pair(j =1,K,i) orthogonalization of V by Gram-Schmidt γ-{sj}+{si} . And stores them for the next iteration.
And 4, step 4: and (6) updating.
1: if the number of the selected users is smaller than the maximum number of the users supported by the system, updating the set omega of the users to be selected by adopting a user set reduction strategy i+1 ：
a. The set of the users to be selected by the (i + 1) th user is omega i+1 ＝Ω i -{s i }。
b. C, each to-be-selected k is equal to omega i+1 Calculating
If it is used
Deleting k, namely omega, of the user to be selected from the user set to be selected i+1 ＝Ω i+1 -{k}。
2: if Ω is i+1 ≠ i ← i +1, moving to step 2, select the i +1 th user.
3: and ending the selection. The selected user set γ is the final result of the user selection.
To better compare the present invention with the existing methods, the computational complexity of the improved method of the present embodiment was analyzed. An analytical approach is employed that expresses computational complexity as a number of floating point operations. For a complex matrix:
n r ≤n t and
(i-1)n r ≤n t table 1 lists the number of floating point operations for a typical operation.
TABLE 1 number of floating point operations for typical operation
| Typical matrix operations | Number of floating point operations |
| ‖H‖ F 2 | 4n r n t |
| SVD | 24n r n t 2 +48n r 2 n t +54n r 3 |
| GSO(H) | 8n r 2 n t -2n r n t |
| H-HV γ H V γ | 16(i-1)n r 2 n t -2(i-1)n r 2 |
| HGSO(V γ ，H) | 16(i-1)n r 2 n t -2(i-1)n r 2 +8n r 2 n t -2n r n t |
If two random channel matrices H can be calculated i ，H j Xi of i，j The number of users in the user set to be selected can be estimated by giving a threshold value alpha. But xi i，j Is difficult to estimate, assuming only thatWhere | represents the aggregate potential, the specific result is in valueThe simulated figures are given.
The computational complexity ψ of the improved method can be divided into three parts: psi A Is introduced by selecting the first user; psi B Introduced by other user's selection; psi C Is to adopt USSR strategy to calculate xi i，j And the additional computational complexity introduced:
ψ＝ψ A +ψ B +ψ C
ψ A ＝4Kn r n t +8n r 2 n t -2n r n t
the relative complexity is defined as the ratio of the number of floating point operations in the improved method to the existing method. FIG. 1 shows (n) t ＝12，n r = 4) and (n) t ＝8，n r = 2) relative complexity and number of users in a MIMO system, where
3,4 respectively. The curves in fig. 1 are characterized by:
(1) Without USSR, i.e.
The relative complexity reduction is due to the heuristic Gram-Schmidt orthogonalization employed.
(2) Even in the worst case of USSR, i.e.
The user selection set is not reduced, and the improved method is still much less in computational complexity than the existing method.
(3)
The larger the reduction in computational complexity.
Fig. 2 shows the total throughput versus α for the improved method in two MIMO systems with SNR =20dB, K =10,100,1000, each simulation based on 10000 independent channel realizations. The curve of fig. 2 is characterized by:
(1) The larger K, the larger the multi-user diversity gain.
(2) The larger the alpha is, the less the candidate user set is reduced, the larger the multi-user diversity gain is, and the larger the throughput is.
Fig. 3 gives the relative complexity results considering only the USSR policy impact, without considering the heuristic Gram-Schmidt orthogonalization. The curve of fig. 3 is characterized by:
(1) Considering only the relative complexity under the USSR policy is an increasing function with respect to a, independent of the number of users.
(2) A suitable a may achieve a good compromise between system performance and computational complexity.
FIGS. 4 and 5 show (n) t ＝8，n r = 2) system takes α =0.1, (n) t ＝12，n r = 4) system takes a =0.0729, the present embodiment improves the throughput performance and the relative complexity of the method as a function of the number of users. Also the simulation results of the optimal multi-user selection algorithm (BDOptimal) over all possible user sets are given, which, due to its computational complexity, only gives results for up to 40 users at the maximum. The curves in fig. 4,5 show the following characteristics:
(1) With fewer users, the improved method results in a slight decrease in throughput over the prior art method due to the reduction in the set of users.
(2) As the number of users increases, the improved method can achieve almost the same throughput performance as the existing method.
(3) The improved method can greatly reduce the computational complexity in (n) t ＝12，n r = 4) relative complexity in the system is only 18% of the existing method in (n) t ＝8，n r = 2) only 7% of the existing methods in the system.
The invention provides an improved method by taking the complexity of a multi-user selection method based on norm in a multi-user MIMO system with reduced block diagonalization as a starting point. In the design of the block diagonalized precoding matrix, the existing result is fully utilized, and a heuristic Gram-Schmidt orthogonalization method is adopted, so that the design flow of the precoding matrix is simplified; after each user is selected, updating the set of users to be selected, so that the users to be selected in the set and the users in the selected user set meet certain orthogonality, and reducing the search range selected by the next user; the improved method provided by the invention can greatly reduce the computational complexity by selecting proper parameters on the basis of keeping the throughput rate performance of the existing method, and is suitable for being used in an actual system.
Claims (3)
1. The improved multi-user selection method for the block diagonalization multi-input multi-output system based on the norm is characterized by comprising the following steps of:
(1) Initialization
Selecting a to-be-selected user set omega of the 1 st user 1 Set of all users, i.e. omega 1 =1,2, k }; selecting a set of selected users gamma as null, namely gamma =; 1 st selected user s 1 Is the set omega of the candidate users with the maximum channel matrix Frobenius norm 1 Users of (i), i.e.
For the selected user s 1 Of the channel matrix H s1 Orthogonalizing by adopting Gram-Schmidt (Gram-Schmidt) to obtain an orthogonal base V s1 (ii) a To be selected users s 1 Adding the set of selected users gamma, i.e. gamma = { s = {(s) } 1 }; and will be orthogonal base V s1 Joining the orthogonal bases V of all selected users γ I.e. by
Updating the user set to be selected to obtain a user set omega to be selected of the 2 nd user 2 ；
(2) Select the ith user, i ≧ 2
For the selected user set omega of the ith user i Each user k in (i.e., k ∈ Ω) i Calculating its equivalent channel matrixThen H k ％ Orthogonal basis V falling on all selected users γ A null space of (a); for each selected user s in the selected user set gamma j ，s j E gamma (j =1,2, L, i-1), and updating the equivalent channel matrix of each selected user added to the user k according to the following two steps:
a. obtaining a channel matrix H of a user k by adopting a heuristic Gram-Schmidt orthogonalization method k Joining subscriber s j Orthogonal basis V of all other selected users γ-{sj} (j =1,2,L,i-1) introduction of a new orthogonal group V k，γ-{sj} I.e. by
HGSO is a heuristic Gram-Schmidt orthogonalization method;
b. selected subscriber s j The equivalent channel matrix of (1) is updated as follows:
selecting an equivalent channel H for user k k ％ And updated selected user equivalent channel H sj，γ-{sj}+{k} ％ The user with the maximum Frobenius norm sum is the ith selected user s i I.e. by
(3) Storing
Adding the ith selected user s according to the result of the step (2) i Equivalent channel H after updating of selected user sj，γ-{sj}+{si} ％ (j =1,K, i) orthogonalizing with Gram-Schmidt to obtain the orthogonal base V γ-{sj}+{si} And store them for the next iteration;
(4) Updating
If the number of the selected users is less than the maximum number of users supported by the system, updating and selecting the set omega of the users to be selected of the (i + 1) th user i+1 (ii) a If omega i+1 If not, increasing 1 for i, and turning to the step (2) to select the (i + 1) th user; otherwise, ending the selection.
2. The improved norm-based block diagonalized multiple-input multiple-output (memo) system multiuser selection method of claim 1, wherein: the updating of the user set to be selected in the step (1) and the step (4) adopts a user set reduction method USSR, which comprises the following steps:
(1) Initialization: let the i-th user selection result in the selection of user s i . The set omega of the users to be selected by the (i + 1) th user i+1 To select the candidate user set omega of the ith user i Removing user s i I.e. omega i+1 ＝Ω i -{s i }；
(2) And (3) set reduction: for omega i+1 Calculating user k and user s for each user k in the set i Is | Nm (H) of the channel matrix correlation s i)H si H k H Nm(H k )‖ F 2 /(n r，si ·n r，k ) If the correlation result is greater than the set threshold alpha, then the set omega of the users to be selected i+1 Delete user k, i.e. Ω i+1 ＝Ω i+1 -{k}。
3. The improved norm-based block diagonalized multiple-input multiple-output (memo) system multiuser selection method according to claim 1, wherein: the heuristic Gram-Schmidt orthogonalization method in the step (3) comprises the following steps:
(1) K channel matrix H of user to be selected k Mapping to orthogonal space V γ In the method, an equivalent channel matrix H of a user k to be selected is obtained k，γ ％ ：
(2) If the user k to be selected is connectedNumber of receiving antennas is greater than 1, for H k，γ ％ Orthogonalizing with Gram-Schmidt to obtain V k，γ 。
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| CN102710394A (en) * | 2012-06-04 | 2012-10-03 | 电子科技大学 | Spatial modulation method based on transmitting antenna selection for MIMO (Multi-Input Multi-Output) system |
| CN102710394B (en) * | 2012-06-04 | 2014-07-02 | 电子科技大学 | Spatial modulation method based on transmitting antenna selection for MIMO (Multi-Input Multi-Output) system |
| CN102891711A (en) * | 2012-09-06 | 2013-01-23 | 东南大学 | User selection method in multipoint coordination scene |
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| CN104868943B (en) * | 2015-04-23 | 2019-02-05 | 山东大学 | Multiuser MIMO user choosing method based on conditional number |
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| CN105871439A (en) * | 2016-05-31 | 2016-08-17 | 华南理工大学 | Iteration BD precoding method based on projection operator |
| CN105871439B (en) * | 2016-05-31 | 2019-05-14 | 华南理工大学 | A kind of iteration BD method for precoding based on projection operator |
| CN106209191A (en) * | 2016-07-20 | 2016-12-07 | 南京邮电大学 | A kind of MU mimo system true environment low complex degree user choosing method |
| CN106209191B (en) * | 2016-07-20 | 2019-05-31 | 南京邮电大学 | A kind of MU-MIMO system true environment low complex degree user choosing method |
| CN107462809A (en) * | 2017-07-19 | 2017-12-12 | 中国科学院电工研究所 | Phase-model transformation matrix design method for three-phase power circuit fault diagnosis |
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