CN106230493B - A kind of selection of multiuser MIMO uplink antenna and user scheduling method - Google Patents
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Abstract
The present invention relates to a kind of selection of multiuser MIMO uplink antenna and user scheduling methods, downward branch-and-bound (Downwards Branch and Bound based on the selection of user's semi-orthogonal, DBAB), local iteration's optimizing algorithm search channel matrix maximum MSV realizes joint antenna selection and user's scheduling；For the algorithm using channel capacity as evaluation index, the rate capability of local optimum is more preferable, approaches exhaust algorithm (Brute-Force Search, BFS)；Meanwhile the computation complexity of the algorithm is far below the method for exhaustion, has larger application value, is a kind of promising day line options and user scheduling method in multi-user MIMO system.
Description
Technical Field
The present invention relates to the field of fourth and fifth generation mobile communications. In order to solve the above problems, the present invention provides a Joint Antenna Selection and User Scheduling (JASUS) method for multi-user MIMO uplink, which has better local optimal rate performance and approaches to the exhaustive algorithm (Brute-ForceSearch, BFS); meanwhile, the calculation complexity of the algorithm is far lower than that of an exhaustion method, and the algorithm has a large application value. Therefore, the invention is a promising antenna selection and user scheduling method in a multi-user MIMO system.
Background
In modern and future mobile communication systems, a base station serves Multiple users simultaneously by deploying an antenna array, thereby forming a Multiple-Input Multiple-Output (MIMO) system.
In the past decade, MIMO technology in wireless communication has received much attention from researchers worldwide due to its high system capacity and spectral efficiency [ see document 1: xu, A.Liu, W.Jiang, H.Xiang, and W.Luo, "journal user scheduling and anti-na selection in distributed massive MIMO system with limited background capacity," China Communications, vol.11, No. 5, pp.17-30,2014 ]. In the commercial LTE system, the communication system based on the MIMO technology has brought a great improvement to the internet access experience of the mobile user.
In point-to-point MIMO communication, both the signal transmitter and the receiver include multiple antennas, which can achieve spatial diversity and multiplexing of communication. Theoretically, the capacity achieved by the MIMO system increases linearly with the minimum number of transmit and receive antennas of the system without increasing the extra bandwidth and the transmission power [ see document 2: rusek, D.Persson, L.Buon Kiong, E.G.Larsson, T.L.Marzetta, O.Edfors, and F.Tufvesson, "Scaling up MIMO: opportunities and variations with large array," IEEE Signal processing Mag., vol.30, pp.40-60,2013 ]. In mobile cellular communication, a Multi-User MIMO (MU-MIMO) communication system has been widely used. When the mobile base station obtains Channel State Information (CSI) of its own and different users, the base station may provide Information services to multiple users simultaneously by using a suitable precoding (generalized beamforming) technique, so as to improve the communication rate by multiple times [ see documents 3 to 5: h.q.ngo, e.g.larsson, and t.l.marzetta, "Energy and spectral efficiency of top large multiuser mimo systems," IEEE trans. commun., vol.61, No.4, pp.1436-1449, apr.2012; l.dai, z.wang, and z.yang, "spectral efficiency time-frequency training OFDM for mobile large-scale MIMO systems," IEEE j.sel.areas command, vol.31, No.2, pp.251-263, feb.2013; lu, J.Ning, Y.Zhang, T.Xie, and W.Shen, "Richardson method based on decoding with low complexity for massive MIMO systems," in Proc.of IEEE 81st VTC Spring,2015, pp.1-4 ]. Currently, a small-scale MIMO (small-scale MIMO) including only 8 antennas at most is included in the LTE-Advanced protocol specification of one of the 4G standards [ document 5: lu, j.ning, y.zhang, t.xie, and w.shen, "Richardson method based linear coding with low complexity for Massive MIMO systems," in proc.of IEEE 81st VTC Spring,2015, pp.1-4 ", while Massive MIMO (also known as large-scale MIMO) technology requires that the base station end contain 64 or even hundreds of antennas, which is considered to be the most promising and promising technology in future 5G communications [ see documents 6-7: e.larsson, o.edfors, f.tufvesson, and t.marzetta, "Massive MIMO for next generation wireless systems," ieee commun.mag., vol.52, No.2, pp.186-195, feb.2014; y, Wang and Y.Dong, "A genetic selection algorithm for a massive MIMO system with channel estimation error," in Proc. of Advances in Wireless and Optical Commun (RTUWO),2015, pp.1-4 ]. In multi-user MIMO, especially Massive MIMO systems, when the number of base station antennas is sufficiently large, the channels from different users to the base station are approximately orthogonal to each other [ see document 6: wang and y. dong, "a genetic anti-selective algorithm for a massive MIMO system with channel estimation Error," in proc. of advances in Wireless and Optical command (RTUWO),2015, pp.1-4], small-scale channel fading and uncorrelated noise can also be eliminated [ see document 8: m. Benmimoune, E.Driouch, W.ajib, and D.Massicotte, "Joint transmit anti-selectivity and user scheduling for major MIMOsystems," in Proc. of IEEE WCNC,2015, pp.381-386 ]; if proper precoding technology is adopted, the interference of information among different users can be completely eliminated. However, in order to fully utilize the antennas of the base station, the number of AFE modules equal to the number of antennas needs to be deployed in the design, which is not applicable in the actual design. Since the number of base station Analog Front-End (AFE) modules is limited, the number of antennas that can be simultaneously selected for the uplink and the users served are constrained.
In order to fully utilize the diversity and multiplexing gain of a large antenna array and save radio frequency front end resources, antenna selection is a very suitable choice [ see document 8: m. Benmimoune, E.Driouch, W.ajib, and D.Massicotte, "Jointtransmit antenna selection and user scheduling for massive MIMO systems," InProc.of IEEE WCNC,2015, pp.381-386 ]. In the case of limited AFE resources, antenna selection can select the "best" set of antennas for communication, e.g., the set of antennas with the best channel conditions or the highest output signal-to-noise ratio. Researchers have had many efforts in antenna selection. In the uplink, see document 9: y. gao, w.jiang, andt.kaiser, "Bidirectional branch and Bound based antenna selection in a massive mimo system," in proc.of IEEE 26th PIMRC, 2015, pp.563-568, proposes a Bidirectional branch and Bound (BBAB) algorithm based on finding the Minimum Singular Value (MSV) of the maximum matrix to achieve antenna selection; due to monotonicity of matrix singular values, the antenna selection can search a global optimal solution and is much lower in complexity than an exhaustive method. In the case of channel errors, [ document 7] an antenna selection based on the water-filling principle can be realized by using a genetic algorithm; the algorithm can achieve better channel capacity than the conventional algorithm at low Signal-to-Noise Ratio (SNR). [ document 10: S.E.El-Khamy, K.H.Moussa, A.A.El-Sherif, "On the performance of a massive multiuser MIMO with differential transmission beamforming techniques and antenna selection," in Proc.of 20151st URSI orthogonal Radio Science (URSI AT-RASC),2015, pp.1-10] proposes an antenna selection algorithm based On user channel vector two-norm maximization, which can achieve (Bit Error Rate, BER) performance improvement in beamforming.
On the other hand, due to the constraint of the AFE module, the number of users that can be served at most simultaneously when the base station transmits and receives signals cannot exceed the number of AFE resource modules, and the orthogonality of users also affects the performance of the multi-user MIMO system. User scheduling is also very important in system performance implementation. Based on user distributed evaluation, the user scheduling algorithm based on competitive channel feedback is proposed by [ document 11: X.Xie and X.Zhang, "Scalable user selection for MU-MIMO networks," in Proc.of IEEE INFOCOM,2014, pp.808-816], and the algorithm can effectively save CSI acquisition time. Using Zero-Forcing Beamforming (ZFBF) precoding, [ document 1] proposing three antenna selection and user scheduling algorithms for finding a local optimal solution based on loop capacity constraints; on the basis of the existing local antenna set and user set, the local optimal solution is jumped out by exchanging antennas and user elements to approach the global optimal solution. To reduce complexity, document 8 proposes antenna selection and user scheduling based on user subspace orthogonality in the downlink, which algorithm is able to achieve the optimal performance of the near-exhaustive method, see document 8.
Further, [ document 12: Y.Cao and V.Kariwala, "Bidirectional branch and bound for controlled variable selection: Part I.principles and minimum singular value selection," Computers & Chemical Engineering, vol.32, No.10, pp.2306-2319,2008] and [ document 13: antenna selection and user scheduling algorithms are also proposed in t.yoo and a.goldsmith, "On the optimization of multiantenna hybrid-castscheduling using zero-shaping beamforming," IEEE j.select.areas command, vol.24, No.3, pp.528-541, ma.2006 ].
However, it is difficult to implement various algorithms to achieve excellent system rate, rate standard deviation, and other performances, and to reduce the complexity of calculation.
Disclosure of Invention
In order to solve the above problems, the present invention provides a multi-User MIMO uplink Antenna Selection and User Scheduling method (named Joint Antenna Selection and User Scheduling, JASUS), which has a better local optimal rate performance, but the algorithm complexity is lower.
2. Therefore, the method for selecting the multi-user MIMO uplink antenna and scheduling the user comprises the following steps: s1, a downward branch-and-bound algorithm based on semi-orthogonality user selection: finding a local optimal solution of an antenna set A and a user set U which enable the minimum singular value of a channel matrix to be maximum; s2, local iterative optimization algorithm based on antenna and user set element exchange: in the case where a and U have been obtained, sets A, U are fixed, respectively, exchanging the selected user elements and antenna elements; if the set A, U after switching elements is found to be able to make the channel rate larger, then jumping out from the current locally optimal solution to another locally optimal solution with better performance; and S3, repeating the step S2 until the antenna set A and the user set U are not changed any more.
The method provided by the invention is based on the downward branch and Bound (DBAB) selected by the user semi-orthogonality and the local iterative optimization algorithm to search the maximum MSV of the channel matrix, thereby realizing the joint antenna selection and the user scheduling; the algorithm takes the channel capacity as an evaluation index, has better local optimal rate performance and approaches to an exhaustive algorithm (BFS); meanwhile, the calculation complexity of the algorithm is far lower than that of an exhaustion method, and the algorithm has a large application value. Therefore, the invention is a promising antenna selection and user scheduling method in a multi-user MIMO system.
Drawings
FIG. 1 is a diagram illustrating a downward branch-and-bound algorithm according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of a local iterative optimization algorithm according to an embodiment of the present invention.
FIG. 3 is a flow chart of a downward branch-and-bound algorithm (DBAB) based on semi-orthogonal user selection according to an embodiment of the present invention.
Fig. 4 is a flowchart of a local iterative optimization algorithm according to an embodiment of the present invention.
Fig. 5 is a diagram illustrating uplink and rate variations with signal-to-noise ratio for different algorithms according to an embodiment of the present invention.
Fig. 6 is a diagram illustrating the variation of different algorithm uplink and rate standard deviation with signal-to-noise ratio according to the embodiment of the present invention.
FIG. 7 is a graphical representation of sum rates of different algorithms as a function of analog front end count for embodiments of the present invention.
FIG. 8 is a graph illustrating the variation of the average number of iterations of different algorithms with the simulation front end, in accordance with an embodiment of the present invention.
Detailed Description
As described above, in a multi-user MIMO communication system, especially a Massive MIMO communication system, the cost of antennas of a base station is low, and the antennas can be deployed in a large scale to form an antenna array; however, the analog front end resources are relatively expensive, and deploying one AFE for each antenna greatly increases the cost and wastes resources. In consideration of the limited practical application scene of the AFE module, the embodiment of the invention provides an antenna selection and user scheduling method for searching the maximum MSV based on the combination of user semi-orthogonality downward branch-and-bound and local iterative optimization, and the complexity is not obviously increased under the condition of improving the performance. The following illustrates aspects of the algorithm description, method steps and performance analysis.
Description of the Algorithm
1.1 System model and Rate problem
1.1.1 System model
Suppose that in a multi-user MIMO cell, a base station deploys M antennas and N AFE modules, and M > N. Meanwhile, suppose there are k single antenna users waiting for service in the cell, k > N. Because of the number limitation of the base station AFE modules, the base station can only select the N antennas with the best channel quality from the M antennas at most to transmit and receive signals at each time, and can only serve N users at most simultaneously. If the uplink channel of multi-user MIMO is considered, the signal received by the base station antenna satisfies the following formula:
whereinY is the received antenna signal vector, andthe channel matrix is a quasi-static independent identically distributed Rayleigh channel matrix from a user to a base station;is the transmitted signal vector uploaded to the base station by k users,is Additive White Gaussian Noise (AWGN) superimposed on the received signals of the M antennas, and each component is subjected to a complex Gaussian random distribution with a mean value of 0 and a variance of 1, i.e., zi～CN(0,1)。
At the receiving end of the base station, the optimal reception can be realized by adopting a linear receiver such as zero forcing detection and the like. Wherein,is the receive matrix of a multi-user MIMO system, and W ═ HHH)-1HH/||(HHH)-1HH||2Wherein | | | purple2Is a two-norm' ()HIs the conjugate transpose of the matrix.
The user transmission signal detected by the receiver is as follows:
wherein τ ═ l (H)HH)-1HH||2. The SNR of user k satisfies [9 ]]：
Wherein λ ismin(H)Representing the smallest singular value of the matrix H.
1.1.2 problem description
If the uplink transmission power P of a single user is fixed and the number N of the AFE modules deployed by the base station is fixed, the base station can only utilize N antennas at most each time to form an antenna set A, and the system can provide communication service for N users at most simultaneously to form a user set U; the channel matrix actually used at last is:
HA,U＝H(A,U) (4)
because the communication process is a random process, the maximum ergodic history and rate of the system are as follows:
in the formula, E { } is a mathematical expectation, and the antenna set and the user set need to satisfy a constraint condition:
|A|≤N
|U|≤N (6)
where, | | is the set cardinality. As can be seen from the formulas (4), (5), and (6), when the rate of the communication system is maximum, the number of elements in the user set U and the antenna set a is N. As can be seen from equations (3) and (5), to maximize the rate of the system, the following condition is satisfied:
λmin(HA,U)≥λmin(H′)
H∈{Hs|Hs∈CN×N,Hs＝H(N,N)} (7)
i.e. the channel matrix H finally selected on the basis of the antenna set a and the user set UA,UIn H all NxN dimensional sub-matrices H(N,N)Of which there is the largest MSV [9 ]]。
For the NP-hard problem, an exhaustive method can find a global optimal solution, but the calculation complexity is extremely high. In order to meet the practical application, the invention provides an antenna selection and user scheduling method (Largest MSV based-JASUS, LMSV-JASUS) based on the maximum MSV to search a local optimal solution. The algorithm is equivalent to the Complexity of the existing joint antenna selection and user scheduling method (JASUS) algorithm, the current local optimal thought can be skipped by exchanging elements by means of the (TCB-JASUS) algorithm, the performance is further improved, and the algorithm is close to the global optimal solution.
1.2 JASUS Algorithm to search for maximum MSV
Based on the problem analysis in section 1.1, this section will introduce in detail the LMSV-JASUS algorithm based on the combination of user semi-orthogonality, downward branch-and-bound, and local iterative optimization. The algorithm is mainly divided into two parts:
1) down branch-and-bound algorithm based on semi-orthogonality user selection
The antenna set A and the user set U with system performance close to an exhaustion method can be found as much as possible through the algorithm;
2) local iteration optimization algorithm based on antenna and user set element exchange
Where a and U have been obtained, the sets are fixed A, U, respectively, exchanging the selected user elements and antenna elements. If the set A, U of exchanged elements is found to be able to make the channel rate larger, then the current locally optimal solution is skipped to another locally optimal solution with better performance. Because the global optimal solution is the maximum value in the local optimal solution, the method has a higher probability of obtaining the global optimal solution.
1.2.1 Down branch-and-bound Algorithm based on semi-orthogonality
1) Downward branch and bound algorithm
The downward branching and delimiting algorithm is an unsupervised classification algorithm, and global optimum can be searched when downward monotonicity is met. The classification theory is as follows:
target: assuming that the existing set X {1,2,3,4,5} contains 5 elements, a set X of2 elements needs to be selected from the set2Satisfying the objective function j (x):
downward monotonicity: if there is a set XnWhen is coming into contact withIn time, there are always:
J(Xn)≥J(Xm)(9)
the objective function j (x) is said to satisfy downward monotonicity. If set XnSatisfies the following conditions:
then set XSThe branch is the optimal search direction.
Global optimum: based on the downward monotonicity of the objective function J (X), the algorithm can obtain a global optimal solution X through multiple iterations2。
As shown in fig. 1, the branch-and-bound algorithm is divided into two processes of searching for branches and determining boundaries. The method comprises the following steps:
a) the root node is the original set X ═ {1,2,3,4,5}, and contains 5 elements.
b) Branch search: the set X is n in size and can be divided into n search branches, and each branch represents one element i removed from the set X to form the set X-iI is 1, …, n; as in the first round, the set X has 5 elements and can therefore be divided into 5 branches; the number on a branch represents the element removed from set X, so there are 5 branches.
c) And (3) boundary determination: according to the principle of b), a set X is generated by each branch-iCarry over to the objective function, calculate J (X)-i) Taking the value of (A); find J (X)-i) Set X in which the function value is maximizedS(satisfying the formula (10)). Set X with element 3 removed as in the first rounds1,2,4,5 is the optimal search direction.
d) Will gather XSAnd replacing by X, and calculating whether the number of the elements of the set meets the requirement. If the number of the cells is more than 2, turning to the step b) to execute; if it equals 2, the search process is ended.
Based on a) to d), removing elements 3, 2 and 5 in sequence in each round through three rounds of search; finally, obtaining the global optimal solution X21, 4. The algorithm needs a search (M-N) round in all, and the total computation complexity is not high.
2) Down branch-and-bound algorithm based on semi-orthogonality user selection
If J (X)n) The downward monotony is satisfied, and the global optimal solution can be found according to the branch-and-bound algorithm principle. In [9 ]]When the served user fixes, only the antenna selection is carried out; the maximum MSV of the channel matrix H is J (A) lambdamin(H(A,:)) Satisfying downward monotony [9,12 ]]A global optimal solution can be obtained.
In the present invention, when the number of users is greater than the number of AFEs (k)>N), antenna and user selection may need to be performed simultaneously, where J (a, U) ═ λmin(H(A,U)) Downward monotony is not completely satisfied, so that a globally optimal solution cannot be obtained.
Based on the analysis, the LMSV-JASUS algorithm of the invention provides a downward branch-and-bound algorithm for realizing JASUS by using the principle of searching local maximum MSV, and the algorithm adopts three steps of antenna subset branching, semi-orthogonal user selection and search direction determination to select the antenna. To select the most appropriate N users from the k users, the present invention utilizes [13 ]]The user half with the best semi-orthogonality and the maximum amplitude after the orthogonality is provided in the methodThe orthogonal selection (SUS) algorithm. Therefore, each node in fig. 1 will first select the most suitable user set U by using SUS algorithm, and then solve the antenna branches based on the currently served user set UDetermining an optimal search directionThe single antenna m that has the greatest impact on system performance is removed. Through (M-N) iterations, the locally optimal set A, U under this condition can be obtained.
1.2.2 local iteration optimization algorithm
In general, the antenna and user set A, U solved by the 1.2.1 algorithm may be trapped in local optimum rather than global optimum, and the local optimum solution has great volatility. In order to reduce the volatility of the local optimal solution, the local iterative optimization algorithm designed based on the [1] can jump out of the current local optimal solution to find the local optimal solution with better performance, and the possibility of obtaining the global optimal solution is increased. The specific idea is shown in fig. 2:
assuming that a two-dimensional planar space exists, each point on the plane is assembled by an antenna and a user (A)i,Uj) To representThe goal is to find the optimal point to maximize the sum rate of the system.
a) The locally optimal antenna and user set A, U is obtained according to the 1.2.1 downward branch-and-bound algorithm and is set as the initial point P (a1, U1).
b) A fixed antenna set A1, and a user set U2 determined by searching the antenna set by using an SUS algorithm; the set (a1, U2) constitutes point q. And if the sum rate of the system obtained by calculation at the point q is greater than the sum rate at the point p, updating the optimal solution (A, U) to be (A1, U2).
c) And (4) finding an optimal antenna set A2 by using a fixed user set U2 and a DBAB algorithm to form a point R. If the system sum rate at the point R is greater than the system sum rate at the point q, the optimal solution is updated to (a, U) — (a2, U2).
d) Repeating steps c) and d) until the system and rate no longer increase. The solution sets (a, U) at this time are the final output antenna set and user set.
Second, concrete implementation steps of each algorithm
In section 1.2, the invention analyzes the structure composition and the implementation principle based on LMSV-JASUS algorithm in detail. The method mainly comprises a downward branch-and-bound algorithm, a semi-orthogonal user selection algorithm and a local iteration optimization algorithm. The specific implementation steps of each algorithm are as follows.
2.1 Down Branch-and-bound Algorithm (DBAB)
The downward branch-and-bound algorithm of the invention is composed of three steps of antenna subset branching, semi-orthogonal user selection and search direction determination, and according to 1.2.1 subsection analysis, the algorithm can obtain a local optimal antenna set A and a user set U. The specific step flow is shown in fig. 3:
a) a base station acquires a channel matrix H, and acquires the number N of AFE modules, the number M of antennas and the number k of users of a system; initializing a set A of antennas to be selected and the round number t of search circulation:
A＝{1,…,M} (11)
t＝1 (12)
b) for any antenna element i ∈ A, the set A is generated after the antenna i is removed from the antenna set A-iAnd obtaining the current channel matrix H based on the antenna set-i；
c) Invoking a semi-orthogonal user selection (SUS) algorithm (2.2 detailed analysis) to deliver a corresponding channel matrix H-iAnd the number N of users which can be served once generates a corresponding user set U-i；
d) According to A-i、U-iCalculating minimum singular values of corresponding channel matrixFinding out antenna set and user set A with maximum minimum singular value-i、U-iIt indicates that:
A←{i∈A,i≠m} (14)
U＝U-m (15)
e) repeating b) -d) if | A | > N, t ← t + 1); if | a | ═ N, the iterative process is stopped, and the locally optimal antenna set and user set are output A, U.
2.2 semi-orthogonal user selection (SUS) [8]
The semi-orthogonal user selection algorithm is to select the N users U with the best orthogonality for service under the condition that the antenna set A is fixed, and the algorithm is completed through N rounds of search. And each round of selecting one user with the best orthogonality with the selected user set from the user set to be selected to join the served user set until the served user set comprises N elements. The input parameter is CSI matrix H ═ H1,…,hk]And the number N of users that can be served simultaneously. The method comprises the following implementation steps:
a) initializing parameters:
according to the CSI information, the total number of users in the cell is k. Initializing a candidate set of users T1And ith selected user:
T1＝{1,…,k} (16)
i＝1 (17)
the user set U of the selected service is an empty set:
b) for each user k ∈ TiBased on the channel vector hkCalculate it and expand space { g(1),…,g(i-1)The quadrature component g ofk：
When i is 1, gk＝hk. Wherein, the orthogonal vector base g(j)For the selected user j-1, …, the effective quadrature component of (i-1).
c) Finding the ith best served user pi (i) (the symbol refers to the ith round from the candidate user set TiNumber of best served user selected from):
U←U∪π(i) (21)
g(i)＝gπ(i) (22)
d) if | U |<N, i ← i +1, updating the antenna set T to be selectedi+1Comprises the following steps:
Ti+1＝{k∈Ti,k≠π(i)} (23)
repeating steps b) to d); otherwise, go to e);
e) returning a selected set of users U of spatial size N.
2.3 local iterative optimization solution
A set of locally optimal solutions (a, U) can be obtained by JASUS based on user semi-orthogonality constructed by 2.1 and 2.2. The flow of the main steps of the local iterative optimization algorithm performed on the basis is shown in fig. 4:
f) the locally optimal antenna and user set A, U is obtained according to the 2.1 downward branch-and-bound algorithm and set as the initial point (a, U).
g) And saving the current optimal antenna and user set (A _ t, U _ t) ═ A, U.
h) In the ith round (i is 1,2, … is the number of iteration rounds), an antenna set A is fixed, and an optimal user set U is solved by utilizing an SUS algorithmi. If point (A, U) on the plane at this timei) Let the system rate R (A, U)i)>If R (A, U) is satisfied, updating the user set U ═ UiThe sum rate of the system R (a, U) ═ R (a, U)i) (ii) a Otherwise, U and R (A, U) are not updated.
i) A fixed user set U, and a current optimal antenna set A can be solved by utilizing a downward branch and bound algorithm (containing no SUS)i. If the point (A) on the plane at this timeiU) let the system rate R (A)i,U)>R (A, U), updating the antenna set A ═ AiThe sum rate of the system R (a, U) ═ R (a)iU); otherwise, the target solutions A and R (A, U) are not updated.
j) And comparing whether the optimal solution (A _ t, U _ t) is the same as the optimal solution (A, U) updated after iteration. If not, c) to e) are executed again; if so, the iterative process is stopped and method k) is performed.
k) And obtaining the optimal solution (A, U) of the algorithm, and solving the sum rate R of the system by using the formulas (4) and (5).
Third, performance analysis
3.1 evaluation of numerical results
In this section, the system performances of the LMSV-JASUS algorithm proposed by the present invention are compared with algorithms such as JASUS [8], TCB-SUS [1], exhaustion method (BFS), etc., to analyze the merits of various methods. In a simulation experiment, due to the fact that the calculation complexity of the exhaustive method is too high, when the performance of the exhaustive method is compared, the parameter setting is small.
Fig. 5 is a graph of average rate versus SNR for different joint antenna selection and user scheduling algorithms. Because the wireless channel is a random process, the rate and the standard deviation of the system are taken as measurement indexes in the test; and the parameters are simplified because of the high complexity of the exhaustive approach. Assuming that in a single cell of a cellular system, a base station deploys 10 antennas and 5 AFE modules, there are 10 users to be served. Due to the limited number of AFEs, only a maximum of 5 users can be served at a time in upstream communication. The base station selects a maximum of five antennas to serve 5 users simultaneously at a time. Assuming the system ergodicity, the mean of 50 rates is solved herein as the expectation of the system rate. When the SNR of the system is gradually increased from 0dB to 30dB, the LMSV-JASUS algorithm has better rate expectation than the existing JASUS and TCB-SUS, and the system and the rate solved by the LMSV-JASUS algorithm in the patent approach the optimal value of BFS.
Fig. 6 is a graph comparing the standard deviation of the mean sum rate versus SNR for different joint antenna selection and user scheduling algorithms. The main parameters of which are consistent with the arrangement of fig. 5. As the SNR is increased, the sum rate standard deviation of the exhaustive method is minimum, the sum rate standard deviation of the LMSV-JASUS algorithm approaches the exhaustive method, the sum rate standard deviation has lower values than the existing JASUS and TCB-SUS, and the sum rate of the system is relatively more stable.
Fig. 7 is a graph of rate versus AFE for different joint antenna selection and user scheduling algorithms. Suppose that 64 antennas are deployed in a base station in a single cell of a cellular system, the cell has 25 users in total, and the SNR at the transmitting end of the user is 10 dB. Because of the large number of antennas and users, the BFS rates are not compared. When the number of the AFEs is gradually increased from 4 to 12, TCB-JASUS relying on element exchange only quickly loses advantages and falls into a locally optimal solution; the rates of the JASUS and LMSV-JASUS algorithms can continue to increase and the algorithm of the present invention performs better than JASUS.
Fig. 8 is a graph of average number of iterations of different antenna selection and user scheduling algorithms as AFE increases. JASUS has no iterative process and is not shown in the figure. It can be seen that as the number of AFEs increases, the number of iterations of TCB-JASUS is about 2, and the number of iterations of the local iterative optimization algorithm proposed in the article is always slightly less than 1 and is relatively constant. This shows that in most cases, the result of the downward branch-and-bound algorithm based on user semi-orthogonality selection can be optimized again through iteration, but a significant improvement in performance can be achieved through one iteration.
Based on the analysis of fig. 5-8, the LMSV-JASUS algorithm achieves a system rate, a standard deviation of the rate that is better than the TCB-JASUS, and closer to the performance of the exhaustive method. The existing downward branch and bound algorithm can cause the JASUS solution to be trapped in local optimization, and the performance of the iterative optimization algorithm only depending on element exchange is easy to lose effect when the selected set is increased. The method provided by the invention not only gives full play to the advantages of the two algorithms, but also does not increase the iteration times. Therefore, the LMSV-JASUS algorithm combining downward branch and delimitation and local iterative optimization based on user semi-orthogonality selection is very significant.
3.2 complexity analysis
The computational complexity of the LMSV-JASUS algorithm provided by the invention is mainly composed of the computational complexity of a downward branch-and-bound algorithm and a local iterative optimization algorithm selected based on the user semiorthogonality.
Based on the 1.2.1 analysis, the calculation complexity based on the downward branch-and-bound algorithm is mainlyThe computation complexity of the objective function J (x) includes the selection algorithm SUS of the orthogonal user set and the complexity of the SVD after determining the user set, namelyThe complexity of the down-branch-and-bound algorithm is
Based onSection 1.2.2 analysis shows that a round of local iterative optimization contains separate SUS and downward branch-and-bound algorithms. The computational complexity at this time is
Therefore, the computational complexity of the LMSV-JASUS algorithm is aboutt is the number of iteration rounds. Since the average iteration number of the actual simulation is lower than one time, the total average calculation complexity is less thanSo its computational complexity is equal to [8]]Compared with the JASUS algorithm in the prior art, the JASUS algorithm is not obviously increased.
Claims (9)
1. A multi-user MIMO uplink antenna selection and user scheduling method is characterized in that: the method comprises the following steps:
s1, a downward branch-and-bound algorithm based on semi-orthogonality user selection: finding a local optimal solution of an antenna set A and a user set U which enable the minimum singular value of a channel matrix to be maximum;
s2, updating an optimal solution based on a local iterative optimization algorithm of antenna and user set element exchange, wherein the method comprises the following steps:
s2a, setting the local optimal antenna and user set A, U obtained by the downward branch-and-bound algorithm according to the step S1 as an initial point P (A1, U1);
s2b, fixing an antenna set A1, and searching a user set U2 by utilizing an SUS algorithm based on the determined antenna set A1; the set (A1, U2) constitutes a point q, and if the sum rate of the system obtained by calculation at the point q is larger than the sum rate at the point p, the optimal solution (A, U) is updated to be (A1, U2);
s2c, fixing a user set U2, and finding an optimal antenna set A2 by using a DBAB algorithm to form a point R; if the system sum rate at the point R is larger than that at the point q, updating the optimal solution to be (A, U) — (A2, U2);
and S3, repeating the step S2 until the antenna set A and the user set U are not changed any more.
2. The multi-user MIMO uplink antenna selection and user scheduling method of claim 1, wherein: in step S1, antenna selection is performed by first branching downward, then selecting a semi-orthogonal user set, and finally determining a boundary.
3. The method for multi-user MIMO uplink antenna selection and user scheduling according to claim 2, wherein the step S1 is as follows: firstly, using SUS algorithm to select the most suitable user set U of each antenna branch, and then solving J (A) of each antenna branch-i,U)＝λmin(H(A-i,U)) Determining the optimal search direction A-iThrough (M-N) iterations, the locally optimal set A, U under the current channel matrix can be obtained.
4. The multi-user MIMO uplink antenna selection and user scheduling method of claim 1 wherein said step S1 is more specifically as follows:
s1a, the base station acquires a channel matrix H, and acquires the number N of AFE modules, the number M of antennas and the number k of users of the system; initializing a set A of antennas to be selected and the round number t of search circulation:
A＝{1,…,M}
t＝1
s1b RenmayAn antenna element i belongs to A, and a set A is generated after the antenna i is removed from the antenna set A-iAnd obtaining the current channel matrix H based on the antenna set-i；
S1c, calling a semi-orthogonal user selection (SUS) algorithm, and transmitting a corresponding channel matrix H-iAnd the number N of users which can be served once generates a corresponding user set U-i；
S1d, according to A-i、U-iCalculating minimum singular values of corresponding channel matrixFinding out antenna set and user set A with maximum minimum singular value-i、U-iIt indicates that:
A←{i∈A,i≠m}
U＝U-m
s1e, if | A | > N, t ← t +1, repeating S1 b-S1 d; if | a | ═ N, the iterative process is stopped, and the locally optimal antenna set and user set are output A, U.
5. The method for multi-user MIMO uplink antenna selection and user scheduling according to claim 1, wherein said step S3 is: and S2d, repeating the steps S2b and S2c until the system and the rate are not increased any more, wherein the solution set at the moment is the final output antenna set and the final output user set.
6. The method of claim 2, wherein the downward branch-and-bound algorithm used in the downward branch step of step S1 comprises three steps of antenna subset branching, semi-orthogonal user selection, and search direction determination.
7. The multi-user MIMO uplink antenna selection and user scheduling method of claim 6, wherein: the antenna subset branch comprises the following steps:
a) a base station acquires a channel matrix H, and acquires the number N of AFE modules, the number M of antennas and the number k of users of a system; initializing a set A of antennas to be selected and the round number t of search circulation:
A＝{1,…,M}
t＝1
b) for any antenna element i ∈ A, the set A is generated after the antenna i is removed from the antenna set A-iAnd obtaining the current channel matrix H based on the antenna set-i；
c) Invoking a semi-orthogonal user selection (SUS) algorithm to transfer a corresponding channel matrix H-iAnd the number N of users which can be served once generates a corresponding user set U-i；
d) According to A-i、U-iCalculating minimum singular values of corresponding channel matrixFinding out antenna set and user set A with maximum minimum singular value-i、U-iIt indicates that:
A←{i∈A,i≠m}
U＝U-m
repeating b) -d) if | A | > N, t ← t + 1); if | a | ═ N, the iterative process is stopped, and the locally optimal antenna set and user set are output A, U.
8. The multi-user MIMO uplink antenna selection and user scheduling method of claim 6,
characterized in that the semi-orthogonal user selection comprises:
initializing parameters: initializing a user set T to be selected according to the CSI information and the total number of users in the cell as K1And the ith selected user:
T1＝{1,…,K}
i＝1
the user set U of the selected service is an empty set:
for each user k ∈ TiBased on the channel vector hkCalculate it and expand space { g(1),…,g(i-1)The quadrature component g ofk：
When i is 1, gk＝hkWherein the orthogonal vector base g(j)The effective quadrature component for the selected user j-1, …, (i-1);
finding the ith best served user pi (i), wherein the symbol pi (i) refers to the ith round from the candidate user set TiNumber of the served user with the best conditions selected in (1):
U←U∪π(i)
g(i)＝gπ(i)
if | U |<N, i ← i +1, updating the antenna set T to be selectedi+1Comprises the following steps:
Ti+1＝{k∈Ti,k≠π(i)}
returning a selected set of users U of spatial size N.
9. A multi-user MIMO uplink antenna selection and user scheduling method is characterized by comprising the following steps:
a) obtaining a local optimal antenna and user set A, U according to a downward branch-and-bound algorithm, and setting the local optimal antenna and user set as an initial point (A, U);
b) saving the current optimal antenna and user set (A _ t, U _ t) ═ A, U;
c) fixing an antenna set A in the ith round, and solving an optimal user set U by utilizing an SUS algorithmiI is 1,2, … is iteration round number; if point (A, U) on the plane at this timei) Let the system rate R (A, U)i)>If R (A, U) is satisfied, updating the user set U ═ UiThe sum rate of the system R (a, U) ═ R (a, U)i) (ii) a Otherwise, not updating U and R (A, U);
d) fixing the user set U updated in the step c), and solving the current locally optimal antenna set A by utilizing a downward branch-and-bound algorithmiIf the point (A) on the plane is presentiU) let the system rate R (A)i,U)>R (A, U), updating the antenna set A ═ AiThe sum rate of the system R (a, U) ═ R (a)iU); otherwise, the target solution A and R (A, U) are not updated;
e) comparing whether the optimal solution (A _ t, U _ t) is the same as the optimal solution (A, U) updated after iteration; if not, c) to e) are executed again; if the antenna groups are the same, stopping the iteration process, and outputting the final antenna group A and the user group U.
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