A method and system for calculating optimal antenna spacing in a MIMO system

Abstract

The present invention discloses a method and system for calculating the optimal antenna spacing in a MIMO system. The method comprises the following steps: establishing a relationship between a channel matrix, an antenna vector matrix, and a multipath cluster environment matrix under a random geometric channel model; establishing a relationship between a transmitting antenna vector matrix, a departure angle, and a transmitting antenna spacing; establishing a relationship between a receiving antenna vector matrix, an arrival angle, and a receiving antenna spacing; in the MIMO system, comprehensively considering the condition number of the channel matrix and the sum of squares of the matrix's singular values as optimization targets, setting the case of omnidirectional antennas, calculating and solving the optimal antenna spacing to obtain the best MIMO channel; dividing the problem into three cases: the number of transmitting antennas is equal to the number of environmental clusters, the number of transmitting antennas is greater than the number of environmental clusters, and the number of transmitting antennas is less than the number of environmental clusters, and solving the three cases to obtain the optimal antenna spacing corresponding to the three cases; quantitatively analyzing the influence of the antenna vector matrix on the channel matrix condition number, and providing the optimal antenna spacing.

Description

Technical Field

[0001] The present invention belongs to the field of performance research of MIMO systems in wireless communications, and particularly relates to a method and system for calculating optimal antenna spacing in a MIMO system. Background Art

[0002] With the advancement of wireless communication technology, research on the impact of antennas on communication system performance has received increasing attention. In multi-antenna systems, the question of how to best arrange antennas for optimal channel adaptation is a key research topic. Existing techniques often use simulations to compare the performance of different antenna arrays, while some more complex iterative optimization algorithms are used to achieve antenna sparseness.

[0003] The condition number of the channel matrix of a multiple-input, multiple-output (MIMO) system is a key parameter for evaluating MIMO system performance. The MIMO channel matrix is determined by both the environment cluster and the antenna vector matrix. Given a known environment cluster, the present invention addresses the question of what antenna vector matrix can maintain or even improve the condition number of the environment cluster matrix. Summary of the Invention

[0004] In order to obtain the optimal antenna spacing, the present invention provides a method for calculating the optimal antenna spacing in a MIMO system, obtaining the optimal antenna vector matrix to maintain or even improve the condition number of the environment cluster matrix, and then obtaining the MIMO channel matrix with the optimal condition number.

[0005] To achieve the above object, the present invention adopts a technical solution: a method for calculating the optimal antenna spacing in a MIMO system, comprising the following steps:

[0006] S1, assume that both the receiving and transmitting antennas are omnidirectional antennas. Under the random geometry channel model, establish the relationship between the channel matrix, antenna vector matrix, and multipath cluster environment matrix; establish the relationship between the transmitting antenna vector matrix, departure angle, and transmitting antenna spacing; establish the relationship between the receiving antenna vector matrix, arrival angle, and receiving antenna spacing; the communication environment is a downlink with one transmitter and one receiver, the number of antennas at the transmitter is Tx, and the number of antennas at the receiver is Rx, forming an Rx*Tx MIMO channel; the channel environment is an NLoS multipath cluster environment under random geometry description, and the number of multipaths is L;

[0007] S2, in MIMO systems, takes the condition number of the channel matrix and the sum of the squares of the matrix's singular values as optimization objectives;

[0008] S3, based on the optimization goal described in S2, sets the antenna to an omnidirectional antenna, calculates and solves the optimal antenna spacing, and obtains the best MIMO channel;

[0009] S4, dividing the optimal antenna spacing problem calculated and solved in S3 into three cases: the number of transmitting antennas is equal to the number of environmental clusters, the number of transmitting antennas is greater than the number of environmental clusters, and the number of transmitting antennas is less than the number of environmental clusters, and obtaining the optimal antenna spacing corresponding to the three cases.

[0010] In S1, under the random geometric channel model, the transmitting antenna vector matrix FT is established. L×Tx , receiving antenna vector matrix FR Rx×L and the multipath environment cluster matrix With the channel matrix H Rx×Tx The expression of is shown in formula (1a); the expression of the receiving end antenna vector matrix and the arrival angle is shown in formula (1b); the expression of the transmitting end antenna vector matrix and the departure angle is shown in formula (1c);

[0011]

[0012] α l =κd r *cos(AoA l )cos(ZoA l ), (1b)

[0013] β l =κd t *cos(AoD l )cos(ZoD l ), (1c)

[0014] Among them, α l represents the phase difference caused by the incident light of the lth cluster on two adjacent receiving antennas, β l AoA represents the phase difference caused by the emission of the lth cluster on two adjacent transmitting antennas; l and ZoA l represents the arrival foot (azimuth and elevation angle) of the lth cluster at the receiving antenna side, AoD l and ZoD l represents the departure angle (azimuth and elevation) of the lth cluster on the transmitting antenna side; κ is the wave number of electromagnetic waves propagating in the air; d r Represents the distance between adjacent receiving antennas, d t represents the distance between adjacent transmitting antennas; a1,…,a L represents the environmental gain of the L-bar cluster.

[0015] S2, in MIMO systems, when the condition number of the channel matrix and the sum of the squares of the matrix singular values are used as optimization targets: the problem is transformed into solving the condition number and energy of the product matrix H′ of the transmitter vector matrix and the environment cluster matrix and the matrix and the matrix FT L×TxThe relationship is as shown in Expression (2):

[0016]

[0017] where a i (i = 1, …, L) represents the gains on L clusters, arranged in descending order of modulus value. The smaller the index i, the larger the modulus value.

[0018] In S4, the number of transmit antennas is equal to the number of environmental clusters, i.e., L = Tx. At this time, the transmit antenna vector matrix FT L×Tx is a square matrix;

[0019] H′ L×Tx The sum of the squares of the singular values of is obtained from Expression (3):

[0020]

[0021] where represents the L singular values of H′ L×Tx and are arranged in descending order. The smaller the index i, the larger;

[0022] H′ L×Tx The condition number cond(H′ L×Tx ) satisfies Expression (4)

[0023]

[0024] where is the largest one among the singular values of H′ L×Tx , is the smallest one among the singular values of H′ L×Tx .

[0025] The condition for the equality in Equation (4) is that the rows of the matrix FT L×Tx are orthogonal (the columns are orthogonal). The antenna spacing expression that satisfies row orthogonality is Equation (5)

[0026]

[0027]

[0028] where k l represents any integer, and d t,opt represents the optimal antenna spacing.

[0029] In S4, the number of transmit antennas is greater than the number of environmental clusters, i.e., L < Tx. At this time, the transmit antenna vector matrix FT L×Tx is a matrix with the number of rows less than the number of columns,

[0030] H′L×Tx The sum of the squares of the singular values of is the same as when the number of transmitting antennas and the number of environmental clusters are equal, and is obtained from expression (3):

[0031] H′ L×Tx The condition number satisfies expression (4). The condition for the equality in (4) is that the matrix FT L×Tx The rows are orthogonal, and the antenna spacing expression that satisfies the orthogonality of the rows is (5).

[0032] In S4, the number of transmitting antennas is less than the number of environmental clusters, that is, L>Tx. At this time, the transmitting antenna vector matrix FT L×Tx is a matrix with more rows than columns,

[0033] H′ L×Tx The sum of the squares of the singular values of is the same as when the number of transmitting antennas and the number of environmental clusters are equal, and is obtained from expression (3):

[0034] Taking L = 3, Tx = 2 as an example, the expression of the transmit antenna vector matrix is (6), H′ L×Tx There are two cases for the optimal value of the condition number, a1 2 >a2 2 +a3 2 and a1 2 ≤a2 2 +a3 2 , the expression is (7). a1 2 >a2 2 +a3 2 The derivation process of the singular values in this case is expressed as (8).

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] The optimal antenna spacing needs to meet the following conditions (9):

[0041]

[0042] β l =κd t *cos(AoD l )cos(ZoD l ),l=1,2,3,…,L (9b)

[0043] The sum of squares of the singular values of the channel matrix is expressed as (3), which is only related to the number of transmitting antennas and the channel cluster gain. The optimal antenna spacing is obtained by the optimal condition number of the channel matrix.

[0044] Based on the concept of the method, the present invention also provides a calculation system for the optimal antenna spacing in a MIMO system, including a model construction module, an optimization target construction module and a calculation module; the model construction module assumes that the receiving end antenna and the transmitting end antenna are both omnidirectional antennas, and under a random geometric channel model, establishes a relationship between the channel matrix and the antenna vector matrix and the multipath cluster environment matrix; establishes a relationship between the transmitting end antenna vector matrix and the departure angle and the transmitting antenna spacing; establishes a relationship between the receiving end antenna vector matrix and the arrival angle and the receiving antenna spacing; the communication environment is a downlink of one transmitting end and one receiving end, the number of antennas at the transmitting end is Tx, the number of antennas at the receiving end is Rx, and a MIMO channel of Rx*Tx is formed; the channel environment is an NLoS multipath cluster environment under a random geometric description, and the number of multipaths is L;

[0045] The optimization target building module takes the condition number of the channel matrix and the sum of the squares of the matrix's singular values as optimization targets in the MIMO system;

[0046] The calculation module is used to set the antenna as an omnidirectional antenna based on the optimization target, calculate and solve the optimal antenna spacing, and obtain the best MIMO channel; divide the problem of calculating and solving the optimal antenna spacing into three cases: the number of transmitting antennas is equal to the number of environmental clusters, the number of transmitting antennas is greater than the number of environmental clusters, and the number of transmitting antennas is less than the number of environmental clusters, and obtain the optimal antenna spacing corresponding to the three cases.

[0047] In addition, the present invention also provides a computer device, including a processor and a memory, the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and when the processor executes the computer executable program, it can implement the method for calculating the optimal antenna spacing in the MIMO system described in this article.

[0048] At the same time, a computer-readable storage medium may be provided, in which a computer program is stored. When the computer program is executed by a processor, the method for calculating the optimal antenna spacing in the MIMO system described in this article can be implemented.

[0049] Compared with the prior art, the present invention has at least the following beneficial effects: combining quantitative analysis of the influence of the antenna vector matrix on the channel matrix condition number, a simple method is used to obtain a closed-form solution for the optimal antenna spacing, which provides a reference for antenna layout and array arrangement, gives the optimal antenna spacing, and provides guidance for antenna array arrangement in multiple-input and multiple-output communication systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of the transmitting antenna arrangement and departure angle.

[0051] Figure 2 Schematic diagram of the channel condition number and optimal antenna vector for Example 1 (2 clusters and 2 transmitting antennas).

[0052] Figure 3 Schematic diagram of the channel condition number and optimal antenna vector for Example 2 (3 clusters and 3 transmitting antennas).

[0053] Figure 4 Schematic diagram of the channel condition number and optimal antenna vector for Example 3 (2 clusters and 3 transmitting antennas).

[0054] Figure 5 For example 4 (3 clusters and 2 transmit antennas, a1 2 >a2 2 +a3 2 Schematic diagram of the channel condition number and optimal antenna vector in the case of .

[0055] Figure 6 For example 5 (3 clusters and 2 transmit antennas, a1 2 ≤a2 2 +a3 2 Schematic diagram of the channel condition number and optimal antenna vector in the case of . DETAILED DESCRIPTION

[0056] The present invention provides a method for calculating the optimal antenna spacing in a MIMO system, comprising the following steps:

[0057] Step 1, system modeling: the communication environment is a downlink of a transmitter (usually a base station) and a receiver (usually a user); the number of antennas at the transmitter is Tx, and the number of antennas at the receiver is Rx, forming an Rx*Tx MIMO channel; the channel environment is an NLoS multipath cluster environment under random geometry description, and the number of multipaths is L; it is assumed that both the receiver antenna and the transmitter antenna are omnidirectional antennas; under the random geometry channel model, the relationship between the channel matrix and the antenna vector matrix and the multipath cluster environment matrix is established; the relationship between the transmitter antenna vector matrix and the departure angle and the transmitter antenna spacing is established; the relationship between the receiver antenna vector matrix and the arrival angle and the receiver antenna spacing is established; since the effects of the transmitter and receiver antenna vector matrices on the channel matrix are similar, the calculation method of the optimal antenna spacing of the receiver antenna and the transmitter antenna is similar; the present invention is set to calculate the optimal antenna spacing of the transmitter antenna;

[0058] Step 2: Establish the optimization goal: In a MIMO system, the condition number and energy of the channel matrix (the sum of the squares of the matrix's singular values) are comprehensively considered as the optimization goal. The smaller the condition number, the greater the energy, and the better the channel.

[0059] Step 3: Establish optimization variables: Calculate the optimal antenna spacing for omnidirectional antennas to obtain the best MIMO channel.

[0060] Step 4: Discuss the problem by case: the number of transmitting antennas is equal to the number of environmental clusters, the number of transmitting antennas is greater than the number of environmental clusters, and the number of transmitting antennas is less than the number of environmental clusters. This ensures that the problem can be solved in an orderly and efficient manner.

[0061] Step 5: Solve for Case 1: Find the optimal antenna spacing when the number of transmitting antennas is equal to the number of environmental clusters. The optimal antenna spacing is the one where the rows of the antenna vector matrix are orthogonal.

[0062] Step 6: Solve for Case 2: Find the optimal antenna spacing when the number of transmitting antennas is greater than the number of environmental clusters. The optimal antenna spacing is the one where the antenna vector matrix rows are orthogonal.

[0063] Step 7: Solve for Case 3: Determine the optimal antenna spacing when the number of transmitting antennas is less than the number of environmental clusters. In this case, the optimal antenna spacing is related not only to the departure angle but also to the energy distribution of the environmental clusters.

[0064] Step 8: Draw conclusions: Based on the above three situations, get the overall conclusion.

[0065] In step 1, under the random geometric channel model, the transmitting end antenna vector matrix FT is established. L×Tx , receiving end antenna vector matrix FR Rx×L and the multipath environment cluster matrix With the channel matrix H Rx×Tx The expression of is shown in formula (1a); the expression of the receiving end antenna vector matrix and the arrival angle is shown in formula (1b); the expression of the transmitting end antenna vector matrix and the departure angle is shown in formula (1c); the departure angle is shown in formula (1c). Figure 1 As shown;

[0066]

[0067] α l =κd r *cos(AoA l )cos(ZoA l ), (1b)

[0068] β l =κd t *cos(AoD l )cos(ZoD l ), (1c)

[0069] Among them, αl represents the phase difference caused by the incident light of the lth cluster on two adjacent receiving antennas, β l AoA represents the phase difference caused by the emission of the lth cluster on two adjacent transmitting antennas; l and ZoA l represents the arrival foot (azimuth and elevation angle) of the lth cluster at the receiving antenna side, AoD l and ZoD l represents the departure angle (azimuth and elevation) of the lth cluster on the transmitting antenna side; κ is the wave number of electromagnetic waves propagating in the air; d r Represents the distance between adjacent receiving antennas, d t represents the distance between adjacent transmitting antennas; a1,…,a L represents the environmental gain of the L-bar cluster.

[0070] In step 2, it can be clearly concluded from expression (1a) that the influence of the transmitting antenna vector matrix and the receiving antenna vector matrix on the channel matrix is similar, so the problem is transformed into studying the condition number and energy of the product matrix H′ of the transmitting antenna vector matrix and the environment cluster matrix and the matrix and matrix FT L×Tx The relationship is shown in expression (2);

[0071]

[0072] Among them, a i (i=1,…,L) represents the gains on L clusters, which are arranged in descending order of modulus value. The smaller the index i, the larger the modulus value.

[0073] In step 5, case 1 is the case where the number of transmitting antennas is equal to the number of environment clusters, that is, L=Tx. At this time, the transmitting antenna vector matrix FT L×Tx It is a square array.

[0074] H′ L×Tx The sum of the squares of the singular values of can be obtained by expression (3):

[0075]

[0076] in, Represents H′ L×Tx The L singular values of , and arranged in order from large to small, the smaller the index i, The bigger.

[0077] H′ L×Tx The condition number cond(H′ L×Tx ) satisfies expression (4)

[0078]

[0079] Among them, is the largest one of the L×Tx singular values of H′, is the smallest one of the L×Tx singular values of H′.

[0080] The condition for the equality in Equation (4) is that the rows (columns) of the matrix FT L×Tx are orthogonal to each other.

[0081] The expression for the antenna spacing that satisfies row orthogonality is Equation (5)

[0082]

[0083]

[0084] where k l is an arbitrary integer, and d t,opt is the optimal antenna spacing.

[0085] In Step 6, Case 2 is the case where "the number of transmit antennas is greater than the number of environmental clusters", that is, L < Tx. At this time, the transmit antenna vector matrix FT L×Tx is a matrix with the number of rows less than the number of columns.

[0086] The sum of the squares of the singular values of H′ L×Tx is the same as that in Case 1 and can be obtained from Equation (3).

[0087] The condition number of H′ L×Tx satisfies Equation (4). The condition for the equality in Equation (4) is that the rows of the matrix FT L×Tx are orthogonal to each other. The expression for the antenna spacing that satisfies row orthogonality is Equation (5). That is, the expressions for solving the optimal antenna spacing in Case 2 and Case 1 are the same. However, since Tx > L in Case 2, the solution space of Case 2 is larger than that of Case 1.

[0088] In Step 7, Case 3 is the case where "the number of transmit antennas is less than the number of environmental clusters", that is, L > Tx. At this time, the transmit antenna vector matrix FT L×Tx is a matrix with the number of rows greater than the number of columns.

[0089] The sum of the squares of the singular values of H′ L×Tx is the same as that in Case 1 and can be obtained from Equation (3).

[0090] The condition number of H′ L×Tx is different from that in Case 1 and Case 2. To make the expression clearer, taking L = 3 and Tx = 2 as an example, the expression for the optimal condition number is Equation (7).

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] The condition that needs to be satisfied for the optimal antenna spacing can be rewritten as (9):

[0097]

[0098] β l =κd t *cos(AoD l )cos(ZoD l ),l=1,2,3,…,L (9b)

[0099] In step 8, the summary is as follows:

[0100] (1) The sum of squares of the singular values of the channel matrix is expressed as (3), which is only related to the number of transmit antennas and the channel cluster gain, and has nothing to do with the antenna spacing. Therefore, the optimal antenna spacing is obtained from the optimal condition number of the channel matrix.

[0101] (2) The condition number of the channel matrix satisfies expression (4) in cases 1 and 2. The optimal condition number is the case where the equality of expression (4) holds, which corresponds to the optimal antenna spacing, given by expression (5).

[0102] (3) The optimal condition number of the channel matrix satisfies expression (7) in case 3, and the optimal antenna spacing satisfies expression (9).

[0103] Example 1: When the number of transmitting antennas is 2 and the number of environment clusters is 2, the channel matrix H is expressed as (10)

[0104]

[0105] At this time, the conditions satisfied by the transmitting antenna vector are shown as follows: Figure 2 Right (two vectors are evenly distributed on the unit circle), the relationship between the derivative of the condition number and the antenna vector is Figure 2 Left.

[0106] Example 2: When the number of transmitting antennas is 3 and the number of environment clusters is 3, the channel matrix H is expressed as (11)

[0107]

[0108] At this time, the conditions satisfied by the transmitting antenna vector are shown as follows: Figure 3Right (3 vectors are evenly distributed on the unit circle), the relationship between the derivative of the condition number and the antenna vector is Figure 3 Left.

[0109] Example 3: When the number of transmitting antennas is 3 and the number of environment clusters is 2, the channel matrix H is expressed as (12)

[0110]

[0111] At this time, the conditions satisfied by the transmitting antenna vector are shown as follows: Figure 4 Any two of the right ones are fine, and the relationship between the derivative of the condition number and the antenna vector is Figure 4 Left.

[0112] Example 4: When the number of transmitting antennas is 2 and the number of environment clusters is 3, the channel matrix H is expressed as (13)

[0113]

[0114] At this time, the conditions satisfied by the transmitting antenna vector are shown as follows: Figure 5 Right, the relationship between the derivative of the condition number and the antenna vector is Figure 5 Left.

[0115] Example 5: When the number of transmitting antennas is 2 and the number of environment clusters is 3, the channel matrix H is expressed as (14)

[0116]

[0117] At this time, the conditions satisfied by the transmitting antenna vector are shown in the right side of Figure (6). The relationship between the derivative of the condition number and the antenna vector is: Figure 6 Left.

[0118] The present invention also provides a calculation system for optimal antenna spacing in a MIMO system, comprising a model construction module, an optimization target construction module, and a calculation module; the model construction module assumes that both the receiving end antenna and the transmitting end antenna are omnidirectional antennas, and under a random geometric channel model, establishes a relationship between a channel matrix, an antenna vector matrix, and a multipath cluster environment matrix; establishes a relationship between the transmitting end antenna vector matrix and the departure angle and the transmitting antenna spacing; establishes a relationship between the receiving end antenna vector matrix and the arrival angle and the receiving antenna spacing; the communication environment is a downlink of one transmitting end and one receiving end, the number of antennas at the transmitting end is Tx, the number of antennas at the receiving end is Rx, and a MIMO channel of Rx*Tx is formed; the channel environment is an NLoS multipath cluster environment under a random geometric description, and the number of multipaths is L;

[0119] The optimization target building module takes the condition number of the channel matrix and the sum of the squares of the matrix's singular values as optimization targets in the MIMO system;

[0120] The calculation module is used to set the antenna as an omnidirectional antenna based on the optimization target, calculate and solve the optimal antenna spacing, and obtain the best MIMO channel; divide the problem of calculating and solving the optimal antenna spacing into three cases: the number of transmitting antennas is equal to the number of environmental clusters, the number of transmitting antennas is greater than the number of environmental clusters, and the number of transmitting antennas is less than the number of environmental clusters, and obtain the optimal antenna spacing corresponding to the three cases.

[0121] In addition, the present invention can also provide a computer device, including a processor and a memory, the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and when the processor executes part or all of the computer executable program, it can implement the method for calculating the optimal antenna spacing in the MIMO system described in the present invention.

[0122] On the other hand, the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can implement the method for calculating the optimal antenna spacing in the MIMO system described in the present invention.

[0123] The computer device may be a laptop computer, a desktop computer or a workstation.

[0124] The processor may be a central processing unit (CPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), or an off-the-shelf field programmable gate array (FPGA).

[0125] The memory of the present invention may be an internal storage unit of a laptop computer, desktop computer or workstation, such as a memory or a hard disk; or an external storage unit, such as a mobile hard disk or a flash memory card.

[0126] Computer-readable storage media may include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. Computer-readable storage media may include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSD) or optical disks, etc. Among them, random access memory may include resistance random access memory (ReRAM) and dynamic random access memory (DRAM).

[0127] On the other hand, the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can implement the method for calculating the optimal antenna spacing in the MIMO system described in the present invention.

[0128] The computer device may be a laptop computer, a desktop computer or a workstation.

[0129] The processor may be a central processing unit (CPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), or an off-the-shelf field programmable gate array (FPGA).

[0130] The memory of the present invention may be an internal storage unit of a laptop computer, desktop computer or workstation, such as a memory or a hard disk; or an external storage unit, such as a mobile hard disk or a flash memory card.

[0131] Computer-readable storage media may include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. Computer-readable storage media may include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSD) or optical disks, etc. Among them, random access memory may include resistance random access memory (ReRAM) and dynamic random access memory (DRAM).

Claims

1. A method for calculating the optimal antenna spacing in a MIMO system, characterized in that: The following steps are involved: S1, assume that both the receiving and transmitting antennas are omnidirectional antennas. Under the random geometry channel model, establish the relationship between the channel matrix, antenna vector matrix, and multipath cluster environment matrix; establish the relationship between the transmitting antenna vector matrix, departure angle, and transmitting antenna spacing; establish the relationship between the receiving antenna vector matrix, arrival angle, and receiving antenna spacing; the communication environment is a downlink with one transmitter and one receiver, the number of antennas at the transmitter is Tx, and the number of antennas at the receiver is Rx, forming an Rx*Tx MIMO channel; the channel environment is an NLoS multipath cluster environment under random geometry description, and the number of multipaths is L; S2, in MIMO systems, takes the condition number of the channel matrix and the sum of the squares of the matrix's singular values as optimization objectives; S3, based on the optimization goal described in S2, sets the antenna to an omnidirectional antenna, calculates and solves the optimal antenna spacing, and obtains the best MIMO channel; S4, dividing the optimal antenna spacing problem calculated and solved in S3 into three cases: the number of transmitting antennas is equal to the number of environmental clusters, the number of transmitting antennas is greater than the number of environmental clusters, and the number of transmitting antennas is less than the number of environmental clusters, and obtaining the optimal antenna spacing corresponding to the three cases; In S4, the number of transmitting antennas is equal to the number of environmental clusters, that is, L = Tx. At this time, the transmitting antenna vector matrix FT L×Tx For the square array; H′ L×Tx The sum of the squares of the singular values of is given by expression (3): in, Represents H′ L×Tx The L singular values of , and arranged in order from large to small, the smaller the index i, The larger the α i represents the phase difference caused by the incident of the i-th cluster on two adjacent receiving antennas; H′ L×Tx The condition number cond(H′ L×Tx ) satisfies expression (4) in, is H′ L×Tx The largest singular value, is H′ L×Tx The smallest singular value; The condition for the equality in formula (4) is that the matrix FT L×Tx The rows are orthogonal, and the antenna spacing expression that satisfies the orthogonality of the rows is (5) Among them, k l represents any integer, d t,opt represents the optimal antenna spacing; β l represents the phase difference caused by the emission of the lth cluster on two adjacent transmitting antennas; β l+1 AOD represents the phase difference caused by the emission of the l+1th cluster on two adjacent transmitting antennas; l+1 and ZoD l+1 AoD represents the departure angle of the l+1th cluster on the transmitting antenna side; l and ZoD l represents the departure angle of the lth cluster on the transmitting antenna side; The number of transmit antennas is greater than the number of environmental clusters, i.e., L < Tx. At this time, the transmit antenna vector matrix FT L×Tx is a matrix with the number of rows less than the number of columns, H′ L×Tx The sum of the squares of the singular values of is the same as when the number of transmitting antennas and the number of environmental clusters are equal, and is obtained from expression (3): H′ L×Tx The condition number satisfies expression (4). The condition for the equality in (4) is that the matrix FT L×Tx Each row is orthogonal, and the antenna spacing expression that satisfies the orthogonality of each row is (5); the number of transmitting antennas is less than the number of environmental clusters, that is, L>Tx, at this time, the transmitting antenna vector matrix FT L×Tx is a matrix with more rows than columns, H′ L×Tx The sum of squares of the singular values of is the same as when the number of transmitting antennas and the number of environmental clusters are equal, and is obtained by expression (3).

2. The method for calculating the optimal antenna spacing in a MIMO system according to claim 1, wherein: In S1, under the random geometric channel model, the transmitting antenna vector matrix FT is established. L×Tx , receiving antenna vector matrix FR Rx×L and the multipath environment cluster matrix With the channel matrix H Rx×Tx The expression of is shown in formula (1a); the expression of the receiving end antenna vector matrix and the arrival angle is shown in formula (1b); the expression of the transmitting end antenna vector matrix and the departure angle is shown in formula (1c); a l =κd r *cos(AoA l )cos(ZoA l ), (1b) b l =κd t *cos(AoD l )cos(ZoD l ), (1c) Among them, α l represents the phase difference caused by the incident light of the lth cluster on two adjacent receiving antennas, β l AoA represents the phase difference caused by the emission of the lth cluster on two adjacent transmitting antennas; l and ZoA l represents the angle of arrival of the lth cluster at the receiving antenna side, AoD l and ZoD l represents the departure angle of the lth cluster on the transmitting antenna side; κ is the wave number of electromagnetic waves propagating in the air; d r Represents the distance between adjacent receiving antennas, d t represents the distance between adjacent transmitting antennas; a1,…,a L represents the environmental gain of the L-bar cluster.

3. The method for calculating the optimal antenna spacing in a MIMO system according to claim 1, wherein: S2, in MIMO systems, when the condition number of the channel matrix and the sum of the squares of the matrix singular values are used as optimization targets: the problem is transformed into solving the condition number and energy of the product matrix H′ of the transmitter vector matrix and the environment cluster matrix and the matrix and the matrix FT L×Tx The relationship is shown in expression (2): Among them, a i (i=1,…,L) represents the gains on L clusters, which are arranged in descending order of modulus value. The smaller the index i, the larger the modulus value.

4. The method for calculating the optimal antenna spacing in a MIMO system according to claim 1, wherein: In S4, taking L=3, Tx=2 as an example, the expression of the transmit antenna vector matrix is (6), H′ L×Tx There are two cases for the optimal value of the condition number, a1 2 >a2 2 +a3 2 and a1 2 ≤a2 2 +a3 2 , the expression is (7); a1 2 >a2 2 +a3 2 The derivation process of the singular values in this case is expressed as (8): The optimal antenna spacing needs to meet the following conditions (9): β l =κd t *cos(AoD l )cos(ZoD l ),l=1,2,3,…,L (9b).

5. The method for calculating the optimal antenna spacing in a MIMO system according to claim 1, wherein: The sum of squares of the singular values of the channel matrix is expressed as (3), which is only related to the number of transmitting antennas and the channel cluster gain. The optimal antenna spacing is obtained by the optimal condition number of the channel matrix.

6. A system for calculating optimal antenna spacing in a MIMO system, characterized in that: It includes a model construction module, an optimization target construction module and a calculation module; the model construction module assumes that the receiving antenna and the transmitting antenna are both omnidirectional antennas, and under the random geometric channel model, establishes the relationship between the channel matrix and the antenna vector matrix and the multipath cluster environment matrix; establishes the relationship between the transmitting antenna vector matrix and the departure angle and the transmitting antenna spacing; establishes the relationship between the receiving antenna vector matrix and the arrival angle and the receiving antenna spacing; the communication environment is a downlink with one transmitter and one receiver, the number of antennas at the transmitter is Tx, and the number of antennas at the receiver is Rx, forming an Rx*Tx MIMO channel; the channel environment is an NLoS multipath cluster environment under random geometric description, and the number of multipaths is L; The optimization target building module takes the condition number of the channel matrix and the sum of the squares of the matrix's singular values as optimization targets in the MIMO system; The calculation module is used to set the antenna as an omnidirectional antenna based on the optimization goal, calculate and solve the optimal antenna spacing, and obtain the best MIMO channel; The problem of calculating and solving the optimal antenna spacing is divided into three cases: the number of transmitting antennas is equal to the number of environmental clusters, the number of transmitting antennas is greater than the number of environmental clusters, and the number of transmitting antennas is less than the number of environmental clusters, and the optimal antenna spacing corresponding to the three cases is obtained; the number of transmitting antennas is equal to the number of environmental clusters, that is, L = Tx. At this time, the transmitting antenna vector matrix FT L×Tx For the square array; H′ L×Tx The sum of the squares of the singular values of is given by expression (3): in, Represents H′ L×Tx The L singular values of , and arranged in order from large to small, the smaller the index i, The larger the α i represents the phase difference caused by the incident of the i-th cluster on two adjacent receiving antennas; H′ L×Tx The condition number cond(H′ L×Tx ) satisfies expression (4) in, is H′ L×Tx The largest singular value, is H′ L×Tx The smallest singular value; The condition for the equality in formula (4) is that the matrix FT L×Tx The rows are orthogonal, and the antenna spacing expression that satisfies the orthogonality of the rows is (5) Among them, k l represents any integer, d t,opt represents the optimal antenna spacing; β l represents the phase difference caused by the emission of the lth cluster on two adjacent transmitting antennas; β l+1 AoD represents the phase difference caused by the emission of the l+1th cluster on two adjacent transmitting antennas; l+1 and ZoD l+1 AoD represents the departure angle of the l+1th cluster on the transmitting antenna side; l and ZoD l represents the departure angle of the lth cluster on the transmitting antenna side; The number of transmit antennas is greater than the number of environmental clusters, that is, L < Tx. At this time, the transmit antenna vector matrix FT L×Tx is a matrix with the number of rows less than the number of columns. H′ L×Tx The sum of the squares of the singular values of is the same as when the number of transmitting antennas and the number of environmental clusters are equal, and is obtained from expression (3): H′ L×Tx The condition number satisfies expression (4). The condition for the equality in (4) is that the matrix FT L×Tx Each row is orthogonal, and the antenna spacing expression that satisfies the orthogonality of each row is (5); the number of transmitting antennas is less than the number of environmental clusters, that is, L>Tx, at this time, the transmitting antenna vector matrix FT L×Tx is a matrix with more rows than columns, H′ L×Tx The sum of squares of the singular values of is the same as when the number of transmitting antennas and the number of environmental clusters are equal, and is obtained by expression (3).

7. A computer device, characterized in that: The invention comprises a processor and a memory, the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and when the processor executes the computer executable program, it can implement the method for calculating the optimal antenna spacing in the MIMO system as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that A computer program is stored in a computer-readable storage medium. When the computer program is executed by a processor, the method for calculating the optimal antenna spacing in the MIMO system according to any one of claims 1 to 5 can be implemented.

Images