Method and system for computing optimal antenna pattern in a frequency selective channel

Abstract

The application discloses a method and system for calculating optimal antenna pattern in a frequency selective channel. The method comprises the following steps: two-dimensional modeling of the antenna pattern in frequency and space; dividing a space region of interest into M*N space regions according to a spherical surface, and the radiation characteristics of the antenna are the same in each space region; establishing the relationship among the antenna pattern matrix, the multipath environment matrix and the channel matrix based on the downlink system of the transmitting end and the receiving end; listing the relationship among the channel capacity, the antenna pattern and the multipath environment in the frequency selective channel; making the antenna pattern with the maximum channel capacity as the optimal antenna pattern, and obtaining an optimization problem by constraining the total power of the transmitting antenna as P; solving the optimization problem to obtain the optimal antenna pattern and determine the power distribution of the transmitting antenna, and giving the optimal antenna directivity in the frequency selective channel; and giving the capacity upper limit that can be reached by the wireless environment in the frequency selective channel.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication, specifically relating to a method and system for calculating the optimal antenna pattern in a frequency-selective channel. Background Technology

[0002] With the development of wireless communication technology, the impact of antennas on communication system performance has received increasing attention, and finding the right antenna directivity to better adapt to the communication channel has become a key research focus. Based on the mathematical modeling of random geometric channels using TR38.961, antenna directivity is a crucial parameter for calculating channel coefficients. Capacity describes the maximum achievable communication rate of a channel. In frequency-selective channels, the channel is often divided into multiple flat-fading channels across various frequency bands, and the sum of the capacities of each band describes the capacity of the frequency-selective channel. In this invention, the antenna directivity corresponding to the maximum capacity is defined as the optimal antenna pattern. Summary of the Invention

[0003] To address the problem of finding the optimal antenna pattern in a frequency-selective channel, this invention provides a method for calculating the optimal antenna pattern in a frequency-selective channel, offering design guidelines for antenna directivity and specifying the channel's capacity limits.

[0004] To achieve the above objectives, the technical solution adopted by this invention is: a method for calculating the optimal antenna pattern in a frequency-selective channel, comprising the following steps:

[0005] S01, perform two-dimensional modeling of the antenna pattern in frequency and space: In the frequency dimension, within the frequency range of interest, the antenna pattern does not change with frequency; in the spatial dimension, the spatial region of interest is divided into spherical regions, that is, theta is divided into M intervals and phi is divided into N intervals, thus forming M×N spatial regions, in which the antenna radiation characteristics are the same.

[0006] S02, System Modeling and Optimization Problem: The communication environment consists of a downlink between the transmitter and receiver, with users distributed across... Within a sector-shaped region; the number of antennas at the transmitting end is Tx, and the number of antennas at the receiving end is Rx, forming an Rx*Tx MIMO channel; the transmitting antennas are pattern-reconfigurable antennas, and the receiving antennas are omnidirectional antennas; the channel environment is a frequency-selective channel, and an NLos multipath environment described by random geometry, with L multipaths; the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix is ​​established; based on the relationship between channel capacity, antenna pattern, and multipath environment under a frequency-selective channel; the antenna pattern that maximizes the channel capacity is the optimal antenna pattern, with the constraint that the total power of the transmitting antenna is P, thus obtaining the optimization problem;

[0007] S03, Solving the optimization problem: Based on the optimization problem described in S2, use auxiliary variables and an alternating optimization algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antenna.

[0008] In S01, theta is divided into M intervals, each interval being 60° / M within the range of -30° to +30°, and phi is divided into N intervals, each interval being 120° / N within the range of -60° to +60°.

[0009] In S02, establishing the relationship between the antenna pattern matrix, multipath environment matrix, and channel matrix includes: under the stochastic geometric channel model, frequency points... Channel matrix on It is expressed as the product of the transmitting antenna pattern matrix and the multipath environment matrix, as shown in expression (1):

[0010] (1a)

[0011] (1b)

[0012] (1c)

[0013] in, ( () indicates frequency point Upper Gain on stripe clusters; Indicates the first The transmitting antenna is at the ... The directionality of the strip cluster in the direction it is located. This indicates the frequency point. Upper The departure azimuth and elevation angles of the stripe cluster; Frequency point wavenumber on; This represents the distance between two adjacent antennas in a uniform receiving linear array; This represents the distance between two adjacent antennas in a uniform transmitting antenna array; Indicates frequency point The two adjacent receiving antennas are in the first... Path phase difference on the stripe cluster due to distance; Indicates frequency point The two adjacent transmitting antennas are at the 1st Path phase difference on the stripe cluster due to distance;

[0014] At different frequency points, the size of the transmitting antenna pattern matrix is ​​expanded to MN×MN; the environmental cluster matrix is ​​expanded from Rx*L dimensions to Rx×MN dimensions, where L clusters reside in the spatial region. For the original cluster gain, in other spatial regions, The value is 0, as shown in expression (2).

[0015] (2)

[0016] in, This represents the gain of a cluster in the MN spatial angles. If there is no cluster in a certain spatial angle, a virtual cluster with a gain of 0 is created.

[0017] After dimension expansion, frequency is ignored as a function of wavenumber. The influence of wavenumber at any frequency point is uniformly expressed as Rewrite expression (1) as (3).

[0018] (3a)

[0019] (3b)

[0020] (3c)

[0021] in, and For the M×N regions, the first The median angles of phi and theta corresponding to each region; Indicates falling on the 1st The path phase difference between clusters in a region on two adjacent receiving antennas due to distance; Indicates falling on the 1st Clusters in a region exhibit path phase differences on two adjacent transmitting antennas due to distance.

[0022] In S02, the capacity expression for the frequency-selective channel is shown in (4). The frequency-selective channel is divided into K frequency bands:

[0023] (4a)

[0024] (4b)

[0025] (4c)

[0026] (4d)

[0027] in, Indicates channel capacity; The dimension is unit array; It is the total power at the source; The noise power at the receiving end is denoted by K; K represents the number of frequency points. Indicates the first Cross-correlation matrix of the transmitted data streams at each frequency point; Indicates the first The first frequency point The power on the first antenna; will the power on the second antenna The matrix at each frequency point, composed of the environmental cluster gain and the phase difference of the receiving antenna, is represented as follows: The matrix composed of the transmit antenna directivity and the transmit antenna phase difference is represented as: .

[0028] The optimization problem constructed in S02 is shown in expression (5):

[0029] (5a)

[0030] (5b)

[0031] (5c).

[0032] Solving optimization problems in S03 includes: using alternating optimization F and The method for finding the maxima of C is given by... If F is a concave function, we can directly use convex optimization tools to solve it; C is a convex function for F, and the maximum point is obtained on the boundary. We can use the method of auxiliary variables to transform the problem and then solve it.

[0033] The specific process is as follows:

[0034] S11, Set initial value , Number of iterations ,calculate

[0035] S12, fixed (Right now ),optimization ;

[0036] S13, Fixed ,optimization ;

[0037] S14, number of iterations ,calculate ;

[0038] S15, if or End, otherwise skip to S12.

[0039] Optimization in S13 In the initial stage, the CVX optimization tool was used to solve the problem; when optimizing F in S13, K was introduced as an auxiliary variable. Define function As shown in expression (6), the expression of C relative to F is transformed into equation (7), and the optimization problem is transformed into equation (8);

[0040] (6)

[0041] (7)

[0042] (8a)

[0043] (8b)

[0044] In optimization problem (8), C targets Both are concave functions. The specific solution steps are as follows:

[0045] S1, fixed according to expressions (9) and (10) beg and ;

[0046] S2, Fixed and Find F, as shown in expression (11), and solve it using the Lagrange multiplier method;

[0047] S3 is optimized by alternating between S1 and S2 until... , This represents the number of iterations.

[0048] (9)

[0049] (10)

[0050] (11a)

[0051] (11b)

[0052] The optimization problem of (11) is solved using the Lagrange multiplier method, as shown in expression (12).

[0053] (12a)

[0054] (12b)

[0055] in, It is introduced A Lagrange multiplier.

[0056] Solving (12b) yields the optimal F, as shown in expression (13).

[0057] (13)

[0058] The specific steps are as follows:

[0059] S21 initialization ;

[0060] S22 Order ;

[0061] S23 uses expression (13) to obtain the tx-th column of F;

[0062] S24 If the sum of squares of the elements in column tx of F is greater than 1... ,otherwise ;if End, otherwise skip to S22.

[0063] Simultaneously, a calculation system for the optimal antenna pattern in a frequency-selective channel is provided, including an antenna model construction module, an optimization problem construction module, and a solution module. The antenna model construction module is used to perform two-dimensional modeling of the antenna pattern in terms of frequency and space: in the frequency dimension, within the frequency range of interest, the antenna pattern does not change with frequency; in the spatial dimension, the spatial region of interest is divided into spherical regions, that is, theta is divided into M intervals and phi is divided into N intervals, thus forming M×N spatial regions. In each spatial region, the antenna radiation characteristics are the same.

[0064] The optimization problem building module is used to construct optimization problems: the communication environment is a downlink between the sender and receiver, and the users are distributed in... Within a sector-shaped region; the number of antennas at the transmitting end is Tx, and the number of antennas at the receiving end is Rx, forming an Rx*Tx MIMO channel; the transmitting antennas are pattern-reconfigurable antennas, and the receiving antennas are omnidirectional antennas; the channel environment is a frequency-selective channel, and an NLos multipath environment described by random geometry, with L multipaths; establish the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix; list the relationship between channel capacity, antenna pattern, and multipath environment under a frequency-selective channel; the antenna pattern that maximizes the channel capacity is the optimal antenna pattern, with the constraint that the total power of the transmitting antennas is P, thus obtaining the optimization problem;

[0065] The solution module is used to solve the optimization problem: based on the optimization problem, it uses auxiliary variables and an alternating optimization algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antenna.

[0066] This invention also provides a calculation system for the optimal antenna pattern in a frequency-selective channel, including an antenna model construction module, an optimization problem construction module, and a solution module. The antenna model construction module is used to perform two-dimensional modeling of the antenna pattern in terms of frequency and space: in the frequency dimension, the antenna pattern does not change with frequency within the frequency range of interest; in the spatial dimension, the spatial region of interest is divided into spherical regions, that is, theta is divided into M intervals and phi is divided into N intervals, thus forming M×N spatial regions, in which the antenna radiation characteristics are the same;

[0067] The optimization problem building module is used to construct optimization problems: the communication environment is a downlink between the sender and receiver, and the users are distributed in... Within a sector-shaped region; the number of antennas at the transmitting end is Tx, and the number of antennas at the receiving end is Rx, forming an Rx*Tx MIMO channel; the transmitting antennas are pattern-reconfigurable antennas, and the receiving antennas are omnidirectional antennas; the channel environment is a frequency-selective channel, and an NLos multipath environment described by random geometry, with L multipaths; establish the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix; list the relationship between channel capacity, antenna pattern, and multipath environment under a frequency-selective channel; the antenna pattern that maximizes the channel capacity is the optimal antenna pattern, with the constraint that the total power of the transmitting antennas is P, thus obtaining the optimization problem;

[0068] The solution module is used to solve the optimization problem: based on the optimization problem, it uses auxiliary variables and an alternating optimization algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antenna.

[0069] In addition, the present invention also provides a computer device, including a processor and a memory, the memory for storing a computer executable program, the processor reading the computer executable program from the memory and executing it, and the processor executing the executable program can realize the method for calculating the optimal antenna pattern in the frequency selective channel described herein.

[0070] Simultaneously, a computer-readable storage medium may be provided, which stores a computer program that, when executed by a processor, enables the calculation method for the optimal antenna pattern in a frequency-selective channel as described herein.

[0071] Compared with the prior art, the present invention has at least the following beneficial effects:

[0072] The method described in this invention innovatively provides the optimal antenna directivity under frequency-selective channels, offering a reference for the target radiation pattern of antenna synthesis; it also derives the achievable upper bound of capacity in a wireless environment under frequency-selective channels, providing a reference for the design of communication systems; furthermore, it provides a complete calculation method for the optimal antenna directivity under frequency-selective channels and a calculation method for the achievable upper bound of capacity in a wireless environment under frequency-selective channels. Attached Figure Description

[0073] Figure 1 This shows the cluster distribution at two frequency points in Example 1;

[0074] Figure 2 For the corresponding Figure 1 The optimal antenna pattern (two transmit antennas) is shown in the frequency-selective channel. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] A method for calculating the optimal antenna pattern in a frequency-selective channel includes the following steps:

[0077] Step 1: Perform two-dimensional modeling of the antenna pattern in frequency and space. In the frequency dimension, it is assumed that the antenna pattern does not change with frequency within the frequency range of interest (the antenna's bandwidth). In the spatial dimension, the spatial region of interest is divided spherically, that is, theta is divided into M intervals (each interval is 60° / M within -30° to +30°) and phi is divided into N intervals (each interval is 120° / N within -60° to +60°), thus forming M×N spatial regions. It is assumed that the antenna's radiation characteristics are the same in each spatial region.

[0078] Step 2, System Modeling and Optimization Problem: The communication environment consists of a downlink with one transmitter (usually a base station) and one receiver (usually a user), with users distributed across... Within a sector-shaped region; the number of antennas at the transmitting end is Tx, and the number of antennas at the receiving end is Rx, forming an Rx*Tx MIMO channel; the transmitting antennas are pattern-reconfigurable antennas, and the receiving antennas are omnidirectional antennas; the channel environment is a frequency-selective channel, and an NLos multipath environment described by random geometry, with L multipaths; establish the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix; list the relationship between channel capacity, antenna pattern, and multipath environment under a frequency-selective channel; define the antenna pattern that maximizes the channel capacity as the optimal antenna pattern, with the constraint that the total power of the transmitting antennas is P, thus obtaining the optimization problem;

[0079] Step 3, Solve the optimization problem: Based on the optimization problem, use auxiliary variables and an alternating optimization algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antenna.

[0080] In step 2), under the random geometric channel model, the frequency point Channel matrix on It is expressed as the product of the transmitting antenna pattern matrix and the multipath environment matrix, as shown in expression (1):

[0081] (1a)

[0082] (1b)

[0083] (1c)

[0084] in, ( () indicates frequency point Upper Gain on stripe clusters; Indicates the first The transmitting antenna is at the ... The directionality of the strip cluster in the direction it is located. This indicates the frequency point. Upper The departure azimuth and elevation angles of the stripe cluster; Frequency point wavenumber on; This represents the distance between two adjacent antennas in a uniform receiving linear array; This represents the distance between two adjacent antennas in a uniform transmitting antenna array; Indicates frequency point The two adjacent receiving antennas are in the first... Path phase difference on the stripe cluster due to distance; Indicates frequency point The two adjacent transmitting antennas are at the 1st The path phase difference on the stripe cluster caused by distance.

[0085] At different frequencies, the multipath environment differs, meaning the departure angle and cluster gain vary. To facilitate subsequent calculations, the size of the transmitting antenna pattern matrix is ​​expanded to MN×MN, covering the directivity of each spatial region. The environmental cluster matrix is ​​also expanded from Rx*L dimensions to Rx×MN dimensions, representing the spatial regions containing L clusters. For the original cluster gain, in other spatial regions, It is 0, as shown in expression (2).

[0086] (2)

[0087] in, This represents the gain of a cluster in the MN spatial angles. If there is no cluster in a certain spatial angle, a virtual cluster with a gain of 0 is created.

[0088] After dimension expansion, frequency is ignored as a function of wavenumber. The influence of wavenumber at any frequency point is uniformly expressed as Rewrite expression (1) as (3).

[0089] (3a)

[0090] (3b)

[0091] (3c)

[0092] in, and For the M×N regions, the first The median angles of phi and theta corresponding to each region; Indicates falling on the 1st The path phase difference between clusters in a region on two adjacent receiving antennas due to distance; Indicates falling on the 1st The path phase difference between clusters in a region on two adjacent transmitting antennas due to distance;

[0093] In step 2), the capacity expression for the frequency-selective channel (divided into K frequency bands) is listed as shown in (4):

[0094] (4a)

[0095] (4b)

[0096] (4c)

[0097] (4d)

[0098] in, Indicates channel capacity; The dimension is unit array; It is the total power at the source; The noise power at the receiving end is denoted by K; K represents the number of frequency points. Indicates the first Cross-correlation matrix of the transmitted data streams at each frequency point; Indicates the first The first frequency point The power on each antenna.

[0099] For the convenience of further analysis, the first The matrix at each frequency point, composed of the environmental cluster gain and the phase difference of the receiving antenna, is represented as follows: The matrix composed of the transmit antenna directivity and the transmit antenna phase difference is represented as: .

[0100] The optimization problem constructed in step 2) is expression (5).

[0101] (5a)

[0102] (5b)

[0103] (5c).

[0104] In step 3), the optimization problem is solved using alternating optimization F and... The method described above is used to find the maximum value of C. The specific algorithm flow is shown in Table 1. C is used to find the maximum value of C. If F is a concave function, it can be solved directly using convex optimization tools; C is a convex function for F, and the maximum point is obtained on the boundary. The problem can be transformed and solved by using the method of auxiliary variables.

[0105] Table 1: Steps of the Alternating Optimization Algorithm

[0106]

[0107] In step 3), the optimization problem is solved, and the optimization... At that time, the CVX optimization tool was used to solve the problem:

[0108] In step 3), when solving the optimization problem and optimizing F, K is introduced as an auxiliary variable. Define auxiliary functions As shown in expression (6), the expression for C relative to F is transformed into expression (7). Therefore, the optimization problem is transformed into expression (8).

[0109] (6)

[0110] (7)

[0111] (8a)

[0112] (8b)

[0113] In optimization problem (8), C targets All are concave functions, and the solution steps are shown in Table 2.

[0114] Table 2: Auxiliary variable method for obtaining... Steps

[0115]

[0116] (9)

[0117] (10)

[0118] (11a)

[0119] (11b)

[0120] The optimization problem of (11) is solved using the Lagrange multiplier method, as shown in expression (12).

[0121] (12a)

[0122] (12b)

[0123] in, It is introduced A Lagrange multiplier.

[0124] Solving (12b) yields the optimal F, as shown in expression (13).

[0125] (13)

[0126] The solution is obtained using the bisection method, and the specific steps are shown in Table 3:

[0127] Table 3: Solution steps

[0128]

[0129] Example 1: 2 transmit antennas, 2 receive antennas, 15 clusters, channel cluster distribution at 2 frequency points (3.0 GHz and 3.1 GHz) is as follows. Figure 1 As shown in (a) and (b), the 15 lines represent 15 clusters, the direction of the line segments represents the direction of the clusters, and the length of the line segments represents the gain of the cluster. Figure 2 For the optimal transmitter antenna pattern calculated according to the method of this invention, refer to Figure 2 (a) and (b).

[0130] Based on the concept of the method described above, the present invention can also provide a calculation system for the optimal antenna pattern in a frequency-selective channel, including an antenna model construction module, an optimization problem construction module, and a solution module; the antenna model construction module is used to perform two-dimensional modeling of the antenna pattern in terms of frequency and space: in the frequency dimension, within the frequency range of interest, the antenna pattern does not change with frequency; in the spatial dimension, the spatial region of interest is divided into spherical regions, that is, theta is divided into M intervals and phi is divided into N intervals, thus forming M×N spatial regions, in which the antenna radiation characteristics are the same;

[0131] The optimization problem building module is used to construct optimization problems: the communication environment is a downlink between the sender and receiver, and the users are distributed in... Within a sector-shaped region; the number of antennas at the transmitting end is Tx, and the number of antennas at the receiving end is Rx, forming an Rx*Tx MIMO channel; the transmitting antennas are pattern-reconfigurable antennas, and the receiving antennas are omnidirectional antennas; the channel environment is a frequency-selective channel, and an NLos multipath environment described by random geometry, with L multipaths; establish the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix; list the relationship between channel capacity, antenna pattern, and multipath environment under a frequency-selective channel; the antenna pattern that maximizes the channel capacity is the optimal antenna pattern, with the constraint that the total power of the transmitting antennas is P, thus obtaining the optimization problem;

[0132] The solution module is used to solve the optimization problem: based on the optimization problem, it uses auxiliary variables and an alternating optimization algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antenna.

[0133] In addition, the present invention can also provide a computer device, including a processor and a memory, wherein 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 executable program, it can realize the method for calculating the optimal antenna pattern in the frequency selective channel described in the present invention.

[0134] On the other hand, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the calculation method for the optimal antenna pattern in a frequency-selective channel as described in the present invention.

[0135] The computer device may be a laptop, a desktop computer, or a workstation.

[0136] The processor can be a central processing unit (CPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).

[0137] The memory described in this invention can be an internal storage unit of a laptop, desktop computer, or workstation, such as memory or hard disk; or it can be an external storage unit, such as a portable hard disk or flash memory card.

[0138] Computer-readable storage media can include computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media can include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSDs), or optical discs, etc. Random access memory can include resistive random access memory (ReRAM) and dynamic random access memory (DRAM).

Claims

1. A method for calculating the optimal antenna pattern in a frequency-selective channel, characterized in that, Includes the following steps: S01, perform two-dimensional modeling of the antenna pattern in frequency and space: In the frequency dimension, within the frequency range of interest, the antenna pattern does not change with frequency; in the spatial dimension, the spatial region of interest is divided into spherical regions, that is, theta is divided into M intervals and phi is divided into N intervals, thus forming M×N spatial regions, in which the antenna radiation characteristics are the same. S02, System Modeling and Optimization Problem: The communication environment consists of a downlink between the transmitter and receiver, with users distributed across... Within a sector-shaped region; the number of antennas at the transmitting end is Tx, and the number of antennas at the receiving end is Rx, forming an Rx*Tx MIMO channel; the transmitting antennas are pattern-reconfigurable antennas, and the receiving antennas are omnidirectional antennas; the channel environment is a frequency-selective channel, and an NLos multipath environment described by random geometry, with L multipaths; establish the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix; establish the relationship between channel capacity, antenna pattern, and multipath environment under a frequency-selective channel; the antenna pattern that maximizes the channel capacity is the optimal antenna pattern, with the constraint that the total power of the transmitting antenna is P, thus obtaining the optimization problem; Establishing the relationship between the antenna pattern matrix, multipath environment matrix, and channel matrix includes: under the stochastic geometric channel model, frequency points Channel matrix on It is expressed as the product of the transmitting antenna pattern matrix and the multipath environment matrix, as shown in expression (1): (1a) (1b) (1c) in, ( () indicates frequency point Upper Gain on stripe clusters; Indicates the first The transmitting antenna is at the ... The directionality of the strip cluster in the direction it is located. This indicates the frequency point. Upper The departure azimuth and elevation angles of the stripe cluster; Frequency point wavenumber on; This represents the distance between two adjacent antennas in a uniform receiving linear array; This represents the distance between two adjacent antennas in a uniform transmitting antenna array; Indicates frequency point The two adjacent receiving antennas are in the first... Path phase difference on the stripe cluster due to distance; Indicates frequency point The two adjacent transmitting antennas are at the 1st Path phase difference on the stripe cluster due to distance; At different frequency points, the size of the transmitting antenna pattern matrix is ​​expanded to MN×MN; the environmental cluster matrix is ​​expanded from Rx*L dimensions to Rx×MN dimensions, where L clusters reside in the spatial region. For the original cluster gain, in other spatial regions, The value is 0, as shown in expression (2). (2) in, This represents the gain of a cluster in the MN spatial angles. If there is no cluster in a certain spatial angle, a virtual cluster with a gain of 0 is created. After dimension expansion, frequency is ignored as a function of wavenumber. The influence of wavenumber at any frequency point is uniformly expressed as Rewrite expression (1) as (3). (3a) (3b) (3c) in, and For the M×N regions, the first The median angles of phi and theta corresponding to each region; Indicates falling on the 1st The path phase difference between clusters in a region on two adjacent receiving antennas due to distance; Indicates falling on the 1st The path phase difference between clusters in a region on two adjacent transmitting antennas due to distance; S03, Solving the optimization problem: Based on the optimization problem described in S2, use auxiliary variables and an alternating optimization algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antenna.

2. The method for calculating the optimal antenna pattern in a frequency-selective channel according to claim 1, characterized in that, In S01, theta is divided into M intervals, each interval being 60° / M within the range of -30° to +30°, and phi is divided into N intervals, each interval being 120° / N within the range of -60° to +60°.

3. The method for calculating the optimal antenna pattern in a frequency-selective channel according to claim 1, characterized in that, In S02, the capacity expression for the frequency-selective channel is shown in (4). The frequency-selective channel is divided into K frequency bands: (4a) (4b) (4c) (4d) in, Indicates channel capacity; The dimension is unit array; It is the total power at the source; The noise power at the receiving end is denoted by K; K represents the number of frequency points. Indicates the first Cross-correlation matrix of the transmitted data streams at each frequency point; Indicates the first The first frequency point The power on the first antenna; will the power on the second antenna The matrix at each frequency point, composed of the environmental cluster gain and the phase difference of the receiving antenna, is represented as follows: The matrix composed of the transmit antenna directivity and the transmit antenna phase difference is represented as: .

4. The method for calculating the optimal antenna pattern in a frequency-selective channel according to claim 3, characterized in that, The optimization problem constructed in S02 is shown in expression (5): (5a) (5b) (5c)。 5. The method for calculating the optimal antenna pattern in a frequency-selective channel according to claim 4, characterized in that, Solving optimization problems in S03 includes: using alternating optimization F and The method for finding the maxima of C is given by... If F is a concave function, we can directly use convex optimization tools to solve it; C is a convex function for F, and the maximum point is obtained on the boundary. We can use the method of auxiliary variables to transform the problem and then solve it. The specific process is as follows: S11, Set initial value , Number of iterations ,calculate ; S12, fixed (Right now ),optimization ; S13, Fixed ,optimization ; S14, number of iterations ,calculate ; S15, if or End, otherwise skip to S12.

6. The method for calculating the optimal antenna pattern in a frequency-selective channel according to claim 5, characterized in that, Optimization in S13 In the initial stage, the CVX optimization tool was used to solve the problem; when optimizing F in S13, K was introduced as an auxiliary variable. Define function As shown in expression (6), the expression of C relative to F is transformed into equation (7), and the optimization problem is transformed into equation (8); (6) (7) (8a) (8b) In optimization problem (8), C targets Both are concave functions. The specific solution steps are as follows: S1, fixed according to expressions (9) and (10) beg and ; S2, Fixed and Find F, as shown in expression (11), and solve it using the Lagrange multiplier method; S3 is optimized by alternating between S1 and S2 until... , This represents the number of iterations. (9) (10) (11a) (11b) The optimization problem of (11) is solved using the Lagrange multiplier method, as shown in expression (12). (12a) (12b) in, It is introduced One Lagrange multiplier; Solving (12b) yields the optimal F, as shown in expression (13). (13) The specific steps are as follows: S21 initialization ; S22 Order ; S23 uses expression (13) to obtain the tx-th column of F; S24 If the sum of squares of the elements in column tx of F is greater than 1... ,otherwise ;if End, otherwise skip to S22.

7. A system for calculating the optimal antenna pattern in a frequency-selective channel, characterized in that, The method for calculating the optimal antenna pattern in a frequency-selective channel as described in any one of claims 1-6 includes an antenna model construction module, an optimization problem construction module, and a solution module. The antenna model construction module is used to perform two-dimensional modeling of the antenna pattern in terms of frequency and space: in the frequency dimension, the antenna pattern does not change with frequency within the frequency range of interest; in the spatial dimension, the spatial region of interest is divided into spherical regions, that is, theta is divided into M intervals and phi is divided into N intervals, thus forming M×N spatial regions, in which the antenna radiation characteristics are the same; The optimization problem building module is used to construct optimization problems: the communication environment is a downlink between the sender and receiver, and the users are distributed in... Within a sector-shaped region; the number of antennas at the transmitting end is Tx, and the number of antennas at the receiving end is Rx, forming an Rx*Tx MIMO channel; the transmitting antennas are pattern-reconfigurable antennas, and the receiving antennas are omnidirectional antennas; the channel environment is a frequency-selective channel, and an NLos multipath environment described by random geometry, with L multipaths; establish the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix; list the relationship between channel capacity, antenna pattern, and multipath environment under a frequency-selective channel; the antenna pattern that maximizes the channel capacity is the optimal antenna pattern, with the constraint that the total power of the transmitting antennas is P, thus obtaining the optimization problem; The solution module is used to solve the optimization problem: based on the optimization problem, it uses auxiliary variables and an alternating optimization algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antenna.

8. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading the computer-executable program from the memory and executing it, and the processor executing the calculation executable program is able to implement the method for calculating the optimal antenna pattern in the frequency-selective channel as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores a computer program that, when executed by a processor, enables the calculation method for the optimal antenna pattern in a frequency-selective channel as described in any one of claims 1 to 6.

Images