A calculation method and system for an antenna pattern adapted to a wireless channel

Abstract

The present invention discloses a calculation method for an antenna pattern adapted to a wireless channel. The method is as follows: Discretely model the antenna pattern: Divide the spatial sphere into N equal parts, and within each part of the spatial angle, the radiation characteristics of the antenna are the same; The communication environment is the downlink of a base station and a mobile phone user. The number of antennas of the base station as the transmitting end is Tx, and the number of antennas of the mobile phone user as the receiving end is Rx. Under the random geometric channel model, establish the antenna pattern and the channel matrix, obtain the relationship between the channel capacity and the antenna pattern, and use the channel capacity as the performance index of the system; The antenna pattern that maximizes the channel capacity is defined as the best-adapted antenna pattern for the wireless channel, with the constraint that the total power of the transmitting antennas is P; Use SVD decomposition and the water-filling algorithm to calculate the optimal antenna pattern and determine the power allocation of each transmitting antenna; The optimal pattern adapted to the wireless channel is given, which can be used as the target pattern for antenna synthesis.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication capacity optimization, and particularly relates to a method and system for calculating an antenna pattern that optimally adapts to a wireless channel. Background Art

[0002] The influence of antennas on the performance of communication systems has been increasingly emphasized in current research. What kind of "antenna directivity" can better adapt to the communication channel is a current research hotspot. Based on the channel model of TR38.961, the directivity of an antenna is an important parameter for calculating channel coefficients in a stochastic geometric channel model, and thus is also an important parameter affecting channel capacity. In current research, due to the lack of mathematical modeling of antenna patterns, there is no direct method for calculating antenna patterns. In existing methods, most integrate antenna design parameters into the channel capacity calculation model, first calculate antenna parameters, and then obtain the antenna pattern. In these methods, different antenna structures require re-modeling and re-optimization calculations, and the calculation complexity is relatively high. Moreover, due to the parameter constraints of the antenna, the calculated pattern in this case is not the optimal pattern that adapts to the wireless channel, but a sub-optimal pattern constrained by antenna parameters. Summary of the Invention

[0003] To explore the influence of antenna directivity on the performance of communication systems and find the optimal antenna pattern that adapts to the wireless channel, the present invention establishes a mathematical relationship between antenna directivity and channel capacity, and uses an optimization algorithm to calculate the antenna pattern that maximizes the capacity and the upper bound of the capacity.

[0004] To achieve the above object, the technical solution adopted by the present invention is: a method for calculating an antenna pattern that adapts to a wireless channel, comprising the following steps:

[0005] Step 1, perform discrete modeling on the antenna pattern: divide the spherical surface of space into N equal parts, and the solid angle of each part of the spatial angle is The corresponding surface area is where r is the distance from the observation point to the phase center of the antenna. In each part of the spatial angle, the radiation characteristics of the antenna are the same;

[0006] Step 2, system modeling and construction of optimization problem: The communication environment is the downlink of a transmitter and a 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 environment under random geometric description, and the number of multipaths is L; it is assumed that the receiver antenna is an omnidirectional antenna, and the transmitter antenna is a reconfigurable antenna whose radiation pattern can be dynamically adjusted according to the environmental channel; under the random geometric channel model, establish the relationship between the antenna radiation pattern matrix, the multipath environment matrix, and the channel matrix; according to the MIMO channel capacity formula, obtain the relationship between the channel capacity and the antenna radiation pattern and the multipath environment; the antenna radiation pattern F that maximizes the channel capacity L×Tx is defined as the optimal adaptation antenna radiation pattern for the wireless channel, with the constraint that the total power of the transmitting antenna is P, and the optimization problem is obtained;

[0007] Step 3, solving the optimization problem: Based on the optimization problem, use SVD decomposition and water-filling algorithm to calculate the optimal antenna radiation pattern and determine the power allocation of the transmitting antenna.

[0008] In Step 1, in each spatial angle, the same radiation characteristics of the antenna mean that the electric field, magnetic field, and power flow density of the antenna are the same.

[0009] In Step 1, if N = 1, it represents an omnidirectional antenna, and the relationship between the power flow density and the radiation power is expressed as Equation (1), and the relationship between the radiation intensity and the radiation power is expressed as Equation (2)

[0010]

[0011] If N≠1, it means that the antenna radiation has non-uniformity in the whole space, and the radiation power is obtained by superimposing the power flow density or radiation intensity, as shown in Equation (3). When N approaches infinity, the discrete representation of Equation (3) is equivalent to the integral representation under continuity.

[0012]

[0013] In Step 1, for a directional antenna, the power concentration factor is the ratio of the radiation power in the concerned radiation space to the total radiation power, as shown in Equation (4). Among N spatial angles, there are K concerned radiation directions, where K < N.

[0014]

[0015] For a directional antenna, the radiation concentration factor is the ratio of the sum of the radiation intensities in the concerned radiation space to the radiation intensity of the omnidirectional antenna, as shown in Equation (5). The radiation factor characterizes the sum of the radiation capabilities of the beams in the concerned radiation directions.

[0016]

[0017] In Equation (5), in the ideal case, assuming that the radiation intensity in the non-primary radiation space is 0, then γ = 1, ρ = N. The greater the spatial subdivision strength, the smaller the primary radiation space, that is, the larger N and the smaller K, and the greater the radiation convergence factor.

[0018] In step 2, under the random geometric channel model, establish the antenna pattern matrix F L×Tx , the multipath environment matrix and the channel matrix H Rx×Tx are expressed as in Equation (6):

[0019]

[0020] where α l is the phase difference caused by the l-th path between two adjacent receiving antennas; β l is the phase difference caused by the l-th path between two adjacent transmitting antennas; represents the physical channel, which is a known parameter, and h l represents the gain on the l-th path in the multipath environment; F L×Tx represents the matrix of the influence of antenna directivity on the channel, which is the quantity to be solved, where represents the gain of the n-th transmitting antenna on the l-th path.

[0021] In step 2, the relationship between the channel capacity and the antenna pattern is as shown in Equation (7)

[0022]

[0023] where R ss is the covariance matrix of the transmitted stream, and the sum of the diagonal elements represents the total transmitted power

[0024]

[0025] In step 3, when using SVD decomposition and the water-filling algorithm to calculate the optimal antenna pattern and determine the power allocation between the transmitting antennas:

[0026]

[0027] where ρ is the radiation convergence factor.

[0028] In step 3, when using SVD decomposition and the water-filling algorithm to calculate the optimal antenna pattern and determine the power allocation between the transmitting antennas:

[0029] Perform SVD decomposition on as shown in Equation (10), and the right singular value matrix is the optimal pattern of F L×Tx as shown in Equation (11)

[0030]

[0031] F L×Tx opt = V(11)

[0032] Use the water-filling algorithm to calculate the covariance matrix R of the transmitted streams according to the S matrix and ρ ss , and determine the power distribution between the transmitting antennas.

[0033] Based on the technical concept of the present invention, a calculation system for the antenna pattern adapted to the wireless channel is further provided, including a model construction module, an optimization problem construction module, and a solution module;

[0034] The model construction module is used to discretely model the antenna pattern. Specifically: divide the spherical surface of space into N equal parts, and the solid angle of each part of the spatial angle is The corresponding surface area is where r is the distance from the observation point to the antenna phase center. In each part of the spatial angle, the radiation characteristics of the antenna are the same;

[0035] The optimization problem construction module is used to model the antenna communication system and construct an optimization problem, specifically as follows: the communication environment is the downlink of a transmitter and a 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 environment under random geometric description, and the number of multipaths is L; set the receiver antenna as an omnidirectional antenna, and the transmitter antenna as a reconfigurable antenna whose pattern can be dynamically adjusted according to the environmental channel; under the random geometric channel model, establish the relationship between the antenna pattern matrix, the multipath environment matrix, and the channel matrix; according to the MIMO channel capacity formula, obtain the relationship between the channel capacity and the antenna pattern and the multipath environment; the antenna pattern F L×Tx defined as the best-adapted antenna pattern to the wireless channel, with the constraint that the total power of the transmitting antennas is P, to obtain an optimization problem;

[0036] The solution module uses SVD decomposition and the water-filling algorithm to calculate the optimal antenna pattern and determine the power distribution of the transmitting antennas.

[0037] The present invention can also provide a computer device, including a processor and a memory. The memory is used to store computer-executable programs. The processor reads the computer-executable programs from the memory and executes them. When the processor executes the computer-executable programs, it can implement the calculation method of the antenna pattern adapted to the wireless channel of the present invention.

[0038] Compared with the prior art, the present invention has at least the following beneficial effects:

[0039] 1) Based on the random geometric channel model of TR38.961, the MIMO channel matrix is written in the form of the product of the antenna directivity matrix and the multipath environment matrix;

[0040] 2) Mathematically discretize the antenna pattern, and establish the power constraint expression of the antenna directivity matrix on the spatial multipaths of interest, so that the optimal pattern and the power allocation among the transmitting antennas can be obtained by using singular value decomposition and the water-filling algorithm;

[0041] 3) The invention gives the optimal pattern adapted to the wireless channel and gives the upper bound of the capacity;

[0042] 4) The optimal antenna pattern obtained in the invention can be used as the target pattern for antenna synthesis and further used to optimize the antenna parameters. Description of the Drawings

[0043] Figure 1 It is a schematic diagram of the system model Detailed Embodiment

[0044] The present invention provides a method for calculating an antenna pattern adapted to a wireless channel, including the following steps:

[0045] Step 1 Discretely model the antenna pattern

[0046] 1.1 Divide the spherical surface of space into N equal parts, and the solid angle of each part of the spatial angle is The corresponding surface area is (where r is the distance from the observation point to the antenna phase center, in meters)

[0047] 1.2 It is considered that in each part of the spatial angle, the radiation characteristics of the antenna are the same, that is, the electric field, magnetic field, and power flow density of the antenna are the same.

[0048] If N = 1, it represents an omnidirectional antenna, and the relationship between the power flow density and the radiation power is expressed by Equation (1), and the relationship between the radiation intensity and the radiation power is expressed by Equation (2)

[0049]

[0050] If N ≠ 1, it means that the antenna radiation is non-uniform in the whole space (such as a directional antenna). At this time, the radiation power can be obtained by superimposing the power flow density or radiation intensity, as shown in Equation (3).

[0051] When N approaches infinity, the discrete representation of Equation (3) is equivalent to the integral representation under continuity.

[0052]

[0053] 1.3 For a directional antenna, the power concentration factor is defined as the ratio of the radiated power in the concerned radiation space to the total radiated power, as shown in Equation (4). There are K concerned radiation directions (K < N) among N spatial angles.

[0054]

[0055] 1.4 For a directional antenna, the radiation concentration factor is defined as the ratio of the sum of the radiation intensities in the concerned radiation space to the radiation intensity of an omnidirectional antenna, as shown in Equation (5). The radiation factor characterizes the radiation ability of the beam in the concerned radiation direction.

[0056]

[0057] In Equation (5), in the ideal case, assuming that the radiation intensity in the non-primary radiation space is 0, then γ = 1 and ρ = N. At this time, the larger the spatial subdivision degree (the larger N), the smaller the primary radiation space (the smaller K), and the larger the radiation concentration factor.

[0058] Step 2 System modeling and optimization problem formulation

[0059] 2.1 Determine the number of transmitting and receiving antennas and the communication environment

[0060] The communication environment is the downlink of a base station (BS) and a mobile phone user (UI). The number of antennas of the BS as the transmitting end is Tx, the number of antennas of the UI as the receiving end is Rx, the channel environment is an NLos multipath environment under random geometric description, the number of multipaths is L, and the receiving-end antenna is an omnidirectional antenna.

[0061] 2.2 Under the random geometric channel model, establish the antenna pattern and the channel matrix H Rx×Tx The expression is as shown in Equation (6)

[0062]

[0063] where α l is the phase difference caused by the l-th path between two adjacent receiving antennas; β l is the phase difference caused by the l-th path between two adjacent transmitting antennas; represents the physical channel, which is a known parameter in this method; F L×Tx represents the matrix of the influence of antenna directivity on the channel, which is an unknown quantity to be solved.

[0064] 2.3 Obtain the relationship between the channel capacity and the antenna pattern, as shown in Equation (7)

[0065]

[0066] where R ssis the covariance matrix of the transmitted stream, and the sum of the diagonal elements represents the total transmitted power

[0067] 2.4 Determine the optimization problem

[0068] In wireless communication, the capacity is often used as the performance metric of the system. The antenna pattern F that maximizes Equation (7) L×Tx can be defined as the optimal antenna pattern for adapting to the wireless channel, with the constraint that the total power of the transmitting antennas is P; the optimization problem is formulated as follows:

[0069]

[0070] subject to tr(R ss ) = P, (9.b)

[0071]

[0072] where ρ is the radiation concentration factor defined in (5).

[0073] Step 3 Use SVD decomposition and the water-filling algorithm to calculate the optimal antenna pattern and determine the power allocation pairs for each transmitting antenna Perform SVD decomposition, and the right singular value vector is the optimal pattern of F L×Tx

[0074]

[0075] F L×Tx opt = V H (12)

[0076] Use the water-filling algorithm to calculate the covariance matrix R according to the S matrix and ρ*P ss , and determine the power allocation among the transmitting antennas.

[0077] The following takes the case where both the transmitter and receiver have 2 antennas and there are 3 paths in the wireless space as an example to illustrate the method described in the present invention.

[0078] System modeling: Figure 1 For the system model schematic diagram, two transmitting antennas are arranged on the x-axis, and the antenna distance is half a wavelength; the receiving antenna distance is half a wavelength, the system operates in the 2 GHz frequency band, and the angles and coefficients of the 3 paths are shown in Table 1.

[0079] Table 1 Three-path model parameters

[0080]

[0081] Obtain the multipath environment matrix

[0082] ​

[0083] Perform SVD decomposition

[0084]

[0085] Obtain the optimal radiation pattern according to Equation (11)

[0086]

[0087] According to the signal-to-noise ratio and the obtained S matrix, calculate the power allocation on the two transmitting antennas by the water-filling algorithm; when the noise power is 10 -9 mW and the total power P at the transmitting end is 10 3 mW, the transmitting power of the first transmitting antenna is 508.9889 mW, and the transmitting power of the second transmitting antenna is 491.0111 mW.

[0088] Calculate the maximum capacity: According to the above power allocation and the optimal radiation pattern F opt , obtain the maximum capacity C = 8.8159 bits / s / Hz from Equation (7).

[0089] Based on the above inventive concept, the present invention provides a calculation system for an antenna radiation pattern adapted to a wireless channel, including a model construction module, an optimization problem construction module, and a solution module;

[0090] The model construction module is used to discretely model the antenna radiation pattern, specifically: divide the spherical surface of space into N equal parts, and the solid angle of each part of the spatial angle is The corresponding surface area is where r is the distance from the observation point to the antenna phase center. In each part of the spatial angle, the radiation characteristics of the antenna are the same;

[0091] The optimization problem construction module is used to model the antenna communication system and construct an optimization problem, specifically as follows: The communication environment is a downlink of one transmitting end and one receiving end; 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 channel environment is an NLos multipath environment under random geometric description, and the number of multipaths is L; it is assumed that the receiving end antenna is an omnidirectional antenna, and the transmitting end antenna is a reconfigurable antenna whose radiation pattern can be dynamically adjusted according to the environmental channel; in the random geometric channel model, establish the relationship between the antenna radiation pattern matrix, the multipath environment matrix, and the channel matrix; according to the MIMO channel capacity formula, obtain the relationship between the channel capacity and the antenna radiation pattern and the multipath environment; the antenna radiation pattern F L×Tx defined as the best-adapted antenna radiation pattern for the wireless channel, with the constraint that the total power of the transmitting antennas is P, to obtain an optimization problem;

[0092] The solving module uses SVD decomposition and water filling algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antennas.

[0093] In summary, the present invention first provides a method for directly calculating the antenna pattern, which does not require re-modeling and re-optimization calculation for the antenna structure; under the random geometric channel model, the relationship between the antenna pattern matrix, the multipath environment matrix and the channel matrix is established; the antenna pattern is discretely modeled mathematically, and the power constraint expression of the antenna directivity matrix on the spatial multipath of interest is established, so that the optimal pattern and the power allocation between the transmitting antennas can be obtained by using singular value decomposition and water filling algorithm; the calculation process is simple; the present invention gives the optimal pattern adapted to the wireless channel, gives the upper bound of the antenna capacity, and can approach the parameter constraints of the antenna itself as much as possible; the obtained optimal antenna pattern can be used as the target pattern for antenna synthesis and can be further used to optimize the antenna parameters and approach the upper bound of the antenna capacity.

[0094] In addition, the present invention can also provide a computer device, including a processor and a memory. The memory is used to store computer-executable programs. The processor reads part or all of the computer-executable programs from the memory and executes them. When the processor executes part or all of the computer-executable programs, it can implement the calculation method of the antenna pattern adapted to the wireless channel according to the present invention.

[0095] The computer device can be a laptop computer, a desktop computer or a workstation.

[0096] The processor can be a central processing unit (CPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA).

[0097] For the memory of the present invention, it can be an internal storage unit of a laptop computer, a desktop computer or a workstation, such as a memory or a hard disk; it can also use an external storage unit, such as a mobile hard disk or a flash card.

Claims

1. A calculation method for an antenna pattern adapted to a wireless channel, characterized in that, It includes the following steps: Step 1, discretely model the antenna pattern: Divide the spherical space into N equal parts, and the solid angle of each spatial angle is The corresponding surface area is where r is the distance from the observation point to the antenna phase center. In each spatial angle, the radiation characteristics of the antenna are the same; Step 2, system modeling and constructing an optimization problem: The communication environment is the downlink of a transmitter and a 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 environment under random geometric description, and the number of multipaths is L; it is assumed that the receiver antenna is an omnidirectional antenna, and the transmitter antenna is a reconfigurable antenna whose radiation pattern can be dynamically adjusted according to the environmental channel; Under the random geometric channel model, establish the relationship between the antenna radiation pattern matrix, the multipath environment matrix, and the channel matrix; According to the MIMO channel capacity formula, the relationship between channel capacity, antenna pattern, and multipath environment is obtained; the antenna pattern F that maximizes the channel capacity L×Tx is defined as the optimal antenna pattern for the wireless channel, with the constraint that the total power of the transmitting antenna is P, and an optimization problem is obtained; under the random geometry channel model, an antenna pattern matrix F L×Tx , multipath environment matrix and channel matrix H Rx×Tx are expressed as shown in Equation (1): where α l is the phase difference caused by the l-th path on two adjacent receiving antennas; β l is the phase difference caused by the l-th path on two adjacent transmitting antennas; represents the physical channel, which is a known parameter, h l represents the gain on the l-th path in the multipath environment; F L×Tx represents the influence matrix of antenna directivity on the channel, which is a quantity to be determined, where represents the gain of the n-th transmitting antenna on the l-th path; Step 3, solving the optimization problem: Based on the optimization problem, use SVD decomposition and the water-filling algorithm to calculate the optimal antenna radiation pattern and determine the power allocation of the transmit antennas.

2. The calculation method of the antenna pattern adapted to a wireless channel according to claim 1, wherein In Step 1, within each spatial angle, the same radiation characteristics of the antenna mean that the electric field, magnetic field, and power flow density of the antenna are the same.

3. The calculation method of the antenna pattern adapted to a wireless channel according to claim 1, wherein In Step 1, if N = 1, it represents an omnidirectional antenna, and the relationship between the power flow density and the radiation power is expressed as Equation (2), and the relationship between the radiation intensity and the radiation power is expressed as Equation (3) If N≠1, it means that the antenna radiation is non-uniform in the whole space, and the radiation power is obtained by superimposing the power flow density or radiation intensity, as shown in Equation (4). When N approaches infinity, the discrete representation of Equation (4) is equivalent to the integral representation under continuity.

4. The calculation method of the antenna pattern adapted to a wireless channel according to claim 1, characterized in that, In Step 1, for a directional antenna, the power concentration factor is the ratio of the radiation power in the concerned radiation space to the total radiation power, as shown in Equation (5). Among N spatial angles, there are K concerned radiation directions, where K < N. For a directional antenna, the radiation concentration factor is the ratio of the sum of the radiation intensities in the concerned radiation space to the radiation intensity of an omnidirectional antenna, as shown in Equation (6). The radiation factor characterizes the sum of the radiation capabilities of the beams in the concerned radiation directions; In Equation (6), in the ideal case, assuming that the radiation intensity in the non-primary radiation space is 0, then γ = 1, ρ = N. The finer the spatial subdivision, the smaller the primary radiation space, that is, the larger N and the smaller K, the larger the radiation concentration factor.

5. The calculation method of the antenna pattern adapted to a wireless channel according to claim 1, wherein In Step 2, the relationship between the channel capacity and the antenna radiation pattern is as shown in Equation (7): Among them, R ss is the covariance matrix of the transmitted stream, and the sum of the diagonal elements represents the total transmitted power 6. The calculation method of the antenna pattern adapted to a wireless channel according to claim 1, characterized in that In Step 2, the optimization problem is formulated as follows: subject to tr(R ss )=P, (9.b) where ρ is the radiation concentration factor.

7. The calculation method of the antenna pattern adapted to a wireless channel according to claim 1, characterized in that In Step 3, when using SVD decomposition and the water-filling algorithm to calculate the optimal antenna radiation pattern and determine the power allocation between the transmit antennas: Pair Perform SVD decomposition as shown in formula (10), and the right singular value matrix is F L×Tx The optimal radiation pattern of F L×Tx opt = V(11) Use the water-filling algorithm to calculate the covariance matrix R of the transmit streams based on the S matrix and ρ ss , and determine the power allocation among the transmit antennas.

8. A computing system for calculating an antenna pattern adapted to a wireless channel, characterized in that, It includes a model construction module, an optimization problem construction module, and a solution module; The model construction module is used to discretely model the antenna pattern. Specifically, the spherical space is divided into N equal parts, and the solid angle of each part of the spatial angle is The corresponding surface area is where r is the distance from the observation point to the antenna phase center. In each part of the spatial angle, the radiation characteristics of the antenna are the same; The optimization problem construction module is used for antenna communication system modeling and constructing an optimization problem, specifically as follows: The communication environment is the downlink of a transmitter and a 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 environment under random geometric description, and the number of multipaths is L; it is assumed that the receiver antenna is an omnidirectional antenna, and the transmitter antenna is a reconfigurable antenna whose radiation pattern can be dynamically adjusted according to the environmental channel; Under the random geometric channel model, establish the relationship between the antenna radiation pattern matrix, the multipath environment matrix, and the channel matrix; The relationship between channel capacity and antenna pattern and multipath environment is obtained according to the MIMO channel capacity formula; the antenna pattern F that maximizes the channel capacity L×Tx is defined as the optimal adaptive antenna pattern for the wireless channel, with the constraint that the total power of the transmitting antenna is P, and an optimization problem is obtained; under the random geometry channel model, an antenna pattern matrix F L×Tx , multipath environment matrix and channel matrix h Rx×Tx are expressed as shown in the following formula: where α l is the phase difference caused by the l-th path on two adjacent receiving antennas; β l is the phase difference caused by the l-th path on two adjacent transmitting antennas; represents the physical channel, which is a known parameter, h l represents the gain on the l-th path in the multipath environment; F L×Tx represents the influence matrix of antenna directivity on the channel, which is a quantity to be determined, where represents the gain of the n-th transmitting antenna on the l-th path; The solution module uses SVD decomposition and water-filling algorithm to calculate the optimal antenna pattern and determine the power allocation of the transmitting antennas.

9. A computer device, characterized in that, It includes a processor and a memory. The memory is used to store computer-executable programs. The processor reads the computer-executable programs from the memory and executes them. When the processor executes the computational executable programs, it can implement the calculation method of the antenna pattern for adapting to the wireless channel described in any one of claims 1 to 7.

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