CN112737653A - Non-uniform antenna array system design method using spherical wave model - Google Patents
Non-uniform antenna array system design method using spherical wave model Download PDFInfo
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- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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Abstract
The invention relates to the technical field of wireless communication, and discloses a method for designing a non-uniform antenna array system by using a spherical wave model, which comprises the following steps: s1, establishing an antenna array structure of the non-uniform transceiving antenna array; s2, establishing a channel model containing spherical wave characteristics according to the established antenna array architecture; s3, designing the optimal transmitting direction and the power distribution thereof by using the statistical channel information; and S4, finally, based on the maximum capacity criterion, under the optimal transmission strategy, giving the optimal antenna array element design criterion. The invention can provide the antenna design method criterion under different signal-to-noise ratios, so that the performance of the array antenna design method is better than that of other array antenna design methods.
Description
Technical Field
The invention relates to the technical field of wireless communication, in particular to a non-uniform antenna array system design method using a spherical wave model.
Background
In recent years, with the widespread use of smart terminals such as mobile phones and tablets, the volume of mobile data traffic has increased explosively, and the existing wireless communication systems have been gradually unable to meet such enormous business demands. Therefore, research on the fifth Generation mobile communication technology (5th Generation,5G) has been successively conducted in the academic world and the industrial world. Compared with the existing fourth Generation mobile communication technology (4th Generation,4G), the massive MIMO (Multiple Input Multiple Output, MIMO) technology is one of the key technologies of 5G, and has become a hot spot of domestic and foreign research because it can significantly improve the spectral efficiency and energy efficiency of a communication system.
In MIMO systems, the use of plane wave models for communication severely underestimates the channel capacity of the system. Compared with plane waves, the system capacity can be remarkably increased by using a spherical wave model for communication; for the MIMO system of the spherical wave model, most of the prior arts relate to the design scheme of the uniform antenna array, and most of the design schemes are all studied on the influence of the antenna spacing, the antenna azimuth angle, the distance between the transmitting and receiving antennas, and the like of the uniform antenna on the system performance under the direct-view channel. Under the condition of a uniform antenna array in a three-dimensional space, the optimal precoding design method of the system is only researched at present.
However, how to study the non-uniform linear antenna array design and the precoding design method under rice channel and how to design the placement positions of the non-uniform antennas is a technical problem that needs to be solved in the field.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a non-uniform antenna array system design method using a spherical wave model, which can provide criteria of an antenna design method under different signal-to-noise ratios, so that the performance of the antenna array design method is better than that of other antenna array design methods.
The invention solves the technical problems by the following technical means:
a method for designing a non-uniform antenna array system by using a spherical wave model is characterized by comprising the following steps: the method for designing the precoding and array antenna design of the non-uniform antenna array system according to the spherical wave model specifically comprises the following steps:
s1, establishing an antenna array framework with non-uniform antenna arrays for receiving and transmitting, and establishing a signal model according to a spherical wave model;
s2, establishing a channel model, and assuming that the receiving end knows all state information of the channel and the transmitting end knows the statistical state information of the channel, obtaining the system capacity expression as follows:
wherein Q is a correlation matrix Q ═ E { SS ] of the transmitted signalHρ is ES/N0U isIs a matrix of eigenvectors ofFeature decomposition diagonal matrix, ΛQIs a eigen-decomposition diagonal matrix of Q;
and deducing the upper bound of the traversal capacity of the channel by using a Jensen inequality and statistical information as follows:
s3, designing the optimal transmitting direction of the 2-transmitting M-receiving system: the method for obtaining the optimal transmitting direction and the optimal power distribution scheme of the 2-transmitting-M-receiving non-uniform antenna array system by utilizing the statistical information specifically comprises the following steps: deducing an optimal transmitting direction as a channel response matrix right singular matrix according to a receiving signal expression, and solving a 2-transmitting M receiving non-uniform linear antenna array system transmission matrix right singular matrix by using matrix analysis knowledge; proving that the capacity upper bound expression is a convex function about power, and solving an optimal power distribution scheme by using a KKT condition;
s4, solving the array antenna design method under different signal-to-noise ratios according to the capacity closed solution after the power distribution scheme specifically comprises the following steps: analyzing the concave-convex property of the capacity closed-type solution to obtain that the closed-type solution is a composite function, and obtaining a conclusion that the capacity of the non-uniform array antenna parameter is the maximum value of the endpoint value according to the monotonicity of the subfunction in the composite function; according to the capacity closed type solution function property, judging the monotonicity of a capacity function subfunction under different signal-to-noise ratios, and determining the optimal nonlinear uniform array antenna parameter value of the system;
s5, designing the optimal array antenna distribution according to the optimal transmission strategy; carrying out closed solution analysis on the transmission power distribution scheme, and designing an antenna method according to different signal-to-noise ratios; the method comprises the following specific steps:
when it is satisfied withAnd isThe design criteria for an optimal irregular antenna array are as follows:
further, in the step S3, the system performance of the signal is optimized according to the eigenvector matrix when the optimal transmission direction of the signal is equal to the channel response covariance matrix, and the optimal transmission direction of the system is obtained as
Wherein
Wherein L ist、LrRespectively, the length of the transmitting and receiving antenna arrays, λ the wavelength of the signal, D the distance between the antenna arrays, αr,lIndicating the normalized position of the l-th receiving antenna from the starting position.
Further, in step S3, according to the capacity upper bound obtained by the statistical information, a power allocation scheme of the transmit antenna of the 2-transmit-M-receive system is obtained, which optimizes the capacity; the method comprises the following specific steps:
Wherein
The invention has the beneficial effects that:
under the irregular array antenna system, the non-uniform antenna array design method utilizing the spherical wave characteristics is better than the performance of the precoding scheme under the existing equal power, and under different signal-to-noise ratios, the array antenna design method provided by the invention is better than the performance of the existing array antenna design method.
Drawings
FIG. 1 is a diagram of a non-uniform antenna array of the present invention in three dimensions;
FIG. 2 is a graph comparing equal power to unequal power distribution for a Rice channel system of the present invention;
fig. 3 is a graph comparing system performance for different array antenna design methods with different signal-to-noise ratios.
Wherein, T in FIG. 1X、RXRespectively representing transmit and receive antenna arrays, thetat、θrRespectively representing the angles between the transmit antenna array and the receive antenna array and the longitudinal axis, D representing the distance between the transmit antenna array and the receive antenna array, phirIndicating the angle of the projection of the receiving antenna array with respect to the horizontal.
Detailed Description
The invention will be described in detail below with reference to the following drawings:
as shown in fig. 1-3:
examples 1,
In this embodiment, a non-uniform antenna array method design scheme using spherical wave characteristics is adopted when the number of antennas is 4, 24, and 100, as shown in fig. 1, the method includes the following steps:
s1, building an antenna array architecture of the non-uniform transmit-receive antenna array, and building a signal model according to the spherical wave model, specifically as follows:
wherein the content of the first and second substances,is a received signal vector, ESIs the total energy of the transmitted signal per unit period,is a matrix of the response of the channel,is the vector of the transmitted signals and,is an independent and identically distributed complex additive white Gaussian noise vector;
s2, establishing a channel model, specifically as follows:
wherein the content of the first and second substances,is the channel response matrix for the direct path in the rice channel,is a channel response matrix of a scattering path in the rice channel, and K represents the ratio of the powers of the direct path and the scattering path;
and assuming that the receiving end knows all the state information of the channel and the transmitting end knows the statistical state information of the channel, the system capacity expression is as follows:
wherein Q is a correlation matrix Q ═ E { SS ] of the transmitted signalHρ is ES/N0U isIs a matrix of eigenvectors ofFeature decomposition diagonal matrix, ΛQIs a eigen-decomposition diagonal matrix of Q;
by using the Jensen inequality, the upper bound of the traversal capacity of the channel is as follows:
s3, obtaining the optimal transmitting direction of the 2-transmitting M-receiving system as
Wherein
S4, obtaining the optimal power distribution scheme of the transmitting antenna of the 2-transmitting-M-receiving system according to the capacity upper bound obtained by the statistical information; the method comprises the following specific steps:
Wherein
Example 2
Example 2 is compared with example 1, the only difference being that the antenna process is being designed.
In this embodiment when satisfyingThe optimal non-uniform receiving antenna array design method is as follows:
example 3
Example 3 is compared with example 1, the only difference being that the antenna process is being designed.
In this embodiment when satisfyingThe optimal receiving antenna design method comprises the following steps:
example 4
Example 4 is compared with example 1, the only difference being that the antenna process is being designed.
comparative examples
In the comparative example, when the number of antennas is selected to be 4, 24, and 200, the antennas are designed by using the existing unequal power allocation method in the rice channel system.
Finally, as shown in fig. 2, when the number of antennas is 4, 24, and 200, the performance of the non-equal power allocation algorithm proposed by us adopted under the rice channel system is improved compared with the traditional equal power allocation algorithm; system performance increases as the signal-to-noise ratio increases.
As shown in fig. 3, the system performance varies with the snr under different non-uniform antenna design methods under the condition that the number of receiving antennas is 4. It is apparent from the figure that the performance is optimal when the antenna design method is the antenna design method in embodiment 2 under low signal-to-noise ratio, and the performance of the system is optimal when the antenna design method is designed by adopting the method in embodiment 3 under high signal-to-noise ratio.
Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims. The techniques, shapes, and configurations not described in detail in the present invention are all known techniques.
Claims (3)
1. A method for designing a non-uniform antenna array system by using a spherical wave model is characterized by comprising the following steps: the method for designing the precoding and array antenna design of the non-uniform antenna array system according to the spherical wave model specifically comprises the following steps:
s1, establishing an antenna array framework with non-uniform antenna arrays for receiving and transmitting, and establishing a signal model according to a spherical wave model;
s2, establishing a channel model, and assuming that the receiving end knows all state information of the channel and the transmitting end knows the statistical state information of the channel, obtaining the system capacity expression as follows:
wherein Q is a correlation matrix Q ═ E { SS ] of the transmitted signalHρ is ES/N0U isIs a matrix of eigenvectors ofFeature decomposition diagonal matrix, ΛQIs a eigen-decomposition diagonal matrix of Q;
and deducing the upper bound of the traversal capacity of the channel by using a Jensen inequality and statistical information as follows:
s3, designing the optimal transmitting direction of the 2-transmitting M-receiving system: the method for obtaining the optimal transmitting direction and the optimal power distribution scheme of the 2-transmitting-M-receiving non-uniform antenna array system by utilizing the statistical information specifically comprises the following steps: deducing an optimal transmitting direction as a channel response matrix right singular matrix according to a receiving signal expression, and solving a 2-transmitting M-receiving non-uniform linear antenna array system transmission matrix right singular matrix by utilizing matrix analysis; proving that the capacity upper bound expression is a convex function about power, and solving an optimal power distribution scheme by using a KKT condition;
s4, solving the array antenna design method under different signal-to-noise ratios according to the capacity closed solution after the power distribution scheme, which specifically comprises the following steps: analyzing capacity closed type solution concave-convex performance to obtain a closed type solution composite function, and obtaining a conclusion that the capacity of the non-uniform array antenna parameter is maximum by taking the endpoint value according to monotonicity of sub-functions in the composite function; according to the capacity closed type solution function property, judging the monotonicity of a capacity function subfunction under different signal-to-noise ratios, and determining the optimal nonlinear uniform array antenna parameter value of the system;
s5, designing the optimal array antenna distribution according to the optimal transmission strategy; carrying out closed solution analysis on the transmission power distribution scheme, and designing an antenna method according to different signal-to-noise ratios; the method comprises the following specific steps:
when it is satisfied withAnd isThe design criteria for an optimal irregular antenna array are as follows:
2. the method of claim 1, wherein the method further comprises: the step S3 of pushing to the optimal transmitting direction specifically includes: according to the characteristic vector matrix when the optimal signal transmitting direction is equal to the channel response covariance matrix, the system performance of the signal is optimal, and the optimal system transmitting direction is obtained
Wherein
Wherein L ist、LrRespectively representing transmit and receive antenna arraysλ represents the wavelength of the signal, D represents the distance between the antenna arrays, αr,lIndicating the normalized position of the l-th receiving antenna from the starting position.
3. The method of claim 2, wherein the method further comprises: the step S3 of solving the optimal power distribution scheme is specifically to obtain a 2-transmission M-reception system transmitting antenna power distribution scheme with optimal capacity according to the capacity upper bound obtained by the statistical information; the method comprises the following specific steps:
Wherein
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CN114389660A (en) * | 2021-12-02 | 2022-04-22 | 重庆邮电大学 | Transmission method containing spherical wave characteristics in super-large-scale MIMO |
CN114520682A (en) * | 2022-01-14 | 2022-05-20 | 重庆邮电大学 | Low-complexity signal detection method using spherical wave characteristics in super-large-scale MIMO |
CN114553275A (en) * | 2022-03-02 | 2022-05-27 | 西安科技大学 | Improved codebook design method suitable for non-uniform line/area array MIMO system |
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Cited By (5)
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CN114520682A (en) * | 2022-01-14 | 2022-05-20 | 重庆邮电大学 | Low-complexity signal detection method using spherical wave characteristics in super-large-scale MIMO |
CN114553275A (en) * | 2022-03-02 | 2022-05-27 | 西安科技大学 | Improved codebook design method suitable for non-uniform line/area array MIMO system |
CN114553275B (en) * | 2022-03-02 | 2022-11-22 | 西安科技大学 | Improved codebook design method and device suitable for non-uniform line/area array MIMO system |
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