WO2020000655A1 - 多天线系统中高功效数模混合波束成形方法、装置及设备 - Google Patents

多天线系统中高功效数模混合波束成形方法、装置及设备 Download PDF

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WO2020000655A1
WO2020000655A1 PCT/CN2018/104918 CN2018104918W WO2020000655A1 WO 2020000655 A1 WO2020000655 A1 WO 2020000655A1 CN 2018104918 W CN2018104918 W CN 2018104918W WO 2020000655 A1 WO2020000655 A1 WO 2020000655A1
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optimization
constraints
optimization problem
variable
analog
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PCT/CN2018/104918
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English (en)
French (fr)
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黄永明
章建军
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东南大学
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Priority to US16/612,761 priority Critical patent/US11031980B2/en
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • 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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H04B7/043—Power distribution using best eigenmode, e.g. beam forming or beam steering
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Definitions

  • the invention belongs to the technical field of wireless communication and radar, and relates to a wireless communication and radar system using a large-plan antenna array at a transmitting / receiving end, and particularly relates to a high-efficiency digital-analog mixed beam forming method, device and equipment in a multi-antenna system.
  • the demand for high-speed data services and ubiquitous access is showing an explosive growth.
  • the next-generation 5G mobile communication technology will have increasing demands on capacity, energy consumption and bandwidth.
  • the multi-antenna array is of great significance in the communication system.
  • For millimeter-wave communications in order to use antenna array gains to compensate for large path losses, large-scale multi-antenna arrays are even more necessary.
  • Multi-antenna arrays are of great significance not only for communication systems, but also for radar systems, because the use of more antennas can further improve spatial resolution and better suppress interference.
  • Multi-antenna arrays can effectively improve the performance of the system, but also increase the difficulty of system design accordingly, and put forward higher requirements for related hardware.
  • millimeter-wave communication compared with the traditional microwave frequency band, the communication distance and coverage are very limited due to the higher frequency and higher path loss of the millimeter-wave signal. It is necessary to compensate the path loss through the array gain provided by the large-scale antenna array, and further improve the system transmission rate and transmission quality by adopting digital-analog hybrid beamforming and space division multiplexing technology.
  • beamforming design plays a central role. Channel estimation, high-resolution direction of arrival estimation, array gain acquisition, interference suppression, and multi-user communication (such as precoding) all rely on efficient beamforming. design. Therefore, both in industry and academia, beam design has attracted great attention and obtained extensive and in-depth research.
  • analog-digital hybrid precoding is usually performed based on a digital-analog hybrid structure, and the analog precoding is implemented by a phase shifter.
  • the current beamforming design method first designs a digital beam according to a given index or requirement, and performs a digital-analog hybrid mapping (assuming that the designed digital beamforming vector is mapped into an analog precoding matrix and Digital precoding vector), and each phase shifter is quantized using nearest distance quantization.
  • the quantization accuracy of the actual phase rotator is limited.
  • the transmit power of each antenna corresponding to the designed beam is very different.
  • the number of quantization bits is small (such as 4 bits)
  • the traditional When using the nearest distance quantization method the degradation of the beam performance is very serious.
  • the purpose of the present invention is to provide a high-efficiency digital-analog mixed beam forming method, device and equipment in a multi-antenna system, which can effectively reduce the peak-to-average ratio of the transmit power of different antennas and improve the Amplifier efficiency.
  • a high-efficiency digital-analog hybrid beamforming method in a multi-antenna system includes the following steps:
  • the optimization problems include three sets of constraints.
  • the first set of constraints is the value of the transmit power of each antenna within a specified range, and the second set Constraints take values within the specified range for the main lobe and sidelobe.
  • the third set of constraints is that the phase of each phase shifter is taken within the specified set.
  • the optimization goal is to minimize the main lobe and sidelobe. Fluctuate, by solving this optimization problem to obtain the corresponding hybrid beamforming analog RF matrix and digital baseband vector;
  • CCCP ConstrainedConcave-ConvexProcedure
  • BCD Block Coordinate Descent
  • the step of using the BCD method to solve the transformed optimization problem in step (3) includes: fixing other optimization variables, constructing and solving the first sub-problem with the simulated RF matrix as the optimization variable; fixing other optimizations Variable, construct and solve the second sub-problem with the digital baseband vector as the optimization variable; fix other optimization variables, construct and solve the third sub-problem with the introduced new optimization variable and the variable that controls fluctuations as the optimization variable; alternately solve
  • the above three sub-problems are updated with multiplier variables and penalty parameters, and iterate until convergence or meet the specified number of iterations.
  • the objective function of the optimization problem obtained in step (2) is:
  • ⁇ is a variable for controlling fluctuations
  • f is a new optimization variable introduced
  • a and d are analog radio frequency matrix and digital baseband vector
  • ⁇ is a penalty parameter
  • u is an introduced multiplier variable.
  • the constraint condition of the first sub-problem constructed in step (3) is that the phase of each phase shifter takes a value within a specified set, and the objective function is:
  • f is a new optimization variable introduced previously
  • a and d are analog radio frequency matrix and digital baseband vector, respectively
  • u is a multiplier variable introduced.
  • the second sub-problem constructed in step (3) is:
  • f is a new optimization variable introduced previously
  • a and d are analog radio frequency matrix and digital baseband vector, respectively
  • u is a multiplier variable introduced.
  • the constraint conditions of the third sub-problem constructed in step (3) are power constraints and fluctuation constraints after constraint transformation, and the objective function is:
  • ⁇ is a variable for controlling fluctuations
  • f is a new optimization variable introduced previously
  • a and d are an analog radio frequency matrix and a digital baseband vector
  • ⁇ is a penalty parameter
  • u is an introduced multiplier variable.
  • a high-efficiency digital-to-analog hybrid beamforming device in a multi-antenna system that implements the high-efficiency digital-to-analog hybrid beamforming method in a multi-antenna system includes:
  • a model initialization module is used to mathematically model a hybrid beamforming design to obtain a corresponding optimization problem.
  • the optimization problem includes three sets of constraints.
  • the first set of constraints is the value of the transmit power of each antenna within a specified range.
  • the second set of constraints takes values within the specified range for fluctuations in the main lobe and side lobes
  • the third set of constraints takes the phase of each phase shifter within the specified set, and the optimization goal is to minimize the main lobe and side Fluctuations in the lobe, and by solving this optimization problem, the corresponding hybrid RF beamforming analog RF matrix and digital baseband vector are obtained;
  • the optimization problem conversion module is used to replace the product of the analog radio frequency matrix and the digital baseband vector in the constraints of the optimization problem with a new optimization variable.
  • the penalty function method is used to transfer the corresponding equation constraints to the objective function. Constraints introduce multiplier variables to transform the original optimization problem into an augmented Lagrange penalty function problem;
  • an optimization problem solving module which uses the CCCP method to convert the transmit power constraints of each antenna of the optimization problem obtained by the optimization problem conversion module and the lower bound non-convex constraints of the fluctuation constraints in the main lobe into convex constraints, and uses a BCD-type method Solve the optimization problem after transformation constraints.
  • the optimization problem solving module includes:
  • the first solving unit is used to fix other optimization variables, and construct and solve the first sub-problem with the simulated RF matrix as the optimization variable;
  • a third solving unit for constructing and solving a third sub-problem that uses the introduced new optimization variables and variables that control fluctuations as optimization variables;
  • an iteration control unit which is used to sequentially call the above three solving units to solve and update the multiplier variables and penalty parameters in each iteration until the iteration converges or the specified number of iterations is satisfied.
  • a computer device includes a memory, a processor, and a computer program stored on the memory and executable on the processor.
  • the computer program is loaded into the processor, the high-efficiency digital-analog hybrid beamforming in the multi-antenna system is realized. method.
  • the high-efficiency digital-to-analog hybrid beamforming method and device suitable for multi-antenna array communication and radar systems provided by the present invention can meet various application requirements in different fields.
  • the beneficial effects are:
  • the high-efficiency digital-to-analog hybrid beamforming method disclosed in the present invention can meet various requirements. Not only can a wide main lobe beam be designed to quickly scan the entire beam space, but also a narrow main lobe beam can be designed to obtain High array gain.
  • each power amplifier corresponding to the beam designed by the present invention is extremely small, so that the peak-to-average ratio is small and the power amplifier efficiency of the power amplifier is very high.
  • the normalized transmit power of each antenna is strictly limited, the designed beam still has good performance, that is, the fluctuations in the main lobe and the side lobe are small, and the transition band is very narrow.
  • the hybrid beamforming method disclosed in the present invention can handle various constraints on the phase value of the phase shifter, including the case where the phase takes continuous values (infinite precision) and the case where the phase takes discrete values (limited precision), and when When the quantization accuracy is very low, very good beam performance can also be obtained.
  • FIG. 1 is a flowchart of a high-efficiency digital-analog hybrid beamforming method according to an embodiment of the present invention.
  • FIG. 2 is a schematic diagram of beam design / optimization in an embodiment of the present invention.
  • FIG. 3 is a normalized amplitude response of a beam designed in an embodiment of the present invention.
  • FIG. 4 is a comparison diagram of normalized amplitude responses of a beam designed in an embodiment of the present invention and a beam designed using other methods.
  • FIG. 5 is a comparison diagram of normalized power of each antenna corresponding to a beam designed in an embodiment of the present invention and a beam designed using other methods.
  • FIG. 6 is a schematic structural diagram of a high-efficiency digital-analog hybrid beamforming device according to an embodiment of the present invention.
  • an embodiment of the present invention discloses a high-efficiency digital-to-analog hybrid beamforming method in a multi-antenna system.
  • the method is applicable to multi-antenna array communication and radar systems.
  • the method is firstly obtained by mathematically modeling the hybrid beamforming design.
  • Corresponding optimization problems which include power constraints, fluctuation constraints, and phase shifter phase constraints; then replace the product of the analog RF matrix and the digital baseband vector in the constraints of the optimization problem with new optimization variables, using penalty
  • the function method transfers the corresponding equation constraints to the objective function, and introduces multiplier variables for the equation constraints, transforming the original optimization problem into an augmented Lagrange penalty function problem; finally, the constraint of the transmit power of each antenna and the main lobe
  • the non-convex constraint of the lower bound of the internal wave constraint is transformed into a convex constraint, and the BCD-type method is used to solve the transformed optimization problem. Specific steps are as follows:
  • Step (1) Perform mathematical modeling on the hybrid beamforming design to obtain the corresponding optimization problem.
  • the index of the beam to be designed is determined according to the application requirements.
  • the relevant input parameters include: 1) the number of array antennas N and the number of radio frequency links K; 2) the main lobe I M , the side lobe I S and the transition band I T ; 3 ) Sampling accuracy in main lobe and side lobe (for uniform linear arrays, the recommended value is 0.5 / N); 4) the set S of phase values (discrete or continuous) that each phase shifter can take; 5) each antenna
  • the dynamic range of the transmit power of the corresponding power amplifier, especially the point or range with the highest power amplifier efficiency, and the normalized transmit power c i (i 1, ..., N) (for a certain actual transmission power value) and the robustness control parameter ⁇ i > 0. It should be noted that the normalized transmit power ⁇ c i ⁇ of each power amplifier may be different, because different types of power amplifiers are allowed.
  • the designed wave combining beam Ad can be modeled as the following optimization problem:
  • e i (0 i-1 , 1,0 Ni ) represents a unit vector in Euclidean space, that is, the i-th element is 1 and the other elements are 0.
  • a T ( ⁇ ) represents the antenna array steering vector, and its specific representation depends on the antenna array form. For example, for a uniform linear array, a T ( ⁇ ) is as follows:
  • the amplifier can not be strictly specified power output, in order to improve the robustness of the design of the beam, the normalized transmission power to the relaxation to the center c i of inter-cell [c i - ⁇ i, c i + ⁇ i] And minimize fluctuations in the main and side lobes.
  • the optimization problem (1) can be further written as
  • the optimization problem modeled in this step includes three sets of constraint conditions.
  • the first group corresponds to the power constraint conditions, that is, the transmit power of each antenna takes a value within a specified range, which can be expressed mathematically as
  • the second group corresponds to the fluctuation constraint conditions, that is, the fluctuations in the main lobe and side lobe take values within a specified range, which can be expressed mathematically as
  • the third group of constraints corresponding to the phase value of the phase shifter can be expressed mathematically as
  • the optimization goal is to minimize the fluctuations in the main and side lobes, and obtain the analog part A * and the digital part d * of the hybrid beamforming vector.
  • Step (2) By introducing new optimization variables and equation constraints, the coupling caused by the multiplication of the analog part and the digital part is processed, and the penalty function method is further used to deal with the equation constraints. Because the analog part A and the digital part d are coupled (in the form of a product) in the optimization problem (3), the product form of A and d makes it extremely difficult to directly optimize A and d. To this end, a new optimization variable and the corresponding equality constraints are introduced to obtain a new optimization problem equivalent to the original optimization problem. However, the introduction of equality constraints also brings new difficulties. For this reason, it is considered to use the penalty function method to transfer the introduced equality constraints to the objective function.
  • the decoupling analog part and the digital part are mainly divided into three sub-steps.
  • the new optimization problem and the original optimization problem are mutually equivalent;
  • the penalty function method usually the quadratic penalty function method
  • Step (3) Use the CCCP method to convert the non-convex part of the transmit power constraint of each antenna (ie, the lower bound of the power constraint) into a convex constraint. Similarly, the non-convex part of the wave constraint in the main lobe (ie the lower bound of the wave constraint) is transformed into a convex constraint.
  • the BCD method is used to solve it. Specifically, the solution of the optimization problem in this embodiment is mainly divided into two sub-steps:
  • the CCCP method is used to transform the non-convex part of the transmit power constraint of each antenna (that is, the lower bound of the power constraint) into a convex constraint, and the non-convex part of the fluctuation constraint in the main lobe (that is, the lower bound of the wave constraint) is transformed into a convex Constraints to facilitate the solution using the BCD method.
  • Step 1 Use the CCCP method to constrain the non-convex part of the transmit power of each antenna (that is, the lower power constraint) Converted into a convex constraint. Specifically, let among them Let f 0 be some initial point, then
  • Step 2 Use the BCD method to solve the optimization problem (8).
  • the specific optimization sub-problems are as follows:
  • the first optimization subproblem is as follows:
  • the optimization problem (9) is equivalent to the following optimization problem
  • b A (m, n) P (n, n)-[AP] (m, n) + R (m, n), [AP] (m, n) represents the (m, n) th of the matrix AP ) Elements.
  • the solution of the optimization problem (11) depends on the set S under consideration.
  • the present invention mainly considers two typical cases.
  • the specific algorithm flow for solving problem (10) is as follows:
  • the second sub-optimization problem is as follows:
  • Step 3 Update the multiplier (dual) variable u and the penalty parameter ⁇ , where the multiplier variable u is updated as follows:
  • u k + 1 u k + (f k -A k d k ) / ⁇ k , (14)
  • a k and d k respectively represent the analog radio frequency matrix and digital baseband vector of the k-th iteration
  • u k and ⁇ k represent multiplier (dual) variables and penalty parameters of the k-th iteration, respectively.
  • the penalty parameters are updated as follows:
  • ⁇ ⁇ (0,1) and ⁇ ⁇ (0,1) are real numbers, and the parameter ⁇ is used to control the growth rate of the penalty parameter ⁇ .
  • the specific algorithm flow for solving the optimization problem (4) using the BCD method is as follows:
  • the high-efficiency digital-to-analog hybrid beamforming method provided by the embodiment of the present invention can restrict the normalized transmission power of each antenna to a small range, and the difference between the normalized transmission power of different antennas is very small. Effectively reduce peak-to-average ratio. It should be pointed out that limiting the normalized transmit power of the antenna within a small range is a very strong constraint. But even so, the designed beam still has very good beam performance, that is, the fluctuations in the main lobe and side lobe are small, and the transition band is very narrow. Not only that, because the phase value constraint of the phase shifter is explicitly considered and optimized, even when the resolution of the phase shifter (ie, the number of quantization bits) is relatively low, a beam with very good performance can be designed.
  • the hybrid beamforming method disclosed in the present invention can be applied not only to communication systems and radar systems, but also to other wireless systems based on antenna arrays; it can be applied not only to uniform linear arrays, but also to planar arrays, etc. Other antenna arrays.
  • the beam space is the interval [-1,1] (the largest space that can be considered).
  • Step (1) mathematically model the hybrid beamforming design to obtain the corresponding optimization problem.
  • the designed hybrid beam Ad can be modeled as the following optimization problem:
  • I M and I S are continuous or uncountable, they must be discretized or sampled. If the sampling interval is set to 1/128, I M and I S are discretized to
  • Step (2) By introducing new optimization variables and corresponding equation constraints, the coupling caused by the multiplication of the analog part and the digital part is processed, and the penalty function method is further used to deal with the equation constraints. Specifically, it is divided into three steps:
  • Step (3) Use the CCCP method to convert the non-convex part of the transmit power constraint of each antenna (ie, the lower bound of the power constraint) into a convex constraint. Similarly, the non-convex part of the wave constraint in the main lobe (ie the lower bound of the wave constraint) is transformed into a convex constraint.
  • the BCD method is used to solve it. Specifically, it is mainly divided into two steps:
  • Step 1 Use the CCCP method to constrain the non-convex part of the transmit power of each antenna (that is, the lower power constraint) ) Into convex constraints. make then Let f 0 be the initial point of some choice, f n represents the value of the variable f at the nth iteration. For n ⁇ 0,
  • f n + 1 can be obtained by solving the following optimization problem
  • Step 2 Use the BCD-type method to solve the optimization problem (8).
  • the optimization problem (8) is decomposed into three optimization sub-problems and iteratively solved.
  • the first optimization subproblem is
  • b A (m, n) P (n, n)-[AP] (m, n) + R (m, n), [AP] (m, n) represents the (m, n) th of the matrix AP ) Elements, to solve the optimization problem (11), only one-dimensional search is required.
  • the optimization problem (13) is a standard convex optimization problem, which can be solved using a standard convex optimization method (such as the interior point method). Solve the optimization subproblems (10), (12), and (13) alternately until convergence, and then obtain the solution of the optimization problem (8)
  • Step 3 Update the multiplier (dual) variable u and the penalty parameter ⁇ , where the multiplier variable u is updated as follows:
  • u k + 1 u k + (f k -A k d k ) / ⁇ k , (14)
  • a k and d k respectively represent the analog radio frequency matrix and digital baseband vector of the k-th iteration
  • u k and ⁇ k represent multiplier (dual) variables and penalty parameters of the k-th iteration, respectively.
  • the penalty parameters are updated as follows:
  • the convergence condition is
  • HBDA Hybrid Beam Design Algorithm
  • other methods including the least square method-LS, beam pattern approximation method-BPSA, and all-digital high-efficiency digital-to-analog mixed beam
  • GMM geometric hybrid mapping method Geometry Hybrid Mapping
  • the transmit power is shown in Figure 5. It can be seen that the hybrid beam design method proposed by the present invention not only has the best beam performance (that is, the fluctuation in the main lobe and the sidelobe is the smallest, and the transition band is very narrow), but the transmission power difference between the antennas is very small, so PAPR is very Low power amplifier with high power efficiency. Since DBDA imposes the same constraints on the transmit power of each antenna as HBDA when designing the beam, the normalized transmit power is the same as HBDA.
  • the phase shifter phase constraint is not taken into account when designing the beam of the DBDA, the beam performance of the designed beam is worse than that of the HBDA, that is, the fluctuation in the main lobe and the side lobe is greater than that in the HBDA.
  • a high-efficiency digital-analog hybrid beamforming device in a multi-antenna system disclosed in an embodiment of the present invention includes a model initialization module, an optimization problem conversion module, and an optimization problem solving module.
  • the model initialization module is used to mathematically model the hybrid beamforming design to obtain corresponding optimization problems.
  • the optimization problems include three sets of constraints. The first set of constraints is that the transmit power of each antenna is taken within a specified range.
  • the second set of constraints is to take values within the specified range for the main lobe and sidelobe fluctuations
  • the third set of constraints is to take the phase of each phase shifter within the specified set
  • the optimization goal is to minimize the main lobe
  • the optimization problem conversion module is used to multiply the analog RF matrix and the digital baseband vector in the constraints of the optimization problem.
  • each antenna used for the optimization problem obtained by using the CCCP method to transform the optimization problem into modules is approximately Lower bound non-convex constraint constraint fluctuations within the main lobe into convex constraints, and the BCD type process optimization problems constraint after conversion.
  • the optimization problem solving module includes: a first solving unit for fixing other optimization variables, constructing and solving a first sub-problem using an analog radio frequency matrix as an optimization variable; and a second solving unit for constructing and solving a digital baseband vector
  • the second sub-problem is the optimization variable
  • the third solving unit is used to construct and solve the third sub-problem with the introduced new optimization variable and the variable controlling fluctuations as the optimization variable
  • an iterative control unit for In the round of iteration, the above three solving units are called in turn to solve and update the multiplier variables and penalty parameters until the iteration converges or meets the specified number of iterations.
  • the embodiment of the high-efficiency digital-to-analog hybrid beamforming device in the multi-antenna system is used to implement the high-efficiency digital-to-analog hybrid beamforming method embodiment in the multi-antenna system.
  • the high-efficiency digital-to-analog hybrid beamforming method embodiment in the multi-antenna system I won't repeat them here.
  • the high-efficiency digital-to-analog hybrid beamforming device in the above multi-antenna system also includes some other well-known structures, such as a processor, a memory, and the like, where the memory includes, but is not limited to, a random access memory, a flash memory, a read-only memory, and a register
  • the processors include, but are not limited to, CPLD, FPGA, DSP, ARM, and MIPS processors.
  • modules in the embodiment can be adaptively changed and set in one or more devices different from the embodiment.
  • the modules or units or components in the embodiments may be combined into one module or unit or component, and furthermore, they may be divided into a plurality of sub-modules or sub-units or sub-components.
  • an embodiment of the present invention further provides a computer device.
  • the computer device may include a memory, a processor, and a computer program stored in the memory and executable on the processor. Wherein, when the computer program is loaded into the processor, each step in the embodiment of the high-efficiency digital-analog hybrid beamforming method in the above-mentioned multi-antenna system is implemented.

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Abstract

本发明公开了一种多天线系统中高功效数模混合波束成形方法、装置及设备，该方法首先对波束成形设计进行数学建模，构造最小化主瓣及旁瓣内波动的波束成形优化问题，该优化问题包括功率约束、波动约束和相移器相位约束，具体为指定每根天线的发送功率的取值范围，要求主瓣与旁瓣内的波动均很小，并且每个相移器仅取指定集合内的相位值；然后使用罚函数方法将原始优化问题转化为约束可分离的优化问题，最后使用块坐标下降方法进行迭代求解。本发明设计的波束峰均比非常小，功率放大器的功放效率很高，并且考虑了相移器的有限分辨率特性。设计的波束主瓣与旁瓣内的波动很小且过渡带很窄，即使对于量化精度很低的相移器，性能损失也较小。

Description

多天线系统中高功效数模混合波束成形方法、装置及设备 技术领域
本发明属于无线通信与雷达技术领域，涉及到发送/接收端使用大规划天线阵列的无线通信与雷达系统，具体涉及一种多天线系统中高功效数模混合波束成形方法、装置及设备。
背景技术
随着无线通信技术的不断发展，高速数据业务以及无处不在的接入需求正呈现出一种爆炸式的增长。下一代5G移动通信技术，对容量、能耗和带宽的需求将越来越高。通过在发送端或接收端使用(大规模)多天线阵列，采用简单的信号处理技术即可以极大地提高通信系统的频谱效率，因此多天线阵列在通信系统中具有非常重要的意义。对于毫米波通信，为了利用天线阵列增益补偿大的路径损失，大规模多天线阵列更是必不可少的。多天线阵列不仅对通信系统具有重要的意义，对于雷达系统也非常重要，因为采用更多的天线能够进一步提高空间分辨率、更好地抑制干扰等。
多天线阵列可以有效地提高系统的性能，但是也相应地增加了系统设计的困难，对相关硬件提出了更高的要求。以毫米波通信为例，与传统微波频段相比，由于毫米波信号的频率较高路径损耗更大，因此通信距离与覆盖范围十分有限。需要通过大规模天线阵列提供的阵列增益补偿路径损失，并通过采用数字-模拟混合波束成形及空分复用技术，进一步提高系统传输速率和传输质量。在通信与雷达系统中，波束成形设计起到了中心作用，信道估计、高分辨率波达方向估计、 阵列增益获取、干扰抑制以及多用户通信(比如预编码)等，均依赖于高效的波束成形设计。因此，无论在工业界还是学术界，波束设计引起了极大的关注，获得了广泛而深入的研究。
尽管波束成形设计获得了深入的研究，已经提出了各种各样的波束成形设计方法，并且取得了较好的性能，但是若干极其重要的问题仍然没有得到切实的解决。首先，尽管通过波束方向图逼近技术可以获得非常好的波束性能，比如主瓣与旁瓣内的波动很小、过渡带非常窄以及可以获得一致的波束对齐性能。但是不同天线的发送功率差异或峰均比(PAPR)可能很大，因而需要功率放大器的动态范围很大，从而对硬件提出了很高的要求。不仅如此，功率放大器的动态范围大，意味着功放的功率效率很低。其次，对于毫米波系统完全在数字域进行预编码非常困难，因此通常基于数字-模拟混合结构进行模拟-数字混合预编码，模拟预编码通过相移器实现。现行的波束成形设计方法先按照给定指标或要求设计数字波束，在假定相位旋转器具有无限分辨率的条件下执行数字-模拟混合映射(即将设计的数字波束形成向量映射成模拟预编码矩阵与数字预编码向量)，并采用最近距离量化方法量化每个相移器。但是，实际的相位旋转器的量化精度是有限的，使用现有的波束设计算法，设计的波束对应的各个天线的发送功率差异很大，当量化比特数较小时(比如4比特)，采用传统的最近距离量化方法时，波束性能的退化非常严重。
发明内容
发明目的：针对现有技术中存在的问题，本发明目的在于提供一 种多天线系统中高功效数模混合波束成形方法、装置及设备，有效降低不同天线发送功率的峰均比，提高功率放大器的功放效率。
技术方案：为实现上述发明目的，本发明采用如下技术方案：
多天线系统中高功效数模混合波束成形方法，包括如下步骤：
(1)对混合波束成形设计进行数学建模得到相应的优化问题，所述优化问题包括三组约束条件，第一组约束条件为每根天线的发送功率在指定范围内取值，第二组约束条件为主瓣与旁瓣内的波动在指定范围内取值，第三组约束条件为每个相移器的相位在指定集合内取值，优化目标为最小化主瓣与旁瓣内的波动，通过求解此优化问题获得相应的混合波束成形的模拟射频矩阵和数字基带向量；
(2)将优化问题的约束条件中模拟射频矩阵与数字基带向量的乘积替换成新的优化变量，使用罚函数方法将相应的等式约束转移到目标函数上，并针对等式约束引入乘子变量，将原始优化问题转化为增广Lagrange罚函数问题；
(3)使用Constrained Concave-Convex Procedure(CCCP)方法将步骤(2)得到的优化问题的每根天线发送功率的约束与主瓣内的波动约束下界的非凸约束转化为凸约束，并使用Block Coordinate Descent(BCD)型方法求解经过转化后的优化问题。
作为优选实施方案，所述步骤(3)中使用BCD方法求解转化后的优化问题的步骤包括：固定其他优化变量，构造并求解以模拟射频矩阵为优化变量的第一个子问题；固定其他优化变量，构造并求解以数字基带向量为优化变量的第二个子问题；固定其他优化变量，构造并 求解以所引入的新的优化变量与控制波动的变量为优化变量的第三个子问题；交替求解上述三个子问题并更新乘子变量及罚参数，迭代直到收敛或满足指定迭代次数。
作为优选实施方案，所述步骤(2)中得到的优化问题的目标函数为：
Figure PCTCN2018104918-appb-000001
其中，ε为控制波动的变量，f为引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，ρ为罚参数，u为引入的乘子变量。
作为优选实施方案，所述步骤(3)中构造的第一个子问题的约束条件为每个相移器的相位在指定集合内取值，目标函数为：
Figure PCTCN2018104918-appb-000002
其中，f为先前引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，u为引入的乘子变量。
作为优选实施方案，所述步骤(3)中构造的第二个子问题为：
Figure PCTCN2018104918-appb-000003
其中，f为先前引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，u为引入的乘子变量。
作为优选实施方案，所述步骤(3)中构造的第三个子问题的约束条件为约束转化后的功率约束和波动约束，目标函数为：
Figure PCTCN2018104918-appb-000004
其中，ε为控制波动的变量，f为先前引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，ρ为罚参数，u为引入的乘子变量。
实现上述多天线系统中高功效数模混合波束成形方法的多天线系统中高功效数模混合波束成形装置，包括：
模型初始化模块，用于对混合波束成形设计进行数学建模得到相应的优化问题，所述优化问题包括三组约束条件，第一组约束条件为每根天线的发送功率在指定范围内取值，第二组约束条件为主瓣与旁瓣内的波动在指定范围内取值，第三组约束条件为每个相移器的相位在指定集合内取值，优化目标为最小化主瓣与旁瓣内的波动，通过求解此优化问题获得相应的混合波束成形的模拟射频矩阵和数字基带向量；
优化问题转化模块，用于将优化问题的约束条件中模拟射频矩阵与数字基带向量的乘积替换成新的优化变量，使用罚函数方法将相应的等式约束转移到目标函数上，并针对等式约束引入乘子变量，将原始优化问题转化为增广Lagrange罚函数问题；
以及优化问题求解模块，用于使用CCCP方法将优化问题转化模块得到的优化问题的每根天线的发送功率约束与主瓣内的波动约束的下界非凸约束转化为凸约束，并使用BCD型方法求解转化约束后的优化问题。
作为优选实施方案，优化问题求解模块包括：
第一求解单元，用于固定其他优化变量，构造并求解以模拟射频 矩阵为优化变量的第一个子问题；
第二求解单元，用于构造并求解以数字基带向量为优化变量的第二个子问题；
第三求解单元，用于构造并求解以所引入的新的优化变量与控制波动的变量为优化变量的第三个子问题；
以及迭代控制单元，用于在每轮迭代中，依次调用上述三个求解单元求解并更新乘子变量及罚参数，直到迭代收敛或满足指定迭代次数。
一种计算机设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，所述计算机程序被加载至处理器时实现所述的多天线系统中高功效数模混合波束成形方法。
有益效果：本发明提供的适用于多天线阵列通信和雷达系统的高功效数模混合波束成形方法和装置，可以满足不同领域中各种应用需求，其有益效果在于：
(1)本发明公开的高功效数模混合波束成形方法可以满足各种需求，不仅可以设计主瓣较宽的波束以实现快速扫描整个波束空间，也可以设计主瓣较窄的波束以获得较高的阵列增益。
(2)本发明设计的波束对应的各个功率放大器的发送功率差异极小，从而峰均比很小、功率放大器的功放效率很高。尽管对每根天线的归一化发送功率作了非常严格的限制，但是设计的波束依然具有很好的性能，即主瓣与旁瓣内的波动很小、过渡带非常窄等。
(3)本发明公开的混合波束成形方法可处理相移器的相位取值 的各种约束，包括相位取连续值(无限精度)的情形和相位取离散值(有限精度)的情形，并且当量化精度很低时，也可以获得非常好的波束性能。
附图说明
图1为本发明实施例的高功效数模混合波束成形方法流程图。
图2为本发明实施例中波束设计/优化示意图。
图3为本发明实施例中设计的波束的归一化幅度响应。
图4为本发明实施例中设计的波束与使用其他方法设计的波束的归一化幅度响应对比图。
图5为本发明实施例中设计的波束与使用其他方法设计的波束对应的各个天线的归一化功率对比图。
图6为本发明实施例的高功效数模混合波束成形装置的结构示意图。
具体实施方式
下面结合附图和具体实施例，进一步阐明本发明。
如图1所示，本发明实施例公开了一种多天线系统中高功效数模混合波束成形方法，该方法适用于多天线阵列通信和雷达系统，方法首先对混合波束成形设计进行数学建模得到相应的优化问题，该优化问题包括功率约束条件、波动约束条件和相移器相位约束条件；然后将优化问题的约束条件中模拟射频矩阵与数字基带向量的乘积替换成新的优化变量，使用罚函数方法将相应的等式约束转移到目标函数上，并针对等式约束引入乘子变量，将原始优化问题转化为增广 Lagrange罚函数问题；最后再将每根天线发送功率的约束与主瓣内的波动约束下界的非凸约束转化为凸约束，并使用BCD型方法求解经过转化后的优化问题。具体步骤如下：
步骤(1)：对混合波束成形设计进行数学建模得到相应的优化问题。
本步骤中，根据应用需求确定待设计波束的指标，相关输入参数包括：1)阵列天线数N，射频链路数K；2)主瓣I M、旁瓣I S及过渡带I T；3)主瓣与旁瓣内的采样精度(对于均匀线性阵列，推荐值为0.5/N)；4)每个相移器可取的相位值(离散或连续)构成的集合S；5)每根天线对应的功率放大器的发射功率的动态范围，特别是功放效率最高的点或范围，并依据每个功率放大器发射功率的动态范围确定其归一化发送功率c i(i＝1,...,N)(针对某个实际发送功率值)以及鲁棒性控制参数δ i＞0。需要指出的是，每个功放的归一化发送功率{c i}可能不同，因为允许使用不同类型的功放。
对于模拟与数字混合天线阵列结构，设计的波束可以表示成Ad，其中A表示模拟射频部分(矩阵维数为N×K)，d表示数字基带部分(向量维数为K×1)。由于A由相移器实现，A的每个元素可以表示为
Figure PCTCN2018104918-appb-000005
其中j表示虚数单位，S表示相移器可取值构成的集合，R表示全体实数构成的集合。将天线阵列的集合记作N＝{1,2,…,N}，设第i个天线的归一化发送功率为c i。
一般而言，希望设计的波束的主瓣与旁瓣内的波动尽可能小，本发明设计波束的基本思想是：约束每根天线对应的功放取预先指定值，并最小化主瓣与旁瓣内的波动。数学上，设计的波合波束Ad可以建模为如下优化问题：
Figure PCTCN2018104918-appb-000006
其中，e i＝(0 i-1,1,0 N-i)表示欧几里得空间中的单位向量，即第i个元素为1，其他元素为0。a T(φ)表示天线阵列导引向量，其具体表示形式取决于天线阵列形态。例如，对于均匀线性阵列，a T(φ)如下：
Figure PCTCN2018104918-appb-000007
其中，φ＝2πd/λ(d和λ分别表示相邻天线之间的距离和信号的波长)。优化问题(1)对应的几何意义如图2所示。
实际中功放并不能严格地输出指定功率，为了提高所设计波束的鲁棒性，将归一化发送功率松弛为以c i为中心的小区间[c i-δ i,c i+δ i]，并最小化主瓣与旁瓣内的波动。数学上，优化问题(1)可以进一步写成
Figure PCTCN2018104918-appb-000008
通过对主瓣与旁瓣进行采样，将具有无穷个约束的优化问题转化为具有有限个约束的优化问题。具体地，由于I M和I S是连续的或者不可数的，必须对其进行离散化或采样，按指定采样精度将I M和I S分别离散化为D M＝{φ 1,φ 2,…}和D S＝{φ' 1,φ' 2,…}，则相应的优化问题可以重新写为
Figure PCTCN2018104918-appb-000009
综上，本步骤所建模的优化问题包括三组约束条件，第一组对应功率约束条件，即每根天线的发送功率在指定范围内取值，数学上可表示为
Figure PCTCN2018104918-appb-000010
第二组对应波动约束条件，即主瓣与旁瓣内的波动在指定范围内取值，数学上可表示为
Figure PCTCN2018104918-appb-000011
第三组对应相移器的相位取值构成的约束，数学上可以表示为
Figure PCTCN2018104918-appb-000012
优化目标为最小化主瓣与旁瓣内的波动，并获得混合波束成形向量的模拟部分A *与数字部分d *。
步骤(2)：通过引入新的优化变量及等式约束，处理由于模拟部分与数字部分相乘而形成的耦合，并进一步使用罚函数方法处理等式约束。由于优化问题(3)中模拟部分A和数字部分d是耦合的(乘积的形式)，A和d的乘积形式导致直接优化A和d极其困难。为此引入新的优化变量及与之相对应的等式约束，获得与原优化问题等价的新的优化问题。但是等式约束的引入也带来了新的困难，为此考虑使用罚函数方法将引入的等式约束转移到目标函数上。为了处理由于罚参 数很小时导致的病态性，考虑针对等式约束引入相应的乘子(对偶)变量，获得增广Lagrange罚函数问题。具体而言，本实施例中解耦模拟部分与数字部分主要分成三个子步骤。
步骤(2.1)：引入新的优化变量及相应的等式约束，构造一个新的优化问题，新的优化问题与原始优化问题是相互等价的；
步骤(2.2)：为了处理引入的新的等式约束，使用罚函数方法(通常是二次罚函数方法)将等式约束转移到目标函数上；
步骤(2.3)：为了处理由于罚参数趋于0时可能引起的病态性，引入乘子(对偶)变量，从而得到增广Lagrange罚函数问题。
下面基于数学表示对本步骤中的求解思路做详细解释说明。
第一步：处理模拟部分与数字部分由于乘积形式构成的耦合，引入新的优化变量f并令f＝Ad，得到如下新的优化问题
Figure PCTCN2018104918-appb-000013
可以证明，优化问题(4)与原始优化问题(3)是等价的。
第二步：为了处理引入的新的等式约束f＝Ad，使用二次罚函数方法将其转移到目标函数上，得到如下优化问题
Figure PCTCN2018104918-appb-000014
需要注意的是，当罚参数ρ很小时(趋于0时)，相应的优化问题极有可能是病态的。
第三步：为了处理由于罚参数很小时导致的病态性，针对等式约束f＝Ad引入乘子(对偶)变量u，得到如下的增广Lagrange罚函数问题
Figure PCTCN2018104918-appb-000015
可以验证，优化问题(6)等价于如下优化问题:
Figure PCTCN2018104918-appb-000016
步骤(3)：使用CCCP方法将每根天线的发送功率约束的非凸部分(即功率约束下界)转化为凸的约束。类似地，将主瓣内波动约束的非凸部分(即波动约束下界)转化为凸的约束。针对转化后的优化问题，进一步使用BCD型方法进行求解。具体而言，本实施例中优化 问题的求解主要分成两个子步骤：
(3.1)使用CCCP方法将每根天线的发送功率约束的非凸部分(即功率约束下界)转化为凸的约束，将主瓣内波动约束的非凸部分(即波动约束下界)转化为凸的约束，从而方便使用BCD方法进行求解。
(3.2)使用BCD方法求解转化后的优化问题，主要是分解成三个子问题，具体优化问题及优化变量为：
(3.1.1)使用BCD方法求解的第一个子问题为固定其他优化变量时，优化每个相移器的取值，相应的优化问题可以进一步使用BCD方法进行求解；
(3.1.2)使用BCD方法求解的第二个子问题为固定其他优化变量时，优化混合波束的数字部分，使用最小二乘法可以获得闭式解；
(3.1.3)使用BCD方法求解的第三个子问题为固定其他优化变量时，联合优化引入的新的优化变量与控制波动的变量，相应的优化问题为凸优化问题，可以转化为二阶锥规划使用内点方法直接求解。
交替求解上述3个子问题并更新乘子(对偶)变量及罚参数，迭代直到收敛或满足指定的迭代次数。
下面基于数学表示对本步骤中的求解思路做详细解释说明。
第一步：使用CCCP方法将每根天线的发送功率约束的非凸部分(即功率下界约束
Figure PCTCN2018104918-appb-000017
转化为凸的约束。具体地，令
Figure PCTCN2018104918-appb-000018
其中
Figure PCTCN2018104918-appb-000019
令f 0为某个初始点，则有
Figure PCTCN2018104918-appb-000020
使用线性部分
Figure PCTCN2018104918-appb-000021
取代原始约束中的二次部分，可以得到如下凸的约束
Figure PCTCN2018104918-appb-000022
类似地，将主瓣内波动约束的非凸部分(即波动下界约束
Figure PCTCN2018104918-appb-000023
)转化为如下凸的约束
Figure PCTCN2018104918-appb-000024
其中，
Figure PCTCN2018104918-appb-000025
令f n表示第n次迭代时变量f的取值，通过使用CCCP方法线性化非凸约束
Figure PCTCN2018104918-appb-000026
及
Figure PCTCN2018104918-appb-000027
第(n+1)次迭代时变量f的取值f n+1可以通过求解如下优化问题
Figure PCTCN2018104918-appb-000028
可以看出，优化问题(8)的约束是可分离的，因此可以使用块坐标下降(BCD)型方法进行求解。
第二步：使用BCD方法求解优化问题(8)，通过将优化问题(8)分解成三个子问题，具体的优化子问题如下：
第一个优化子问题如下：
Figure PCTCN2018104918-appb-000029
优化问题(9)等价于如下优化问题
Figure PCTCN2018104918-appb-000030
其中，矩阵P＝dd H及矩阵R＝(f+ρu)d H。
注意到优化问题(10)的约束仍然是可分离的，因此仍然可以使用块坐标下降方法。具体地，记相应于元素A(m,n)的目标函数为h(A(m,n))，则函数h(A(m,n))可以写成二次型的形式，即
h(A(m,n))＝a|A(m,n)| 2-2Re{b *A(m,n)},
相应的优化问题可以写成
Figure PCTCN2018104918-appb-000031
考虑到
Figure PCTCN2018104918-appb-000032
上述优化问题可以进一步写成
Figure PCTCN2018104918-appb-000033
其中，b＝A(m,n)P(n,n)-[AP](m,n)+R(m,n)，[AP](m,n)表示矩阵AP的第(m,n)个元素。
优化问题(11)的求解依赖于所考虑的集合S，本发明主要考虑两种典型情况。第一种情形为S＝为连续实数集(或S＝[0,2π])，此时最优解为
Figure PCTCN2018104918-appb-000034
第二种情形为S＝为离散有限集合，此时只要进行一维搜索即可。为方便起见，求解问题(10)的具体算法流程如下：
Figure PCTCN2018104918-appb-000035
第二个子优化问题如下：
Figure PCTCN2018104918-appb-000036
相应的最优解(闭式解)为
d *＝(A HA) -1A H(f+ρu).       (12)
第三个子优化问题：
Figure PCTCN2018104918-appb-000037
注意到上述子优化问题为标准的凸优化问题，可以使用标准的凸优化方法(比如内点方法)求解。基于上述三个子问题求解问题(8)的具体算法流程如下：
Figure PCTCN2018104918-appb-000038
第三步：更新乘子(对偶)变量u以及罚参数ρ，其中乘子变量u的更新方法如下：
u k+1＝u k+(f k-A kd k)/ρ k,         (14)
其中，A k与d k分别表示第k迭代的模拟射频矩阵与数字基带向量，而u k与ρ k分别表示第k迭代的乘子(对偶)变量与罚参数。罚参数按下述方式更新：
Figure PCTCN2018104918-appb-000039
其中，β∈(0,1)和γ∈(0,1)为实数，参数β用于控制罚参数ρ的增长速率。使用BCD方法求解优化问题(4)的具体算法流程如下：
Figure PCTCN2018104918-appb-000040
本发明实施例提出的高功效数模混合波束成形方法，由于每个天线的归一化发送功率约束在一个很小的范围内，并且不同天线归一化发送功率的差异非常小，从而可以非常有效地降低峰均比。需要指出的是，限制天线的归一化发送功率在一个很小的范围内是非常强的约束。但是即使如此，设计的波束依然具有非常好的波束性能，即主瓣与旁瓣内的波动很小以及过渡带很窄等。不仅如此，由于对相移器的相位取值约束进行了显式的考虑和优化，即使当相移器的分辨率(即量化比特数)比较低，也可以设计出性能非常好的波束。
需要指出的是，本发明公开的混合波束成形方法不仅可以应用于通信系统与雷达系统中，也适用于其他基于天线阵列的无线系统；不仅可以应用于均匀线性阵列，也可以应用于平面阵等其他天线阵列。为了便于理解本发明方案和效果，本发明提供另一示例性实施例，该实施例考虑发射端为均匀线性阵列的多天线系统，阵列的天线数为 N＝64，射频链路数为K＝3，相邻两根天线之间的间距d＝3λ/8，其中λ为信号波长。为简单起见，假设接收端只安装单根天线。需要注意的是，虽然本实例只考虑发送端安装有天线阵列，但接收端安装天线阵列时本发明也可以使用。
由于为一维线性阵列，波束空间为区间[-1,1](可考虑的最大空间)，波束设计输入参数为：(1)主瓣设置为I M＝[-1,-33/64]，旁瓣设置为I S＝[-31/64,1]，过渡带设置为I T＝[-33/64,-31/64]；(2)主瓣与旁瓣内的采样精度设置为1/128；(3)每天线归一化发送功率均设为1，即c 1＝…＝c N＝1；(4)鲁棒性控制参数均设为0.05，即δ 1＝…＝δ N＝0.05；(5)每个相移器使用4比特进行量化，从而每个相移器可取值构成的集合为
Figure PCTCN2018104918-appb-000041
本实施例提供的多天线系统中高功效数模混合波束成形方法，包括如下步骤：
步骤(1)对混合波束成形设计进行数学建模以得到相应的优化问题。为了最小化设计波束主瓣与旁瓣内的波动，所设计的混合波束Ad可以建模为如下优化问题：
Figure PCTCN2018104918-appb-000042
其中，e i＝(0 i-1,1,0 64-i)表示欧几里得空间中的单位向量(即第i个元素为1，其他元素为0)，集合N＝{1,2,…,64}。
为了提高设计波束的鲁棒性，依据给定的鲁棒性控制参数 δ 1,...,δ N，将归一化发送功率松弛为小区间[0.95,1.05]，相应的优化问题可以写为
Figure PCTCN2018104918-appb-000043
由于I M和I S是连续或不可数的，必须进行离散化或采样，设置采样间距为1/128，则I M和I S分别被离散化为
Figure PCTCN2018104918-appb-000044
和
Figure PCTCN2018104918-appb-000045
相应的优化问题可以重新写为
Figure PCTCN2018104918-appb-000046
步骤(2)：通过引入新的优化变量及相应的等式约束，处理由于模拟部分与数字部分相乘而形成的耦合，并进一步使用罚函数方法处理等式约束。具体而言，分成三个步骤：
第一步：处理模拟部分与数字部分由于乘积形式构成的耦合，为此引入新的优化变量f并令f＝Ad，得到如下新的优化问题
Figure PCTCN2018104918-appb-000047
需要指出的是优化问题(4)与原始优化问题(3)是等价的。
第二步：为了处理引入的新的等式约束f＝Ad，使用二次罚函数方法将其转移到目标函数上，得到如下优化问题：
Figure PCTCN2018104918-appb-000048
第三步：为了处理当罚参数ρ很小时导致的病态性，针对等式约束f＝Ad引入乘子(对偶)变量u，得到如下的增广Lagrange罚函数问题
Figure PCTCN2018104918-appb-000049
计算可得，优化问题(6)等价于如下优化问题:
Figure PCTCN2018104918-appb-000050
步骤(3)：使用CCCP方法将每根天线的发送功率约束的非凸部分(即功率约束下界)转化为凸的约束。类似地，将主瓣内波动约束的非凸部分(即波动约束下界)转化为凸的约束。针对转化后的优化问题，进一步使用BCD型方法进行求解。具体而言，主要分成两个步骤：
第一步：使用CCCP方法将每根天线的发送功率约束的非凸部分(即功率下界约束
Figure PCTCN2018104918-appb-000051
)转化为凸的约束。令
Figure PCTCN2018104918-appb-000052
则
Figure PCTCN2018104918-appb-000053
令f 0为某个选择的初始点，f n表示第n次迭代时变量f的取值，对于n≥0有
Figure PCTCN2018104918-appb-000054
使用线性部分
Figure PCTCN2018104918-appb-000055
取代原始约束中的二次部分，可以得到如下凸的约束
Figure PCTCN2018104918-appb-000056
令
Figure PCTCN2018104918-appb-000057
类似地，将主瓣内波动约束的非凸部分(即波动下界约束
Figure PCTCN2018104918-appb-000058
转化为如下凸的约束
Figure PCTCN2018104918-appb-000059
在已知f n时，f n+1可以通过求解如下优化问题获得
Figure PCTCN2018104918-appb-000060
可以看出，优化问题(8)的约束是可分离的，因此可以使用块坐标下降(BCD)型方法进行求解。
第二步：使用BCD型方法求解优化问题(8)，通过将优化问题(8)分解成三个优化子问题并交替迭代求解。第一个优化子问题为
Figure PCTCN2018104918-appb-000061
令P＝dd H及R＝(f+ρu)d H，优化问题(9)可以等价地写成
Figure PCTCN2018104918-appb-000062
注意到优化问题(10)的约束仍然是可分离的，因此仍可以使用块坐标下降方法。具体地，记相应于元素A(m,n)的目标函数为h(A(m,n))，则h(A(m,n))可以写成如下二次型的形式，即
h(A(m,n))＝a|A(m,n)| 2-2Re{b *A(m,n)},
相应的优化问题可以写成
Figure PCTCN2018104918-appb-000063
考虑到
Figure PCTCN2018104918-appb-000064
上述优化问题可以进一步写成
Figure PCTCN2018104918-appb-000065
其中，b＝A(m,n)P(n,n)-[AP](m,n)+R(m,n)，[AP](m,n)表示矩阵AP的第 (m,n)个元素，求解优化问题(11)只要进行一维搜索即可。
针对每个m∈{1,2,...,64}及n∈{1,2,3}，构造优化问题(11)并使用一维搜索求解，交替迭代直到收敛。可以采用不同的收敛条件，此处收敛条件为目标函数tr(A HAP)-2Re{tr(A HR)}的函数值的变化小于10 -4。
第二个子优化问题为
Figure PCTCN2018104918-appb-000066
相应的最优解(闭式解)为
d *＝(A HA) -1A H(f+ρu).
第三个子优化问题为
Figure PCTCN2018104918-appb-000067
优化问题(13)为标准的凸优化问题，可以使用标准的凸优化方法(比如内点方法)求解。交替求解优化子问题(10)、(12)和(13)直到收敛，即可获得优化问题(8)的解
第三步：更新乘子(对偶)变量u以及罚参数ρ，其中乘子变量u的更新方法如下：
u k+1＝u k+(f k-A kd k)/ρ k,         (14)
其中，A k与d k分别表示第k迭代的模拟射频矩阵与数字基带向量，而u k与ρ k分别表示第k迭代的乘子(对偶)变量与罚参数。罚参数按下 述方式更新：
Figure PCTCN2018104918-appb-000068
其中，β＝0.95和γ＝0.95，罚参数ρ的初始值为ρ 0＝15，乘子(对偶)变量u的初始值为u 0＝[1,1,...,1] T。为求解优化问题(8)，只要按照上述三步进行迭代/更新直至收敛，收敛条件为||f k-A kd k||≤0.2，收敛后获得的A和d(分别记作A *和d *)即为设计的混合波束的模拟分量与数字分量。
本实施例设计的波束f opt＝A *d *的归一化幅度响应如图3所示，需要指出的是，由于本发明在设计波束时将相移器的相位取值考虑在内，因此不需要考虑相位值的量化问题。为了显示本发明公开的方法(记作HBDA，即Hybrid Beam Design Algorithm)的优越性，使用其他方法(包括最小二乘方法-LS、波束方向图逼近方法-BPSA及全数字高功效数模混合波束设计方法-DBDA，三种方法设计的波束的相移器的相位取值均采用几何混合映射方法Geometry Hybrid Mapping，即GHM)设计的波束的归一化幅度响应如图4所示。定义归一化发送功率为10log(|f(i)|/max{|f(i)|})，可用于反应各个天线对应功放的发送功率的差异，4种方法设计的波束对应的归一化发送功率如图5所示。可以看出，本发明提出的混合波束设计方法，不仅波束性能最好(即主瓣与旁瓣内波动最小、过渡带很窄)，而且各个天线之间的发送功率差异极小，因此PAPR很低、功放的功率效率很高。由于DBDA在设计波束时，对每根天线的发送功率施加了与HBDA相同的约束，因此归一化发送功率与HBDA相同。但是，由于DBDA设计波束时未将相移 器相位约束考虑在内，因此设计的波束的波束性能比HBDA差，即主瓣与旁瓣内的波动比HBDA大。
如图6所示，本发明实施例公开的多天线系统中高功效数模混合波束成形装置，包括：模型初始化模块、优化问题转化模块以及优化问题求解模块。其中，模型初始化模块，用于对混合波束成形设计进行数学建模得到相应的优化问题，所述优化问题包括三组约束条件，第一组约束条件为每根天线的发送功率在指定范围内取值，第二组约束条件为主瓣与旁瓣内的波动在指定范围内取值，第三组约束条件为每个相移器的相位在指定集合内取值，优化目标为最小化主瓣与旁瓣内的波动，通过求解此优化问题获得相应的混合波束成形的模拟射频矩阵和数字基带向量；优化问题转化模块，用于将优化问题的约束条件中模拟射频矩阵与数字基带向量的乘积替换成新的优化变量，使用罚函数方法将相应的等式约束转移到目标函数上，并针对等式约束引入乘子变量，将原始优化问题转化为增广Lagrange罚函数问题；优化问题求解模块，用于使用CCCP方法将优化问题转化模块得到的优化问题的每根天线的发送功率约束与主瓣内的波动约束的下界非凸约束转化为凸约束，并使用BCD型方法求解转化约束后的优化问题。
其中优化问题求解模块包括：第一求解单元，用于固定其他优化变量，构造并求解以模拟射频矩阵为优化变量的第一个子问题；第二求解单元，用于构造并求解以数字基带向量为优化变量的第二个子问题；第三求解单元，用于构造并求解以所引入的新的优化变量与控制波动的变量为优化变量的第三个子问题；以及迭代控制单元，用于在 每轮迭代中，依次调用上述三个求解单元求解并更新乘子变量及罚参数，直到迭代收敛或满足指定迭代次数。
上述多天线系统中高功效数模混合波束成形装置实施例用于实现上述多天线系统中高功效数模混合波束成形方法实施例，具体细节参考上述多天线系统中高功效数模混合波束成形方法实施例，此处不再赘述。
本领域技术人员可以理解，上述多天线系统中高功效数模混合波束成形装置还包括一些其他公知结构，例如处理器、存储器等，其中，存储器包括但不限于随机存储器、闪存、只读存储器、寄存器等，处理器包括但不限于CPLD、FPGA、DSP、ARM、MIPS处理器等。
本领域技术人员可以理解，可以对实施例中的模块进行自适应性地改变并且把它们设置在与该实施例不同的一个或多个设备中。可以把实施例中的模块或单元或组件组合成一个模块或单元或组件，以及此外可以把它们分成多个子模块或子单元或子组件。
基于与方法实施例相同的技术构思，本发明实施例还提供了一种计算机设备，该计算机设备可以包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序。其中，计算机程序被加载至处理器时实现上述多天线系统中高功效数模混合波束成形方法实施例中的各步骤。

Claims (9)

  1. 多天线系统中高功效数模混合波束成形方法，其特征在于，包括如下步骤：
    (1)对混合波束成形设计进行数学建模得到相应的优化问题，所述优化问题包括三组约束条件，第一组约束条件为每根天线的发送功率在指定范围内取值，第二组约束条件为主瓣与旁瓣内的波动在指定范围内取值，第三组约束条件为每个相移器的相位在指定集合内取值，优化目标为最小化主瓣与旁瓣内的波动，通过求解此优化问题获得相应的混合波束成形的模拟射频矩阵和数字基带向量；
    (2)将优化问题的约束条件中模拟射频矩阵与数字基带向量的乘积替换成新的优化变量，使用罚函数方法将相应的等式约束转移到目标函数上，并针对等式约束引入乘子变量，将原始优化问题转化为增广Lagrange罚函数问题；
    (3)使用CCCP方法将步骤(2)得到的优化问题的每根天线发送功率的约束与主瓣内的波动约束下界的非凸约束转化为凸约束，并使用BCD型方法求解经过转化后的优化问题。
  2. 根据权利要求1所述的多天线系统中高功效数模混合波束成形方法，其特征在于，所述步骤(3)中使用BCD方法求解转化后的优化问题的步骤包括：固定其他优化变量，构造并求解以模拟射频矩阵为优化变量的第一个子问题；固定其他优化变量，构造并求解以数字基带向量为优化变量的第二个子问题；固定其他优化变量，构造并求解以所引入的新的优化变量与控制波动的变量为优化变量的第三个子 问题；交替求解上述三个子问题并更新乘子变量及罚参数，迭代直到收敛或满足指定迭代次数。
  3. 根据权利要求1所述的多天线系统中高功效数模混合波束成形方法，其特征在于，所述步骤(2)中得到的优化问题的目标函数为：
    Figure PCTCN2018104918-appb-100001
    其中，ε为控制波动的变量，f为引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，ρ为罚参数，u为引入的乘子变量。
  4. 根据权利要求2所述的多天线系统中高功效数模混合波束成形方法，其特征在于，所述步骤(3)中构造的第一个子问题的约束条件为每个相移器的相位在指定集合内取值，目标函数为：
    Figure PCTCN2018104918-appb-100002
    其中，f为先前引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，u为引入的乘子变量。
  5. 根据权利要求2所述的多天线系统中高功效数模混合波束成形方法，其特征在于，所述步骤(3)中构造的第二个子问题为：
    Figure PCTCN2018104918-appb-100003
    其中，f为先前引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，u为引入的乘子变量。
  6. 根据权利要求2所述的多天线系统中高功效数模混合波束成形方法，其特征在于，所述步骤(3)中构造的第三个子问题的约束条件为约束转化后的功率约束和波动约束，目标函数为：
    Figure PCTCN2018104918-appb-100004
    其中，ε为控制波动的变量，f为先前引入的新的优化变量，A和d分别为模拟射频矩阵和数字基带向量，ρ为罚参数，u为引入的乘子变量。
  7. 实现根据权利要求1-6任一项所述的多天线系统中高功效数模混合波束成形方法的多天线系统中高功效数模混合波束成形装置，其特征在于，包括：
    模型初始化模块，用于对混合波束成形设计进行数学建模得到相应的优化问题，所述优化问题包括三组约束条件，第一组约束条件为每根天线的发送功率在指定范围内取值，第二组约束条件为主瓣与旁瓣内的波动在指定范围内取值，第三组约束条件为每个相移器的相位在指定集合内取值，优化目标为最小化主瓣与旁瓣内的波动，通过求解此优化问题获得相应的混合波束成形的模拟射频矩阵和数字基带向量；
    优化问题转化模块，用于将优化问题的约束条件中模拟射频矩阵与数字基带向量的乘积替换成新的优化变量，使用罚函数方法将相应的等式约束转移到目标函数上，并针对等式约束引入乘子变量，将原始优化问题转化为增广Lagrange罚函数问题；
    以及优化问题求解模块，用于使用CCCP方法将优化问题转化模块得到的优化问题的每根天线的发送功率约束与主瓣内的波动约束的下界非凸约束转化为凸约束，并使用BCD型方法求解转化约束后的优化问题。
  8. 根据权利要求7所述的多天线系统中高功效数模混合波束成形装置，其特征在于，优化问题求解模块包括：
    第一求解单元，用于固定其他优化变量，构造并求解以模拟射频矩阵为优化变量的第一个子问题；
    第二求解单元，用于构造并求解以数字基带向量为优化变量的第二个子问题；
    第三求解单元，用于构造并求解以所引入的新的优化变量与控制波动的变量为优化变量的第三个子问题；
    以及迭代控制单元，用于在每轮迭代中，依次调用上述三个求解单元求解并更新乘子变量及罚参数，直到迭代收敛或满足指定迭代次数。
  9. 一种计算机设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，其特征在于，所述计算机程序被加载至处理器时实现根据权利要求1-6任一项所述的多天线系统中高功效数模混合波束成形方法。
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