CN102998660A

CN102998660A - Robustness multi-beam forming method in near field scope

Info

Publication number: CN102998660A
Application number: CN2012104872471A
Authority: CN
Inventors: 廖艳苹; 焦艳敏; 陈立伟; 刘玉梅; 汤春明
Original assignee: Harbin Engineering University
Current assignee: Harbin Engineering University
Priority date: 2012-11-26
Filing date: 2012-11-26
Publication date: 2013-03-27

Abstract

The present invention provides a near-field robust multi-beam forming method. Including determining the signal source, the location parameters of the receiving antenna array, and related environmental parameters; using the influence of the near-field and far-field environments on the signal, determining the near-field spherical wave signal and the steering vector; determining the indicators for evaluating signal reception performance; The process of robust beamforming method in a poor environment determines the possible incoming wave direction of the source signal, and obtains the weight vector of the array antenna at this time; performs spatial scanning on the range where the signal exists after detection, and uses the sidelobe power minimization criterion to determine the The precise position of the source signal within the range obtains the weight vector at this time; use the two weight vectors obtained in the above steps to receive the source signal step by step, so as to realize the precise positioning of the incoming wave signal. The multi-beam forming algorithm adopted in the present invention well solves the problem of near-field direction vector mismatch, the algorithm has good robustness, is easy to implement, and improves the performance of the output signal.

Description

A Robust Multi-beamforming Method in the Near Field

技术领域technical field

本发明涉及一种阵列信号处理方法，特别是涉及一种近场鲁棒多波束形成的方法。The invention relates to an array signal processing method, in particular to a near-field robust multi-beam forming method.

背景技术Background technique

波束形成算法实质是天线阵列对准某一特定方向接收信号并处理，使得传感器阵列的输出信号性能最佳，进而达到实现空间指向性的目的，信号与干扰噪声的比常作为衡量算法优劣的标准。随着阵列信号处理的发展以及实际应用的需要，单一方向指向的波束形成算法已经不能满足实际需求。同时对多个方向上的来波信号进行接收并保证波束形成方法的鲁棒性，改善波束形成方法输出性能已经逐步成为波束形成方法研究的主要方向。由于多波束形成方法在多目标多任务信号接收上的优势，其在海洋探测、雷达以及卫星通信等领域有着较高的实用性。The essence of the beamforming algorithm is that the antenna array is aligned in a specific direction to receive and process the signal, so that the output signal performance of the sensor array is the best, and then achieve the purpose of spatial directivity. The ratio of signal to interference noise is often used as a measure of the algorithm. standard. With the development of array signal processing and the needs of practical applications, the single-directional beamforming algorithm can no longer meet the actual needs. Simultaneously receiving incoming signals from multiple directions and ensuring the robustness of the beamforming method, improving the output performance of the beamforming method has gradually become the main direction of beamforming method research. Due to the advantages of the multi-beamforming method in multi-target and multi-task signal reception, it has high practicability in the fields of ocean detection, radar and satellite communication.

多波束形成方法一类是Victor I.Djigan在第九届东西设计与测试讨论会（ESDTS）上发表的Adaptive signal processing in multi-beam arrays文章中使用子阵列模型实现多波束的接收方法。在文章中使用递推最小二乘法（RLS）对每个来波信号分别进行优化。在对某一方向进行优化时，其他方向上的信号都被当作干扰信号抑制掉。优化后会形成不同的权重向量，然后综合输出，可以得到所有的信号。采用子阵列模型的多波束接收需要阵列有较多的阵元个数，应用起来不方便，不容易调整，而且在信号采样时可能会出现不同时性，这样子信号输出就不能保证最优。为了改善子阵列模型在多波束形成方面的不足。另一类为YuLei在文章A Robust Adaptive Beamformer for Multi-path Signal Reception中采用的一个天线阵列完成多个信号的接收。这种只使用一副天线完成多个信号的接收方法相对于前者来说，接收信号时只需要对不同的算法进行优化，而不需要硬件的调整，阵列也不需要很多的阵元个数，减少了优化过程中的数据量，相比而言具有一定的优势。The multi-beam forming method is a multi-beam receiving method using a sub-array model in the Adaptive signal processing in multi-beam arrays article published by Victor I.Djigan at the Ninth East-West Design and Test Symposium (ESDTS). In this paper, each incoming wave signal is optimized separately using the recursive least squares (RLS) method. When optimizing a certain direction, signals in other directions are suppressed as interference signals. After optimization, different weight vectors will be formed, and then integrated and output, all signals can be obtained. The multi-beam reception using the sub-array model requires a large number of array elements, which is inconvenient to apply and difficult to adjust. Moreover, there may be asynchrony during signal sampling, so the sub-signal output cannot be guaranteed to be optimal. In order to improve the insufficiency of the subarray model in multi-beamforming. The other is an antenna array used by YuLei in the article A Robust Adaptive Beamformer for Multi-path Signal Reception to complete the reception of multiple signals. Compared with the former, this method of receiving multiple signals using only one antenna only needs to optimize different algorithms when receiving signals, without requiring hardware adjustments, and the array does not require a large number of array elements. The amount of data in the optimization process is reduced, which has certain advantages in comparison.

Yu Lei采用的方法主要思想是将整个空间域分成相互独立的几个部分，在每个小空间内假定都有不同的来波信号，然后在每个小空间域中都利用适用于导向向量失配鲁棒波束形成方法进行优化。每个空间内的优化都是互不影响的，这样一方面保证了信号接收的鲁棒性，另一方面也确保了每个空间域的信号信息可以完全采集，提高了信号的输出性能。虽然Yu Lei的方法实现了对多信号的接收，不过由于提高信号接收的鲁棒性，在算法优化过程中，将实际导向向量约束在一个不确定集中，然后对不确定集进行处理，而实际应用中，不确定集边界的不同选择将会影响算法的性能。不确定集的确定会使得一定范围内的信号无法正确检测，即相邻的信号间隔过小，该鲁棒性算法将不能很好的分辨每个来波信号。The main idea of the method adopted by Yu Lei is to divide the entire space domain into several independent parts, assuming that there are different incoming wave signals in each small space, and then using the suitable steering vector loss method in each small space domain. Optimized with a robust beamforming method. The optimization in each space does not affect each other, so that on the one hand, it ensures the robustness of signal reception, and on the other hand, it also ensures that the signal information in each space domain can be completely collected, improving the output performance of the signal. Although Yu Lei's method realizes the reception of multiple signals, in order to improve the robustness of signal reception, in the process of algorithm optimization, the actual steering vector is constrained in an uncertain set, and then the uncertain set is processed, while the actual In the application, different choices of the boundary of the uncertain set will affect the performance of the algorithm. The determination of the uncertain set will make the signals within a certain range unable to be detected correctly, that is, the interval between adjacent signals is too small, and the robust algorithm will not be able to distinguish each incoming signal well.

发明内容Contents of the invention

本发明的目的在于提供一种能够提高信号接收的鲁棒性，减小导向向量误差对算法性能的影响，能够抑制干扰和噪声对输出信号的影响，在干扰方向上产生较深的零陷的鲁棒多波束形成方法。The purpose of the present invention is to provide a method that can improve the robustness of signal reception, reduce the influence of steering vector errors on algorithm performance, suppress the influence of interference and noise on output signals, and produce deep nulls in the direction of interference. Robust multi-beamforming method.

本发明的目的是这样实现的：The purpose of the present invention is achieved like this:

(1)确定信号源，接收天线阵列的位置参数，以及相关的环境参数；(1) Determine the signal source, the location parameters of the receiving antenna array, and related environmental parameters;

(2)利用近场与远场环境对信号的影响，确定近场球面波信号以及导向向量；(2) Using the influence of the near-field and far-field environment on the signal, determine the near-field spherical wave signal and the steering vector;

(3)确定评估信号接收性能的指标，即信号与干扰噪声比准则；(3) Determine the index for evaluating signal reception performance, that is, the criterion of signal to interference and noise ratio;

(4)通过最差环境下鲁棒波束形成方法过程，确定源信号可能的来波方向，求得此时阵列天线的权重向量；(4) Determine the possible direction of arrival of the source signal through the process of the robust beamforming method in the worst environment, and obtain the weight vector of the array antenna at this time;

(5)对经过检测后存在信号的范围进行空间扫描，采用旁瓣功率最小化准则确定该范围内源信号的精确位置得到此时的权重向量；(5) Carry out spatial scanning to the range that exists signal after detection, adopt the sidelobe power minimization criterion to determine the precise position of source signal in this range to obtain the weight vector at this moment;

(6)使用上述步骤中得到的两个权重向量分步对源信号进行接收，实现来波信号的精确定位。(6) Using the two weight vectors obtained in the above steps to receive the source signal step by step, so as to realize the precise positioning of the incoming wave signal.

所述的最差环境下鲁棒波束形成方法是将所有可能的实际导向向量看作一个不确定集，而对不确定集中的所有向量进行期望响应无畸变输出，可以转化为对不确定集中向量对应的实际响应值的最差性能进行最优化，转变为最差环境下鲁棒波束形成问题。The robust beamforming method in the worst environment is to regard all possible actual steering vectors as an uncertain set, and to output the expected response without distortion for all vectors in the uncertain set, which can be transformed into the uncertain set vector The worst performance corresponding to the actual response value is optimized, and transformed into the problem of robust beamforming in the worst environment.

所述的对经过检测后存在信号的范围进行空间扫描的方法是在同一时刻对存在信号的空间域逐点进行采样，求相应的旁瓣均方响应，然后使得该响应最小，进而求得此时的最优权重向量，用以获取精确的信号来波方向以及对应的输出性能。The method for spatially scanning the range of existing signals after detection is to sample the spatial domain of existing signals point by point at the same time, to find the corresponding sidelobe mean square response, and then make the response minimum, and then obtain the The optimal weight vector of time is used to obtain the accurate signal incoming wave direction and the corresponding output performance.

本发明的主要优点是：The main advantages of the present invention are:

本发明的核心技术内容在于复杂的近场环境中来波信号的精确定位。本发明解决了一般鲁棒波束形成方法无法精确定位小间隔信号的不足。其主要思想是解决不确定集边界选择存在偏差时，对距离较近的来波信号不可以正确的分辨，从而导致系统的输出性能下降的问题。在鲁棒波束形成方法中，实际方向向量误差值的选择源于实际经验，但是这样选择的边界值往往存在一定的偏差，无法保证在有偏差边界值选择的前提下系统有最优的输出性能。而本发明中，在采用鲁棒波束形成方法之后，再次对感兴趣范围内的信号再次进行检测，避免了对信号的漏检，错检等问题。总之，本发明克服信号不能完全被检测的不足，在保证算法鲁棒性之后，对同一时刻的特定空间进行扫描，加入算法准则，对小范围内的信号进行精确的检测。The core technical content of the invention lies in the precise positioning of the incoming wave signal in the complex near-field environment. The invention solves the deficiency that the general robust beam forming method cannot accurately locate signals with small intervals. Its main idea is to solve the problem that when there is a deviation in the selection of the boundary of the uncertain set, the incoming wave signal at a relatively short distance cannot be correctly distinguished, resulting in a decrease in the output performance of the system. In the robust beamforming method, the selection of the actual direction vector error value is derived from actual experience, but the boundary value selected in this way often has a certain deviation, and it cannot guarantee that the system has optimal output performance under the premise of biased boundary value selection . However, in the present invention, after adopting the robust beamforming method, the signals in the range of interest are detected again, so as to avoid problems such as missed detection and false detection of signals. In a word, the present invention overcomes the deficiency that signals cannot be completely detected, and after ensuring the robustness of the algorithm, scans a specific space at the same time, adds algorithm criteria, and accurately detects signals in a small range.

附图说明Description of drawings

图1为发散播近场与远场不同波前示意图；Figure 1 is a schematic diagram of different wavefronts in the near field and far field of divergent propagation;

图2为本发明中适用的M元均匀圆形阵列，其中各个阵元性质相同且具有全向响应特性；Fig. 2 is the uniform circular array of M element applicable among the present invention, wherein each array element property is identical and has omnidirectional response characteristic;

图3为本发明接收系统示意图。Fig. 3 is a schematic diagram of the receiving system of the present invention.

具体实施方式Detailed ways

下面结合附图和具体实施例对本文作进一步具体说明：Below in conjunction with accompanying drawing and specific embodiment this paper is described in further detail:

近场信号与远场信号的波前示意图如图1所示，从图中可以清晰的看出近场信号是球面波前，而远场信号时平面波前。在远场范围内，由于距离对信号的影响并不显著，所以远场信号可看作是平面波，而天线阵列各个阵元接收到的来波信号的区别在于距离差产生的延迟，这样，在处理的时候就会简单很多。而在近场范围内，距离对信号产生的影响显著，在设计信号模型时，若再以平面波信号作为传输信号，那么算法的输出性能会下降。因此在这种情况下，就不能再用平面波检验算法的性能，因而采用球面波信号就很好必要性。这也是近场与远场的主要区别。在近场范围，距离除了会使接收信号产生一个延迟，同时对信号的能量也产生影响，距离越远，信号强度越小。The schematic diagram of the wave front of the near-field signal and the far-field signal is shown in Figure 1. It can be clearly seen from the figure that the near-field signal is a spherical wave front, while the far-field signal is a plane wave front. In the far-field range, because the distance has no significant influence on the signal, the far-field signal can be regarded as a plane wave, and the difference between the incoming wave signals received by each element of the antenna array lies in the delay caused by the distance difference. In this way, in It will be much easier to deal with. In the near-field range, the distance has a significant impact on the signal. When designing the signal model, if the plane wave signal is used as the transmission signal, the output performance of the algorithm will decrease. Therefore, in this case, it is no longer possible to use plane waves to test the performance of the algorithm, so it is very necessary to use spherical wave signals. This is also the main difference between near field and far field. In the near-field range, the distance not only causes a delay in receiving the signal, but also affects the energy of the signal. The farther the distance is, the smaller the signal strength is.

假定信号源位于接收天线阵列的近场范围，在此空间域中有来自不同方向上的干扰信号以及带提取的期望信号，同时存在有白噪声。信源P与阵列的相对位置为其中，r为信号源到阵列中心的距离，θ为信源的俯仰角，

则为方位角。阵列是由M个性质相同也具有全向响应的传感器组成的半径为R的均匀圆形阵列，其示意图是图2所示。It is assumed that the signal source is located in the near-field range of the receiving antenna array. In this space domain, there are interference signals from different directions and the desired signal with extraction, and white noise exists at the same time. The relative position of the source P and the array is Among them, r is the distance from the signal source to the center of the array, θ is the pitch angle of the signal source,

is the azimuth angle. The array is a uniform circular array with a radius R composed of M sensors with the same properties and omnidirectional response. The schematic diagram is shown in Figure 2.

1.近场模型1. Near-field model

假定圆形阵列第m个阵元与x轴的夹角为

信源在x-y平面投影与其的距离为l_m，信源与第m个阵元的距离为d_m。可得第m个阵元接收到球面波信号为Assume that the angle between the mth element of the circular array and the x-axis is

The distance between the signal source and its projection on the xy plane is l _m , and the distance between the signal source and the mth array element is d _m . It can be obtained that the spherical wave signal received by the mth array element is

${s the s}_{m m} ((t t)) = = \frac{A A}{{d d}_{m m}} exp exp ((jωt jωt - - {jkd jkd}_{m m})) = = {a a}_{m m} s the s ((t t)) - - - - - - ((11))$

其中A是与天线阵列相关的常数，t为时间，j为虚数单位，j²=-1，ω为角频率，波长为λ，对应的波数

与信源和阵列的相对位置关系有关，s(t)＝exp(jωt)。是一个指数信号，对算法性能优劣不产生影响。Where A is a constant related to the antenna array, t is time, j is an imaginary unit, j ² =-1, ω is angular frequency, wavelength is λ, and the corresponding wave number

It is related to the relative position relationship between the source and the array, s(t)=exp(jωt). It is an exponential signal and has no effect on the performance of the algorithm.

天线阵列的接收信号可以表示为：The received signal of the antenna array can be expressed as:

x(n)＝s(n)+i(n)+n(n) (2)x(n)=s(n)+i(n)+n(n)

＝as(n)+i(n)+n(n)=as(n)+i(n)+n(n)

x(n)＝[x₁(n),...,x_M(n)]^T是在n时刻阵列接收到的样本信号，s(n)，i(n)，n(n)分别为互不相关的期望信号，干扰信号以及噪声信号向量分量。a＝[a₁,a₂...,a_M]^T为阵列导向矢量，s(n)则是球面信号中与阵列位置关系无关的成分。x(n)=[x ₁ (n),...,x _M (n)] ^T is the sample signal received by the array at time n, s(n), i(n), n(n) are respectively Uncorrelated desired signal, interference signal and noise signal vector components. a=[a ₁ ,a ₂ ...,a _M ] ^T is the steering vector of the array, and s(n) is the component of the spherical signal that has nothing to do with the positional relationship of the array.

经过化简后，导向向量a可以表示为：After simplification, the steering vector a can be expressed as:

本发明中，解决信号源和基阵在同一平面内的问题，此时导向向量为In the present invention, the problem that the signal source and the matrix are in the same plane is solved, and the steering vector is

从导向向量的表达式可以看到，信号源与天线阵列之间的距离不仅使得不同的阵元之间接收的信号在相位上有所区别，同时改变了信号的能量值。导向向量的变化，使得传统波束形成方法性能严重恶劣。为此，本发明中，将已有波束形成方法改进，解决了传统波束形成方法鲁棒性不佳以及输出性能下降的问题。It can be seen from the expression of the steering vector that the distance between the signal source and the antenna array not only makes the signals received by different array elements differ in phase, but also changes the energy value of the signal. The variation of the steering vector makes the performance of the traditional beamforming method seriously poor. Therefore, in the present invention, the existing beamforming method is improved to solve the problems of poor robustness and output performance degradation of the traditional beamforming method.

2.性能量度2. Performance metrics

假定本发明中窄带波束形成器的权重向量为w，则输出信号可以表示为Assuming that the weight vector of the narrowband beamformer in the present invention is w, then the output signal can be expressed as

y(n)＝w^Hx(n) (5)y(n)=w ^H x(n) (5)

权重向量w可以通过最大化信号与干扰噪声比(SINR)准则获得。The weight vector w can be obtained by maximizing the Signal to Interference and Noise Ratio (SINR) criterion.

$SINR SINR = = \frac{{σ σ}_{s the s}^{22} {| | {w w}^{H h} a a | |}^{22}}{{w w}^{H h} {R R}_{i i + + n no} w w} - - - - - - ((66))$

其中R_i+n＝E{[i(n)+n(n)][i(n)+n(n)]^H}是干扰信号与噪声的互相关矩阵，是期望信号能量。Wherein R _i+n =E{[i(n)+n(n)][i(n)+n(n)] ^H } is the cross-correlation matrix of interference signal and noise, is the expected signal energy.

3.鲁棒波束形成方法3. Robust beamforming method

在最小方差无畸变准则下，对最大信干噪比求解，可以转化为下面的优化问题：Under the minimum variance and no distortion criterion, the solution to the maximum SINR can be transformed into the following optimization problem:

$\begin{matrix} \underset{w w}{min min} {w w}^{H h} {R R}_{i i + + n no} w w & s the s . . t t . . {w w}^{H h} a a = = 11 - - - - - - ((77)) \end{matrix}$

然而在实际应用中，精确的互相关矩阵是不可获得的，因此通常情况下采用采样互相关矩阵

才代替干扰噪声互相关矩阵R_i+n：However, in practical applications, the exact cross-correlation matrix is not available, so the sampling cross-correlation matrix is usually used

to replace the interference noise cross-correlation matrix R _i+n :

$\overset{&OverBar; &OverBar;}{R R} = = \frac{11}{N N} {Σ Σ}_{n no = = 11}^{N N} x x ((n no)) {x x}^{H h} ((n no)) - - - - - - ((88))$

式中N为采样个数，使用该替代后，利用拉格朗日因子法可以求得最佳的权重向量为In the formula, N is the number of samples. After using this substitution, the best weight vector can be obtained by using the Lagrange factor method as

${w w}_{opt opt} = = \frac{{\overset{&OverBar; &OverBar;}{R R}}^{- - 11} a a}{{a a}^{H h} {\overset{&OverBar; &OverBar;}{R R}}^{- - 11} a a} - - - - - - ((99))$

上述算法在导向向量恰好对准来波方向时，算法有很好的输出性能，能够很好的接收信号。不过在实际应用中，期望导向向量与实际导向向量之间不可能完全匹配，在误差存在的情况下，输出信号产生较大的衰减，算法性能急剧下降，鲁棒性欠佳。鲁棒性指的是当信号的实际方向和期望方向存在一定误差的时候，算法仍然能够保证有较好的输出信号，即输出信号与干扰和噪声的比值保持在一定水平内。在实际中，实际导向向量

和期望导向向量a的关系可以表示为：The above algorithm has good output performance and can receive signals well when the steering vector is just aligned with the incoming wave direction. However, in practical applications, it is impossible to completely match the expected steering vector with the actual steering vector. In the case of errors, the output signal will be greatly attenuated, the performance of the algorithm will drop sharply, and the robustness is not good. Robustness means that when there is a certain error between the actual direction of the signal and the expected direction, the algorithm can still guarantee a good output signal, that is, the ratio of the output signal to interference and noise remains within a certain level. In practice, the actual steering vector

The relationship with the expected steering vector a can be expressed as:

$\overset{~ ~}{a a} = = a a + + Δ Δ - - - - - - ((1010))$

Δ表示未知的导向失配复向量，假设实际中Δ为有限值，且由一个正实数限定，即|Δ|≤ε。在这种情况下，SINR准则转变为：Δ represents an unknown steering mismatch complex vector, assuming that Δ is a finite value in practice and is limited by a positive real number, ie |Δ|≤ε. In this case, the SINR criterion transforms into:

$SINR SINR = = \frac{{σ σ}_{s the s}^{22} {| | {w w}^{H h} \overset{~ ~}{a a} | |}^{22}}{{w w}^{H h} {R R}_{i i + + n no} w w} - - - - - - ((1111))$

由SINR的变化，可知当存在导向向量误差的时候，由于天线阵列没有准确对准来波方向，会使得输出SINR下降，换言之，输出性能下降。为了解决该问题，适用于导向向量失配的鲁棒波束形成方法引起研究者的关注。在应用时，实际导向向量

可以用以下的不确定集表示：From the change of SINR, it can be seen that when there is a steering vector error, the output SINR will decrease because the antenna array is not accurately aligned with the incoming wave direction, in other words, the output performance will decrease. In order to solve this problem, the robust beamforming method suitable for steering vector mismatch has attracted the attention of researchers. When applied, the actual steering vector

It can be represented by the following uncertain set:

$A A ((\overset{~ ~}{a a})) \overset{Δ Δ}{= =} {{\overset{~ ~}{a a} | | \overset{~ ~}{a a} = = a a + + e e,, | | | | e e | | | | \leq \leq ϵ ϵ}} - - - - - - ((1212))$

e为实际导向向量与假定导向向量误差，并且是范数有界的，其范数用一个已知的正数ε进行限定。

可以是集合中的任一向量值，为了是算法的性能达到最优，应该令该集合中的最差性能最优，此时可以保证该集合中的其他向量也会是算法的最优值，这样问题转化为最差环境的最优化问题。为了保证信号接收不失真，优化问题可以进一步改写为：e is the error between the actual steering vector and the assumed steering vector, and its norm is bounded, and its norm is limited by a known positive number ε.

It can be any vector value in the set. In order to achieve the optimal performance of the algorithm, the worst performance in the set should be optimized. At this time, it can be guaranteed that other vectors in the set will also be the optimal value of the algorithm. This problem is transformed into the optimization problem of the worst environment. In order to ensure that the signal reception is not distorted, the optimization problem can be further rewritten as:

$\underset{w w}{min min} {w w}^{H h} \overset{&OverBar; &OverBar;}{R R} ws ws . . t t min min | | {w w}^{H h} \overset{~ ~}{a a} | | &GreaterEqual; &Greater Equal; 11,, &ForAll; &ForAll; \overset{~ ~}{a a} &Element; &Element; A A ((\overset{~ ~}{a a})) - - - - - - ((1313))$

对于集合中的任一向量，

都为非线性同时也是非凸约束，这样导致在实际应用时，最佳权重不易获得。然而由于目标函数以及约束条件的特殊形式，优化问题可以经过化简，转变为凸优化问题，同时利用内点法有效地获取最优权重向量。在这样的考虑下，

的不确定集约束条件可以该写为：For any vector in the set,

Both are non-linear and non-convex constraints, which makes it difficult to obtain the optimal weight in practical applications. However, due to the special form of the objective function and constraints, the optimization problem can be simplified and transformed into a convex optimization problem, and the optimal weight vector can be obtained effectively by using the interior point method. Under such consideration,

The uncertain set constraints of can be written as:

min|w^Ha+w^He|≥1 (14)min|w ^H a+w ^H e|≥1 (14)

应用柯西-施瓦茨不等式以及||e||≤ε将约束条件再次化简后，可以得到：After applying the Cauchy-Schwartz inequality and ||e||≤ε to simplify the constraints again, we can get:

min|w^Ha+w^He|＝|w^Ha|-ε||w|| (15)min|w ^H a+w ^H e|＝|w ^H a|-ε||w|| (15)

|w^Ha|-ε||w||≥1 (16)|w ^H a|-ε||w||≥1 (16)

然而由于化简后的等式中仍有绝对值的运算，该约束依然为非凸约束。但由于权重向量的相位旋转不改变目标函数值的特点，在实际中应用中，可以将绝对值运算加以旋转，使得约束条件满足：However, since there are still absolute value operations in the simplified equation, the constraint is still a non-convex constraint. However, since the phase rotation of the weight vector does not change the value of the objective function, in practical applications, the absolute value operation can be rotated so that the constraints are satisfied:

w^Ha≥ε||w||+1，Im{w^Ha}=0 (17)w ^H a≥ε||w||+1, Im{w ^H a}=0 (17)

经过一系列的化简后，优化问题最终转变为最差环境下的凸优化问题，可以写作：After a series of simplifications, the optimization problem is finally transformed into a convex optimization problem in the worst environment, which can be written as:

$\underset{w w}{min min} {w w}^{H h} \overset{&OverBar; &OverBar;}{R R} ws ws . . t t . . {w w}^{H h} a a &GreaterEqual; &Greater Equal; ϵ ϵ | | | | w w | | | | + + 11 - - - - - - ((1818))$

Im{w^Ha}=0Im{w ^H a}=0

在多波束形成中，由于期望信号由不同的方向传播而来，因此只对一个方向上的来波信号进行接收，会造成信号流失，输出性能也随之下降，为此，将上述鲁棒约束算法引入到多波束形成问题中，需要对多个方向上的导向向量进行约束。多波束形成中，来波信号导向向量可以用下述集合A′表示，其中，θ∈[θ₀,…,θ_p-1]表示p个来波方向，p为多波束的个数，

表示各自的实际方向向量，a(θ)对应各自的假定方向向量，而e^′则是每个方向向量各自对应的误差。In multi-beamforming, since the desired signal is transmitted from different directions, only receiving the incoming signal in one direction will cause signal loss and the output performance will also decrease. Therefore, the above robust constraints When the algorithm is introduced into the multi-beamforming problem, it is necessary to constrain the steering vectors in multiple directions. In multi-beam forming, the incoming signal steering vector can be represented by the following set A′, where θ∈[θ ₀ ,…,θ _p-1 ] represents p incoming directions, and p is the number of multi-beams,

represent the respective actual direction vectors, a(θ) corresponds to the respective assumed direction vectors, and e ^' is the error corresponding to each direction vector.

${A A}^{' '} = = {{{\overset{~ ~}{a a}}^{' '} | | {\overset{~ ~}{a a}}^{' '} = = a a ((θ θ)) + + {e e}^{' '},, | | | | {e e}^{' '} | | | | \leq \leq {ϵ ϵ}^{' '} &Element; &Element; {θ θ}_{00},, . . . . . .,, {θ θ}_{p p - - 11}]]}} - - - - - - ((1919))$

多波束情况下，上述鲁棒波束形成方法可以转化为：In the case of multiple beams, the above robust beamforming method can be transformed into:

$\underset{w w}{min min} {w w}^{H h} \overset{&OverBar; &OverBar;}{R R} ws ws . . t t {w w}^{H h} a a ((θ θ)) &GreaterEqual; &Greater Equal; {ϵ ϵ}^{' '} | | | | w w | | | | + + 11$

Im{w^Ha(θ)}=0 (20)Im{w ^H a(θ)}=0 (20)

θ∈[θ₀,…,θ_p-1]θ∈[θ ₀ ,…,θ _p-1 ]

可以看出，在上述鲁棒波束形成方法中，存在一个未知的误差边界ε′。ε′值的不同会使得算法可接收的信号受到一定的限制，而其选择完全是凭借经验所得。上述算法中所获得的权重向量只能够确定来波方向的大概位置，而无法进行精确的定位。这是因为不能保证选取的边界值是最优性能所对应的边界，边界值的不同会导致相距较近的来波信号无法正确分辨。It can be seen that in the above robust beamforming method, there is an unknown error bound ε′. The different values of ε' will limit the signal that the algorithm can receive, and its selection is entirely based on experience. The weight vector obtained in the above algorithm can only determine the approximate position of the incoming wave direction, but cannot perform precise positioning. This is because it cannot be guaranteed that the selected boundary value is the boundary corresponding to the optimal performance, and the difference of the boundary value will cause the incoming wave signals that are relatively close to each other to be incorrectly distinguished.

4.使用旁瓣均方响应最小准则的波束形成方法4. Beamforming method using the minimum criterion of sidelobe mean square response

为了解决边界值不佳对算法性能的影响，本发明在上述算法之上，对经过检测后存在信号的范围进行二次信号处理，精确确定来波信号的位置。在二次信号处理时区别于上述对信号进行时间采样的方式，对同一时刻选定区域内进行空间搜索收集信息，然后应用旁瓣均方响应最小准则确定该区域内精确的来波方向。一定范围内，均方响应ASR为：In order to solve the influence of poor boundary value on the performance of the algorithm, on top of the above algorithm, the present invention performs secondary signal processing on the detected signal range to accurately determine the position of the incoming wave signal. In the secondary signal processing, different from the above-mentioned time sampling method of the signal, the spatial search is carried out to collect information in the selected area at the same time, and then the minimum criterion of the sidelobe mean square response is applied to determine the precise incoming wave direction in the area. Within a certain range, the mean square response ASR is:

$ASR = \frac{1}{Ω} Σ {| w^{' H} x (r_{i}, θ_{j}) |}^{2} = \frac{1}{Ω} Σ w^{' H} x (r_{i}, θ_{j}) x {(r_{i}, θ_{j})}^{H} w^{'}$ (21) $ASR = \frac{1}{Ω} Σ {| w^{' h} x (r_{i}, θ_{j}) |}^{2} = \frac{1}{Ω} Σ w^{' h} x (r_{i}, θ_{j}) x {(r_{i}, θ_{j})}^{h} w^{'}$ (twenty one)

$= = {w w}^{' ' H h} \frac{11}{Ω Ω} Σx Σx (({r r}_{i i},, {θ θ}_{j j})) x x {(({r r}_{i i},, {θ θ}_{j j}))}^{H h} {w w}^{' '} {w w}^{' ' H h} \overset{^^}{R R} {w w}^{' '},, x x (({r r}_{i i},, {θ θ}_{j j})) &Element; &Element; Ω Ω$

其中，w′为此时的权重向量，Ω代表选定的区域，x(r_i,θ_j)为选定区域内的采样信号，r_i和θ_j分别是采样信号所对应的半径和方位角。

为区域内的采样功率，旁瓣均方响应最小准则可以表示为：Among them, w′ is the weight vector at this time, Ω represents the selected area, x(r _i , θ _j ) is the sampling signal in the selected area, r _i and θ _j are the radius and orientation corresponding to the sampling signal horn.

is the sampling power in the area, the minimum criterion of sidelobe mean square response can be expressed as:

$\underset{{w w}^{' '}}{min min} {w w}^{' ' H h} \overset{^^}{R R} ws ws . . t t . . {w w}^{' ' H h} x x (({r r}_{i i},, {θ θ}_{j j})) = = 11 - - - - - - ((22 twenty two))$

由于x(r_i,θ_j)表示在采样区域内某一确定位置的球面波信号，为保证不产生失真，故要求波束指向的输出为1。在利用凸优化方法求解时，为了进一步提高仿真效率，可以将目标函数化简为：Since x(r _i ,θ _j ) represents the spherical wave signal at a certain position in the sampling area, in order to ensure no distortion, the output of the beam pointing is required to be 1. When using the convex optimization method to solve, in order to further improve the simulation efficiency, the objective function can be simplified as:

$w^{H} \overset{&OverBar;}{R} w = {| | Lw | |}^{2}$ (23) $w^{h} \overset{&OverBar;}{R} w = {| | Lw | |}^{2}$ (twenty three)

${w w}^{' ' H h} \overset{^^}{R R} {w w}^{' '} = = {| | | | U u {w w}^{' '} | | | |}^{22}$

其中，L、U分别为

的Cholesky分解函数，

故引入常数τ和υ，将目标函数转化为：

\min_{w, τ} {| | Lw | |}^{2} \leq τ,

(24)Among them, L and U are respectively

The Cholesky decomposition function,

Therefore, constants τ and υ are introduced to transform the objective function into:

\min_{w, τ} {| | Lw | |}^{2} \leq τ,

(twenty four)

$\underset{{w w}^{' '} &upsi; &upsi;}{min min} {| | | | U u {w w}^{' '} | | | |}^{22} \leq \leq &upsi; &upsi;$

把来波信号进行上述两种方法的逐步优化，可以获得精确的来波方向，精确定位来波信号，整个优化过程分两步进行，化简后可能最终的优化算法为：By gradually optimizing the incoming wave signal through the above two methods, the precise incoming wave direction can be obtained, and the incoming wave signal can be precisely positioned. The entire optimization process is divided into two steps. After simplification, the possible final optimization algorithm is:

$\underset{w w,, τ τ}{min min} {| | | | Lw Lw | | | |}^{22} \leq \leq τ τ,,$

s.t.w^Ha(θ)≥ε′||w||+1stw ^H a(θ)≥ε′||w||+1

Im{w^Ha(^θ)}=0，θ∈[θ₀,…,θ_p-1] (25)Im{w ^H a( ^θ )}=0, θ∈[θ ₀ ,…,θ _p-1 ] (25)

$\underset{{w w}^{' '} τ τ}{min min} {| | | | U u {w w}^{' '} | | | |}^{22} \leq \leq &upsi; &upsi;$

s.t.w′^Hx(r_i,θ_j)=1，x(r_i,θ_j)∈Ωstw′ ^H x(r _i ,θ _j )=1，x(r _i ,θ _j )∈Ω

通过一系列的准则细化、化简，上述算法可以对近场范围内间距较小的来波信号进行准确定位，而且具有较好的鲁棒性。本发明在应用上可以延伸为其他的修改、变化、应用和实施例，并且因此认为所有这样的修改、变化、应用、实施例都在本发明的精神和教导范围内。Through a series of criteria refinement and simplification, the above algorithm can accurately locate the incoming wave signals with small spacing in the near-field range, and has good robustness. The present invention extends in application to other modifications, changes, applications and embodiments, and all such modifications, changes, applications and embodiments are therefore considered to be within the spirit and teaching of the present invention.

Claims

1. Robust multi-beamforming method in a near-field range, it is characterized in that comprising the following steps:

(1) Determine the signal source, the location parameters of the receiving antenna array, and related environmental parameters;

(2) Using the influence of the near-field and far-field environments on the signal, determine the near-field spherical wave signal and the steering vector;

(3) Determine the index for evaluating signal reception performance, that is, the criterion of signal to interference and noise ratio;

(4) Determine the possible direction of arrival of the source signal through the process of the robust beamforming method in the worst environment, and obtain the weight vector of the array antenna at this time;

(5) Carry out spatial scanning to the range that exists signal after detection, adopt the sidelobe power minimization criterion to determine the precise position of source signal in this range to obtain the weight vector at this moment;

(6) Using the two weight vectors obtained in the above steps to receive the source signal step by step, so as to realize the precise positioning of the incoming wave signal.

2. The robust multi-beamforming method in the near-field range according to claim 1, characterized in that: the robust beamforming method under the worst environment considers all possible actual steering vectors as an uncertain set, and the undistorted output of the expected response for all vectors in the uncertain set can be transformed into the optimization of the worst performance of the actual response value corresponding to the vector in the uncertain set, and transformed into a robust beamforming problem in the worst environment.

3. The robust multi-beamforming method in the near-field range according to claim 1, characterized in that: the method of spatially scanning the range where signals exist after detection is to scan the space where signals exist at the same time The domain is sampled point by point, and the corresponding sidelobe mean square response is obtained, and then the response is minimized, and then the optimal weight vector at this time is obtained to obtain the accurate signal incoming wave direction and the corresponding output performance.