新体制频率分集阵列（Frequency Diverse Array, FDA）的方向图具有距离-角度二维空间辐射特性，克服了相控阵方向图仅与角度相关的局限性。当对分辨率要求较高时，均匀间距的FDA需要大量阵元，而阵元数的增加将导致成本的升高。为了在几乎保持天线分辨率的同时显著降低成本，对FDA进行非均匀间隔的稀布综合就显得尤为重要。因此，本文对稀布FDA发射-接收波束形成方法展开研究，主要研究内容如下：

（1）针对大型线性FDA阵列成本高和信号处理复杂的问题，首先提出了一种仅稀疏线性FDA发射-接收波束形成方法。具体地，为了解决FDA发射方向图固有的时变问题，提出了一种改进的联合发射-接收域的信号处理链路，该链路仅采用一个混频器和一个模数转换器，显著降低了硬件实现的复杂度；基于该链路，建立了线性FDA发射-接收稀疏模型，通过采用非线性频率步进量，仅在期望的距离-角度二维空间产生时不变聚焦主瓣；采用遗传算法，对所构建的优化模型进行优化，以降低旁瓣区域电平；以采用对数频偏和正弦频偏的两种60元线性FDA为例，仿真结果表明，这两种类型的阵列均可以在旁瓣电平抬高小于1dB的情况下，实现50%的阵元稀疏。

（2）共形阵列具有易与载体平台共形的优势，因此以典型的半圆形共形阵列构型为例，本论文接着对半圆形FDA展开稀疏波束形成研究，提出了一种同时优化稀疏和幅度的半圆形FDA发射-接收优化方法。首先建立半圆形FDA阵列模型并分析其辐射特性；基于此，建立半圆形FDA发射-接收稀疏优化模型，同时考虑激励幅度值，以在期望的距离-角度二维空间产生时不变的点状波束；采用遗传算法对模型进行优化，以采用对数频偏、正弦频偏和双曲正切频偏的三种60元半圆形FDA为例，仿真结果表明，这三种类型的阵列均可在节省50%阵元数的同时，旁瓣电平降低，主瓣展宽。

（3）在工作（2）的基础上，建立了一种优化阵元间距的稀布半圆形FDA发射-接收波束模型，使综合后半圆形FDA的主瓣展宽问题有明显改善。采用遗传算法进行优化，仍然以对数频偏、正弦频偏和双曲正切频偏的三种60元半圆形FDA为例，仿真结果表明，这三种类型的阵列可在节省50%阵元数的同时，旁瓣电平降低，主瓣宽度略微展宽，其中，正弦频偏的半圆形FDA在角度维的主瓣不展宽。可以看出，在其它条件不变的前提下，稀布半圆形FDA发射-接收波束在克服主瓣展宽方面的能力更强，能在大幅降低成本的同时，获得更理想的波束图性能。

      The radiation pattern of the new system Frequency Diverse Array (FDA) is the range and angle two-dimensional spatial radiation characteristics, which overcomes the limitation that the phased array pattern is only related to the angle. When the resolution requirement is high, FDA with uniform spacing requires a large number of elements, and the increase in the number of elements will lead to an increase in cost. In order to significantly reduce the cost while almost maintaining the antenna resolution, it is particularly important to perform non-uniformly spaced sparse synthesis for FDA. Therefore, this thesis studies the sparse FDA transmit-receive beamforming method. The main research contents are as follows:

      (1) Aiming at the problems of high cost and complex signal processing of large linear FDA, a thinned linear FDA transmit-receive beamforming method is proposed. Specifically, in order to solve the inherent time-varying problem of the FDA transmit pattern, an improved transmit-receive domain joint signal processing chain is proposed. The chain only uses a mixer and an analog-to-digital converter, which significantly reduces the complexity of the hardware implementation. Based on this chain, a linear FDA transmit-receive thinned model is established. By using a nonlinear frequency offset, the time-invariant focusing mainlobe is generated only in the desired range-angle two-dimensional space. The genetic algorithm is used to optimize the constructed optimization model to reduce the sidelobe level. Taking two 60-element linear FDAs with logarithmic frequency offset and sinusoidal frequency offset as examples, the simulation results show that both types of arrays can achieve 50% element thinness when the sidelobe level is less than 1dB higher.

      (2) The conformal array has the advantage of being easy to be conformal to the carrier platform. Therefore, taking the typical semicircular conformal array configuration as an example, this thesis then studies the thinned beamforming of the semicircular FDA, and proposes a semicircular FDA transmit-receive thinned optimization method that simultaneously optimizes amplitude. Firstly, a semicircular FDA model is established and its radiation characteristics are analyzed. Therefore, a semicircular FDA transmit-receive thinned optimization model is established, and the excitation amplitude value is considered to generate a time-invariant point beam in the desired range-angle two-dimensional space. The genetic algorithm is used to optimize the model. Taking three semicircular FDAs of sixty elements with logarithmic frequency offset, sinusoidal frequency offset and hyperbolic tangent frequency offset as examples, the simulation results show that the sidelobe levels are reduced and the mainlobes are widened while the number of elements can save 50%.

      (3) On the basis of (2), a sparse semicircular FDA transmit-receive beam model with optimized element spacing is established, which significantly improves the mainlobe broadening problem of the semicircular FDA after synthesis. The genetic algorithm is used for optimization, and three semicircular FDAs of sixty elements with logarithmic frequency offset, sinusoidal frequency offset and hyperbolic tangent frequency offset are still taken as examples. Simulation results show that these three types of arrays can save 50% elements, while the sidelobe levels are reduced and the mainlobe widths are slightly widened. In particularly, a semicircular FDA with sinusoidal frequency offset does not widen the mainlobe in the angle dimension. It can be seen that under the premise of other conditions unchanged, the sparse semicircular FDA transmit-receive beam has a stronger ability to overcome the mainlobe broadening, and can obtain better beampattern performance while greatly reducing the costs.

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