第n个阵元的信号复数加权权值为an。
The signal in branch n is weighted with thecomplex weight an .
若参考阵元接收到的电场强度为E0exp(jΩt)，那么整个阵列接收的总电压E为
For an incoming electric field E0exp(jΩt)at the reference element, the total output voltage E can easily be shown to be(Stutzman and Thiele, 1998; Skolnik, 2001)
式（1.13）与加权序列{an}的离散傅立叶变换DFT形式是相似的。
This is similar in form to the discreteFourier transform (DFT) of the weight sequence {an}.
如同孔径天线一样，线性阵列的天线方向图与傅立叶变换有关，这里的加权序列（加权决定了电流分布的特性）也是如此。
Like the aperture antenna, the antennapattern of the linear array thus involves a Fourier transform, this time of theweight sequence (which determines the current distribution in the antenna).
当an= 1，天线方向图为我们熟悉的"aliased sinc"函数，其幅度为：
For the case where all the an =1, the pattern is the familiar “aliased sinc” function, whosemagnitude is
该函数与式（1.8）和图1.6非常相似。
This function is very similar to that ofEq. (1.8) and Fig. 1.6.
如果天线阵元的数量N非常大（9个或更多），则总的孔径大小D = Nd，3-dB波束宽度为0.89λ/D，第一旁瓣低于主瓣峰值13.2dB（均匀加权条件下）。
If the number of elements N is reasonablylarge (nine or more) and the product Nd is considered to be the total aperturesize D, the 3-dB beamwidth is 0.89λ/D, and the first sidelobe is 13.2 dB belowthe mainlobe peak; both numbers are the same as those of the uniformlyilluminated aperture antenna.
当然，通过改变幅度加权an，可以降低旁瓣电平，但也会带来主瓣宽度的展宽。
Of course, by varying the amplitudes of theweights an , it is possible to reduce the sidelobes at the expenseof a broader mainlobe.
相位中心位于阵列的中心。
The phase center is at the center of thearray.
而真实的天线阵元通常并不是各向同性的全向均匀的辐射器。
Actual array elements are not isotropicradiators.
典型的天线阵元方向图简化模型通常使用一阶近似，即：
A simple model often used as a first-orderapproximation to a typical element pattern Eel(θ) is
式（1.13）的右侧被称为阵列因子AF(θ)，则复合的阵列方向图表达式为：
The right-hand side of Eq. (1.13) is thencalled the array factor AF(θ), and the composite radiation pattern becomes
由于余弦函数随θ变化缓慢，所以尤其在θ = 0°附近考虑阵元方向图的复合阵列方向图的变化并不明显，因此，波束宽度和第一副瓣电平并不会发生很大的变化。
Because the cosine function is slowlyvarying in θ, the beamwidth and first sidelobe level are not greatly changed byincluding the element pattern for signals arriving at angles near broadside(near θ = 0°).
阵元方向图确实降低了远区旁瓣，从而降低了阵列对远离正侧向入射信号的灵敏度。
The element pattern does reduce distantsidelobes, thereby reducing sensitivity to waves impinging on the array fromoff broadside.
到目前为止，我们是根据发射天线方向图（对于孔径天线）或接收方向图（对于天线阵列）进行讨论的，但不是针对两者。
The discussion so far has been phrased interms of the transmit antenna pattern (for aperture antennas) or the receivepattern (for arrays), but not both.
天线方向图都是指单程天线方向图。
The patterns described have been one-wayantenna patterns.
互易性定理保证了接收天线方向图与发射天线方向图是相同的(Balanis，2005)。
The reciprocity theorem guarantees that thereceive antenna pattern is identical to the transmit antenna pattern (Balanis,2005).
因此，对于单基地雷达，双程天线方向图（功率或电压）仅仅是相应的单程方向图的平方。
Consequently, for a monostatic radar, thetwo-way antenna pattern (power or voltage) is just the square of thecorresponding oneway pattern.
此外，天线相位中心在发射和接收模式下都是相同的。
It also follows that the antenna phasecenter is the same in both transmit and receive modes.
——本文译自Mark A. Richards所著的《Fundamentals of Radar Signal Processing（Second edition）》
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