通过功率积分，可以假设每个体积单元的后向散射是非相干的，而不是相干的。

By integrating power, it is being assumedthat the backscatter from each volume element adds noncoherently rather thancoherently.

这意味着由两个或多个散射中心的后向散射形成的复合电磁波功率是所有单个独立功率的总和，而不是单个电压（电场振幅）的总和。（功率叠加！！！）

This means that the power of the compositeelectromagnetic wave formed from the backscatter of two or more scatteringcenters is the sum of the individual powers, as opposed to the voltage(electric field amplitude) being the sum of the individual amplitudes, in whichcase the power would be the square of the voltage sum.

非相干叠加发生在单个散射信号的相位是随机的，并且彼此不相关的情况下，这与它们处于同相位时的相干情况相反。

Noncoherent addition occurs when the phasesof the individual contributors are random and uncorrelated with one another, asopposed to the coherent case when they are in phase.

这个问题将在第2.7节重新进行讨论。

This issue will be revisited in Sec. 2.7.

如果对点、体、面散射的特殊情况进行评估，式（2.17）的结果更为有用。

The general result of Eq. (2.17) is moreuseful if evaluated for the special cases of point, volume, and areascatterers.

考虑点散射体，分辨率单元体积中的微分RCS由权值σ的Dirac脉冲函数表示：

Beginning with the point scatterer, thedifferential RCS in the resolution cell volume is represented by a Diracimpulse function of weight σ :

将式（2.18）代入式（2.17），则(R0 , θ0 , ϕ0)处的点目标距离方程为：

Using Eq. (2.18) in Eq. (2.17) gives therange equation for a point target at (R0, θ0 , ϕ0)

如果点散射体位于天线视轴方向，则θ0 = ϕ0 = 0，P(θ0 , ϕ0) = G，式（2.19）等同于式（2.11）。

If the point scatterer is located on theantenna boresight θ0 = ϕ0 = 0, P(θ0 , ϕ0)= G and Eq. (2.19) is identical to Eq. (2.11).

接下来考虑体散射的情况，其中雷达RCS被假定为均匀分布在整个体积中的散射体，而不是单个散射点。

Next consider the volume scattering casewhere the RCS seen by the radar is presumed to be due to a distribution ofscatterers evenly distributed throughout the volume, rather than associated witha single point.

在这种情况下，σ表示每立方米的RCS，或体反射率，表示为η。

In this case, σ is expressed in terms ofRCS per cubic meter, or volume reflectivity, denoted as η.

反射率的单位为m2/m3= m-1。

The units of reflectivity are m2/m3= m-1.

微分体单元dV的RCS为：

The RCS of a differential volume element dVis then

其中dΩ为微分立体角单元。

where dΩ is a differential solid angleelement.

则雷达距离方程为

The range equation becomes

如果假设大气损失在距离分辨率单元的范围内缓慢变化，则La®可以替换为La(R0)，其中R0为距离分辨率单元的中心，因此可以当作常数处理，不参与积分运算。

If it is assumed that atmospheric loss isslowly varying over the extent of a range resolution cell, then La®can be replaced by La(R0), where R0 is thecenter of the range resolution cell, and removed from the integral.

则距离上的积分如下：

The integral over range that remains is

上式指出，与绝对距离相比，距离分辨率通常是非常小的。

provided the range resolution is smallcompared to the absolute range, which is usually the case.

将式(2.22)代入式(2.21)，得到

Using Eq. (2.22) in Eq. (2.21) gives

在角坐标上的积分需要已知天线方向图。

Integration over the angular coordinatesrequires knowledge of the antenna pattern.

许多天线主瓣方向图的一个常见近似模型是高斯函数(Sauvageot, 1992)。

One common approximate model of themainlobe of many antennas is a Gaussian function (Sauvageot, 1992).

——本文译自Mark A. Richards所著的《Fundamentals of Radar Signal Processing（Second edition）》

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