2.2.2. Distributed TargetForms of the Range Equation
Not all scattering phenomena can be modeledas a reflection from a single point scatterer.
Ground clutter, for example, is bestmodeled as distributed scattering from a surface, while meteorologicalphenomena such as rain or hail are modeled as distributed scattering from athree-dimensional volume.
The radar range equation can be rederivedin a generalized way that accommodates all three cases.
Equation is still applicable as astarting point.
考虑分布式散射问题，由于天线增益随方位角和俯仰角变化，式必须替换为另一个方程，从而考虑天线功率方向图P(θ, ϕ)在特定方向(θ, ϕ)上辐射的功率密度，即：
To consider distributed scatterers, andbecause the gain of the antenna varies with azimuth and elevation angle, Eq. must be replaced with an equation that accounts for the effect of theantenna power pattern P(θ, ϕ) on the power density radiated in a particulardirection (θ, ϕ):
假设天线视距方向对应于θ =ϕ = 0。
Assume that the antenna boresightcorresponds to θ = ϕ = 0.
天线视距通常是最大增益的轴方向，因此P = G。
The antenna boresight is normally the axisof maximum gain so that P = G.
Now consider the scattering from anincremental volume dV located at range and angle coordinates (R, θ, ϕ).
Suppose the incremental RCS of the volumeelement is dσ square meters, and that dσ in general varies with position inspace.
The incremental backscattered power from dVis
As before, dσ is defined such that it isassumed this power is reradiated isotropically, and then collected by theantenna effective aperture, adjusted for the angle of arrival.
After substituting for effective apertureand accounting for losses, this results in an incremental received power of
Again, this power is received 2R/c secondsafter transmission.
The total received power is obtained byintegrating over all space to obtain a generalized radar range equation.
In Eq. , the volume of integration Vis all of three-dimensional space.
However, the backscattered energy from allranges does not arrive simultaneously at the radar.
As discussed in Sec. 1.4.2,only scatterers within a single range resolution cell of extent ΔR contributesignificantly to the radar receiver output at any given instant.
Thus, a more appropriate form of thegeneralized radar range equation gives the received power as a function of time
where ΔR is the range interval of the resolutioncell centered at range R0and Ω represents integration over theangular coordinates.
——本文译自Mark A. Richards所著的《Fundamentals of Radar Signal Processing（Second edition）》