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2019-08-27 08:51



As an example, consider an X-band radar with a peak transmitted power of 1 kW and a pencil beam antenna with a 1°beamwidth, and suppose an echo is received from a jumbo jet aircraft with anRCS of 100 m2at arange of 10 km.

2.2.2. Distributed TargetForms of the Range Equation



The received power can be determined usingEq. .

Not all scattering phenomena can be modeledas a reflection from a single point scatterer.

天线增益可由式估算为G = 26000/= 26000 = 44dB。


The antenna gain can be estimated from Eq. to be G = 26,000/ = 26,000 = 44 dB.

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.

图片 1



The radar range equation can be rederivedin a generalized way that accommodates all three cases.

Even though this example is a large targetat short range, the received power is only 3.07 nW, nearly 12 orders ofmagnitude less than the transmitted power!



Equation is still applicable as astarting point.

Nonetheless, this signal level is adequatefor reliable detection in many cases.

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):

This example illustrates the huge dynamicranges observed in radar between transmitted and received signal powers.

图片 2


假设天线视距方向对应于θ =ϕ = 0。

An important consequence of Eq. isthat for a point target, the received power decreases as the fourth power ofrange from the radar to the target.

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。

Thus, the ability to detect a target of agiven radar cross section decreases rapidly with range.

The antenna boresight is normally the axisof maximum gain so that P = G.


现在考虑距离和角度坐标(R,θ, ϕ)上增量体积为dV的散射情况。

Range can be increased by increasingtransmitted power, but because of the R4dependence, the power mustbe raised by a factor of 16 just to double the detection range.

Now consider the scattering from anincremental volume dV located at range and angle coordinates (R, θ, ϕ).



Alternatively, the antenna gain can beincreased by a factor of 4 , implying an increase in antenna area by afactor of 4.

Suppose the incremental RCS of the volumeelement is dσ square meters, and that dσ in general varies with position inspace.



On the other hand, designers of"stealth" aircraft and other target vehicles must reduce the RCS σ bya factor of 16 inorder to halve the range at which they can be detected by a given radar system.

The incremental backscattered power from dVis


图片 3

The range equation is a fundamental radarsystem design and analysis tool.



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.

More elaborate or specialized versions ofthe equation can be formulated to show the effect of other variables, such aspulse length, intermediate frequency bandwidth, or signal processinggains.



After substituting for effective apertureand accounting for losses, this results in an incremental received power of

Several such variations are given inRichards et al. .

图片 4



The range equation also provides the basisfor calibrating a radar system.

Again, this power is received 2R/c secondsafter transmission.



If the system power, gain, and losses arecarefully characterized, then the expected received power of echoes from testtargets of known RCS can be computed.

The total received power is obtained byintegrating over all space to obtain a generalized radar range equation.


图片 5

Calibration tables equating receivervoltage observed due to those signal processing techniques can increase theeffective received power, and therefore increase the obtainable range.



In Eq. , the volume of integration Vis all of three-dimensional space.

The effect of each technique on receivedpower is discussed as they are introduced in later chapters.


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

However, the backscattered energy from allranges does not arrive simultaneously at the radar.

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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

图片 7


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)》

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