Is the ratio of the power density incident on the

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is the ratio of the power density incident on the receiving station at a distance or range R to the equivalent isotropic power density or the average power density radiated in all directions at that range. The receiving antenna intercepts some of the power density incident upon it, producing an output signal with some amount of power. The factor that expresses how much power is its effective area, A eff = P rx ( W ) /P inc ( W/m 2 ) . The effective area has units of area and is sometimes (but not always) related to the physical area of the antenna. This picture is modified somewhat for a radar link, which also involves some kind of target. The transmitter and receiver are also frequently collocated in a radar, as shown in Figure 1.2. Here, the transmitter and receiver share a common antenna connected through a transmit-receive (T/R) switch. P inc ( W/m 2 ) = P tx G tx 4 πR 2 P scat ( W ) = P inc σ radar bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright ( m 2 ) 8
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R Tx Rx G tx A eff σ Figure 1.2: Radar link. The first line above is the power density incident on the radar target. We next define a radar scattering cross section as the ratio of the total power scattered by the target to the incident power density illuminating it. The cross-section has units of area and may or may not be related to the physical area of the target itself. The definition is such that we take the scattering to be isotropic, simplifying the calculation of the power received back at the radar station. P rx ( W ) = P scat A eff 4 πR 2 All together, these expressions for the received power can be combined to form the radar equation : P rx ( W ) = P tx G tx 4 πR 2 bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright P inc ( W/m 2 ) σ radar bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright P scat ( W ) A eff 4 πR 2 R 4 where we have neglected any losses in the system and propagation channel. The radar equation is useful in evaluating the power budget of a radar link. Notice in particular the inverse dependence on the fourth power of the range, which may make long-range detection difficult. While the equation is complete, it has a number of components that require further investigation. These will make up the body of the content of the text. They are: 1. Antenna gain G tx : What is it, and how is it calculated? 2. Antenna effective area A eff : What is it, how is it calculated, and how is it related to gain? 3. Scattering cross section σ radar : How is it defined, and how is it calculated for different kinds of scatterers? 4. Noise, statistical errors: From where does it come, how is it estimated, and how is it mitigated? 5. Propagation effects, polarization, etc.: How do radar signals propagate from place to place? 6. Signal processing: How are radar data acquired and handled?
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