The signal-to-noise ratio form of the search radar equation,
*SNR*, is:

where the terms of the equation are:

*P*_{av} — Average transmit power in
watts

*A* — Antenna effective aperture in square meters

*t*_{s} — Search time in seconds

*σ* — Nonfluctuating target radar cross section in square
meters

*F* — One-way propagation factor for the transmit and receive
paths

*F*_{c} — Combined range-dependent factors that
contribute to the reduction of the received signal energy

*k* — Boltzmann constant

*T*_{s} — System temperature in Kelvin

*R* — Target range in meters. The equation assumes the radar is
monostatic.

*L*_{a} — One-way atmospheric absorption
loss

*L* — Combined system losses

*Ω* — Search volume in steradians

You can derive this equation based on assumptions about the SNR form of the standard
radar equation. For more information about the SNR form of the standard radar equation, see
the `radareqsnr`

function. These are the assumptions:

The radar is monostatic, so that *R* = *R*_{t} =
*R*_{r}, where *R*_{t} is the range from
the transmitter to the target and *R*_{r} is the
range from the receiver to the target.

The search time is the time the transmit beam takes to scan the entire search
volume. As a result, you can express the search time,
*t*_{s}, in terms of the search volume,
*Ω*, the area of the beam in steradians,
*Ω*_{t}, and the dwell time in seconds,
*T*_{d}.

The transmit antenna beam has an ideal rectangular shape. As a result, you can
express the transmit antenna gain, *G*_{t}, in
terms of the angular area of the antenna beam.

The receive antenna is ideal. This means you can express the receive antenna gain,
*G*_{r}, in terms of the antenna effective
aperture, *A*, and the radar operating frequency wavelength,
*λ*.