= sub-clutter visibility in dB, S = number of range samples between each transmit pulse, PRF = maximal design pulse repetition frequency. The antenna type and scan performance is a practical consideration for multi-mode radar systems. Diffraction Choppy surfaces, like waves and trees, form a diffraction grating suitable for bending microwave signals. Pulse-Doppler can be so sensitive that diffraction from mountains, buildings or wave tops can be used to detect fast moving objects otherwise blocked by solid obstruction along the line of sight. This is a very lossy phenomenon that only becomes possible when radar has significant excess sub-clutter visibility. Refraction and ducting use transmit frequency at L-band or lower to extend the horizon, which is very different from diffraction. Refraction for over-the-horizon radar uses variable density in the air column above the surface of the earth to bend RF signals. An inversion layer can produce a transient troposphere duct that traps RF signals in a thin layer of air like a wave-guide. Subclutter visibility Subclutter visibility involves the maximum ratio of clutter power to target power, which is proportional to dynamic range. This determines performance in heavy weather and near the earth surface. Subclutter visibility is the ratio of the smallest signal that can be detected in the presence of a larger signal. A small fast-moving target reflection can be detected in the presence of larger slow-moving clutter reflections when the following is true: Performance The pulse-Doppler radar equation can be used to understand trade-offs between different design constraints, like power consumption, detection range, and microwave safety hazards. This is a very simple form of modeling that allows performance to be evaluated in a sterile environment. The theoretical range performance is as follows. where R = distance to the target, Pt = transmitter power, Gt = gain of the transmitting antenna, Ar = effective aperture (area) of the receiving antenna, σ = radar cross section, or scattering coefficient, of the target, F = antenna pattern propagation factor, D = Doppler filter size (transmit pulses in each Fast Fourier transform), Kb = Boltzmann's constant, T = absolute temperature, B = receiver bandwidth (band-pass filter), N = noise figure. This equation is derived by combining the radar equation with the noise equation and accounting for in-band noise distribution across multiple detection filters. The value D is added to the standard radar range equation to account for both pulse-Doppler signal processing and