Signal-to-Noise (SNR) for SAR (2)

$SNR_"image" = ( P_"avg" * ( n_"ap" ^2 * A_A ^2 ) * rho_r * sigma_(0, ref) * ( f / f_"ref" )^ n * f * a_"wa" ) / ( 8 pi * c * v_x * (k * T * F_N ) * ( L_"radar" * L_r * L_a ) * [ R ^3 * sqrt(1 - (h/R)^2) 10^(( alpha * R )/10)])$

$(P_"avg")"Average power transmitted during the synthetic aperture data collection period"$

$(A_A)"The physical area of the antenna aperture"$

$(n_"ap")"The aperture efficieny of the antenna"$

$(rho_r)"The slant-range resolution"$

$(sigma_(0, ref))"Distributed target reflectivity (m^2/m^2)"$

$(a_"wa")"Azimuth impulse response broadening factor"$

$(f)"Nominal frequency"$

$(f_"ref")"Reference nominal frequency"$

$(n)"RCS frequency dependence"$

$(R)"The magnitude of the distance vector from radar to target"$

$(v_x)"The platform velocity, horizontal and orthogonal to the target direction"$

$(T)"Ambient temperature"$

$(F_N)"System noise factor for the receiver"$

$(L_"radar")"Noise bandwidth at the antenna port"$

$(L_r)"The reduction in SNR gain due to non-ideal range filtering"$

$(alpha)"The two-way atmospheric loss rate (dB/m)"$

$(L_a)"The reduction in SNR gain due to non-ideal azimuth filtering"$

$(h)"The elevation of the radar relative to the target"$