RadarSim uses SI units internally. Angles passed to physics functions are radians unless a name ends in _deg; powers are watts unless a name ends in _dbm; gains and losses bearing _db are power ratios in decibels.
For a point target at slant range (R), the received power is
[ P_r = \frac{P_t G_t G_r \lambda^2 \sigma}{(4\pi)^3 R^4 L_t L_r L_a}. ]
P_t is peak transmit power, G_t and G_r are linear antenna gains, lambda is wavelength, sigma is RCS, L_t and L_r are transmit and receive loss factors, and L_a is the accumulated two-way atmospheric loss factor. The implementation floors range at 1 m to avoid a singular point-target equation at zero separation.
Receiver noise power is (P_n=kT_sB_nF), where (k) is the exact SI Boltzmann constant, (T_s) is system noise temperature, (B_n) is equivalent noise bandwidth, and (F) is receiver noise factor. If no explicit noise bandwidth is supplied, the scalar radar API uses (1/\tau). This is a modelling default, not a claim that every matched filter has exactly that bandwidth.
The displayed single-look SNR is (10\log_{10}(P_r/P_n)). Noncoherent pulse integration is handled by the detection model, so pulse count is not silently multiplied into received power.
calculate_required_snr_albersheim implements the Albersheim closed-form approximation for noncoherent integration using requested (P_d), (P_{fa}), and pulse count. Inputs are constrained to open probabilities and a positive integer pulse count. It is an approximation to square-law, noncoherent detection and should not be used as an exact coherent-detector threshold.
Probability of detection supports nonfluctuating and Swerling I–IV targets. Swerling I/II use exponential RCS power; III/IV use a gamma distribution with shape two. I and III remain fixed over a coherent processing interval; II and IV decorrelate pulse to pulse. Monte Carlo tests check means and variances against the analytic distributions.
Slant range is the Euclidean norm of the radar-to-target position vector. Radial velocity is (v_r=(\mathbf v_t-\mathbf v_r)\cdot\hat{\mathbf R}), with positive velocity defined as receding. Monostatic Doppler is (f_d=2v_r/\lambda). Consequently, approaching targets have negative Doppler in the physics API.
Gaseous loss follows the line-by-line dry-air and water-vapour specific-attenuation structure in ITU-R P.676. Frequency, pressure, temperature, and water-vapour density are explicit. The homogeneous-path result is multiplied by path length and by two for a monostatic round trip.
Rain specific attenuation follows ITU-R P.838: (\gamma_R=kR^\alpha) dB/km. The coefficients are interpolated by frequency and combined for the configured polarization tilt. Path integration assumes uniform rain. It does not include a melting layer, spatially varying rain cells, radome wetting, or cloud/fog attenuation.
User-provided rcs_m2 is a mean point-target RCS. The optional aspect model applies a simple nose/beam/tail interpolation before Swerling fluctuation. It is useful for sensitivity studies but is not a physical-optics or method-of-moments solver. Target-type defaults are generic illustrative medians and must not be interpreted as authoritative signatures for named platforms.
Normalized surface backscatter (\sigma^0) is converted to clutter RCS by multiplying by the illuminated surface resolution-cell area. The area model uses slant-range resolution, azimuth beamwidth, and grazing-angle projection; values near zero grazing are bounded to avoid a singular footprint.
Land options are:
gamma: an empirical terrain-category backscatter level with grazing-angle dependence.oh1992: the Oh, Sarabandi, and Ulaby co-polarized bare-soil formulation using wavelength, incidence angle, complex relative permittivity, and RMS height. Its published domain is bare soil measured at L, C, and X bands and incidence angles of roughly 10–70 degrees; extrapolation is not validated.
The sea option follows the NRL 2012 empirical reflectivity model, including frequency, grazing angle, polarization, wind/sea-state terms, and propagation-factor selection. Inputs outside the report’s empirical region are rejected or bounded as documented in the function.
Weibull and compound K-distributed generators provide stochastic amplitudes for clutter experiments. They do not make the empirical mean-backscatter model itself stochastic. Rain reflectivity uses the Marshall–Palmer drop-size relation for a volume-clutter estimate.
The terrain module provides deterministic synthetic height fields, bilinear elevation lookup, and sampled line-of-sight masking. It is a geometric obstruction model. Earth curvature, refraction, diffraction, digital-elevation-dataset accuracy, and land-cover scattering are outside its present scope.
Physical inputs are validated before logarithms, divisions, filter design, or distribution sampling. Covariances are symmetrized after updates; linear systems are solved rather than explicitly inverted where possible. Floors used solely to prevent floating-point singularities are documented at the corresponding API.