Radar Systems: From Maxwell to Synthetic Aperture
The physics, signal processing, and applications of electromagnetic remote sensing โ from Watson-Watt's 1935 invention to modern phased arrays, weather radar, and spaceborne SAR imaging.
Radar (RAdio Detection And Ranging) emerged from wartime urgency and now underpins aviation safety, meteorology, autonomous driving, planetary science, and climate observation. This graduate-level course develops radar systematically from Maxwell's equations through pulse-Doppler processing, phased-array antennas, CFAR detection, and synthetic aperture imaging. Each of the nine modules contains full mathematical derivations, SVG diagrams, and executable Python simulations you can run in the browser.
Radar System Block Diagram
Key Equations
Radar Equation
$$P_r = \frac{P_t\, G^2\, \lambda^2\, \sigma}{(4\pi)^3\, R^4\, L}$$
Doppler Shift
$$f_d = \frac{2 v_r}{\lambda}$$
Range Resolution
$$\Delta R = \frac{c\,\tau}{2} = \frac{c}{2B}$$
Matched Filter SNR
$$\text{SNR} = \frac{2E_s}{N_0}$$
SAR Azimuth Resolution
$$\delta_a = \frac{L}{2}$$
PRF Constraints
$$\frac{2 v_{\max}}{\lambda} \le \text{PRF} \le \frac{c}{2 R_{\max}}$$
Nine Modules
EM Wave Foundations
Maxwell equations, plane waves, polarization, Larmor radiation, radar bands (HF through W), atmospheric attenuation.
The Radar Equation
Derive P_r = P_t Gยฒ ฮปยฒ ฯ / ((4ฯ)ยณ Rโด L) from first principles. RCS, max range, monostatic vs bistatic.
Pulse & Modulation
PRI, PRF, duty cycle, range resolution cฯ/2, LFM chirps, Barker codes, matched filter, pulse compression.
Doppler & Moving Targets
Doppler shift f_d = 2v/ฮป, MTI filters, pulse-Doppler, ambiguity function, blind speeds, STAP.
Antennas & Beamforming
Parabolic reflectors, phased arrays, array factor, MIMO radar, Taylor/Chebyshev taper, adaptive nulling.
Signal Processing
CA-CFAR, OS-CFAR detection thresholds, Kalman tracking, Swerling targets, ROC curves, clutter statistics.
Synthetic Aperture Radar
SAR principle, range-Doppler algorithm, stripmap/spotlight/ScanSAR, InSAR phase, polarimetric SAR.
Weather & Atmospheric Radar
Rayleigh scattering from hydrometeors, Z-R relation, dual-pol (Z_DR, ฯ_HV, K_DP), NEXRAD network.
Applications & Defense
ATC, marine, automotive 77 GHz FMCW, GPR, stealth/RAM, AESA, passive radar, electronic warfare.
Prerequisites & Cross-References
Radar fuses three physics domains. Refresh the underlying material in these related courses:
Electrodynamics
Maxwell, radiation, antennas, scattering
Signal Theory
Fourier, sampling, matched filters, FFT
Waves & Optics
Diffraction, interference, aperture synthesis
Earth Observation
Satellite remote sensing context for SAR
Atmospheric Science
Microphysics of hydrometeors for weather radar
Electronics
Mixers, LNAs, ADCs, RF front ends
Recommended Textbooks
- Skolnik, M.I. โ Introduction to Radar Systems, 3rd ed., McGraw-Hill (2001). The canonical systems-engineering reference.
- Richards, M.A. โ Fundamentals of Radar Signal Processing, 2nd ed., McGraw-Hill (2014). Modern DSP perspective.
- Richards, Scheer, & Holm โ Principles of Modern Radar: Basic Principles, SciTech (2010).
- Curlander, J. & McDonough, R. โ Synthetic Aperture Radar: Systems and Signal Processing, Wiley (1991).
- Cumming, I.G. & Wong, F.H. โ Digital Processing of Synthetic Aperture Radar Data, Artech House (2005).
- Doviak, R.J. & Zrnic, D.S. โ Doppler Radar and Weather Observations, 2nd ed., Dover (2006).
- Bringi, V.N. & Chandrasekar, V. โ Polarimetric Doppler Weather Radar, Cambridge (2001).
- Mahafza, B.R. โ Radar Systems Analysis and Design Using MATLAB, 3rd ed., CRC Press (2013).
- Stimson, G.W. โ Introduction to Airborne Radar, 3rd ed., SciTech (2014).