Radar systems

In short

Radar (RAdio Detection And Ranging) transmits radio waves, receives the echo scattered by a target and measures its range, direction, radial velocity and size. Range comes from echo delay, direction from a narrow antenna beam, velocity from the Doppler shift and target size from the radar cross section. It is a standard unit in the communication/microwave papers of Indian universities and appears in ISRO/DRDO entry tests through the radar equation, Doppler and MTI blind speeds, and in placement rounds at DRDO (LRDE), BEL, ISRO, HAL, Astra Microwave, Data Patterns and Tata Advanced Systems. The same physics runs air-traffic radars at AAI airports, IMD Doppler weather radars, ISRO's RISAT SAR satellites and 77 GHz automotive ADAS sensors.

Explained

Fundamentals and block diagram

• Principle: a pulse of duration τ travels to a target and back in time t_R; range R = c·t_R/2, where c = 3 × 10⁸ m/s. The factor 2 is for the two-way path.
• Pulsed radar blocks: trigger/synchroniser → modulator → transmitter (magnetron, klystron, TWT or solid-state GaN amplifier) → duplexer → antenna → low-noise RF amplifier → mixer with local oscillator → IF amplifier (the matched filter) → detector → video amplifier → display/signal processor.
• Duplexer: a TR/ATR gas-tube or ferrite circulator switch that lets one antenna both transmit and receive, isolating the sensitive receiver from megawatt transmit pulses.
• Key timing terms: pulse width τ (µs) sets resolution and energy; pulse repetition frequency f_p (Hz) and pulse repetition interval T = 1/f_p; duty cycle = τf_p (typically 0.001); average power P_av = P_t·τ·f_p.
• Classification by waveform: pulsed, CW, FM-CW, pulse-Doppler, pulse-compression (chirp/phase-coded), noise/stepped-frequency.
• Classification by function: surveillance (search), tracking, track-while-scan, fire-control, navigation, altimeter, weather, imaging (SAR/ISAR), ground-penetrating, secondary (SSR/transponder-based).
• Monostatic radar has transmitter and receiver at the same site; bistatic separates them (useful against stealth and anti-radiation missiles).
• Primary radar relies on the skin echo; secondary surveillance radar (SSR/MSSR, Mode S) interrogates an aircraft transponder which replies with identity and altitude — used with ASR at Indian airports.
• Radar bands (IEEE letter designations) are allotted in India through the National Frequency Allocation Plan administered by the WPC Wing, DoT, under the Indian Telegraph Act 1885 and the Indian Wireless Telegraphy Act 1933.

Range, resolution, ambiguity and the radar equation

• Maximum unambiguous range R_un = c/(2f_p): an echo arriving after the next pulse is transmitted appears as a false close target (second-time-around echo). High PRF gives good Doppler but short unambiguous range — the basic radar trade-off, broken by PRF staggering or multiple PRFs.
• Range resolution ΔR = cτ/2 for an uncoded pulse, or c/(2B) in general, where B is the signal bandwidth. Wide bandwidth, not short pulse, is the real requirement.
• Angular resolution is set by the beamwidth: two targets at range R are resolved in cross-range if separated by more than R·θ_B.
• Radar equation derivation outline: power density at target = P_tG/(4πR²); reradiated power = that × σ; power density back at radar = P_tGσ/(4πR²)² ; received power P_r = that × effective aperture A_e = G λ²/4π. Setting P_r = S_min gives R_max.
• Consequence: received power falls as 1/R⁴, so doubling range needs 16 times the transmitted power — hence long pulses, pulse integration and large antennas rather than brute power.
• Minimum detectable signal S_min = kT₀B·F_n·(S/N)_min, where k = 1.38 × 10⁻²³ J/K, T₀ = 290 K reference temperature, F_n receiver noise figure.
• Integration improvement: n pulses hit a target per scan; coherent integration improves SNR by n, non-coherent integration by roughly n^0.7–n^0.8.
• Detection statistics: threshold detection trades probability of detection P_d against probability of false alarm P_fa; false alarm time T_fa ≈ 1/(P_fa·B). Fluctuating targets are modelled by the Swerling cases I–IV.
• Radar cross section (σ, m²) depends on target size, shape, material and aspect, not just physical area. Regions: Rayleigh (σ ∝ λ⁻⁴, target ≪ λ), resonance/Mie (oscillatory), optical (σ ≈ projected area). For a sphere of radius r in the optical region σ = πr². Stealth shaping and radar-absorbing material reduce σ.

CW, FM-CW and Doppler radar

• CW radar transmits continuously and measures only the Doppler shift f_d = 2v_r/λ, where v_r is the radial (closing) velocity; it gives speed but no range. Used in police speed guns and ground-speed sensors.
• Doppler is positive for an approaching target and negative for a receding one; only the radial component is measured, so a target crossing the beam shows zero Doppler (tangential blindness).
• Isolation problem: in CW radar, transmitter leakage and clutter swamp the receiver; separate transmit/receive antennas and sideband/FM noise limits decide the usable power.
• FM-CW radar adds frequency modulation (usually triangular) so delay appears as a beat frequency, giving range as well. The altimeter relation R = c·f_b/(4·f_m·Δf), with f_m the modulation rate and Δf the frequency sweep (deviation).
• With a moving target the up-sweep and down-sweep beats differ; the range beat is the average and the Doppler is half the difference, which separates range and velocity.
• Applications: aircraft radio altimeters, level gauges in tanks, 77 GHz automotive radar (FMCW chirp sequences giving range–Doppler maps for ADAS).

MTI and pulse-Doppler radar

• Problem: echoes from ground, sea, rain, birds and chaff (clutter) are far stronger than aircraft echoes but have near-zero Doppler. MTI rejects them by cancelling what does not move.
• Coherent MTI uses a stable local oscillator (STALO) and a coherent oscillator (COHO) phase-locked to the transmitted pulse, so a fixed target gives the same video amplitude every sweep.
• Delay-line canceller: subtract the previous sweep from the present one. Frequency response |H(f_d)| = 2|sin(πf_dT)| — zero at f_d = 0 (clutter) and at multiples of f_p.
• Blind speeds: v_n = nλf_p/2 (n = 1, 2, 3…). Targets at these speeds vanish because their phase advances by a whole cycle between pulses. Cured by staggered PRF or multiple PRFs, which push the first blind speed much higher.
• Double (two-delay) canceller response ∝ 4sin²(πf_dT), giving a wider, deeper clutter notch at the cost of attenuating slow targets; three-pulse and N-pulse FIR cancellers and MTI filter banks generalise this.
• Figures of merit: clutter attenuation, MTI improvement factor I = (S/C)_out/(S/C)_in averaged over target velocity, and sub-clutter visibility (dB).
• Limitations: internal clutter motion (wind-blown trees, sea waves) spreads the clutter spectrum; antenna scanning broadens it; equipment instabilities set a floor.
• Pulse-Doppler radar uses high PRF, coherent processing of a whole burst and FFT/doppler filter banks: excellent clutter rejection and velocity resolution, but range ambiguity which multiple PRFs resolve. Airborne MTI (AMTI) must first subtract platform motion.
• CFAR (constant false alarm rate) processing sets the detection threshold from the local noise/clutter estimate (cell-averaging, ordered-statistic CFAR) so the false alarm rate stays constant across changing clutter.

Pulse compression and matched filtering

• Matched filter: maximises output SNR = 2E/N₀, where E is received pulse energy and N₀/2 the noise power spectral density. Its impulse response is the time-reversed conjugate of the transmitted pulse; implemented as a correlator. Detection depends on energy, not peak power.
• Pulse compression transmits a long pulse (energy) with wide bandwidth (resolution). Linear FM chirp: sweep B over τ, then the matched filter compresses it to width ≈1/B.
• Compression ratio = Bτ = τ/τ_compressed = processing gain. Range sidelobes are reduced by amplitude weighting (Hamming/Taylor) or non-linear FM.
• Phase-coded waveforms: Barker codes (lengths up to 13, peak-to-sidelobe 13:1), polyphase Frank codes, and pseudo-random codes for low probability of intercept.
• Ambiguity function χ(τ, f_d) shows the range–Doppler resolution of a waveform; its volume is invariant, so you can shape resolution but not create it from nothing.
• Benefit: a solid-state transmitter of a few kW average power can match an old megawatt magnetron radar's range while keeping fine resolution.

Tracking radar, phased arrays and imaging radar

• Sequential lobing and conical scan (con-scan) compare echo amplitudes in offset beam positions to find the angle error — simple but vulnerable to amplitude fluctuation.
• Monopulse tracking forms sum and difference beams from a four-horn/four-quadrant feed in one pulse; the difference-to-sum ratio gives the angle error. It is the accurate, standard method.
• Range tracking uses early/late split gates driving a servo loop; velocity tracking uses a Doppler frequency tracker.
• Tracking errors: angle noise/glint, amplitude scintillation, servo lag, multipath at low elevation, and range–angle blind spots.
• Phased array radar: the beam is steered electronically by setting the phase of each element; no inertia, so multiple beams, track-while-scan and adaptive nulling are possible. Passive (PESA) uses one transmitter with phase shifters; AESA gives every element its own transmit/receive module (GaAs/GaN), improving reliability (graceful degradation) and bandwidth. Element spacing ≤ λ/2 avoids grating lobes.
• Beam steering: phase gradient Δφ = (2πd/λ)·sinθ₀ across elements; scanning off broadside shrinks the effective aperture (cosθ loss) and widens the beam.
• Synthetic aperture radar (SAR): platform motion synthesises a long aperture; azimuth resolution approaches D/2 (half the real antenna length) and is independent of range — day/night, all-weather imaging. ISAR uses target rotation instead. India's RISAT series and Chandrayaan-2's DFSAR, plus the NISAR mission with NASA, are SAR systems.
• Secondary/other radars: 3D surveillance radars (range, azimuth, elevation), stacked-beam and frequency-scanned antennas, radar altimeters, ground-penetrating radar, and weather radars that measure reflectivity Z plus Doppler velocity and dual-polarisation parameters to classify rain, hail and wind shear.

Key points

• Range from delay - R = ct_R/2; the factor 2 accounts for the two-way trip.
• Radar equation - received power ∝ 1/R⁴, so R_max varies only as the fourth root of transmitted power.
• PRF trade-off - high f_p gives unambiguous Doppler but ambiguous range; low f_p the reverse.
• Range resolution - ΔR = cτ/2 = c/(2B); bandwidth, not pulse length, is what limits it.
• Duty cycle - τf_p; P_av = P_t·τ·f_p, and detection depends on energy P_t·τ.
• Doppler shift - f_d = 2v_r/λ = 2v_rf/c; only the radial velocity is sensed.
• Blind speed - v_n = nλf_p/2, where an MTI canceller nulls a genuine moving target; fixed by staggered PRF.
• Single canceller response - |H| = 2|sin(πf_dT)|; double canceller 4sin²(πf_dT), a deeper and wider notch.
• Radar cross section - an electromagnetic, aspect-dependent area, not the physical area; σ = πr² for a large sphere.
• Minimum detectable signal - S_min = kT₀B·F_n·(S/N)_min; the receiver noise figure sets the floor.
• Matched filter - gives maximum SNR = 2E/N₀; its impulse response is the time-reversed transmitted pulse.
• Pulse compression gain - Bτ; long pulse for energy, chirp for fine resolution, solid-state transmitters practical.
• Monopulse - sum and difference beams give angle error in a single pulse; the accurate tracking method.
• AESA - per-element T/R modules, agile multi-beam operation, graceful degradation; elements spaced ≤ λ/2.
• SAR azimuth resolution - about D/2, set by the real antenna length and independent of range.
• CFAR - adaptive threshold from local clutter statistics keeps the false alarm rate constant.
• Duplexer - lets one antenna transmit and receive while protecting the receiver.
• Indian regulation - radar frequencies are allotted by WPC (DoT) under the NFAP; the Telegraph Act 1885 and Wireless Telegraphy Act 1933 apply.

Formulas and examples

Example 1 — maximum range from the radar equation. S-band radar: P_t = 500 kW, G = 5000 (37 dBi), f = 3 GHz (λ = 0.1 m), σ = 5 m², S_min = 10⁻¹³ W.

• Numerator: 5 × 10⁵ × (5000)² × (0.1)² × 5 = 5 × 10⁵ × 2.5 × 10⁷ × 0.01 × 5 = 6.25 × 10¹¹.
• Denominator: (4π)³ × 10⁻¹³ = 1984.4 × 10⁻¹³ = 1.9844 × 10⁻¹⁰.
• R⁴ = 6.25 × 10¹¹ / 1.9844 × 10⁻¹⁰ = 3.15 × 10²¹ m⁴ → R_max ≈ 2.37 × 10⁵ m = 237 km.
• Aperture check: A_e = Gλ²/4π = 5000 × 0.01/12.566 = 3.98 m²; a 4 m wide antenna gives θ_B ≈ 70 × 0.1/4 = 1.75°.

Example 2 — timing, resolution and average power. Same radar with τ = 1 µs, f_p = 1000 Hz; an echo returns 400 µs after the pulse.

• R_un = 3 × 10⁸/(2 × 1000) = 150 km; the 237 km detection range above is therefore range-ambiguous — a real set would use a lower PRF or multiple PRFs.
• ΔR = 3 × 10⁸ × 1 × 10⁻⁶/2 = 150 m.
• Duty cycle = 1 × 10⁻⁶ × 1000 = 10⁻³ → P_av = 500 kW × 10⁻³ = 500 W.
• Target range = 3 × 10⁸ × 400 × 10⁻⁶/2 = 60 km (inside R_un, so unambiguous).

Example 3 — minimum detectable signal. B = 1 MHz, F_n = 3 dB (ratio 2), (S/N)_min = 15 dB (ratio 31.6), T₀ = 290 K.

• kT₀B = 1.38 × 10⁻²³ × 290 × 10⁶ = 4.0 × 10⁻¹⁵ W (= −114 dBm).
• S_min = 4.0 × 10⁻¹⁵ × 2 × 31.6 = 2.53 × 10⁻¹³ W ≈ −96 dBm (−114 + 3 + 15 dB).

Example 4 — Doppler and blind speeds. X-band radar at 10 GHz (λ = 0.03 m), f_p = 2 kHz, aircraft closing at 300 m/s.

• f_d = 2 × 300/0.03 = 20 kHz.
• Blind speeds v_n = n × 0.03 × 2000/2 = 30n m/s → 30, 60, 90 … m/s (first blind speed 30 m/s = 108 km/h).
• 300 m/s = 10 × 30, so this target sits exactly on the 10th blind speed and would be cancelled; staggering the PRF (say 2 kHz and 2.1 kHz, a 21:20 ratio) pushes the first common null to 21 × 30 = 630 m/s, beyond any aircraft speed.

Example 5 — pulse compression and FM-CW altimeter.

• Chirp: τ = 50 µs, B = 2 MHz → compression ratio = 2 × 10⁶ × 50 × 10⁻⁶ = 100; compressed width = 1/B = 0.5 µs; ΔR = c/(2B) = 3 × 10⁸/(4 × 10⁶) = 75 m, against 7.5 km for the uncompressed 50 µs pulse — same energy, 100 times better resolution.
• Altimeter: f_m = 100 Hz, Δf = 10 MHz, f_b = 1.2 kHz → R = (3 × 10⁸ × 1200)/(4 × 100 × 10⁷) = 3.6 × 10¹¹/4 × 10⁹ = 90 m.

Where it is used

• Defence R&D and production: DRDO's LRDE (Bengaluru) designs the Rajendra phased-array, Ashwini LLTR, Arudhra MPR and Swathi weapon-locating radar; BEL (Bengaluru, Ghaziabad) and Astra Microwave, Data Patterns and Tata Advanced Systems build T/R modules, exciters and processors — roles in RF design, antenna/array design, signal processing and system integration.
• Civil aviation: AAI operates ASR/MSSR and surface-movement radars at Indian airports with ADS-B; radar data feeds air traffic automation systems.
• Meteorology and disaster management: IMD's Doppler weather radar network (S-, C- and X-band) supports cyclone tracking and nowcasting; about 39 radars were operational in the mid-2020s with a large expansion planned under Mission Mausam — check IMD for the current count.
• Space and remote sensing: ISRO's RISAT SAR satellites, Chandrayaan-2 DFSAR, the NISAR L/S-band SAR mission, radar altimeters on oceanography satellites, and ground radars for launch-vehicle tracking at SDSC Sriharikota.
• Automotive and industrial: 77 GHz FMCW radar for adaptive cruise control and blind-spot detection in ADAS now being integrated by Indian OEMs and Tier-1s (Bharat NCAP pushes adoption); level and flow radars in process plants; marine radars on coastal vessels.
• Civil and security infrastructure: ground-penetrating radar for utility and tunnel surveys, perimeter surveillance radars, railway level-crossing and obstacle detection, and coastal surveillance radar chains run by the Indian Coast Guard.

Interview questions

• Q: Why does received echo power fall as 1/R⁴ while a communication link falls as 1/R²? A: The wave spreads on the way out and again on the way back after scattering, so two inverse-square factors multiply.
• Q: What limits the maximum unambiguous range, and how is it extended? A: The PRF: R_un = c/(2f_p). Lower the PRF, or use multiple/staggered PRFs so ambiguous echoes can be resolved.
• Q: How can a radar have 75 m resolution with a 50 µs pulse? A: Pulse compression — a chirp of 2 MHz bandwidth is matched-filtered to 0.5 µs, so resolution follows c/2B, not cτ/2.
• Q: What is a blind speed and how do you avoid it? A: A radial speed v_n = nλf_p/2 at which a target's inter-pulse phase shift is a whole cycle, so the MTI canceller removes it; staggered PRFs move the nulls beyond realistic speeds.
• Q: Why does a double delay-line canceller perform better than a single one? A: Its response 4sin²(πf_dT) gives a wider, deeper clutter notch, improving clutter attenuation — but it also suppresses slow targets more.
• Q: Why is monopulse preferred over conical scan for tracking? A: It derives the angle error from sum and difference channels in a single pulse, so target amplitude fluctuation and scintillation do not corrupt the error signal.
• Q: What does radar cross section depend on? A: Target size relative to wavelength, shape, material, polarisation and aspect angle — not simply physical size; shaping and absorbers can cut it by orders of magnitude.
• Q: What decides radar detection — peak power or energy? A: Energy. A matched filter gives SNR = 2E/N₀, which is why long coded pulses from low-power solid-state transmitters work well.
• Q: Why does a CW radar miss a target crossing in front of it? A: Doppler responds only to radial velocity; a purely tangential target has zero radial component and so zero Doppler.
• Q: How does SAR get fine azimuth resolution from a small antenna? A: Platform motion plus coherent processing synthesise a long aperture, giving resolution of about D/2, independent of range.
• Q: What is CFAR and why is it needed? A: A threshold set adaptively from surrounding cells' noise/clutter estimate, so the false alarm rate stays constant as clutter level changes across the coverage.
• Q: What is the function of the STALO and COHO in an MTI radar? A: The STALO provides a stable down-conversion reference and the COHO a coherent phase reference, so a stationary target's echo phase repeats pulse to pulse and cancels.

Common mistakes

• Omitting the factor 2 in R = ct_R/2 or in f_d = 2v_r/λ, which doubles or halves every answer.
• Treating R_max in the radar equation as proportional to power — it goes as the fourth root, so 16× power doubles range.
• Confusing peak power with average power, or forgetting that duty cycle is τf_p when computing P_av.
• Claiming resolution improves only with shorter pulses; with coding it is bandwidth, c/2B, that matters.
• Mixing up ambiguity types: high PRF causes range ambiguity, low PRF causes Doppler/velocity ambiguity.
• Using total velocity instead of the radial component for Doppler, or forgetting the sign convention for approaching and receding targets.
• Assuming RCS equals physical cross-sectional area, and ignoring aspect and wavelength dependence.

Related topics

Analog modulation: AM and FM · Noise in communication systems · Random signals and noise analysis · Spread spectrum and CDMA · Satellite communication · Antennas and microwave engineering.