CW Radar Applications — ECE 5th Year

Learning Objectives

By the end of this topic, the student should be able to:

Explain the operating principle of simple CW, CW-Doppler and FM-CW radars.
Derive and apply the Doppler frequency relation f_d = 2v_r/λ.
Analyse FM-CW range measurement using the beat-frequency technique R = c·f_b/(2·(ΔF/T_m)).
Describe CW radar applications: police/sports speed radar, Doppler navigation, satellite tracking via Doppler, radar altimeters, weather radar, proximity fuzes and biomedical sensing.
Discuss practical CW radar problems: transmitter–receiver leakage/isolation, noise, and the need for modulation to obtain range.
Solve numerical problems on Doppler shift and FM-CW beat frequency.

1. Theory of CW Radar

1.1 What is CW radar?

A continuous-wave (CW) radar transmits an unbroken (or frequency-modulated) sinusoidal signal rather than pulses. Because there is no time reference between transmission and echo, a simple CW radar cannot measure range directly — but it measures velocity with very high accuracy through the Doppler effect. Adding linear frequency modulation (FM-CW) gives both range and velocity, at low peak power and small hardware size.

Property	Simple CW (Doppler)	FM-CW	Pulsed radar (for reference)
Range measurement	No	Yes — beat frequency	Yes — time delay
Velocity measurement	Excellent (Doppler)	Yes	Needs MTI/Doppler processing
Peak power	Low (continuous)	Low	High
Minimum range / dead zone	None	Small	Limited by pulse width
Main problem	TX→RX leakage, no range	Linearity of modulation, leakage	High-voltage modulators

1.2 The Doppler effect in radar

f_d = 2 v_r / λ = 2 v_r f_c / c
f_d = Doppler shift [Hz]; v_r = radial (line-of-sight) velocity [m/s]; λ = wavelength [m]; f_c = carrier [Hz]; c = 3×10⁸ m/s. Factor 2 because the path is two-way (echo "sees" a moving mirror).

The received frequency is f_c ± f_d: approaching targets → higher (positive Doppler), receding → lower. Only the radial component matters — a target crossing the beam at constant range produces zero Doppler.

1.3 Simple CW Doppler radar — bistatic block diagram

In a bistatic CW Doppler radar the transmitter and receiver are at separate sites, separated by the baseline d. The transmitter chain (oscillator → power amplifier → TX antenna) radiates continuously. The echo is collected by a physically separate RX antenna, amplified by an LNA / RF preamplifier, and mixed with a local-oscillator pick-off taken from the same oscillator (sent over a cable or derived coherently) so the phase coherence needed for Doppler detection is preserved. The mixer output at f_d passes through a Doppler (audio) amplifier and filter to a detector/threshold and processor/display.

Bistatic operation removes the TX→RX leakage problem of monostatic CW radar by antenna spatial separation (the residual direct-path leakage between sites is handled by nulling and Doppler filtering). The bistatic Doppler shift depends on the two look angles θ_t (at transmitter) and θ_r (at receiver):

f_d = (v/λ)·(cos θ_t + cos θ_r) = (2v/λ)·cos(δ/2)·cos β
δ = bistatic angle (TX–target–RX); β = angle between target velocity and the bistatic bisector. Monostatic result f_d=2v_r/λ is recovered when δ→0 and the velocity lies along the line of sight.

Fig. 1 — Textbook block diagram of a CW Doppler radar (bistatic configuration): CW oscillator → power amplifier → transmitting antenna; receiving antenna → RF (LNA) amplifier → balanced mixer (LO = coherent pick-off of transmitted carrier) → IF amplifier/filter → Doppler amplifier → phase-sensitive detector → indicator/recorder. The mixer output is the Doppler beat f_d; only the radial velocity component is measured.

The bistatic arrangement is widely used for fencing (continuous surveillance lines — e.g., the historic SPASUR satellite fence), forward-scatter intrusion detection, and measurement scenarios where placing the receiver away from the transmitter avoids noise, interference or physical crowding at the target site.

1.4 FM-CW radar — adding range capability

If the transmitted frequency is swept linearly (e.g., triangular modulation, bandwidth ΔF, period T_m), the echo — delayed by the two-way time t_r = 2R/c — differs in frequency from the currently-transmitted signal by the beat frequency:

f_b = (2R / c) · (ΔF / T_m) ⇒ R = c · T_m · f_b / (2 ΔF)
If the target also moves, the up-sweep and down-sweep beats differ (f_b↑ = f_r + f_d, f_b↓ = f_r − f_d), giving BOTH range and Doppler. This is the classic altimeter and police-radar configuration.

Worked example (exam standard): An FM-CW radar sweeps 150 MHz in 1 ms (triangular). A stationary target returns a beat of 40 kHz. Find R.
Slope s = ΔF/T_m = 150×10⁶ / 10⁻³ = 1.5×10¹¹ Hz/s. R = c·f_b/(2s) = 3×10⁸·4×10⁴ / (3×10¹¹) = 40 m.

Application 1 — Doppler Speed Measurement (Police & Sports Radar)

The simplest and most common CW application. A Gunn-diode or dielectric-resonance-oscillator (DRO) transmitter at 10.525 GHz (X-band, λ ≈ 2.85 cm) or 24.125 GHz (K-band) illuminates a vehicle; the Doppler echo is down-converted and the audio-frequency beat is counted. Typical values: 1 mph ≈ 31 Hz at 10.5 GHz — the "tone" rises with speed. Modern units add pseudo-random FM to defeat detectors and to reject moving clutter (e.g., patrol-car motion).

v (km/h) = f_d · c / (2 f_c) · 3.6
At 10.525 GHz: v[km/h] ≈ f_d × 0.0513. A 1 kHz beat ⇒ ≈ 51 km/h. Angle error: measured v = v_true·cosθ — a 10° aiming error gives a 1.5 % speed error.

Why CW here?

No minimum range — can measure a car 30 m away with the same unit that reaches 1 km.
Low peak power → compact, battery-operated hand-held units.
Only radial speed is needed — the geometry (roadside beam) makes the cosθ correction small.

Other speed applications: sports radar guns (cricket/baseball), conveyor and industrial speed monitoring, ground-speed measurement of aircraft (Doppler velocity sensors), and water-current measurement (river/sea surface scatter).

Application 2 — Distance Measuring Equipment (DME) & FM-CW Ranging

Technical note: Standard aeronautical DME is a pulsed secondary system (1030/1090 MHz family, covered in the Secondary Radar notes). However, the ranging function itself can equally be implemented with CW techniques, and several modern systems do exactly that — so DME principles are revisited here from the CW/FM-CW viewpoint.

Distance measurement requires a time or frequency reference. CW systems implement it in two ways:

FM-CW two-way ranging: sweep the carrier (e.g., 4.2–4.4 GHz radar-altimeter band or 5.2–5.7 GHz); measure beat frequency → slant range directly. Used in precision distance measuring equipment and in industrial level/position radars.
Phase-comparison CW: transmit a CW tone and compare the phase of the returned tone; range follows from phase ambiguity resolution (used in surveying EDM — electro-optical distance meters are CW phase-comparison systems).

The result is the same slant-range information a pulsed DME provides, with the low-peak-power and short-minimum-range benefits of CW — valuable at small airfields and in helicopter operations.

Application 3 — Satellite Ground Control & Tracking (CW Doppler)

The historic birth of space tracking was pure CW Doppler: the 1957 Sputnik 1 beacon (20.005/40.002 MHz) produced the famous descending-tone recordings from which amateur and professional stations derived orbit parameters. Today every satellite TT&C ground station still relies on coherent CW techniques:

Two-way coherent Doppler: the ground uplinks a stable CW carrier; the satellite transponder coherently turns it around (translates by a fixed ratio, e.g., 221/240 for S-band). The ground measures the received frequency with mHz-class precision → range-rate accuracy of mm/s at GEO distances.
Doppler curve of a pass: as the satellite rises, approaches (max Doppler), passes overhead (zero Doppler — closest point), and sets, the recorded curve f(t) lets a single station determine orbit elements; this is how early networks (Minitrack, SPASUR fence) worked.
Ranging tones / PN codes on the CW carrier (phase-comparison, like EDM) give absolute range to ~1 m, closing the same loop as the DME principle at 36 000 km.
Deep space: DSN combines CW Doppler, ranging tones and delta-DOR (differential VLBI) for interplanetary navigation.

_up (stable CW) Downlink f_dn = k·f_up (coherent) f_d measured over a pass ⇒ range-rate curve ⇒ orbit determination (Sputnik principle, 1957)

Fig. 2 — Coherent two-way CW Doppler: the transponder preserves phase, so the ground recovers a precision Doppler history of the whole pass.

Worked example: A satellite transponder turns around a 2 GHz uplink coherently. The ground observes a Doppler shift of +55 kHz at 2 GHz-equivalent during a pass. What is the range-rate?
v_r = f_d·c/(2f_c) = 5.5×10⁴·3×10⁸/(4×10⁹) = 4 125 m/s ≈ 4.1 km/s (typical LEO approach rate at low elevation).

Application 4 — FM-CW Radar Altimeters

Aviation radio altimeters (4.2–4.4 GHz) must measure height from 0 ft (wheels on runway) to 2 500 ft with feet-class accuracy — impossible for pulsed radar (huge dynamic range, short-range eclipsing). The FM-CW solution: sweep ~150 MHz in ~1 ms, mix TX and RX, count the beat. Because the beat at 40 m is only ~40 kHz, cheap digital counters suffice; because the signal is continuous, there is no minimum range. Modern combined altimeter/weather radar modules use the same FM-CW front-end.

Low-altitude mode: fast sweep (small ΔF) for wide unambiguous range window near ground.
High-altitude mode: slower sweep, larger ΔF for resolution; tracking filters follow the ground return through overpass (e.g., over water the return point migrates with roughness — sea-state bias).

Application 5 — Doppler Weather Radar

Weather radars must measure both reflectivity (rain intensity) and radial velocity of hydrometeors (wind inside storms). The Doppler measurement uses the pulsed-Doppler variant (magnetron/klystron with phase-coherent processing), but the underlying measurement is pure CW-Doppler physics applied per range cell: successive pulses sample the phase of the echo from each cell; the phase progression rate = Doppler frequency.

Velocity aliasing (folding): maximum unambiguous velocity v_max = ±λ/(4·PRI) — at 3 GHz (10 cm) with PRI 1 ms, v_max ≈ ±25 m/s. Beyond this, velocities "fold" — correction requires dealiasing algorithms.
Products: base velocity, storm-relative velocity, spectrum width (turbulence), and mesocyclone/tornado vortex signatures (TVS) that trigger warnings.
Applications: nowcasting, aviation hazard (wind shear, microbursts), rainfall estimation for flood warnings — e.g., Doppler radars such as those operated by national meteorological services and the NEXRAD network.

Application 6 — Other CW Radar Applications

Application	CW variant	Principle / notes
Proximity fuzes	CW Doppler	Artillery shell fuze detonates when Doppler shift from the target rises sharply on final approach (VT fuzes, WWII origin)
Doppler navigator	CW (multi-beam)	Aircraft fires 3–4 beams downward; Doppler of each beam gives ground-speed vector + drift angle — self-contained navigation (used before GNSS, still as backup)
Missile seekers / fuze	CW or FM-CW	Semi-active homing: illuminator CW carrier, missile sees Doppler of target echo; end-game FM-CW for fuzing distance
Vital-sign monitoring	CW Doppler (microwave/60 GHz)	Chest-wall motion (0.1–0.5 Hz respiration, ~1 Hz heartbeat) modulates the echo; contactless monitoring in hospitals and security screening
Intrusion / presence sensors	CW Doppler	X-band (10.5 GHz) door openers, traffic light triggers, security motion sensors
Ground-penetrating & level radar	FM-CW / stepped-CW	Tank level, snow depth, road layer thickness via beat-frequency ranging
Police "photo radar" / speed cameras	FM-CW or pulsed	Adds range gating so only vehicles in a lane window are measured
Surveying (EDM)	CW phase-comparison (IR/laser)	Modulated CW carrier; phase of return gives distance, mm-accuracy over km

Interactive Simulations

Simulation 1 — CW Doppler Speed Radar

Choose carrier band and target speed; the animated wave shows the echo frequency shift, and the readouts give the Doppler beat and measured speed (with cosθ aiming error).

Band

True speed 90 km/h

Aiming angle θ 15°

Doppler shift f_d

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Measured speed (cosθ)

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Speed error

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Beat audio pitch

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Simulation 2 — FM-CW Range Measurement (beat frequency)

Adjust sweep bandwidth, sweep time and target range. The live plot shows TX sweep and delayed echo; the beat frequency and computed range update in real time.

Sweep bandwidth ΔF 150 MHz

Sweep period T_m 1 ms

Target range 40 m

Beat frequency f_b

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Computed range

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Two-way delay

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Simulation 3 — Satellite Pass Doppler Curve (ground control)

Set satellite altitude and carrier. As the satellite flies overhead (animated), the Doppler curve is traced — exactly the record a ground station uses for orbit determination.

Altitude 400 km

Carrier 2.0 GHz

Max Doppler (at rise/set geometry)

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Orbital velocity

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Pass duration (horizon-to-horizon)

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Summary

CW radar trades direct range measurement for simplicity, low peak power and excellent velocity resolution via the Doppler effect (f_d = 2v_r/λ).
Applications span police/sports speed radar, DME-equivalent FM-CW and phase-comparison ranging, satellite ground control via coherent two-way Doppler (the Sputnik principle), radar altimeters, Doppler weather radar, proximity fuzes, Doppler navigators and vital-sign monitors.
FM-CW recovers range from the beat frequency between the swept TX and the delayed echo: R = c·T_mf_b/(2ΔF).
Key engineering issue: TX→RX isolation; key physics issues: cosθ geometry, velocity aliasing in pulsed-Doppler weather radar, and modulation linearity.

Review Questions

Q1. Why can a simple CW radar not measure range? How does FM-CW solve this?

With unmodulated CW there is no time marker distinguishing "now" from "echo delayed"; all echoes mix into one beat. Linear FM tags each instant with a unique frequency; the echo's frequency offset (beat) encodes the two-way delay, hence range.

Q2. A 24.125 GHz police radar measures a beat of 2.43 kHz from a car approaching head-on. Find the car's speed (km/h).

v = f_d·c/(2f_c) = 2430·3×10⁸/(2·2.4125×10¹⁰) = 15.1 m/s ≈ 54.4 km/h.

Q3. Explain how a single ground station tracked Sputnik-1 using only its CW beacon.

The beacon's constant frequency appeared Doppler-shifted as the satellite approached (rising tone), passed overhead (zero shift at closest approach), and receded (falling tone). The curve of f_d(t) contains the range-rate history; fitting it yields the orbit's period, inclination and perigee/apogee.

Q4. An FM-CW altimeter sweeps 4.3→4.45 GHz in 1 ms. The beat is 120 kHz. Find the height.

s = 150 MHz/1 ms = 1.5×10¹¹ Hz/s; R = c·f_b/(2s) = 3×10⁸·1.2×10⁵/3×10¹¹ = 120 m.

Q5. Give three reasons CW radar is preferred for police speed guns and vital-sign monitoring.

(i) No minimum range (continuous transmission); (ii) low peak power → small, battery-powered units; (iii) Doppler output is a simple audio-frequency tone — trivial to process; (iv) high velocity resolution.