ECE 521E — Radar & Satellite Engineering • 5th Year BSc. Electrical & Communication Engineering
Masinde Muliro University of Science and Technology (MMUST)
By the end of this unit, the student should be able to:
Prerequisites: Radar fundamentals (ECE 5xx), communication systems, signals & systems, electromagnetics.
A continuous wave (CW) radar transmits an unbroken (continuous) electromagnetic wave rather than short pulses. While pulsed radar times the gap between transmitted pulse and echo to measure range, a basic CW radar transmits and receives simultaneously and extracts information from the frequency (or phase) of the returned signal rather than its time delay.
Consider a radar transmitting a pure sinusoid st(t) = A·cos(2πf0t). The echo from a target at range R returns after delay td = 2R/c, so the received signal is a delayed copy:
For a stationary target, this is merely a phase-shifted version of the transmitted signal — the delay information is buried in an unobservable constant phase. Worse, if the target moves, the delay changes continuously and the returned wave is frequency-shifted (Doppler effect). A pure CW radar can therefore measure radial velocity via this frequency shift, but it has no time reference with which to measure the delay → range is unmeasurable.
Because the transmitter is always on, its enormous signal (watts) can leak into the sensitive receiver (which must detect echoes of picowatts). Solutions include:
When a target moves with radial velocity vr (positive = approaching), the round-trip path length changes at rate 2vr, producing a Doppler shift on the echo:
where λ = c/f0 is the wavelength. The received frequency is f0 ± fd (sign of the shift depends on the convention; closing targets shift the frequency in one consistent direction).
| Radar Band | Frequency f₀ | Wavelength λ | Doppler shift fd at v = 1 m/s |
|---|---|---|---|
| S (2.7 GHz) | 2.7 GHz | 11.1 cm | 18.0 Hz |
| C (5.8 GHz — police radar) | 5.8 GHz | 5.17 cm | 38.7 Hz |
| X (10 GHz) | 10 GHz | 3.0 cm | 66.7 Hz |
| Ka (35 GHz) | 35 GHz | 8.57 mm | 233 Hz |
To add range capability, the transmitted frequency is swept in a known pattern — typically linear (sawtooth or triangular). The echo returns after delay td = 2R/c, so at any instant the received frequency differs from the currently transmitted frequency by the beat frequency fb, from which range follows.
For a linear sweep of bandwidth B over sweep time Tm, the slope is k = B/Tm Hz/s. The beat frequency is the slope times the delay:
With a triangular sweep (up-ramp then down-ramp), a moving target adds a Doppler shift that increases the beat on one ramp and decreases it on the other:
This elegant two-ramp scheme decouples range and Doppler — one of the most elegant results in radar engineering.
Wider sweep bandwidth B gives finer range resolution, exactly as in pulsed radar (where B ≈ 1/τ). Automotive radars sweeping 1–4 GHz achieve ~10 cm resolution.
| Type | Modulation | Measures | Typical Use |
|---|---|---|---|
| Unmodulated CW (CW Doppler) | None | Radial velocity only | Police speed radar, speed guns, proximity sensors |
| FMCW (sawtooth) | Linear frequency sweep | Range (and velocity if staggered) | Radar altimeters, tank-level radar, automotive ACC |
| FMCW (triangular) | Triangular sweep | Range + velocity simultaneously | Missile seekers, automotive radar |
| Phase-coded CW | BPSK phase coding | Range (correlation), velocity | ECCM-resistant CW radar, long-range surveillance CW |
| Multiple-frequency CW | Two or more discrete tones | Range (phase comparison), velocity | Precision fuzes, short-range measurement |
| Interrupted CW (ICW/FMICW) | CW with TX/RX alternation | Range + velocity, relaxed isolation | Marine/navigation radar, atmospheric radar |
The most familiar CW Doppler radar: a K-band (24 GHz) or Ka-band (35 GHz) Gunn oscillator illuminates vehicles; the reflected wave's Doppler shift gives speed directly (v = fdλ/2). Advantages: instant-on measurement, no minimum range, low cost. Modern units add FMCW or phased arrays for range gating (selecting one vehicle in traffic).
FMCW altimeters sweep ~100–400 MHz near 4.3 GHz (C-band). Range resolution c/2B of ~0.5–1.5 m suits low-altitude flight; space missions (e.g., planetary landers) use similar FMCW or CW concepts for descent ranging. Key advantage: no high peak power needed on a power-limited platform, and no minimum-range "dead zone."
77 GHz FMCW automotive radars measure range and velocity of vehicles ahead with ~0.1–0.4 m resolution, enabling adaptive cruise control and automatic emergency braking — triangulated with cameras and lidar.
CW Doppler detonates artillery shells at preset height above target (the shell's own velocity gives the Doppler signature of approach). Triangular-wave FMCW seekers provide passive-ranging target tracking in air-to-air missiles.
CW Doppler wind lidars/radars measure wind shear and clear-air turbulence by scattering from aerosols — used at airports and for wind-farm optimization.
CW and phase-coded techniques appear in satellite ground stations: coherent CW carriers support precise two-way Doppler for orbit determination (complementing the transponder ranging studied in the secondary-radar unit), and CW beacon signals enable ground-antenna tracking (monopulse and conical-scan tracking receivers lock onto a satellite's CW beacon). Deep-space navigation uses coherent CW Doppler of unprecedented stability to measure line-of-sight velocity to better than 0.1 mm/s.
| Attribute | CW Radar | Pulsed Radar |
|---|---|---|
| Transmit waveform | Continuous, 100% duty cycle | Pulses, low duty cycle |
| Peak power | Low (= average) | Very high |
| Range measurement | Only with modulation (FMCW) | Direct from pulse delay |
| Velocity measurement | Excellent (Doppler) | Good (requires MTI/Doppler processing) |
| Minimum range | None (no eclipsing) | Limited by pulse width τ |
| TX/RX isolation | Difficult (simultaneous) | Easy (duplexer timing) |
| Power consumption | Low average for given performance | High peak, switching losses |
| Typical domains | Short–medium range, velocity-critical | Long range, surveillance |
Satellite engineering exploits CW principles in three important ways:
A traffic radar operates at 24.15 GHz (K-band). It measures a Doppler beat of 2,680 Hz from an approaching car. Find the car's speed.
λ = c/f₀ = 3×108/2.415×1010 = 0.01242 m.
vr = fd·λ/2 = 2680 × 0.01242 / 2 = 16.65 m/s ≈ 59.9 km/h.
An aircraft FMCW altimeter sweeps B = 150 MHz in Tm = 1 ms and measures a beat frequency fb = 40 kHz on the down-ramp. Find the altitude.
R = c·Tm·fb/(2B) = (3×108 × 10−3 × 4×104)/(2 × 1.5×108) = 40 m.
Range resolution: ΔR = c/2B = 3×108/(3×108) = 1 m.
An X-band (λ = 3 cm) automotive radar sweeps B = 300 MHz in Tm = 2 ms per ramp. It measures fup = 42 kHz and fdown = 58 kHz. Find target range and radial velocity.
R = c·Tm(fup+fdown)/(4B) = 3×108 × 2×10−3 × 105 / (1.2×109)
= 50 m.
fd = (58 − 42)/2 = 8 kHz; vr = fdλ/2 = 8000 × 0.03/2 = 120 m/s
(receding or approaching per sign convention).
Doppler shift: — Hz
Q1. State the fundamental reason an unmodulated CW radar cannot measure target range.
Answer: A pure continuous tone carries no time reference; the echo delay appears only as a constant (unobservable) phase shift, so delay — hence range — cannot be extracted.
Q2. A 10 GHz CW radar measures a Doppler shift of 500 Hz. Find the target's radial velocity.
Answer: λ = 0.03 m; vr = fdλ/2 = 500×0.03/2 = 7.5 m/s.
Q3. Why do CW radars typically use two separate antennas?
Answer: To provide isolation between the continuously transmitting power amplifier and the sensitive receiver, whose input must simultaneously detect very weak echoes.
Q4. An FMCW radar sweeps 100 MHz in 1 ms and measures a beat frequency of 20 kHz. Calculate the range.
Answer: R = c·Tm·fb/(2B) = 3×108×10−3×2×104/(2×108) = 30 m.
Q5. Explain the role of coherence between the transmitted wave and the mixer's LO reference.
Answer: The beat note at fd persists only if the reference is phase-locked to the transmitted carrier; an incoherent LO would produce a randomly varying phase difference and the Doppler tone would average to zero.
Q6. For triangular FMCW, write the expressions for range and Doppler in terms of the up-ramp and down-ramp beat frequencies.
Answer: R = c·Tm(fup+fdown)/(4B); fd = (fdown−fup)/2, hence vr = fdλ/2.
Q7. What sweep bandwidth is needed for 10 cm range resolution in an FMCW radar?
Answer: B = c/(2ΔR) = 3×108/0.2 = 1.5 GHz.
Q8. Give two advantages of CW radar over pulsed radar for short-range applications.
Answer: No minimum-range dead zone; low peak power (average = peak, easier solid-state design); simple Doppler processing (any two advantages).
Q9. How does a radar altimeter on a satellite lander benefit from FMCW rather than a short pulse of equivalent bandwidth?
Answer: FMCW achieves the same resolution with continuous low-power transmission rather than a high-peak-power short pulse — easier on a power-limited spacecraft and avoids transmitter/receiver switching at very short ranges.
Q10. A satellite ground station uplinks a stable CW and receives a coherent return whose frequency decreases linearly during a pass. What does this indicate about the satellite's motion?
Answer: A changing Doppler shift means a changing line-of-sight velocity; the Doppler slope provides the range-rate history used in orbit determination.