Continuous-wave_radar

# Continuous-wave radar **Continuous-wave radar** (CW radar) is a radar that transmits a continuous, uninterrupted [[Radio_wave|radio]] signal rather than a series of separated pulses, and finds a target by comparing the frequency of what comes back against the frequency still being sent out. A moving target shifts the returning signal's frequency by the [[Doppler_effect|Doppler effect]], and because the transmitter never falls silent the way a pulsed set does, that shift can be measured continuously rather than pieced together from one echo to the next. The technique trades away everything a pulse's timing would have given it directly, range chief among them, for an extremely clean, continuous measurement of radial velocity and near-total immunity to a large, motionless background. A three.js microsim elsewhere on this page renders the FMCW variant described below directly: a transmitted frequency sweeping in a sawtooth, an echo returning slightly delayed, and the beat tone between the two reading off the target's range. Unmodulated CW radar measures only speed; giving the transmitted frequency a modulation of its own recovers a measurement of range as well, at the cost of new leakage and configuration problems the rest of this article follows in turn, from how a bare carrier and a swept one each operate, through the ways a transmitter and receiver can be arranged around the leakage problem, to where continuous-wave operation earns its keep and where a pulsed set is simply the better tool. ## Operation A continuous-wave radar's transmitter runs constantly rather than firing discrete pulses, so its [[Radio_receiver|receiver]] must listen at the same time the transmitter is active rather than during a quiet gap between pulses. Whatever comes back is compared against a sample of the outgoing signal, taken directly from the transmitter rather than recovered from the target echo alone, and a moving target's echo differs from that sample by the Doppler shift its own radial velocity imposes: `f_d = 2 · v_r / λ` for a wavelength λ and radial speed v_r, the same relation a pulsed radar's Doppler processing extracts across several pulses instead of continuously. Because a genuinely motionless reflector, the ground, a building, a stationary vehicle, returns no shifted frequency at all, a receiver can filter out the unshifted carrier entirely and keep only the moving-target sidebands, which is what gives continuous-wave operation its long-standing reputation for seeing a moving target against a strong, cluttered background that would swamp a simpler amplitude-only receiver. What a bare, unmodulated carrier cannot do is say how far away that moving target is, since a continuous wave carries no marked instant a receiver can time against; that limitation, and the modulation schemes built to remove it, are the subject of the next section. ## Types ### Unmodulated continuous-wave An unmodulated, or bare-carrier, continuous-wave radar transmits a single stable [[Sine_wave|sine wave]] and measures nothing but the Doppler shift on whatever returns, making it in effect a dedicated [[Doppler_radar|Doppler radar]] rather than a general-purpose one. Police and sports radar guns, some proximity switches, and simple intrusion sensors use exactly this form, since a single reliable number, closing speed, is all the application needs and the circuitry to extract it is far simpler than anything that must also time a pulse.[^radargun] Multiple simultaneous targets at different ranges but the same radial speed are indistinguishable to a receiver built this way, and a target moving exactly tangential to the beam, contributing no radial component at all, produces no shift and is effectively invisible regardless of how close it may be. ### Modulated continuous-wave Modulating the transmitted frequency deliberately restores a timing mark a receiver can use for range, without ever switching the transmitter off the way a pulsed radar does. The two common schemes sweep the carrier's frequency on a repeating schedule, a sawtooth ramp or a sinusoid, and each reads range from a slightly different measurement of how the returning, delayed copy of that sweep differs from the sweep being transmitted at that same instant. #### Sawtooth frequency modulation Sweeping the carrier linearly up, or down, across a fixed bandwidth B over a sweep time T and then resetting, a sawtooth, gives the scheme usually called FMCW; the swept waveform is itself a linear [[Chirp|chirp]]. Because the echo left the transmitter, travelled to the target and back, and only then reached the receiver, it arrives carrying whatever frequency the sweep was at slightly earlier, so mixing the live echo against the currently transmitted frequency produces a beat tone at their difference, `f_b = 2 · R · S / c`, where S = B / T is the sweep rate; measuring that single beat frequency, typically with a [[Fast_Fourier_transform|Fast Fourier Transform]] of the sampled beat signal in the [[Frequency_domain|frequency domain]], therefore reads out range directly. This beating of two nearby frequencies into one slow difference tone is the general physics of any two-tone mix.[^beats] Digitizing that beat tone with an [[Analog-to-digital_converter|analog-to-digital converter]] demands sampling faster than twice its bandwidth, the ordinary limit set by the [[Nyquist–Shannon_sampling_theorem|Nyquist–Shannon sampling theorem]]. A moving target adds its own Doppler shift on top of the beat, which on a symmetric up-and-down sawtooth can be separated from the range-beat term by comparing the beat frequency measured on the rising ramp against the one measured on the falling ramp, since Doppler adds to one and subtracts from the other while the range term keeps the same sign on both. #### Sinusoidal frequency modulation Sweeping the carrier sinusoidally rather than as a sawtooth avoids the instantaneous reset a sawtooth needs at the top of every ramp, trading a slightly more complex spectrum, made up of multiple sidebands around the carrier rather than one clean beat tone, for a transmitted signal with no discontinuity for a receiver's automatic gain control or a phase-locked oscillator to settle after. Range is recovered from the relative strength or phase of those sidebands rather than from a single beat frequency, an approach historically favoured in some early frequency-modulated altimeters before sawtooth generation became straightforward enough to dominate the field.[^sinusoidalhist] ## Configurations ### Monostatic A monostatic configuration transmits and receives through the same antenna, or through two antennas mounted close together at one site, matching the simplicity of a typical pulsed radar's layout. Because the transmitter never stops, the transmitted signal reaches the receiver directly as well as through any reflecting target, a leakage path a pulsed radar does not have to manage since its transmitter and receiver are never active at the same instant. Every configuration and leakage-management technique described below exists to make a monostatic, single-site radar practical despite that direct path. ### Bistatic A [[Bistatic_radar|bistatic]] configuration separates the transmitter and receiver, sometimes by a considerable distance, removing the direct leakage path a co-located antenna pair would suffer at the cost of a harder geometry: range and Doppler must now be worked out from the triangle the transmitter, target and receiver form rather than from a single round trip. A passive arrangement, using a transmitter of opportunity such as a broadcast signal the receiver does not control, takes the same idea further and removes the dedicated transmitter altogether; a wartime German system is reported to have exploited British Chain Home transmissions this way, passively and without revealing its own presence by transmitting anything at all.[^bistatichist] ### Monopulse A [[Monopulse_radar|monopulse]] continuous-wave system adds simultaneous, precisely matched receive channels, typically comparing sum and difference beam patterns, to extract a target's angular position from a single continuous return rather than from a mechanical scan across several looks. Because the comparison is made continuously rather than pulse to pulse, a monopulse CW tracker can hold a narrow, precise angular lock on one target's continuous echo, at the cost of the extra receive hardware the comparison itself needs. ### Leakage Leakage, the transmitted signal reaching the receiver directly rather than by reflecting off a target, is continuous-wave radar's defining practical problem, since even a small fraction of a typically much stronger transmitted signal arriving directly can swamp a genuinely weak, distant echo the same receiver is also trying to hear. Two broad remedies exist: filtering the direct path out of a receiver that hears it constantly, and interrupting transmission briefly enough to stop hearing it at all without giving up the continuous-wave waveform's other advantages. #### Filter Because a stationary or slowly drifting leakage path produces no meaningful Doppler shift of its own, the same kind of filter that rejects ground [[Clutter_(radar)|clutter]] in a pulsed moving-target-indication system can reject direct leakage in a continuous-wave one, isolating the shifted echo of a genuinely moving target from the unshifted carrier arriving straight from the transmitter. Physical isolation helps as much as electronic filtering: separating transmit and receive antennas, shielding one from the other, and keeping transmitted power modest all reduce how much leakage a filter has to remove in the first place, since no filter recovers a receiver the direct path has driven beyond its [[Dynamic_range|dynamic range]] into outright saturation. #### Interruption, FMICW Interrupted frequency-modulated continuous-wave operation, FMICW, blinks the transmitter off for brief intervals timed to when an echo from the range of interest is expected, borrowing a pulsed radar's transmit-then-listen discipline without giving up a swept-frequency waveform's ranging method.[^fmicwhist] The interruptions must be short and infrequent enough that the underlying frequency sweep is barely disturbed, so FMICW behaves, from the point of view of the sweep and its beat-frequency ranging, almost exactly like ordinary FMCW while removing the worst of the leakage problem during each brief listening window. The approach costs some average transmitted power and adds switching complexity plain FMCW does not need, a trade accepted mainly where leakage would otherwise be severe, such as a very short desired range. ## Advantages Continuous-wave operation's chief advantage is exactly the one unmodulated CW radar was built around: an extremely clean, continuous measurement of radial velocity, free of the coarser Doppler sampling a pulsed radar's finite [[Pulse-repetition_frequency|pulse-repetition frequency]] imposes and free of the blind speeds that sampling can create. A continuous transmission also spreads a given average power over all of time rather than concentrating it into brief, powerful pulses, letting a continuous-wave transmitter reach a useful average power with far less peak power, and so far less demanding high-voltage components, than a pulsed set radiating the same energy. Because the transmitted power is comparatively modest and constant rather than a sharp, easily intercepted pulse, some continuous-wave designs are also harder for a simple intercept receiver to detect at a distance than an equivalently capable pulsed radar would be. [[Radar_altimeter|Radio altimeters]], proximity fuzes, level gauges, [[Ground-penetrating_radar|ground-penetrating radar]] and traffic or sports radar guns all exploit some mixture of these advantages in preference to a pulsed design of similar range. ## Limitations Continuous-wave operation's limitations mirror its advantages closely. An unmodulated set measures no range at all, and even a modulated, ranging-capable FMCW set generally reaches shorter maximum ranges than a pulsed radar of comparable average power, since a pulsed set can concentrate its energy into brief, very high peak pulses, or stretch a long pulse with [[Pulse_compression|pulse compression]] to gain a long pulse's energy with a short pulse's resolution, neither of which a continuous transmission can do. Leakage is a permanent tax on receiver sensitivity that a pulsed radar's transmit-then-listen cycle avoids by construction, and every leakage remedy above, filtering, physical isolation, or interruption, costs either performance or complexity to hold that tax down rather than eliminating it outright. A target with no radial velocity component, moving exactly tangentially to the beam or not moving at all, produces no Doppler shift for an unmodulated set to detect, the same blind spot that makes continuous-wave operation so effective against a stationary background but equally effective at hiding a stationary target from it, quite apart from any [[Line-of-sight_propagation|line-of-sight]] limit shared with every other radio-based sensor. ## Microsims A three.js microsim elsewhere on this page renders FMCW operation directly: a sawtooth-swept transmitted frequency, a delayed echo tracing the same sawtooth slightly later, and the beat frequency between the two reading out range as a Doppler shift moves the whole picture. Neither this article nor that companion carries a two-dimensional p5.js sketch of its own, so the reader is pointed instead to the sketches on neighbouring articles that already model a moving target's Doppler shift and a pulsed radar's alternative approach to the same ranging problem. *Try:* in the [[Doppler_effect]] sketch, raise the source speed and watch the two observer markers' received frequencies separate from the source's own — the identical split a stationary CW receiver measures between its transmitted carrier and a moving target's echo. *Try:* in the [[Radar]] sketch, compare how a pulsed set times a single round trip directly, `R = c·τ/2`, against continuous-wave operation's very different approach of reading range from a beat frequency instead of a stopwatch.  **Microsim — three.js (Wikitube framework), pending deploy:** *CW gives up range for an exact Doppler tone; FMCW buys range back, biased* will play here once `https://wikitube-3d-microsims.netlify.app/radar/Continuous-wave_radar.html` is live.  *Built from `MICROSIM_GUIDE/specs/sims/Continuous-wave_radar.json`; part of the [[PORTAL_Radar|Radar]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Continuous-wave_radar) : [Wikitube](https://en.wikitube.io/wiki/Continuous-wave_radar) Skeleton mirrored at revision 1362106365. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Radar]] - [[Doppler_effect]] - [[Bistatic_radar]] - [[Monopulse_radar]] - [[Radar_altimeter]] - [[Ground-penetrating_radar]] - [[Doppler_radar]] - [[Chirp]] - [[Pulse-Doppler_radar]] ## Bibliography - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory - Don Johnson. *Fundamentals of Electrical Engineering I*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 - Michael Stiber; Bilin Stiber; Eric Larson. *Signal Computing: Digital Signals in the Software Domain*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain - Allen Downey. *Think DSP: Digital Signal Processing in Python*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python - Steven Ellingson. *Radio Systems Engineering, Revised First Edition*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - John Dyer; Chad Davis. *Measurement and Instrumentation: An Introduction to Concepts and Methods, 1st Edition*. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/measurement-and-instrumentation-an-introduction-to-concepts-and-methods ## References The Doppler relation `f_d = 2·v_r/λ`, the FMCW beat-frequency relation `f_b = 2·R·S/c`, and the classification of continuous-wave radar into unmodulated and modulated forms are standard radar-engineering material and are not separately footnoted, per the Wikitube style guide's §6.1. Page numbers below are PDF pages of the open edition linked in Bibliography. [^beats]: Two phasors at nearby frequencies sum to a slow envelope times a fast carrier, `(a1 + a2·e^{jδt})·e^{jωt}`, the beat physics underlying an FMCW receiver's range-reading beat tone: Stiber, M.; Stiber, B.; Larson, E. *Signal Computing: Digital Signals in the Software Domain*. 2016, pp. 32-33 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. [^radargun]: Citation needed: a primary manufacturer or police-department record of the first traffic radar gun placed into service would confirm its date and the department or company involved. [^sinusoidalhist]: Citation needed: a primary account of a specific early sinusoidally frequency-modulated radio altimeter would confirm the manufacturer and date this article otherwise describes only generically. [^bistatichist]: Citation needed: a primary wartime or postwar technical account of the German passive bistatic system reported to have exploited Chain Home transmissions would confirm its name, dates and demonstrated performance. [^fmicwhist]: Citation needed: a primary account of the first interrupted-FMCW (FMICW) system fielded would confirm its date, designer and intended application. ## External links This article's only interactive companion is the three.js microsim named in the Microsims section above; the current build has no p5.js sketch about continuous-wave radar specifically, so there is no separate live-sketch or editor-fork link to add here.