Radar_signal_characteristics

# Radar signal characteristics **Radar signal characteristics** are the properties of the signal a [[Radar|radar]] transmits and receives that, between them, decide most of what the radar can and cannot measure. A single carrier frequency, timed into pulses of a chosen width and repeated at a chosen rate, fixes how finely two nearby targets can be told apart, how far away a target can be before its echo is mistaken for a much closer one, and how fast a target must move before its measured speed repeats; changing any one of these numbers moves the other limits with it, so no radar design is free to set them independently. Every one of these time-domain choices has a mirror image in the frequency domain, since a pulse repeated at a fixed rate and held to a fixed width has a spectrum as constrained as its timing, and the two views describe the same signal rather than two different ones. A three.js microsim elsewhere on the site renders one of these constraints directly, putting pulse width, pulse-repetition frequency and duty cycle on a single live readout. The [[Pulse-repetition_frequency|pulse-repetition frequency]] a radar chooses is usually the single most consequential of these numbers, since it alone trades range reach against speed reach, and the limit it imposes on how finely a long pulse can resolve two close targets is what motivates [[Pulse_compression|pulse compression]], the technique described next in this sequence for escaping that trade rather than accepting it. ## In the time domain A pulsed radar's signal can be read directly off an oscilloscope trace, as a sequence of on-and-off pulses at a fixed carrier, and every parameter of that trace has a direct consequence for what the radar can measure. ### Carrier The carrier is the radio-frequency oscillation the pulse switches on and off; its frequency sets the physical antenna size needed for a given beamwidth, how well the signal penetrates weather, and how much bandwidth the surrounding spectrum can spare for it. A [[Microwave|microwave]] carrier of a few gigahertz is typical of search and weather radar, where a manageable antenna and modest atmospheric attenuation both matter, while far higher carriers trade both away for the finer angular resolution a much smaller antenna can then achieve.[^band-choice] ### Pulse width Pulse width, the duration the transmitter stays on for each pulse, sets range resolution directly: two targets on the same bearing appear as separate echoes only if their round-trip delays differ by more than the pulse width, giving a minimum separation `ΔR = c·τ/2` for a pulse of width τ. A short pulse therefore resolves targets finely, but a short pulse also carries little energy unless the peak power is raised to match, and peak power is one of the more expensive things to buy in a transmitter; escaping that trade rather than accepting it is the whole motivation for pulse compression, which lets a long, energetic pulse be processed back down to a short pulse's resolution after it returns. ### Pulse repetition frequency (PRF) The pulse-repetition frequency is the rate at which pulses go out, and its reciprocal, the pulse-repetition interval, is the longest round-trip delay the radar can time before the next pulse complicates the picture. Raising the PRF sends out more pulses per second to integrate against noise and lets a pulsed-Doppler radar sample a moving target's phase more often, but it shortens the interval available for a distant echo to return before the next pulse leaves, so PRF choice alone forces a trade between how far and how fast a radar can see, taken up again under Unambiguous range and Unambiguous velocity below. ### Staggered PRF Because a single, fixed PRF leaves some target ranges and some target speeds ambiguous no matter how it is chosen, many radars instead transmit a short repeating sequence of two or more different PRFs rather than one constant rate. A target genuinely at an ambiguous range, or at a blind speed, for one PRF in the sequence is very unlikely to be ambiguous or blind at the others as well, so comparing what each PRF in the sequence reports resolves an ambiguity that no single PRF could resolve on its own.[^stagger-origin] ### Clutter Not every echo comes from an intended target: the ground, the sea, rain and even birds and insects scatter the same transmitted pulse back, and their returns, collectively called [[Clutter_(radar)|clutter]], can be far stronger than a distant aircraft's. Ground and sea clutter cluster near zero Doppler shift because the reflecting surface is stationary or nearly so, which is what lets a [[Doppler_radar|Doppler radar]]'s [[Moving_target_indication|moving-target indication]] separate them from a genuinely moving target even when their amplitude would otherwise swamp it; rain and sea clutter also depart from the simple statistics a receiver's detection threshold is designed around, with amplitude distributions running heavier-tailed than the noise floor and so demanding a threshold set adaptively rather than fixed.[^clutter-stats] ### Sensitivity time control (STC) A target's echo weakens with the fourth power of its range, so a receiver sensitive enough to hear a distant target would be driven far into saturation by strong, nearby clutter arriving only microseconds after the pulse leaves. Sensitivity time control addresses this by programming the receiver's gain to start low immediately after transmission and rise smoothly as range increases, trading away near-range sensitivity, where clutter would dominate in any case, to keep the receiver usable at every range within a single pulse; the same idea, applied more generally to a receiver whose input level cannot be predicted in advance, is what an [[Automatic_gain_control|automatic gain control]] loop does.[^stc-name] ### Unambiguous range Because pulses repeat, an echo that has not returned by the time the next pulse leaves is indistinguishable from a near echo of that later pulse, so the greatest range a radar can measure without confusion is set purely by the pulse-repetition interval: `R_ua = c/(2·PRF)`. A PRF of one kilohertz, for instance, allows an unambiguous range of about 150 kilometres; doubling the PRF to look at targets twice as fast halves that reach. A target beyond the unambiguous range does not disappear, but folds back and reports a false, short range, a range-domain instance of the same [[Aliasing|aliasing]] that governs any signal sampled too slowly for what it is trying to represent. ## In the frequency domain ### Pulse profiling A rectangular pulse of width τ has a spectrum shaped like a sinc function centred on the carrier, with a main lobe roughly `1/τ` wide and sidelobes falling away only slowly on either side; shortening the pulse to sharpen range resolution spreads that spectrum wider still, so a radar cannot choose a fine range resolution without occupying more spectrum, whatever waveform it ultimately transmits. The abrupt on-and-off switching of a simple rectangular pulse also throws a surprising amount of energy into sidelobes far from the carrier, energy that can interfere with other spectrum users; shaping the pulse's rise and fall with a [[Window_function|window function]] rather than switching it abruptly trades a slightly wider main lobe for sidelobes that fall away far faster, the same trade a spectral analyst makes when choosing a window for a Fourier transform. ### Unambiguous velocity The sequence of echoes a pulsed radar collects from one range cell, one sample per pulse, is itself a signal sampled at the pulse-repetition frequency, so the [[Nyquist–Shannon_sampling_theorem|sampling theorem]] that limits any digitised signal limits the Doppler frequency a pulsed radar can measure without ambiguity as well: a shift beyond half the PRF aliases to a lower, incorrect value, the same stroboscopic effect that makes a wagon wheel in film appear to spin backwards once its rotation rate passes half the frame rate. Because the Doppler shift itself is `f_d = 2·v_r/λ`, the unambiguous velocity works out to `v_ua = PRF·λ/4`, which sets up the central dilemma of PRF choice: a low PRF favours a large unambiguous range and leaves velocity ambiguous, a high PRF favours a large unambiguous velocity and leaves range ambiguous, and a radar that needs both without accepting either limit is exactly the case staggered PRF, described above, exists to handle. ## Typical system parameters No single set of numbers describes every radar, since the parameters above are chosen to fit a role rather than to hit any universal target, but a commonly quoted illustrative example puts the scale of a mid-band search radar in perspective: a carrier near a few gigahertz, a pulse width near a microsecond and a PRF near a kilohertz together give a duty cycle, the fraction of time the transmitter is actually on, of only about one part in a thousand, so a transmitter capable of a megawatt of peak power averages only about a kilowatt.[^typical-params] Weather and long-range search radars typically choose a low PRF to keep the unambiguous range generous at the cost of an ambiguous Doppler reading, while fire-control and airborne-intercept radars, which need an unambiguous speed far more than a long unambiguous range, typically choose a much higher PRF and accept range ambiguity as the price. ## Microsims A three.js companion elsewhere on the site puts pulse width, pulse-repetition frequency and duty cycle on one live readout, showing directly how moving any one of these numbers changes the others. This article carries no p5.js sketch of its own, so the reader who wants to see these trade-offs animated is better served by two neighbouring articles' sketches. The Radar sketch puts a complete pulsed radar on a rotating display and lets pulse-repetition frequency and pulse width be dragged directly, with the unambiguous-range ring and a pair of close targets responding live to each. The Doppler effect sketch isolates the frequency side of the same physics, letting a source's speed and frequency be set independently so that the size of a Doppler shift, rather than the timing of a pulse train, is what changes. *Try:* in the [[Radar]] sketch, raise the pulse-repetition frequency until the dashed unambiguous-range ring shrinks inside a distant target, and watch that target's echo fold back to a short, false range exactly as the Unambiguous range section above describes. *Try:* in the [[Doppler_effect]] sketch, change the source frequency rather than its speed, and notice that unlike a pulsed radar's Doppler reading, nothing here aliases, because this sketch never samples the shift through a train of pulses. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Radar_signal_characteristics) : [Wikitube](https://en.wikitube.io/wiki/Radar_signal_characteristics) Skeleton mirrored at revision 1320426279. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Radar]] - [[Pulse-repetition_frequency]] - [[Pulse_compression]] - [[Doppler_radar]] - [[Clutter_(radar)]] - [[Moving_target_indication]] - [[Aliasing]] ## References The core relations here — `ΔR = c·τ/2`, `R_ua = c/(2·PRF)`, the Doppler relation `f_d = 2·v_r/λ` and the resulting `v_ua = PRF·λ/4` — are standard pulsed-radar theory, used throughout radar engineering and not separately footnoted, per the Wikitube style guide's §6.1. Page numbers below are PDF pages of the open editions linked in Further reading. [^band-choice]: Citation needed: the IEEE radar-band letter designations (IEEE Std 521) and the specific propagation and antenna-size trade-offs by band would support a precise reference here. [^stagger-origin]: Citation needed: the origin and first operational use of staggered- or jittered-PRF processing in air-surveillance radar would fix a date and a named system. [^clutter-stats]: Citation needed: a specific statistical clutter model, such as the Weibull or K-distribution commonly used for sea clutter, attributed to its originating paper would support a precise reference here. [^stc-name]: Citation needed: the origin of the term "sensitivity time control" and the date of its adoption as a standard radar receiver feature would fix a source. [^typical-params]: Citation needed: a named radar system's published specification sheet would let these illustrative figures be replaced with, or checked against, a real example. **Further reading** — the open textbooks this article draws on, since the pair carries no separate Further reading heading of its own: - Steven Ellingson. *Radio Systems Engineering, Revised First Edition* (2023). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory* (2026). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory - Don Johnson. *Fundamentals of Electrical Engineering I* (2014). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1