Moving_target_indication

# Moving target indication **Moving target indication** (MTI) is a radar processing technique that separates a moving target from stationary background echoes, or [[Clutter_(radar)|clutter]], by comparing what a receiver hears on one pulse against what it heard on the pulse before. A hill, a building or a stretch of open ground returns almost exactly the same echo every time the beam sweeps past it, and MTI processing is built to reject anything that repeats that way; an aircraft, a ship or a vehicle changes its echo slightly with every pulse because it has moved, and that change is what survives the comparison and reaches the display. The technique is older and coarser than the fuller [[Pulse-Doppler_radar|pulse-Doppler]] processing that followed it, which recovers a target's actual velocity rather than merely flagging that something moved, and it differs in aim from the newer stationary target indication, which classifies a return from properties of the echo itself rather than from whether the echo has moved. A three.js companion microsim to this article renders the device at MTI's centre, the delay-line canceller, showing the notch it cuts at zero Doppler shift, the family of blind speeds that notch repeats at, and the staggered pulse timing radar designers use to close them. The canceller's output still has to be tested against a threshold before it becomes a reported detection, and in most modern systems that later step is [[Constant_false_alarm_rate|constant-false-alarm-rate]] processing rather than one fixed level, so the two techniques are usually described in the same breath even though they answer different questions: MTI removes interference that does not move, and constant-false-alarm-rate processing adapts to interference whose strength changes from one range cell to the next. ## Operation Early implementations built the pulse-to-pulse comparison from a single piece of hardware, a delay line tuned to hold one pulse's worth of receiver output for exactly one interpulse period before releasing it to be subtracted from the next return.[^delayline] A modern radar performs the same subtraction in a digital memory rather than a physical delay medium, but the arithmetic, and the trade-offs it imposes, are unchanged. The comparison only works if the receiver preserves each pulse's carrier phase relative to a fixed reference, so that the sole difference between two returns from the same motionless object is the receiver's own noise. A transmitter whose oscillator restarts at a random phase on every pulse, as an early [[Cavity_magnetron|cavity-magnetron]] transmitter's does, cannot supply that reference by itself; such radars instead generate a local reference in the receiver from a sample of the transmitted pulse and hold it steady until the next one arrives, an arrangement generally called coherent-on-receive operation.[^coho] This differs from a true [[Doppler_radar|Doppler radar]], which reads velocity directly from the size of a frequency shift; MTI only asks whether a shift is present at all, and cancels the returns for which it is not. The simplest canceller delays one pulse's video by the interpulse period `T`, the reciprocal of the [[Pulse-repetition_frequency|pulse repetition frequency]], and subtracts it from the current pulse: `y[n] = x[n] - x[n-1]`. Writing this as a general one-tap digital filter, `y(t) = x(t) + b1*x(t-T)`, gives a frequency response `|H| = sqrt(1 + b1^2 + 2*b1*cos(w*T))`, with a maximum where `b1 = +1` would place it and a minimum in the same place `b1 = -1` places its own maximum instead.[^fir057] The canceller is the `b1 = -1` case, and the algebra collapses to the textbook two-pulse response `|H| = 2*|sin(pi*f*T)|`, exactly zero whenever the Doppler frequency `f` is an integer multiple of the pulse repetition frequency, including zero itself. The zero at `f = 0` is the clutter notch: it removes a motionless return regardless of how strong that return is. The response's higher zeros are blind speeds, radial velocities at which a genuinely moving target's Doppler shift happens to land on a multiple of the pulse repetition frequency and is cancelled along with the clutter it was meant to be separated from. Because a target's Doppler frequency is `2*v/lambda` for a radar wavelength `lambda`, raising the pulse repetition frequency pushes the first blind speed higher, but it only moves the whole comb of notches outward; it never removes them. The standard fix interleaves two or more pulse repetition frequencies so that each one's blind speeds fall at a different true velocity, leaving no single speed blind to every interleaved pulse train at once. This staggered-pulse-repetition-frequency scheme is what the three.js companion renders alongside the notch itself. ## Characteristics A moving-target-indication system is judged on a cluster of figures that separately describe how well it finds targets, how well it places them, and how much ground it can search in a given time. ### Probability of detection (Pd) The probability of detection is the fraction of genuinely present targets a system reports on a given look. It rises with the signal-to-noise ratio the canceller delivers and falls whenever the detection threshold is raised to hold down false alarms, a trade governed by the same tail probability of a Gaussian that is used to compute a bit-error rate in a noisy digital link.[^ellQ] In an MTI system that trade is sharpened by the clutter notch itself: a target whose Doppler frequency lands near a blind speed loses signal-to-noise well before receiver noise alone would explain it, so probability of detection is properly quoted against a target's radial velocity rather than as a single number. ### Target location accuracy Location accuracy is how close a reported range and bearing sit to a target's true position, a different question from how finely two nearby targets can be told apart. It depends on the signal-to-noise ratio at detection and on how finely the system interpolates within a range or angle cell, for instance by comparing amplitude across adjacent beam positions or, more precisely, by the sum-and-difference comparison a [[Monopulse_radar|monopulse]] antenna performs on a single dwell. ### Target range resolution (high range resolution; HRR) Range resolution is set by the transmitted pulse's duration or, once [[Pulse_compression|pulse compression]] is used, by the bandwidth of the compressed pulse rather than its transmitted length. A high-range-resolution waveform can separate two targets, or resolve a target from a competing clutter cell, at spacings that a simple long pulse would blur together into one return. ### Minimum detectable velocity (MDV) Minimum detectable velocity is the slowest radial speed a real target can have and still be told apart from the stationary background, and it is set directly by how wide the delay-line canceller's notch is around zero Doppler. A narrow notch trims away only truly motionless clutter and lets slow targets through it; a notch widened to reject clutter that has some internal motion of its own, such as wind-driven foliage, raises the minimum detectable velocity and can hide a genuinely slow-moving target inside the widened notch. ### Area search rate Area search rate is how much ground a radar can cover per unit time, and it competes directly with the figures above it: a canceller needs several pulses on each patch of sky or ground to build its comparison, so widening the beam or shortening the dwell to search faster leaves fewer pulses to cancel with, which degrades detection and minimum detectable velocity together. ### Stand-off distance Stand-off distance is how far back from the area under surveillance a radar, and the platform carrying it, can sit while still meeting its other performance figures. It matters most for an airborne or ship-based system trading detection range for survivability by remaining outside a threat's own reach. ### Coverage area size (breadth and depth) Coverage area size states the searched region as an angular breadth and a range depth rather than a single number, since a system can trade one for the other: narrowing the azimuth fan searched extends the range at which a given probability of detection still holds, for a fixed area search rate. ### Coverage area revisit rate Revisit rate is how often the same patch of the coverage area is looked at again, and it bounds how a [[Radar_tracker|tracker]] downstream can behave. A slow revisit rate forces wider prediction gates between looks and makes it harder to keep a track continuously associated with a manoeuvring or slow-moving object. ## Microsims A three.js companion built for this article renders the delay-line canceller as a live frequency-response plot: the notch sitting at zero Doppler, the repeating comb of blind speeds it creates at multiples of the pulse repetition frequency, and the effect of interleaving a second, staggered pulse-repetition frequency to close the gaps the first one leaves. Beyond that neutral summary, its controls and readouts are not described here; the two sketches below are carried by neighbouring articles and are reached from this one by cross-reference. *Try:* in the [[Doppler_effect]] sketch, raise the source speed and watch the observed frequency pull away from the source frequency; that split, for a source that never moves, is zero, which is exactly the return a delay-line canceller is built to remove. *Try:* in the [[Radar]] sketch, drag the PRF control and watch the dashed unambiguous-range ring move; the same pulse repetition frequency that sets that ring also sets the spacing between an MTI canceller's blind speeds.  **Microsim — three.js (Wikitube framework), pending deploy:** *Moving target indication: notches at the blind speeds* will play here once `https://wikitube-3d-microsims.netlify.app/radar/Moving_target_indication.html` is live.  *Built from `MICROSIM_GUIDE/specs/sims/Moving_target_indication.json`; part of the [[PORTAL_Radar|Radar]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Moving_target_indication) : [Wikitube](https://en.wikitube.io/wiki/Moving_target_indication) Skeleton mirrored at revision 1309959860. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Pulse-Doppler_radar]] - [[Clutter_(radar)]] - [[Pulse-repetition_frequency]] - [[Doppler_radar]] - [[Radar]] - [[Constant_false_alarm_rate]] - [[Radar_tracker]] ## References [^delayline]: Citation needed: a primary engineering source (manufacturer report, patent or textbook edition, with date) describing an early acoustic or mercury delay-line moving-target-indication canceller would fix the date and the equipment concerned. [^coho]: Citation needed: a primary source naming the radar programme and date at which coherent-on-receive operation was first fielded against a non-coherent cavity-magnetron transmitter would settle this claim precisely. [^fir057]: Stiber, M.; Stiber, B.; Larson, E. *Signal Computing: Digital Signals in the Software Domain*. 2020, pp. 69-70, 72, 74 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. [^ellQ]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 145-148 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC.