Chapter 13 Continuous Wave Radar

Chapter 13 Continuous Wave Radar Radar ypes CW systes CW radar - No range inforation - single target - Unabiguous veloity inforation FM-CW systes - easure both range and veloity - broaden the transitted freq. spetru Pulsed Systes Pulsed radar - easureent of range Pulsed Doppler radar - easure both range and veloity 13-1

CW Radar Priary useful where no range inforation is required Advantage of CW radar - Sipliity; Saller and lighter - Peak transit is equal to average transit power X is lower than the peak power of a pulsed radar; no high voltage odulators are required for siple CW radar; radar ability to detet targets is deterined by the average power - Good for short range appliation; pulsed radars use R swith or tube to protet reeiver eho returns fro short-range targets will not reah the reeiver these targets will not be deteted. CW radars do not use R tubes; X/ RX isolation is ahieved by using other types of duplexer (ferrite irulators) or FM teh. - It is generally sipler to extrat Doppler inforation for a CW syste than fro a pulsed syste. Pulsed radar requires additional signal proessing (gate filter, delay aneller, FF) P peak P ave R in CW spetru Pulsed Radar Wave Shape Pulsed spetru Isolation 13-2 CW Radar Disadvantage of CW radar - No target range foration for a siple radar ability to deterine target range is poor - Rather poor X/ RX isolation - an be overoe using proper CW wavefor design Coon appliations - Siple (enoded), no range inforation: Weapon fuses, weapon seeker, lightweight portable personnel detetor, polie radar - Radar airraft altieter: frequeny CW radars apable of airraft-to-terrain range deterination. 13-3

CW Radar and Doppler Effet CW radar as a speed onitor devie Doppler effet (frequeny shift): only indiates targets oving toward or away fro radar for 2v ------, v: speed, f General for R 2 v R ----------- ----- R v f 10G. v 1ile/hour, 30Hz. 13-4 Siple CW Radar Systes Hoodyne reeiver X/RX Isolation required of irulator: power level of the X signal and sensitivity - HP series 35200 lower power, solid-state, X- band, Doppler radar: 18 db of isolation is required - Cirulators with 30 ~ 40 db of isolation and higher have also been built - In high-power radars, ore isolation ay be required - Other isolation teh. suh as dual antennas ay have to be used. - ajor shortoing sensitivity: al low Doppler freq. fliker noise is very strong aplify reeived signal at a high freq. Superheterodyne reeiver Superheterodyne reeiver IF ~ 60 MHz fliker noise is negligible Baseband Filtering: sweeping LO + a single filter, analog filter bank (IF stage), digital filters or FF proessor (Baseband stage) 13-5 Isolation

CW Radar Doppler Abiguity For infinite period of tie, the reeived signal (ignoring ap. fixed-phase ters): s t osw 0 w d t osw d tos w 0 t sinw d tsin w 0 t I Q Down to baseband (Video band) s t os w d t osw d t, S f 1 2 --f + 1 2 --f reeding approahing f Nothing additional is done, then the sign of the Doppler frequeny shift will be lost Relative target otion (approahing or reeding) will be indeterinate. he proble of abiguous relative otion IF signal into two hannels, I and Q hannels. ounter s t osw d t jsinw d t e j2f d t, S f 1, sign for approahing 2 --f 90 o Phase detetion: DC output FF sinw d t jsinw d t 1 2. 13-6 CW Radar Spetru and Resolution Reall that we talked about spreading of the signal spetru due to finite length signals fro Finite tie in bea, if B : beawidth ; s : san rate se t 0 B s ex: B 2, s 36se, t 0 2 36 1 18 se Bandwidth ooppler filter BW 18Hzse Cross-setion flutuation during tie target is in bea (effetively an ap. odulation) Moving arget oponents. e.g. propeller 13-7

Doppler filtering If we selet the IF beawidth so as to enopass all possible Doppler frequenies, the S/N will be poor. For exaple: ideally, we would like to use a athed filter Analog approahes to optiizing Could also use a single tunable BP filter that sweeps over the IF bandwidth. Siple digital filters Adaptive proessing None of these approahes by theselves will aount for sign of. Ipleent at IF or RF stage. selet so that overlap ours at -3dB Mathed Doppler filter BW in ax 3dB BW BW IF f IF 13-8 f IF Doppler filtering 13-9

Doppler filtering and PRF 13-10 CW Radar Range Equation A single Pulsed SNR SNR PG 2 2 ---------------------------------------- 4 3 R 4 kbfl Single pulse integrated over a dwell period - Coherent or inoherent pulsed radar - CW Radar (~ ) P: Peak power P t. Single pulsed power P t B: IF bandwidth, 1 B IF 1 for a athed filter S N SNR For CW,, ns N single pulse P t f r G 2 2 ------------------------------------------------------- 4 3 R 4 k1 d FL P P avg B B vid 1 d For a single (I) hannel CW 3dB loss Integrated Pulses Integrated Pulse SNR integrated SNR during a target dwell period, d. r 1 f r Nuber of Pulses, n, during d. n f r d, f r 1 r PRF (Pulse repetition freq.) P P avg P t f r B B vid 1 d d B 1 d 13-11

CW Radar Maxiu Range Exaple: Consider a CW polie radar with single hannel. Dual antenna antenna, a irulator a single P 100W, G 20dB, f 10.525G, 2.85, F 6dB, L 9dB, f 1ph 30Hz B: Veloity resolution. RCS 30 2, Required SNR 10dB. For CW, P P avg 100W B, 30Hz Max. R 4.2 k ~ 2.6 iles S iin A 2 e ------G 4 F kb S o N o in 114 db + 10logB MHz + F db + S o N o + L 2.85 10 2 -------------------------------------------100 2 4 6.467 10 3 114 + 10log30 10 6 + 6 + 10 + 10 133.229dB 4.755 10 14 W L indb R ax P t GA e ------------------------------- 4 2 S iin 1 4 0.1 ----------------------------------------------------------------------------------- 100 6.467 10 3 30 1 4 4 2 4.755 10 17 4010.4 4.01k 13-12 CW Ranging In order to easure range, it is neessary to plae a tie arker (odulation) in the transitted signal - aplitude, frequeny, phase - Pulsed radar AM. CW ranging - Frequeny-odulated CW (FMCW) - Multiple-frequeny CW - Phase-oded-CW FM-CW radar - Correlation of frequeny of X and RX signals - a easure of target s range and radial speed. - Linear frequeny odulation 13-13

FM-CW Ranging (No Doppler) Frequeny Modulation rate f 1 arget Range R ------ 2R ------ 2 f o f: Ap. of frequeny odulation f ----- b f We have --------- 4 2R 4 f ------ ---------- 8Rf 8Rff -------------- --------------------- + f f o f 4 1 f t R f ----------------- b 8ff BW 2f ransitted (Carlson s rule) Maxiu unabiguous range R ax -- 2 --------- 2f R ax 13-14 FM-CW Radar (Low Doppler) (1) - For positive slopes 8Rff f+ b f d --------------------- f d (toward) f+ b (negative sign) (away) - For negative slopes 8Rff f- b + f d --------------------- + f d (toward) f- b + f (negative sign) d (away) f+ + f- b b ------------------ f 2 b 8R ff --------------------- R --------------------- f 8Rf f- f+ b d ------------------ 2 v 2v ------ -- f - 4 b f+ b f o + arget oving toward Radar - arget oving away Radar + f f o f - + f+ b 4 13-15 - - arget oving away Radar 1 f + arget oving toward Radar + - t

FM-CW Radar (high Doppler) (2) - For positive slopes 8Rff f+ b f d --------------------- (toward) f+ b f (negative sign) b (away) - For negative slopes 8Rff f- b + f b --------------------- + f d (toward) f- b + (negative sign) (away) f- f+ b b ------------------ f 2 b 8R ff --------------------- R --------------------- f 8Rf f- + f+ b d ------------------ 2 v 2v ------ -- f - 4 b + f+ b f o + arget oving toward Radar - arget oving away Radar + f f o f - + f+ b 4 - - arget oving away Radar 1 f + arget oving toward Radar + - t 13-16 FM-CW Range Resolution Range resolution (auray) R : the frequeny differene,, an be easured. B 2f For a linear FM, (thus R ) depends on the BW and linearity of the odulation. - Nonlinearity is given by f B. f : deviation in odulation fro linear. - Nonlinearity ust be uh less than f B. Maxi. range resolution R 2B, ( «1 f ) For a givenr ax and R ax, nonlinearity «f B R R. EXaple: For a range resolution of 1ft and a axi. unabiguous range of 3000 ft. the nonlinearity of the FM wavefor ust be less than R R 1 3000 0.03%. 13-17

FM-CW for Multi-target Ghost Identifying - Adding another segent - Adding ore slopes - Siilar to Multi-PRF f transitter Reeived ehoes Ghost - Multi-target (wo targets, hree targets) - Ipossible to tell the paired differenes Ghost FF, Filter bank 13-18 FM-CW Radar Design X 10dB RF Aplifier f 10G Modulator VCO (8-12G) Wavefor Generator iing signal Average Frequeny ounter Veloity Range 10dB f IF 1G Average Frequeny ounter Filter Bandwidth BW 5% ~ 50% f RF Sideband Filter (f 9G) BW 500M IF OSC Video Ap. RX f + RF Aplifier 20dB f f IF 9G 10dB f IF + IF Aplifier 20dB IF Sideband Filter (f 1G) BW 200M Low pass Filter 13-19

Sinusoidal-FM Ranging (1) Modulation with an instantaneous frequeny of f t f 0 + f os2f t he transitted signal in this ase is s t A 1 sint, where t 2f tt d 2f o t + f ------ sin2f t f he reeived wavefor for a point target is a replia of the transitter wavefor, in other words, r t A 2 sint A 2 sin 2f o t + ------ f sin2f f t After ixing and filtering of the two signals in the reeiver, the output is r ts t A 1 A 2 f ------------ os 2f 2 0 + ------ sin 2f f t sin 2f t A 1 A ------------ 2 os 2f 2 0 + 2 ---------- f sinf f t os 2f t 2 -- If one assue that «1 f, 8Rff sina sin A B B 2sin -- A B 2 os 2 -- 13-20 Sinusoidal-FM Ranging (2) r ts t A 1 A 2 2f ------------ os2f 2 0 ---------- sinf f 2f t 2 -- os os 2f sin2f 0 sin ---------- sinf 2f f t 2 -- os A 1 A 2 2f ------------ os2f 2 0 J 0 ---------- sinf f 2J2 22f t 2 -- os + 2J 4 os 2f 2sin2f 0 J 1 ---------- sinf 2f os t 2 -- J 3 os 22f t 2 -- + f We use expansion of the for Bessel funtion osz os J o z + 2 1 k J 2k z os2k k 1 sinz os 2 1 k J 2k + 1 z os 2k + 1 k 1 13-21

Sinusoidal-FM Ranging (3) If we add a Doppler oponent, the net result look like D J 0 D os2 t 0 + 2J 1 D sin2 t 0 os 2f t 2J 2 D sin2 t 0 os 22f t + 2J 3 D sin2 t 0 os 3 2f t + 0 2f ---------- sinf f 2f o 2f -- 2 2vf o 2R ------------- 0 2f o ------ R 2 f 2f -- D R ---------- 2f sin -- he haronis of f are odulated by the doppler frequeny and weighted in aplitude by a Bessel funtion Advantage: J o gives a axiu weighting at J n D D n R n for a sall arguent low D, (i.e. near range) and lower weighting at far range (for exaple: far lutter) J o D J 1 D J 2 D J 3 D - When the reeived signals are fro lose-in lutter, higher-order haronis should be hosen Disadvantages: - Insuffiient use of energy - Probably ost suitable for a single target f 2R ------ 13-22 Multiple-Frequeny Ranging (1) arget range ould be deterined by easuring the reeive phase differene between the transitted and reeived waves he relative differene,, is given by RX X 2d 4R 4fR ---------- ---------- -------------- R he axiu unabiguous range 2 R ax 2 ---------- ---------- 4 4f - 15 at L-band (1GHz) to 1.6 at 95 GHz he approah we intend to look at use two or ore CW signals that are very lose-in frequeny. If we have a suffiiently iff f 2 f 1, then range easureent ay be possible sine diff 2 1 is large We exained the ase of two frequeny that only differed by khz - Advantage: Large unabiguous range - Disadvantage: poor range resolution wo CW signals withf 1 andf 2 v 1R v 2R ransitter signal v 1 sin2f 1 t + 1 v 2 sin2f 2 t + 2 Reeiver signal sin2f 1 f D1 t 4f 1 R + 1 sin2f 2 f D2 t 4f 2 R + 2 13-23

Multiple-Frequeny Ranging (2) Low side of ixingv 1 v 1d v 2d tov 1R sin 2f D1 t 4f 1 R sin 2f D2 t 4f 2 R Phase differene betweenv 1d andv 2d 4R 2f D1 f D2 + ---------- f 1 f 2 4R ---------- f 1 f 2 f 1 f 2 If and are nearly the sae. f f 1 f 2. therefore 4R f ------------------ R -------------- 4f Assue R 0 0 Deterine R neessary to give 0 2 - R unab 2 -------------- 4f - If, and then However, a sall f resolution degree ---------- 2f f 1.5kHz 3 10 R 8 unab 2 ----------------------------------- 1.5 10 3 100k - Range per ( o ) degree for also gives a poor range f 1.5kHz R -------------------------- 180 4f ----------------------------------------------- 3 10 8 180 278 phase 41.5 10 3 - If easureent auray is 5 o, then the range resolution is 5(278) 1.4 k f 1 f 2 f 1 f 2 - For sall as beoes saller, R unab beoes higher asf 1 f 2 beoes saller ability to deterine - Solution: use ore than 2 frequenies. R 13-24 hree-frequeny Ranging (3) 3-frequeny syste f 3 f 1» f 2 f 1, let f 3 f 1 15kHz and f 2 f 1 1.5 khz For f 3 f 1 15kHz (Fine) R unab31 2 f 3 f 1 10k, R 180 4f ------------------------------ 3 f 1 28 For f 2 f 1 1.5 khz (Rude) R unab21 2 f 2 f 1 100k, 180 R 4f ------------------------------ 3 f 1 278 Exaple: Assue we are taking easureents with an atual syste and easured values as 3 1, 2 1 1.2rad 1.3rad hen by oparing phase Rf 3 f 1 3 1 4f ------------------------------ 3 f 1 1.91k Rf 2 f 1 2 1 4f ------------------------------ 2 f 1 20.7k Infer range of R 2 R unab31 + Rf 3 f 1 2 10 + 1.91 21.91k Could use an even greater nuber of frequeny to obtain the best obination of R unab and R. 10k R rude 20.7k R fine 21.91k 10k 1.91k 13-25