# RF Propagation Clutter

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RadarDr. John S. SeyboldNovember 9, 2004IEEE Melbourne COM/SP AP/MTT Chapters

RadarAcronym for RAdio Detection And Ranging Radar can be thought of as a pair of one-way communication links, with the return link being the radar reflection. Consider the radar problem, where in general the transmitter and receiver are co-located and the received signal is a reflection The expression for power density at a distance d is,W= PT GT watts/m 2 4 d 2RF Propagation 2

Typical Radar GeometryTransmitted signal Transmit and receive antenna Reflected signal Reflecting Target, apparent size

A typical radar system consists of a co-located pulsed transmitter and a receiver, usually sharing an antenna A pulse is transmitted and then the receiver listens for the return, similar to sonar The strength of the return signal depends upon the distance to the target and its (electrical) size The radar determines the distance to the target from the time delay before receiving the reflected pulseCopyright September 2002, John S. Seybold, All Rights Reserved

RF Propagation

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Free Space PropagationThe power density at a distance, d, is

W=

EIRP watts/m 2 4 d 2

The power available at the output of a receive antenna would be the product of the power density at that point times the antennas effective area

PR =

PT GT Ae 4 d 2

P G G 2 watts or PR = T T 2 R 2 (4 ) d

Substituting the expression for antenna gain yields the Friis free space loss equation

L=

PR GT GR 2 = (4 d ) 2 PT

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Radar Cross-SectionInstead of a receive antenna effective area, in radar, the signal is determined by the RCS The radar cross-section (RCS) is a measure of the electrical or reflective area of a target It may or may not correlate with the physical size of the object It is usually expressed in m2, or dBsm The symbol for RCS is tCopyright September 2002, John S. Seybold, All Rights Reserved

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The Radar EquationSo, the reflected signal can be determined from the power density at the target times the RCS

Prefl =

PT GT t 4 d 2

The power density at the receiver from the reflected signal is

WR =

PT GT t 1 2 4 d 4 d 2

When multiplied by the effective area of the radar antenna, this becomes 2

PR =

PT GT t Ae PT GT GR t = (4 )2 d 4 (4 )3 d 4RF Propagation

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The Radar Range EquationFor a required received signal level, we can solve the radar equation for d and find the maximum distance at which detection is possibled max = 4 PT GT GR t 3 PR min (4 )2

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Radar ExampleConsider a radar system with the following parameters:f = 2 GHz PT = 1 w = 0 dBw R = 2 km F = 5 dB t = 1 m2 GT = GR = 18 dB B = 50 kHz = 0.15 m

What is the SNR at the receiver?RF Propagation

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Radar ExampleThe received signal level isPR = PT GT GR t (4 )3 d 42

This can be computed in dBW asPR = 0 dBW + 18 dB + 18 dB + 0 dBsm + 20log(0.15) dBsm 30 log(4) - 40log(2000)dBm4 (-16.5 dBsm ) (- 33 dB) (132 dBm4)

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Radar ExampleThe receiver noise power is N = kToBF or,NdBm = -174 dBm/Hz + 10log(50,000)dB-Hz + 5 dB (47 dB-Hz)

NdBm = -122 dBm And the SNR isPR NdBm = -115.5 dBm (-122 dBm) = 6.5 dBCopyright September 2002, John S. Seybold, All Rights Reserved

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CommentsNote that the received power is inversely proportional to R 4, so doubling the distance reduces the signal level by 12 dB The round-trip path loss is NOT equal to 3 (or 6 dB) more than the one-way path loss. It is double the one-way loss in dB (i.e. loss is squared)

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Pulse RadarConventional pulse radar works by transmitting a short RF pulse and measuring the time delay of the return The bandwidth of the matched filter receiver is ~ 1/ where is the pulse width (this is used as the NEB in noise calculations) also determines the range resolution of the radar cr = 212Copyright September 2002, John S. Seybold, All Rights Reserved

RF Propagation

Pulse RadarShorter pulses require larger receive bandwidths (more noise), provide less average power (less signal) but provide better range resolution The matched filter has an impulse response that matches the transmitted pulse The range to the target is

R=

c t 2

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Pulse RadarThe pulses are usually transmitted periodically. This period is called the PRI or the PRT The pulse repetition frequency is 1 PRF PRI The PRI defines the maximum unambiguous range of the systemRunamb = c PRI 2

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Pulse RadarA large target beyond the unambiguous range may be interpreted as a close targetRunamb(N-1)th pulse Nth pulse Ro Multiple time around return from previous pulse Target return

Ro-Runamb

Range RF Propagation 15

Pulse RadarFor multiple time around returns to be an issue, the RCS of the distant reflector must usually be large Ideally, we would like Runamb to be well beyond the maximum detection range of the radar In practice there are ways to mitigate the effect of these returns.Copyright September 2002, John S. Seybold, All Rights Reserved

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Range MeasurementTarget range can be estimated with an accuracy better than the pulse width by using a split-gate tracker By comparing the energy in the early and late gates, an estimate of the target position is obtained

Early Gate

Late Gate

Target ReturnRF Propagation

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Radar ClutterClutter is defined as any unwanted radar echo Ground target returns will include ground clutter (area clutter) Airborne target returns may include volume clutter from precipitation in the propagation pathCopyright September 2002, John S. Seybold, All Rights Reserved

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Area ClutterArea clutter is characterized by the average clutter cross-section per unit area, o (sigma-zero) This is called the backscatter coefficient The units are m2/m2 The amount of clutter received depends upon how much ground area is illuminatedCopyright September 2002, John S. Seybold, All Rights Reserved

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Area ClutterThe width of the clutter patch is defined by the antenna azimuth beamwidth and the range or distance to the clutter patch The length of the clutter patch is determined by eitherthe range gate size (shallow grazing angle) or the elevation beamwidth for steeper grazing angles such as an airborne radar illuminating a ground targetCopyright September 2002, John S. Seybold, All Rights Reserved

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Area ClutterThe width of the clutter cell is Where R is the range to the center of the clutter cell and AZ is the antenna azimuth beamwidth in radiansTop Down ViewAZ W RAZ

W R AZ

R

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Area ClutterThe depth or length of the clutter cell is determined by the smaller of theRange gate projected onto the ground The elevation beamwidth times the total range projected onto the groundRadarL BW =L RG

R EL sin( ) c = 2 cos( )

c/2 LBWRF Propagation

= grazing angle

LRG22

Area ClutterThus the length of the clutter cell can be expressed as c l min( sec( ), R EL csc( )) 2L BW =L RG =

R EL sin( )c 2 cos( )

= grazing angle

LBW23

Area ClutterAs seen from the preceding development, these values are approximate In addition, we know that the antenna beam has a roll-off, it does not drop off to zero gain at the edge of the 3 dB beamwidthCopyright September 2002, John S. Seybold, All Rights Reserved

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Area ClutterSo at shallow grazing angles, when pulse limited Actual Clutter AreaAc R AZ c sec( ) 2 c sec( ) l= 2

W = R AZ

Estimated Clutter Area

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Area ClutterAt steeper angles, when beam limited the clutter area is simply the area of the elliptical footprint

Ac =R EL csc( )

4

R 2 EL AZ csc( )

R AZ

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Clutter Cross-SectionThe actual radar cross-section of the clutter is the clutter patch area multiplied by the backscatter coefficient

c = 0 AcWe will only consider the p

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