Week 5 Flashcards
Targets are detected when
The signal out of envelope detector crosses threshold
Detection criterion
Established using N received pulses from target
Analog radar displays
A-scope and PPI use persistence on tube to integrate signals
PPI tube persistence»_space; pulse repetition interval
Returns from target contribute to brightness of spot on screen
Analog integration - no automatic detection
A-scope, PPI display requires a human observer (read range and angle from PPI)
Analog displays - observers
Can interpret signals
Get fatigued when staring at screen
Can fail to notice targets
Can misread range or angle
Automatic target detection
Removes observer as a detector
Threshold circuit deletes all targets below threshold
Has no intelligence, does not get fatigued, always reports range and angle correctly
Used by modern radar systems (present processed info to observer for interpretation, i.e., removes noise from targets and screen and labels target with additional info)
Air traffic control radar labels target on screen with
ID, altitude
Range gating
Dividing up received signal in time
A sample of the receiver output at an instant of time
Integration cannot be carried out without range gates
Natural time step for range gating
τ, the pulse width (corresponds to a step in range equal to ΔR the range resolution)
How does range gating work
Output of receiver is sampled at discrete instants of time after each pulse
Integration proceeds by adding up the samples returned by the pulses for each delay time
Threshold then applied to decide whether each range gate contains a target
Range dimension of the radar display will be divided into segments (cells)
For each cell a decision will be made as to whether a target is present - the cell might ‘light up’
There will be no ability to resolve multiple targets within a cell
M out of N detector
Signal pulses appear in same range gate, noise pulses appear randomly in time
Require M detections in N tries to declare that there is a target
In each range gate try N times (usually number of pulses per target)
1 for detection, 0 for no detection
Threshold at M detections
M out of N detector - Pfa
Pfa: Probability that a noise spike occurs in the same range gate on successive radar transmission falls rapidly with increase in N
Pd: probability that a target pulse appears in the same range gate on successive radar transmission falls slowly with increase in N
Probability of N noise pulse crossing threshold in the same range gate
m-out-of-n tries
Cost of improvement is an extended dwell time in order to conduct test N times
Improvement to Pd and Pfa
With M out of N detection we can meet spec with a smaller radar (can meet spec with a lower single-pulse S/N with M out of N processing than with single-pulse detection
Processing gain
Reduction in the S/N from M out of N detection required to meet spec
Target RCS Fluctuations
Targets typically have dimensions much larger than wavelength (ships, aircraft, people, except for raindrops where D
Two scatterer case
Equal RCS
Electric fields of reflected waves from target 1 and 2 can:
- add in phase (E1+E2=2E)
- add in anti phase (E1-E2=0)
Received power is proportional to E^2
Received power varies between 0 and 4P
Meaning of RCS for complex targets
RCS not single-valued
Because its RCS is the average value of σ over its PDF, the variability of σ needs to be handled statistically
Statistical models for RCS fluctuation
Case 0 - no fluctuating σ
2 PDFs x 2 fluctuation rates = 4 models (SW1, SW2, SW3, SW4)
Choice depends on the nature of the target
2 types of PDFs
Rayleigh and 4th degree chi-square
Two types of fluctuations
Fast, with σ varying from pulse to pulse
Slow, with σ varying from scan to scan (dwell to dwell)
SW1
Rayleigh, slow
Most commonly applied
Higher detection probabilities require larger increases in (S/N) - curve diverges
SW3
Chi-square, degree 4; slow
SW2
Rayleigh, fast
SW4
Chi-square, degree 4; fast
Targets made up of many small scatterers
SW1, SW2
Target made up of a combination of one large scatterer and many small scatterers
SW3, SW4
Finding (S/N) with Swerling Targets
Find the (S/N) needed to meet spec with a non fluctuating model
Decide which swerling model best fits target
Read off additional S/N needed for the Swerling target
Add additional S/N to that needed for SW0 target
Typical values of additional S/N needed to meet the Pd spec with a fluctuating target
SW1 or 2: 7-8dB
SW3 or 4: 3-4dB
Impact of target fluctuations on pulse integration
Coherent integration requires ‘coherence’ in the pulse-to-pulse returns (the returns need to be highly correlated in phase)
Fast fluctuations of SW2 and SW4 targets defeat coherent integration of pulse returns
Does not affect non-coherent integration
Efficiency of envelope detection
The output SNR from an envelope detector is less than the input S/N
Efficiency of detector gets worse as (S/N)in approaches 1 or 0 dB
When noise voltage > signal voltage
Noise ‘captures’ the detector
Does not allow the single pulse S/N for non-coherent integration to fall below +3dB at threshold (does not apply to coherent detection)
range ambiguity
PRF corresponds to a max unambiguous range
R = Run + x with x < Run, R’ = x = R-Run; real target can have any value {R} = mRun + x; correct target is R=R’=x
Echo from the first pulse is associated with the second pulse (R>Run)
All ranges > Run are aliased to the measurement interval {0, Run}
{R} < Rmax if targets do not occur beyond Rmax
Only if Rmax < Run have we eliminated the range ambiguity
Resolving range ambiguity
Using two PRFs can resolve the range ambiguity that arise with individual PRFs
mRun1 = nRun2
If new Run is too far away, there is no possibility of a target being present of or of it having a large enough RCS to be detected
Up to what range can we avoid ambiguity by combining observations with two PRFs
First occurrence of mRun1 = nRun2 = Run_eff
All target ranges beyond this range will aliase to nearer ranges
Avoid choosing PRFs with common multiples
The atmosphere as a propagation medium includes the effects of
Absorption Refraction Volumetric scattering Turbulence Called atmospherics
In order of increasing altitude, the temperature
False through the troposphere (0-10km)
Rises through the stratosphere (10-50km)
Falls through the mesosphere (50-90km)
Riss through the thermosphere (above 90km)
Structure of the atmosphere
Each layer has an upper boundary where the temp reaches a minimum (tropopause, mesopause) or maximum (stratopause)
At a pause the vertical gradient in temp is zero (dT/dz = 0)
Refraction in the atmosphere
Refraction in the troposphere generally bends radar signal downwards
Causes errors in knowing target’s position but extends the range of radar systems
Obeys Snell’s Law applied to the index of refraction
Fairly predictable but can produce bizarre anomalies and what amount to mirages
Snell’s Law
nsin(i)
n - index of refraction, i - angle of incidence
Effect of earth’s surface
Effectively blocks propagation of E/M waves
Plane of the horizon defines two regions
For a target in the line-of-sight region
Transmissions have direct access
For a target in the shadow region
Transmissions only have access via a diffraction or refraction mechanism
Distance to horizon
Microwave radars are line of sight devices
Some bending of rays occur due to refraction and targets can be detected beyond the physical horizon
The ionosphere and refraction
Ionosphere begins about 80km altitude and extends through a peak at about 300 km to about 1000 km
Has electrical properties because it has ions and electrons
Refraction in the ionosphere is strong on HF frequencies and can cause signals to reflect and propagate downwards
Basis for over-the-horizon (OTH) radar
What reveals the ionosphere
Airglow
How can HF signal skip to great distances
By ‘bouncing’ off the ionosphere and Earth’s surface
Atmospheric attenuation and absorption
An E/M wave loses energy from the intended direction of propagation by absorption and scattering (amounts to loss)
Absorption is largely due to
Oxygen and water vapor
Scattering is due to
Particles that deflect wave energy away from the intended direction of propagation
Major factors in attenuation
Water content and temperature (highly variable)
Clear air and water vapor attenuation
Attenuation in clear air varies strongly with frequency above 10 GHz
-significant peaks in attenuation occur within absorption bands that are due to molecular oxygen and water vapor
Water vapor produces a minor absorption band between 20 and 24 GHz (k-band)
-oxygen produces a major observation band that peaks near 60 GHz at almost 20 dB/km
