1. Detection of Signals in Noise and Clutters
Chapter 5 :
Processing
Or:
Detection of Signals in Noise and Clutters

2. Matched Filters Output of a Matched Filter occurred in IF stage and :
Frequency response a Matched Filter:
S(f) is signal spectrum and tm is signal length
Example: A Rectangular Pulse

3. Other Pulses

4. (Detection Decisions)
Detection Criteria
(Detection Decisions)
1. Neyman Pearson Observer:
Based on a classical statistical theory for decision of detection
Have two types of errors :
1. noise is detected as a target when noise is alone.
False Alarm
2. Signal is present, but it is erroneously considered to be noise.
Missed Detection
2. Likelihood Ratio Receiver:
Based on statistical decision and define:
is probability function of signal plus noise
3. Inverse Probability Receiver:
An analytical basis to model optimum receiver. This method is a academic interest and not practical for decisions.
4. Sequential Detection:
In Neyman Pearson Observer a number of pulses are considered for detection decision.
When S/N is large, no need to further pulses. A small number of pulse is sufficient to decision. This procedure is named as Sequential Detection.

5. Detectors 1. Optimum Envelope detector Law : Linear Detector
IF Amp.
Video Amp.
Rectifier
Optimum detector is based on Likelihood Ratio Receiver :
I0 is model based Bessel function zero order and a is amplitude of the sin wave and v is amplitude of IF.
Suitable approximation is :
Linear Law Detector :
Have High dynamic range and preferred
For large of S/N we have a >>1 and then:
Square Law Detector :
Have distortion for signal
For small of S/N we have:
2. Logarithmic Detectors : Logarithmic receivers
The output of the receiver is proportional to the logarithm of input envelope.
To prevent of saturation of receivers in non-MTI systems similar Log-FTC.
In MTI systems, nonlinearity is caused that the improvement factor is reduced.
The loss due to logarithmic detection is limited up to 1.1 dB with the increasing of number of pulses.

6. Detectors 3. I & Q Detector : In phase and quadrature phase channel
Used in MTI for blind phase phenomena
3. Coherent Detector :
Mixer
A single channel detector similar to in phase channel.
Reference single at the same exact frequency and same exact phase.

7. Automatic Detection Manual Detection (Operator Detection) :
PPI display or A-scope integrates pulses in operator’s eye memory.
Automatic Detection (Machine Detection) :
By computer processing
Automatic Detection and Tracking (ADT) act as following :
Quantization of the radar coverage into range (or angle) resolution cells.
Sampling at least one sample per cell or further.
Analog to digital conversion of input signal.
Signal processing in the receiver to remove noise, clutter and interference.
Integration of pulses in each resolution cell.
CFAR operation when the receiver don’t remove all clutter and interferences.
Clutter map generation to provide location of clutters.
Threshold detection to select of target echo.
Measurement of range and angle of the target.

8. Integration of Pulses
In early radars :
integration of pulses is performed by the operator’s eye memory in cathode ray tube (CRT) .
In Modern radars :
integration of pulses is performed by processing.
These integrators are called detectors in technical literatures.
Several types of integrators are classified as following :
Moving window integrators.
Binary integration.
Batch integrators.
Feedback Integrators.
Mean Integrators.
Median integrators.
Censored (removed) mean detectors.
Adaptive detectors.
Non-parametric detectors.
Distribution detectors are usually considered as CFAR.
Binary detector or
Double detector or
m-of-n detector
M pulse is sufficient from n pulse to detect
Most of these detectors are academic interests and aren't applicable for operational radar systems

9. Optimum Number of Pulses in Binary integration:
Integration of Pulses
Optimum Number of Pulses in Binary integration:
Feedback Integrator:

10. Integration of Pulses Pulse Integration is categorized in two types
Coherent integration
Non-coherent integration

11. Different threshold levels
CFAR Receivers
A false alarm is an erroneous radar target detection decision caused by noise or other interfering signals exceeding the detection threshold.
The False Alarm Rate (FAR) is calculated using the following formula:
If the threshold is set too low, the large number of false alarms will mask detection of valid targets.
Different threshold levels
a threshold is set too high: Probability of Detection (P.d.) = 20%
b threshold is set optimal: P.d. = 80% , but one false alarm arises!. False alarm rate = 1 / 666 = 1,5 x10-3  .  
c threshold is set too low: a large number of false alarms arises!
d threshold is set variable, constant false-alarm rate is occurred .

12. CFAR Receivers
Constant False Alarm Rate (CFAR) generate a adaptive threshold for detection decision.
Cell Averaging CFAR (CA-CFAR) :
Other form of CFAR :
Siebert CFAR: The old version of CFAR in 1960 for AN/FPS-23 ,US air force.
Hard limiter : It is a Dicke fix which has a broad band IF amp. and a hard limiter and narrowband match filter. For anti jamming applications and impulse-like noise.
Log-FTC: It is a CFAR when the noise and clutter have a Rayleigh pdf.

13. CFAR Receivers CFAR Loss is Defined as : Effect of Clutter’s Edges :
Clutter’s Edges are change threshold level.
GO-CFAR reduces this effect by using the greater of the two sets of reference cells.
GO-CFAR introduces an additional loss of dB.
Effect of Multiple Targets:
Multiple targets in res. cells increase threshold level.
In this case a number of res. cells is removed (censored).
This procedure is called ‘’Censored Mean Level Detector’’ (CMLD).
Other method for canceling multiple targets is ‘’ordered statistic’’ (OS-CFAR)

14. Signal Management

15. Signal Management Signal Processing: Data Processing:
Signal processing is detection targets in noise, clutter and interference such as:
Matched filter to maximize S/N.
Detector/ Integrator.
Clutter reduction.
CFAR.
Electromagnetic compatibility (EMC).
Electromagnetic Counter Countermeasures (ECCM).
Threshold detection.
Data Processing:
Data processing is actions after detection of target such as:
Target location: in range angle velocity and ...
Target trajectory: target track that is the time history target location.
Target recognition: type of target e.g. recognition of aircraft from birds and ...
Weapon control : in fire control systems (FCS).