Week 4

Question 1

When no targets are present

Answer 1

Output of radar receiver is noise

Question 2

Noise

Answer 2

Thermal in origin (N = kTB W)

Question 3

Thermal noise

Answer 3

RV with Gaussian statistics

Question 4

False alarm

Answer 4

Large peaks of noise occur occasionally and can be mistaken for radar targets

When noise peaks cross threshold

Occurrence of false alarms depends on threshold setting

Question 5

Thresholds and false alarms

Answer 5

Low threshold - close to noise floor, will generate many false alarms

High threshold - will generate few false alarms but may miss weak targets

Question 6

Detection threshold

Answer 6

Must be set above noise in receiver

Noise peaks may cross detection threshold and create false alarms —> detection of radar targets is statistical (also because thermal noise always fluctuates)

Question 7

Pd

Answer 7

Probability of detection of a given target

Question 8

Pfa

Answer 8

Probability of false alarm due to noise

Question 9

Lowering the threshold

Answer 9

Increases Pd (good) and increases Pfa (bad)

Question 10

Concept of superhet receiver

Answer 10

Transmitted RF carrier wave is modulated by the target in amplitude and phase

Want to extract the amplitude and maybe phase info from received signal

Transforms (downconverts) the RF signal to an intermediate frequency (IF) for processing which retains amplitude and phase info

A final stage detects amplitude and phase

Question 11

RF front end

Answer 11

RF amplifier, frequency converter (mixer + local oscillator)

Converts received RF signal to lower frequency (IF)

Question 12

Intermediate frequency section

Answer 12

Sets bandwidth of received signal, adds gain

The modulation (amplitude, phase) on the original RF signal carries over to the IF signal

Question 13

Envelope detector

Answer 13

Converts AC signal at output of IF section to a varying DC voltage - this measures amplitude

Low pass filter after diode removes IF signal (inserts delay into video signal)

Output of envelope detector is called a video signal

Detects only amplitude, not phase

Question 14

LNA

Answer 14

Low noise amplifier boosts the RF signal following the antenna

Question 15

BPF

Answer 15

Band pass filter selects for the RF frequency interval of interest

Question 16

Mixer and local oscillator

Answer 16

Converts the RF signal from RF frequency to IF frequency

Question 17

Frequency conversion

Answer 17

Achieved by multiplying the radar signal by a fixed frequency from the local oscillator (LO)

Multiplier decided called a mixer

Question 18

IF amplifier

Answer 18

Selects for the desired mixer product (IF frequency)

Amplifies signal

Controls bandwidth

Most easily accomplished at a lower frequency than at the radar RF

Question 19

Typical IF frequencies

Answer 19

30 MHz and 60 MHz

Question 20

Linear detector

Answer 20

Output is proportional to the magnitude of the envelope

Question 21

Probability of false alarm

Answer 21

False alarms should occur infrequently

Must set threshold high enough that noise spike rarely cross threshold

Assume only noise is present at the output

• first find rms noise power
• then determine the statistics of the noise voltage

Question 22

Receiver noise in superhet receiver

Answer 22

Usually dominated by the components in the receiver front end - primarily the LNA and mixer

Passes through the narrow bandwidth IF filter

At output of IF amp, noise waveform looks like an AM signal at IF frequency with noise as AM modulation

Noise modulation has a maximum frequency that is equal to the bandwidth of IF filter

Question 23

Noise and IF filter

Answer 23

Individual blocks in the receiver generate noise

Noise at the receiver output is limited by the bandwidth of the IF filter

RF bandwidth is often much wider than IF bandwidth

Question 24

Bandwidth is defined

Answer 24

Betwee 3dB points of TF

Question 25

Bandpass filter

Answer 25

Passes a specific band of frequencies

Transfer function TF is not rectangular

All practical bandpass filters have Bn = 3dB bandwidth

Question 26

Noise bandwidth

Answer 26

The bandwidth of an equivalent rectangular BPF with the same maximum gain that passes the same amount of white noise power

Bn = B(3dB)

Question 27

Noise

Answer 27

At the input of the IF amplifier assume the noise is wide and thermal noise (AWGN)

Question 28

AWGN

Answer 28

Additive - noise adds to signal
White - equal PSD at all frequencies (constant W/Hz)
Gaussian - noise voltage has zero mean Gaussian statistics

Question 29

False alarms / noise spikes

Answer 29

Rectified IF waveform has f_if positive half cycles per second, any of which could be a noise spike that crosses threshold

At output of envelope detector, max rate of occurrence of spikes is equal to the bandwidth of the IF filter

Question 30

Time between false alarms

Answer 30

Decreases vary rapidly as threshold is lowered

Question 31

CFAR target detector

Answer 31

Constant false alarm rate detector floats threshold at (S/N)_T dB above rms voltage

Maintains desired false alarm rate if noise level at envelope detector input increases

If gain of receiver increases, IF noise output increases

Radar sensitivity varies if noise power varies

Question 32

Probability of detection of signal in noise

Answer 32

When echo is received from target, IF output of receiver is signal pulse + noise waveform (noise voltage adds to signal voltage)

Vs+Vn has probability distribution similar to noise but centered on Vs (Ricean)

Pd depends on the signal power, the noise power, and V_T

Question 33

ROC

Answer 33

Receiver operating curve

V_T can be eliminated so as to relate Pd directly to Pfa and SNR

Triplet {Pfa, Pd, S/N}

Typically around 0.9

Question 34

Parameter triplets and radar design

Answer 34

[B,Pfa,(S/N)_T] - determines (S/N)_T for target detection for selected B and Tfa

[Pfa,Pd,(S/N)] - determines the (S/N) required in the receiver to achieve a desired Pd for a selected Pfa

Radar system is then designed to produce the required S/N for a specified situation