Week 4 Flashcards
When no targets are present
Output of radar receiver is noise
Noise
Thermal in origin (N = kTB W)
Thermal noise
RV with Gaussian statistics
False alarm
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
Thresholds and false alarms
Low threshold - close to noise floor, will generate many false alarms
High threshold - will generate few false alarms but may miss weak targets
Detection threshold
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)
Pd
Probability of detection of a given target
Pfa
Probability of false alarm due to noise
Lowering the threshold
Increases Pd (good) and increases Pfa (bad)
Concept of superhet receiver
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
RF front end
RF amplifier, frequency converter (mixer + local oscillator)
Converts received RF signal to lower frequency (IF)
Intermediate frequency section
Sets bandwidth of received signal, adds gain
The modulation (amplitude, phase) on the original RF signal carries over to the IF signal
Envelope detector
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
LNA
Low noise amplifier boosts the RF signal following the antenna
BPF
Band pass filter selects for the RF frequency interval of interest
Mixer and local oscillator
Converts the RF signal from RF frequency to IF frequency
Frequency conversion
Achieved by multiplying the radar signal by a fixed frequency from the local oscillator (LO)
Multiplier decided called a mixer
IF amplifier
Selects for the desired mixer product (IF frequency)
Amplifies signal
Controls bandwidth
Most easily accomplished at a lower frequency than at the radar RF
Typical IF frequencies
30 MHz and 60 MHz
Linear detector
Output is proportional to the magnitude of the envelope
Probability of false alarm
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
Receiver noise in superhet receiver
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
Noise and IF filter
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
Bandwidth is defined
Betwee 3dB points of TF
Bandpass filter
Passes a specific band of frequencies
Transfer function TF is not rectangular
All practical bandpass filters have Bn = 3dB bandwidth
Noise bandwidth
The bandwidth of an equivalent rectangular BPF with the same maximum gain that passes the same amount of white noise power
Bn = B(3dB)
Noise
At the input of the IF amplifier assume the noise is wide and thermal noise (AWGN)
AWGN
Additive - noise adds to signal
White - equal PSD at all frequencies (constant W/Hz)
Gaussian - noise voltage has zero mean Gaussian statistics
False alarms / noise spikes
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
Time between false alarms
Decreases vary rapidly as threshold is lowered
CFAR target detector
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
Probability of detection of signal in noise
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
ROC
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
Parameter triplets and radar design
[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
