Birth of Radar

• Heinrich Hertz (1887) -Discovery of radio waves
•  Christian Huelsmeyer (1904) -  1)Telemobiloscope 2)No range or speed
• Guglielmo Marconi (1922) -1)Wireless Radio advocate
• Sir Robert Watson-Watt (1935)-1)Daventry Experiment2)Full-scale development begins                                                  

   Continues wave Radar    

•  First Radars were Pulse-Wave -1) Fast decay; High EM interference 
• New technology-1)Slow decay 2)Continuous sinusoid     

   FMCW

•  No single inventor-1)Many different corporations and government bodies discovered it.
•  CW Radar limitations1)Can not measure distance 2) Most developers realized that modulating the frequency will allow distance to be calculated.

System Overview

• Frequency modulated transmitter.
• Transmit signals also used as local oscillator (LO).
•  Received signal amplified and mixed with LO to create a beat. 
• Beat frequency proportional to distance.

Linear modulation

• Simplifies transmitter design 
• Allows for easy signal processing
•  Both allow for a low-cost system 
• The signal is represented as a “chirp” in the time domain and a linear ramp in the frequency domain

Transmitted Signal

• The signal is represented by a frequency modulated sine wave. MATHEMATICS--
• The signal travels a distance and is reflected back 
• Time signal takes to travel back is 

                                      𝑡𝑑 = 2𝑑 /c

•  d = distance to the object.
• c = speed of light in the medium.  

Received Signal and Mixing 

• The received signal is identical to transmitted signal, but delayed in time.

    𝑅𝑥 = sin[2𝜋(t-− 𝑡d)(𝑓0 + 𝑓 ′𝑑𝜏 𝑡−�

• 𝑅𝑥 is mixed with 𝑇𝑥 and passed through a low-pass filter, resulting in a signal proportional in frequency to target distance. 

       𝑓𝑜𝑢𝑡 = 𝑓 ′ ∗ 𝑡d==(( 𝑓1−𝑓0)/ (𝑇𝑚𝑜𝑑)) *( 2𝑑 /c)

 Example Heading

• 𝑓0 = 2.26𝐺𝐻z
• 𝑓1 = 2.59𝐺𝐻z
• 𝑇𝑚𝑜𝑑 = 20𝑚s
• 𝑑 = 10m
• 𝑓𝑟 = ((𝑓1−𝑓0)/( 𝑇𝑚𝑜d))*(2𝑑 /c)= 1.1𝑘𝐻z

Additional Parameter 

• FMCW has a range resolution that varies with the range of frequencies used.   

                     ∆𝑅 =(𝑐/ 2 ∗ (𝑓1 − 𝑓0))

• Power received from reflection modeled by radar equation.

                      𝑃𝑟 =(𝑃𝑡𝐺𝑡𝐴𝑟𝜎)/(𝐹 4 (4𝜋) 2𝑅4)

Signal Processing

• Fast Fourier Transform (FFT)-Transform a time signal into the frequency domain. x(t) ⇒ X(k) 
• Filtering
•  Detection Rules
• Multiple Object Detection

Fast Fourier Transform

• Discrete Fourier Transform: Transform a time domain signal into the frequency domain.

• Evaluating the DFT directly requires O(N2 ) operations. FFT algorithms require O(NlogN) operations which result in a significantly faster speed.1)Example: A signal estimated by 1024 samples : N=1024 O(N2 ) = 1,048,576 computations for DFT O(NlogN) = 10,240 computations for FFT.     

Filtering

• The result of the FFT contains noise as well as the signal. In some cases, the noise may be stronger than the signal itself. 
• The target signal is typically low frequency.
•  Noise is broadband and high frequency.
• Use a Low Pass Filter to get rid of the noise and keep the target signal this will increase the Signal to Noise Ratio.

Detection Rule

•  Data set is now a filtered set of amplitudes some low-frequency noise remains.
• We must now set a minimum amplitude for object detection to occur.
•  If an amplitude at a given frequency does not reach the threshold it should be reset to zero.
  

Object Differentiation

• Objects are identified by spectra that have non-zero amplitude.
• A number of consecutive zero spectra are required to differentiate between objects.1)This number is set arbitrarily and fine-tuned through testing. 

Through wall sensing

• Could be between 0 and 3-Dimensional

1. 0D: Presence detection
2. 1D: Detects movement and velocity
3.  2D & 3D: Imaging, able to detect velocity and angle       

• Operates between 0.5 GHz and 8.0 GHz and split up into 3 sub-bands depending on the material and the thickness of the wall.

1. 0.5-2.0 GHz.
2. 1.0-4.0 GHz
3.  2.0-8.0 GHz 

• Attenuation of the signal is increased as the frequency increases                

Why FMCW for through wall?

• Simple and Cheap to implement
• Fast switching synthesizers, specific DSPs, and fast ADCs are expensive
• Low power consumption

1. Consumption is increased by its pulse integration.
2. Consumption decreased by its low duty cycle

•  Based on FFT so processing is fast and efficient.

Automative Application

•  Anti-Collision – Measures velocity to avoid accidents.
• Parking Sensor – Measures distance to avoid collision.
• Traffic Sensor – Detects flow or speed of traffic

Application: Tracking transit

Why FMCW for Tracking Transmit?

•  Ability to detect stationary and moving objects.
• Only need ONE radar
• Environmental factors won’t affect the accuracy of the radar
• Detects speed and direction.

Application: Tank level Gauging

Why FMCW for tank level Gauging?

• Radar waves are unaffected by the atmosphere above the product
• The only antenna is inside the tank
• The only antenna is inside the tank  
• High accuracy
• Resistance to dust and dirt

Applications: concealed weapon detection

• Finding hidden objects

1. Found in: 1)Furniture 2)Covered cloth 3)Thick clothing

Why FMCW for concealed weapon detection?

• 94 GHz radar
•  reasonable penetration for certain materials (thickness)
• High accuracy
• Resistance for outdoor and indoor use
• Could be used for imaging or non-imaging 
• Low emitted power – no health concern 
• Can be remotely deployed