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�CS60055: Ubiquitous Computing

Contactless Sensing

Part I: Sensing with RF: Basic Principles

INDIAN INSTITUTE OF TECHNOLOGY

KHARAGPUR

Sandip Chakraborty

sandipc@cse.iitkgp.ac.in

Department of Computer Science and Engineering

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Contactless Sensing

IMU-based sensing needs the subject to wear some devices: smartwatch, earable, smart glass, smart ring, …

Might not be very convenient all the times (ex. Sleep monitoring)

Contactless sensing are useful when the user does not want to attach the sensors with their body

Useful for continuous and passive monitoring of human activities
Widely used to monitor objects (materials, liquids, structures, ...)

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Sensing Modalities

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Sensing Modalities

Primarily two modalities

Electromagnetic waves (majority of the sensing devices work on some EM waves)
Mechanical waves (acoustic-based sensing)

The basic operating principles vary depending on the type and the frequency of the waves being used in the sensing applications

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

The objects we sense

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

Long wavelength, low frequency: Penetrate more through physical objects
Medium wavelength, medium frequency: Reflect more from physical objects
Short wavelength, high frequency: Penetrate more through the objects

Penetrate more

Reflect more

Penetrate more

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

Long wavelength, low frequency: Penetrate more through physical objects
Medium wavelength, medium frequency: Reflect more from physical objects
Short wavelength, high frequency: Penetrate more through the objects

Penetrate more

Reflect more

Penetrate more

This is just a general idea; the penetration/reflection capability of the signal also depends on its bandwidth and other channel parameters

Indian Institute of Technology Kharagpur

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

Long wavelength, low frequency: Penetrate more through physical objects
Medium wavelength, medium frequency: Reflect more from physical objects
Short wavelength, high frequency: Penetrate more through the objects

Penetrate more

Reflect more

Penetrate more

Useful for passive contactless sensing

Indian Institute of Technology Kharagpur

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

Long wavelength, low frequency: Penetrate more through physical objects
Medium wavelength, medium frequency: Reflect more from physical objects
Short wavelength, high frequency: Penetrate more through the objects

Penetrate more

Reflect more

Penetrate more

Used widely for sensing, but privacy is a concern

(the vision domain)

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

Long wavelength, low frequency: Penetrate more through physical objects
Medium wavelength, medium frequency: Reflect more from physical objects
Short wavelength, high frequency: Penetrate more through the objects

Penetrate more

Reflect more

Penetrate more

Analyze the signal reflection properties for the long wavelength signals

Indian Institute of Technology Kharagpur

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Fundamentals of EM Waves

The existence of EM was predicted by James Clerk Maxwell in 1864

Heinrich Hertz confirmed the same in 1887
Hertz also demonstrated that EM waves are affected and reflected by solid objects

The frequency and the wavelength characterizes the waves

Long wavelength, low frequency: Penetrate more through physical objects
Medium wavelength, medium frequency: Reflect more from physical objects
Short wavelength, high frequency: Penetrate more through the objects

Penetrate more

Reflect more

Penetrate more

Analyze the signal reflection properties for the long wavelength signals

Analyze the signal penetration properties for the short wavelength signals

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Radio Waves

Image Source: https://www.allaboutcircuits.com/technical-articles/basics-of-millimeter-wave-mmwave-technology/

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Radio Waves

Image Source: https://www.allaboutcircuits.com/technical-articles/basics-of-millimeter-wave-mmwave-technology/

RFID

WiFi

UWB

mmWave

We'll see sensing applications in these ranges

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Signal Interference to Detect Motion: The Concept of Radar

1897: Alexander Popov, a Russian Imperial Navi physicist, was testing an early version of wireless communication between two ships in Baltic Sea

He observed an interference wave pattern caused by a third ship
Popov proposed the idea that this might be used to detect moving objects

https://ieeexplore.ieee.org/abstract/document/5282288

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Signal Interference to Detect Motion: The Concept of Radar

1932: Radar as a technical equipment was proposed by a military engineer Piotr Oshchepkov

"RUS-1": The first industrial radar (1939): 4m wavelength, transmitter and receiver seperated by 35 km

https://ieeexplore.ieee.org/abstract/document/5282288

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Basic Principle: The Doppler Effect

Change in the frequency of the wave in relation to an observer who is moving relative to the wave source

Wave source moves towards the observer: Each successive wave cycle is emitted from a position closer to the observer

Time between cycles is reduced; frequency is increased

Wave source moves away from the observer: Each successive wave cycle is emitted from a position farther from the observer

Time between cycles is increased; frequency is decreased

Image Source: Wikipedia

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The Doppler Effect

Let,

f₀ is the emitted frequency
f is the observed frequency
c is the propagation speed of the wave in the medium
𝑣_r is the speed of the receiver, 𝑣_s is the speed of the source

𝑣_r is added to 𝑐 if the receiver is moving towards the source, subtracted if the receiver is moving away from the source (opposite for 𝑣_s)

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The Doppler Effect

Equivalently, if the source is directly approaching or receding from the observer,

𝑣_wr is the wave speed related to the receiver, 𝑣_ws is the wave speed related to the source
λ is the wavelength

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Doppler Effect for the Sound Sources

Stationary sound source

Image Source: Wikipedia

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The Wave: Concept of Bandwidth

Any arbitrary wave signal can be decomposed into a set of sinusoidal wave of multiple frequencies

Called the frequency components of the wave signal (or simply, the signal)

Image Source: https://towardsdatascience.com/decomposing-signal-using-empirical-mode-decomposition-algorithm-explanation-for-dummy-93a93304c541

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The Wave: Concept of Bandwidth

Any arbitrary wave signal can be decomposed into a set of sinusoidal wave of multiple frequencies

Called the frequency components of the wave signal (or simply, the signal)

The bandwidth of a signal is the�difference between the highest and�the lowest frequency components�of that signal

We assume that any of the frequency�components between the highest�and the lowest can be present in�the signal

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Impact of Bandwidth on Sensing

Higher bandwidth signal means it is likely to have more number of signal components

Therefore, scattering, diffraction, reflection, etc., are likely to be more on high-bandwidth signals

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Impact of Bandwidth on Sensing

Higher bandwidth signal means it is likely to have more number of signal components

Therefore, scattering, diffraction, reflection, etc., are likely to be more on high-bandwidth signals

Although create noises for communication, but good for sensing

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Impact of Bandwidth on Sensing

Higher bandwidth signal means it is likely to have more number of signal components

Therefore, scattering, diffraction, reflection, etc., are likely to be more on high-bandwidth signals

Although create noises for communication, but good for sensing

How do we get the various frequency components of a signal?

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Fourier Analysis

Extracts the frequency components of a signal

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Fourier Analysis

Extracts the frequency components of a signal

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Fourier Analysis

Extracts the frequency components of a signal

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Fourier Analysis

Extracts the frequency components of a signal

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Fourier Analysis

Extracts the frequency components of a signal

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Fourier Analysis

Extracts the frequency components of a signal

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Fourier Analysis

Extracts the frequency components of a signal

How do we perform Fourier Analysis of a complex signal?

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Representation of a Signal

What is the significance of frequency of this signal?

y(t) = A sin (ωt + φ)

A: Amplitude

ω: Angular frequency

φ: Phase

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Fourier Representation in Complex Domain

y(t) = A sin (2πft + φ)

A: Amplitude

f: Ordinary frequency

φ: Phase

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The Notion of Phase

The fraction of the cycle covered upto some time instance t
An important metric for sensing

The phase of the reflected/scattered signal depends on the type of the material where the transmitted signal hitted
Introduces a shift in the reflected/scattered signal

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The Notion of Phase

The fraction of the cycle covered upto some time instance t
An important metric for sensing

The phase of the reflected/scattered signal depends on the type of the material where the transmitted signal hitted
Introduces a shift in the reflected/scattered signal

Phase difference/phase shift:

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Fourier Representation in Complex Domain

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Fourier Representation in Complex Domain

Check this video for a nice explanation of Fourier transformation

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Discrete Fourier Transformation

In practice, we record the samples of a continuous signal

Discrete representation of the signal

So, we need to perform the Fourier�transformation on the discrete samples�of the signals

Discrete Time Fourier Transform (DTFT)

However, the input and the output of�the samples are also finite

Discrete Fourier Transform (DFT): Works on the finite time series data

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DTFT and DFT

A Continuous signal and its Fourier transform

Periodic summation of the original signal and its Fourier transform

Original signal discretized and its Fourier transform (DTFT)

Periodic summation of the discrete signal, DFT computes discrete samples of the continuous DTFT

Image Source: Wikipedia

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Discrete Fourier Transformation (DFT)

Let be complex numbers. The DFT is defined by the formula,

Where is the primitive n^th root of 1

Evaluating the above equation needs O(n²) operations

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Discrete Fourier Transformation (DFT)

Let be complex numbers. The DFT is defined by the formula,

Where is the primitive n^th root of 1

Evaluating the above equation needs O(n²) operations

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DFT Matrix

An N-point DFT is represented as

x is the original input signal
W is NxN DFT matrix

ω is a primitive N^th root of unity

For different values of j, W can be �represented as a matrix

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Example: 8-point DFT

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Example: 8-point DFT

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Example: 8-point DFT

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Example: 8-point DFT: Pictorial Representation

Cosine wave: Solid Line

Sine wave: Dashed line

Fractional frequency +5/8

or –3/8

cos (2π - φ) = cos φ

sin (2π - φ) = -sin φ

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Example: 8-point DFT: Pictorial Representation

Cosine wave: Solid Line

Sine wave: Dashed line

Fractional frequency +3/4

or –1/4

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Example: 8-point DFT: Pictorial Representation

Cosine wave: Solid Line

Sine wave: Dashed line

Fractional frequency +7/8

or –1/8

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Discrete Fourier Transformation (DFT)

Let be complex numbers. The DFT is defined by the formula,

Where is the primitive n^th root of 1

Evaluating the above equation needs O(n²) operations

Can we reduce the complexity?

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Fast Fourier Transform (FFT)

Divide the DFT matrix recursively into smaller DFTs and then combine them

Based on the multiplications on complex root of unity

Radix-2 decimation-in-time (DIT) FFT

Divide between odd and even inputs

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Fast Fourier Transform (FFT)

Divide the DFT matrix recursively into smaller DFTs and then combine them

Based on the multiplications on complex root of unity

Radix-2 decimation-in-time (DIT) FFT

Divide between odd and even inputs

By rearranging,

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FFT for N = 8

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Application of FFT in Sensing -- Filters

Extract a portion of the signal components

Example: Acoustic data processing

You want to analyze the acoustic chirp�sent from your smartphone
However, the sound emitted may get�mixed with other environmental�noises
Pass the received signal through a�band-pass filter to extract only the�components of the target frequency�band

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In Summary

Signal propagation, distortion, reflection, etc., can help us sense the environment

Doppler analysis helps in identifying moving objects or movement patters
The reflection patterns (frequency components, time of flight, etc.) can be used to compute the distance of the object from the transmitter, angle of arrival, etc.
Phase shift can be used to identify material properties

Fourier transform helps us to identify the frequency components in the signal

Helpful for signal analysis (we'll see the details later)
Useful for preprocessing the signals – removing unwanted signal components – low-pass/ high-pass/ bandpass filters

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Happy Learning!

Some resources related to this topic

Introduction	Related Work	Background	Observation	Methodology	Evaluation	Conclusion