Physical Layer

Core Questions

• What purpose does the physical layer serve in OSI network model?
• What is a frequency band for radio signal?
  • How can we modulate a baseband signal to fit in the frequency band?
• What is the fundamental limit for reliable data transmission?
• How does multi-path deteriorate the communication channel?
  • How to counter the multi-path effect using diversity?
• What considerations do we have for choosing PHY protocols?

Learning Objectives

• Definition of physical layer in the OSI network model
• Frequency band of radio signal
  • Digital modulation and demodulation
• The capacity of a AWGN channel
• Coherence bandwidth and time due to multi-path
• Time/Space/Frequency diversity
• Various communication protocols and the comparison between them

Table of Contents

OSI 7-Layer Network Model

OSI Physical Layer

• The physical layer defines the means of transmitting raw bits over a physical data link connecting network nodes.
• Deals with accessing the physical medium
  • Mechanical characteristics
  • Electrical characteristics
  • Functional characteristics
  • Procedural characteristics

Wireless PHY protocols

Electromagnetic Spectrum

Radio Frequency (RF) Signal

RF Band Allocation

• Frequency band is a very rare & important resource!

ISM Band

• Radio spectrum reserved internationally for industrial, scientific and medical (ISM) purposes
  • e.g., microwave ovens
• Fastest-growing use for low power wireless communications systems
  • e.g., WiFi, Bluetooth, Zigbee, LoRa
• Communications equipment must tolerate interference generated by ISM applications

Modulation Overview

• Modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted.
• In digital modulation, an analog carrier signal is modulated by a discrete signal.
• The most fundamental digital modulation techniques are based on keying:
  • ASK (amplitude-shift keying): a finite number of amplitudes are used.
  • FSK (frequency-shift keying): a finite number of frequencies are used.
  • PSK (phase-shift keying): a finite number of phases are used.
  • QAM (quadrature amplitude modulation): a finite number of at least two phases and at least two amplitudes are used.

Rectangle and Sinc Function

• The simplest digital signal is a rectangle function:

$$rect(x) = \begin{cases} 1 & x \in [-0.5,0.5]\\ 0 & otherwise \end{cases}.$$

• Fourier Transform:

$$F(\omega ) = \int_{-\infty}^\infty f(t) \exp(2\pi i \omega t)dt.$$

• The FT of rectangle function is (normalized) sinc function

$$sinc(\omega) = \frac{\sin(\pi*\omega)}{\pi*\omega}.$$

Rectangle and Sinc Function

Energy Spectrum of Rectangle Function

• Most of the energy are located inside the passband of $\pm 1Hz$.

Properties of Fourier Transform

Modulation

• If we multiply the baseband signal ($rect(t)$) with a carrier signal ($cos(2\pi f_0 t)$)

$$S(t) = rect(t)\times \cos (2\pi f_0 t).$$

• In frequency domain, the signal will be centered around the carrier frequency $f_0$
• Most of the energy is allocated inside $f_0\pm 1$.
• If we reduce the symbol time from $1s$ to $\tau s$:
  • The modulated signal will still be centered around $f_0$
  • However, the zero crossing will happen at $f_0 \pm 1/\tau$.

Modulation

Demodulation

• The baseband signal can be recovered as

• A low pass filter can be used in order to:
  • Filter out the high frequency $rect(t) \times \cos(4\pi f_0 t)$ component;
  • And recover the baseband signal $rect(t)$.

Demodulation

Amplitude-Shift Keying

Amplitude-Shift Keying

• We are allocated with a frequency band between 200-300kHz. If we use 4-ASK modulation scheme:
  • What is the carrier frequency?
  • What is the symbol rate per second?
  • What is the bit rate per second?

Frequency-Shift Keying

Frequency-Shift Keying

• In practice, we can smooth the digital signal
  • e.g., by Gaussian filter
  • the frequency changes more smoothly rather than instantaneously
  • to reduce sideband power
• We are allocated with a frequency band between 200-300kHz. If we use FSK modulation scheme:
  • What are the sub-carrier frequencies if we assume that we use two frequencies that are 10Mhz apart?
  • What is the bit rate per second?

Phase-Shift Keying

QAM

Constellation Diagram

• We could draw the amplitude and phase of the symbol on the complex plane:

Quadrature Amplitude Modulation (QAM)

• We could combine multiple amplitude and multiple phase together to form a constellation
• The most common ones are 16, 64, 256 QAM
  • each symbol carries 4, 6, 8 bits repsectively

• For WiFi 6, up to 1024-QAM can be used depending on the channel quality
• Can we use “infinite”-QAM to transmit at “infinite” bit rate?

Free Space Loss

Channel Impairments

• Free space loss
• Noise
• Fading
  • Multi-path (Next Section)
• Atmospheric absorption

Free Space Transmission

Friis Transmission Equation

• Friss Transmission Equation: $$\frac {P_r}{P_t}=D_rD_t\left(\frac {\lambda}{4\pi d}\right)^2.$$
• where:
  • $P_{t}$ is the power fed into the transmitting antenna input terminals;
  • $P_{r}$ is the power available at receiving antenna output terminals;
  • $D_{r}, D_t$ are the antenna directivities (with respect to an isotropic radiator) of the transmitting and receiving antennas respectively;
  • $d$ is the distance between antennas;
  • $\lambda$ is the wavelength of the radio frequency;

• Friss Transmission Equation: $$\frac {P_r}{P_t}=D_rD_t\left(\frac {\lambda}{4\pi d}\right)^2.$$
• To increase signal strength at the receiving end:
  • Increase transmitting power;
  • Decrease carrier frequency, distance;
  • Better antenna

Noise

• Thermal Noise(John-Nyquist Noise)
  • Noise seen in switching circuits due to electrons
• Inter-modulation noise
  • Noise caused by signals at different frequencies on the same medium
• Crosstalk
  • coupling between signal paths
• Impulse Noise
  • Power spike (e.g. from thunder)

Thermal Noise

• White noise since it contains the same level of power at all frequencies $$N = ktB$$
• $k$ is the Boltzmann’s constant: $1.381\times 10^{-21} W/(K\cdot Hz)$,
• $T$ is the absolute temperature in Kelvin, and
• $B$ is the bandwidth.
• At room temperature, $T = 290K$, the thermal noise power spectral density $kT = –174 dBm/Hz$
• dBm is the ratio between the power and a reference of one milliwatt (mW), expressed in dB.
  • 0dBm = 1mW, 10dBm = 10mW, 20dBm = 100mW
• For 1MHz bandwidth, the power of the noise is

$-174 + 10 log 1M= -114dBm$ or $4\times 10^{-15}W$.

Thermal Noise

Constellation Diagram with Noise

Channel Capacity

Basic of Detection Theory

• Assuming we are using BPSK.
• At the receiving end, we get the following signals:

$$y = x + w = \pm a + w,$$

• $a^2$ can be viewed as the energy of the received signal
• $w\sim \mathcal N(0,N_0)$ is a zero mean Gaussian noise, with average energy $N_0$
• The Signal to Noise Ratio (SNR) can be defined as $SNR = a^2/N_0$.

Probability of Error

• We need to estimate (“detect”) the phase of $x$
• The probability of error is

$$P_e = P(\hat x \neq x).$$

• Bayesian Detector:

  • Calculate the conditional probability
  $$\begin{align*} P(x = a|y) &= \frac{P(x = a)P(y|x = a)}{P(y)},\\ P(x =- a|y) &= \frac{P(x = -a)P(y|x =- a)}{P(y)}. \end{align*}$$
  • If $P(x=a|y)\geq P(x=-a|y)$, then $\hat x = 0$, otherwise $\hat x = \pi$.

Probability of Error

• Assuming $\pm a$ has equal probability, then the decision rule is

$$\hat x = \begin{cases} 0 & if\;y\geq 0\\ \pi& otherwise\end{cases}.$$

• The probability of error is given by

Encoding/Decoding

• To reduce bit error rate, one could
  • increase the SNR.
  • However, this is very expensive
• More clever solution:
  • We could transmit the same bit multiple times (repetition code)
  • or better yet, use error correct code
• Problem: If we use “higher” QAM (assuming the same average signal energy)
  • we pack more symbols into the same area in the constellation diagram
  • the symbols are more difficult to differentiate -> higher error rate per symbol
  • However, we could use better encoder to reduce the bit error rate
  • Can we achieve infinite bit rate (under some constraints on bit error rate)?

Shannon-Hartley Theorem

$$C = B \times log_2( 1 + S/N ) = B \times log_2( 1 + SNR )$$

• where:
  • $C$ the information rate of data that can be communicated at an arbitrarily low error rate;
  • $B$ is the bandwidth of the channel in hertz;
  • $S$ is the average received signal power over the bandwidth measured in watts; and
  • $N$ is the average power of the noise and interference over the bandwidth, measured in watts.
• Fundamental limit: We CANNOT achieve a data rate higher than $C$ regardless of modulation/encoding scheme.
• Achievability: For any data rate lower than $C$, there exists a modulation/encoding scheme to achieve it.
  • Problem: the computational complexity is usually very high
  • Polar code is the first capacity-achieving code with complexity of $O(n\log n)$.

Shannon-Hartley Theorem

$$C = B \times log_2( 1 + S/N )$$

Shannon-Hartley Theorem

$$C = B \times log_2( 1 + SNR )$$

• Even SNR is very bad, we can still have reliable communication:

$$C = B \times log_2( 1 + SNR ) \approx \log_2(e) B \times SNR.$$

• Example: GPS communication
  • $B$: 1 MHz bandwidth,
  • $SNR$: −30 dB, the signal is 1000 times smaller than noise!
  • $C \approx 1.44\times 10^6 \times 10^{-3} = 1440 bit/s$
• Navigation message of GPS is sent at 50 bit/s
  • reliable communication can be established.

Implications

• Good physical layer protocol for intelligent networked system:
  • Long Range
  • High Throughput
  • Low Power
  • Other metrics: low latency, mobility, cost, …
• Shannon-Hartley Theorem & Friis transmission equation: NO communication scheme can achieve long range, high throughput and low power simultaneously.
• Need to consider applications:
  • Surveillance camera for smart city: long range, high throughput
  • Environmental monitoring: long range, low power
  • Smart Building: short range

Multi-path

Impairments

• Free space loss
• Noise
• Fading
  • Multi-path
• Atmospheric absorption

Multi-path

• Multi-path: obstacles reflect signals so that multiple copies with varying delays are received
  • Reflection - occurs when signal encounters a surface that is large relative to the wavelength of the signal
  • Diffraction - occurs at the edge of an impenetrable body that is large compared to wavelength of radio wave
  • Scattering – occurs when incoming signal hits an object whose size in the order of the wavelength of the signal or less

Reflecting Wall Example [Tse2005]

Coherence Bandwidth

• The difference between the max and min delay is called delay spread. In our case, $$T_d = \frac{2(d-r)}{c}.$$
• If the frequency changes by $1/2T_d$, then the phase difference changes by $\pi$.
• $W_c = 1/2T_d$ is called coherence bandwidth.
• For cellular communication, the path length difference is usually less than 300m
• The delay spread is $300m/c = 1\mu s$
• The coherence bandwidth is $(2 \mu s)^{-1} = 500 KHz$.

Flat v.s. Frequency Selective Fading

• Flat fading: $W_c$ is much larger than the bandwidth of the signal.
  • All frequency components of the signal will experience the same magnitude of fading.
  • Narrowband signal: GSM use 200kHz sub-channel
• Frequency-selective fading: $W_c$ is smaller than the bandwidth of the signal.
  • Different frequency components of the signal experience different fading.
  • Countermeasures: equalization, …
  • Wideband signal: cdmaOne uses 1.25Mhz

Flat v.s. Frequency Selective Fading [Tse2005]

Intersymbol Interference

• Delay causes copies of the signal arriving at the receiver at different times
• Part or all of a given symbol will be spread into the subsequent symbols
  • Interfering with the correct detection of those symbols
• To avoid ISI, symbol duration needs to be much larger than delay spread

Coherence Time

• Recall that phase difference of the two signal is $$\Delta \phi = \frac{4 \pi}{c} (d-r)f.$$
• If the frequency is fixed, then the phase changes $\pi$ if the receiver moves

$$\Delta r = c/4f.$$

• For a carrier frequency of 1GHz, $\Delta r \approx 7.5 cm$.

• Consider we are on a vehicle at speed $60km/h \approx 16.7m/s$
  • It takes 4.5ms for $\Delta \phi$ to change $\pi$
  • This time is called coherence time

Fading

Real World Fading

Time Diversity

• Wireless communication is usually an underspread channel
  • Delay spread ($\mu s$) is much smaller than coherence time (ms)
  • A narrowband signal (flat-fading) can transmit hundreds of symbols during a coherent time window
• To ensure that the coded symbols are transmitted through independent or nearly independent fading gains, we can interleave the code.
• Drawbacks: may results in large latency
• GSM use TDMA for voice communication

Time Diversity

Space Diversity: MIMO

• Multiple antenna can be used at the transmitting and receiving end
• Instead of destructive fading, we can achieve constructive fading

  SIMO, MISO and MIMO

Frequency Diversity

Spread Spectrum

• Spread-spectrum: a signal with a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth.
• Benefits
  • Frequency diversity: not all frequencies are in deep fade
  • Used for hiding and encrypting signals

Chirp Spread Spectrum

• A chirp is a sinusoidal signal of frequency increase or decrease over time
• Idea for low energy communication protocols
  • e.g. LoRa

Direct Sequence Spread Spectrum

• Information is encoded and modulated by a pseudonoise (PN) sequence
• The data rate $R$ is much smaller than the transmission bandwidth $W$ Hz
  • e.g., cdmaOne use a bandwidth of 1.2288 MHz
  • and a typical data rate (voice) is 9.6 kbits/s
  • The processing gain is $1228.8/9.6 = 128$
  • 64 chips are used for 1 data bit

Direct Sequence Spread Spectrum

• Assuming BPSK: 1 is coded as +1, and 0 is coded as -1

Direct Sequence Spread Spectrum: Decoding

• The original symbol can be recovered by performing an inner product with the same PN sequence

Direct Sequence Spread Spectrum

• How to combat Intersymbol interference:
  • The shifted PN sequence is “orthogonal” to the original sequence

Frequency Hopping Spread Spectrum

• Frequency-hopping spread spectrum is a method of transmitting radio signals by rapidly changing the carrier frequency among many distinct frequencies occupying a large spectral band
  • e.g. Bluetooth LE uses 37 channels, each occupy 2MHz
  • Channels are switched at a rate of 1600 hops/s ($625\mu s$).

Orthogonal Frequency Division Multiplexing

• Consider the Bluetooth LE example
  • Assuming a symbol rate of $R$
  • The corresponding $sinc$ function will occupy $2R$ bandwidth
  • Hence, $2R + guard\;band\leq 2MHz$
• Is it really necessary?

Orthogonal Frequency Division Multiplexing

Orthogonal Frequency Division Multiplexing

• $sinc(x + k),\, k\in\mathbb Z$ are orthogonal to each other
• For the OFDM scheme
  • If the symbol rate is $R$
  • Each sub-carrier signal only needs to be $R$ apart
  • More than twice spectral efficient
  • Modulation/Demodulation can be done efficiently via Fast Fourier Transform
• OFDM is originally proposed by Bell lab in 1966
• Used in WiFi, 4G, 5G

Bluetooth LE

• Bluetooth is a low-power wireless connectivity technology

  “Bluetooth Logo” by Skarr21 under CC BY-SA 4.0; from Wikipedia

  • cell phones sensors
  • headsets
  • keyboards/mouses
  • video game systems
• The name Bluetooth refers to King Harald Blatand in the region of what is now Norway and Sweden in around 958AD.
  • He got this name due to his liking of blueberries and/or the eating of his frozen enemies.
  • Bluetooth is derived from his name because King Blatand brought together warring tribes.

Bluetooth LE

• Bluetooth Low Energy is used extensively in IoT deployments
  • beacons
  • wireless sensors
  • asset tracking systems
  • remote controls
  • health monitors
  • and alarm systems.
• Throughout its history, Bluetooth and all the optional components have been under GPL license and are essentially open source.

PHY of Bluetooth LE

• Operates in the 2.400–2.4835 GHz ISM band (Same as WiFi and 802.15.4)
• The ISM band is divided into forty 2-MHz channels.
  • 37 of the channels are used to transmit date
  • 3 channels are reserved for advertising
  • frequency hopping is used to provide diversity
• Within a channel, data is transmitted using Gaussian FSK modulation
• The bit rate is 1 Mbit/s, and the maximum transmit power is 10 mW
  • Can be increased to 2Mbit/s and 100 mW in Bluetooth 5

PHY of Bluetooth LE [Lea2018]

Comparison between Bluetooth and Bluetooth LE

IEEE 802.15.4

• The IEEE 802.15.4 is a standard wireless personal area network (PAN) defined by the IEEE 802.15 working group.
  • Defines the physical and MAC layer
  • basis of many other protocols: Thread, Zigbee, WirelessHART, and others.
• The goal is to develop a low-cost WPAN with low power consumption.
• Operates in the ISM spectrum:
  • 868 MHz, 915 MHz, and 2400 MHz.

PHY of IEEE 802.15.4 [Lea2018]

• Direct Sequence SS/Chirp SS/Ultra-wideband can be used for diversity
• Typical range: 200 meters outdoors, 30m indoors

• Typical transmission current: 15~30 mA, and reception current: 18~37mA

  Bluetooth Low Energy Channels

IEEE 802.11 (WiFi)

• First release in June 1997
• The newest is WiFi 6
  • Works in both 2.4Ghz and 5Ghz ISM band
  • Support up to 1024-QAM
  • Use OFDMA for spreading spectrum and multiple user access
  • Use Multi-user MIMO

WiFi Channels

WiFi MIMO [Lea2018]

Comparison between different generations of WiFi

Cellular Communication

• The International Telecommunication Union (ITU) is a UN specialized agency
  • was founded in 1865
  • took its present name in 1932
  • before becoming a specialized agency in the UN.
• the Radio communication Sector (ITU-R) defines the international standards and goals for various generations of cellular communication.

5G Scenarios

1. Enhanced Mobile Broadband (eMBB):
   • 1 to 10 GBps connections to UEs/endpoints in the field (not theoretical)
   • 100% coverage across the globe (or perception of)
   • 10 to 100x the number of connected devices over 4G-LTE
   • Connectivity at a speed of 500 km/h
2. Ultra-Reliable and Low-Latency Communications (URLLC):
   • Sub < 1 ms end-to-end round-trip latency
   • 99.999% availability (or perception of)
3. Massive Machine Type Communications (mMTC):
   • 1000x bandwidth per unit area; this implies roughly 1 million nodes in 1 km 2
   • Up to a 10 year battery life on endpoint IoT nodes
   • 90% reduction in network energy usage

Sub-6 and mmWave

• 4G-LTE systems mainly use frequencies <3 GHz range.
• 5G may use a multitude of frequencies:
  • Sub 6 GHz: More ready for immediate use
    • China Telecom: 3.4-3.5MHz
    • China Unicom: 3.5-3.6MHz
    • China Mobile: 4.8-4.9MHz
  • mmWave (30-60 GHz): High bandwidth available, Gbps throughput
    • Higher free space loss
    • Absorbed by the atmosphere, vegetation, human body
    • Difficult to penetrate walls
    • Solution: Massive MIMO

LoRa

• LoRa is a physical layer for a long-range and low-power IoT protocol
• Originally developed by Cycleo in France and then acquired by the Semtech Corporation in U.S.
• ZTE and Alibaba are in the LoRa Alliance.
• Uses the following ISM band:
  • 915 MHz: In the USA
  • 868 MHz: In Europe
  • 433 MHz: In Asia.
• Chirp Spread Spectrum (CSS) is the modulation technique used in LoRa.
• Typical data rate is 0.3 - 5kbps
• Each LoRa packet contains 51-222 Bytes of Data
• Typical Energy for one message is < 1 $\mu Ah$
• Typical range of communication is 2-3km in cities and 5-7km in rural area
  • The world record is 702km!

The Things Network

• 15669 gateways in 150 countries as of Oct, 2020

  LoRa Gateways

Comparison

• Good physical layer protocol for intelligent networked system:
  • Long Range
  • High Throughput
  • Low Power
  • Other metrics: low latency, mobility, cost, …
• NO communication scheme can achieve long range, high throughput and low power simultaneously.
• Need to consider applications:
  • Surveillance camera for smart city: 4G/5G
  • Environmental monitoring: LoRa
  • Smart Building:
    • WiFi for camera
    • 802.15.4/Bluetooth LE for temperature sensor