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### An Introductionto Computer Networks

Lecture 5: Physical Layer

University of Tehran

Dept. of EE and Computer Engineering

By:

Dr. Nasser Yazdani

Introduction to Computer Network

- Concepts:
- Data
- signal
- Links
- Link functions
- Modulation
- Shannon’s Theorem
- Transmission media

Introduction to Computer Network

Data

- Discrete data: an instance is binary. Computer works with discrete data. Discrete is encoded in 0s and 1s.
- Continuous data: change with time or space.
- It is converted to discrete data by sampling
- Data is delivered by signals in the links

Introduction to Computer Network

Link Functions

- Functions
- Construct Frame with Error Detection Code
- Encode bit sequence into analog signal
- Transmit bit sequence on a physical medium (Modulation)
- Receive analog signal
- Convert Analog Signal to Bit Sequence
- Recover errors through error correction and/or ARQ

Signal

Adaptor

Adaptor

Adaptor: convert bits into physical signal and physical signal back into bits

Introduction to Computer Network

Link Properties

- Function
- Duplex/Half Duplex
- One stream, multiple streams
- Characteristics
- Bit Error Rate
- Data Rate (this sometimes mistakenly called bandwidth!)
- Degradation with distance

Introduction to Computer Network

Example: Optical Links

Introduction to Computer Network

Electromagnetic waves propagating in the light speed.

- Frequency
- Wavelength
- A (periodic) signal can be viewed as a sum of sine waves of different frequencies and strengths.
- Every signal has an equivalent representation in the frequency domain.

» What frequencies are present and what is their strength (energy)

Introduction to Computer Network

Introduction to Computer Network

- Sender changes the nature of the signal in a way that the receiver can recognize.

» Similar to radio: AM or FM

- Digital transmission: encodes the values 0 or 1 in the signal.

» It is also possible to encode multi-valued symbols

- Amplitude modulation: change the strength of the signal, typically between on and off.

» Sender and receiver agree on a “rate”

» On means 1, Off means 0

- Similar: frequency or phase modulation.
- Can also combine method modulation types.

Introduction to Computer Network

Baseband vs. Carrier Modulation

- Baseband modulation: send the “bare” signal.
- Carrier modulation: use the signal to modulate a higher frequency signal (carrier).
- Can be viewed as the product of the two signals
- Corresponds to a shift in the frequency domain

Modulation

- The function of transmitting the encoded signal over a link, often by combining it with another (carrier signal)
- E.g. Frequency Modulation (FM)
- Combine the signal with a carrier signal in such a way that the instantaneous frequency of the received signal contains the information of the carrier
- E.g. Frequency Hopping (OFDM)
- Signal transmitted over multiple frequencies
- Sequence of frequencies is pseudo random

Introduction to Computer Network

- Noise: “random” energy is added to the signal.
- Attenuation: some of the energy in the signal leaks away. We need repeaters.
- Dispersion: attenuation and propagation speed are frequency dependent.

» Changes the shape of the signal

Introduction to Computer Network

Noise

- A signal s(t) sent over a link is generally
- Distorted by the physical nature of the medium
- This distortion may be known and reversible at the receiver
- Affected by random physical effects
- Shot noise
- Fading
- Multipath Effects
- Also interference from other links
- Wireless
- Crosstalk
- Dealing with noise is what communications engineers do

Introduction to Computer Network

Noise limits the link rate

- Suppose there were no noise
- E.g. Send s(t) always receive s(t+Δ)
- Take a message of N bits say b1b2….bN, and send a pulse of amplitude of size 0.b1b2….bN
- Can send at an arbitrarily high rate
- This is true even if the link distorts the signal but in a known way
- In practice the signal always gets distorted in an unpredictable (random) way
- Receiver tries to estimate the effects but this lowers the effective rate
- One way to mitigate noise is to jack up the power of the signal
- Signal to Noise ratio (SNR) measures the extent of the distortion effects

Introduction to Computer Network

Link rate and Distance

Links become slower with distance because of attenuation of the signal Amplifiers and repeaters can help

Introduction to Computer Network

- Every transmission medium supports transmission in a certain frequency range. This is called channel capacity.

» The channel bandwidth is determined by the transmission medium and the nature of the transmitter and receivers

- A noiseless channel of width H can at most transmit a binary signal at a rate 2 x H.

» E.g. a 3000 Hz channel can transmit data at a rate of at most 6000 bits/second Assumes binary amplitude encoding

- Shannon extended this result by accounting for the effects of noise.
- More aggressive encoding can increase the channel bandwidth.

» Example: modems

Introduction to Computer Network

Nyquist’s Theorum

- How is the data rate constrained by bandwidth?
- Maximum data rate(bits/second) =

2 * bandwidth (hz)

- Nyquist’s Theorum considers only the limit imposed by the bandwidth not noise, encoding, or other factors.

Nyquist’sTheorumWhy Double The Bandwidth?

- In addition to looking at a signal in the time domain, we can view it in the frequency domain.
- In other words, instead of asking the question, “What is the amplitude at time X?”, we can ask the question, “How much energy is present every X units of time?”
- For some signals this is a meaningless measure – but many are periodic. For discrete signals (like data signals), we just assume that they repeat forever.

Energy

Frequency

Nyquist’s TheorumWhy Double The Bandwidth?

- As an analog signal is transmitted through some media, it is filtered by that media.
- Not only is noise introduced, but energy at certain frequencies is lost – and nearly completely so above and below some threshold frequencies.
- As a result, the signal has no harmonics above a certain frequency or below another.

Nyquist’s TheorumWhy Double The Bandwidth?

- A fundamental theoretical finding is that to reproduce an analog signal accurately at a certain frequency, we must sample it twice as frequently. Otherwise, we could lose information.
- If we sample less often, we might miss an event – we sample just before it happens.
- If we sample more often, we just sample the same thing twice – we can’t get more information than is there – and the data has already been limited to a certain bandwidth of information.

Nyquist’s TheorumWhy Double The Bandwidth?

We need to have two points within the same period to know exactly which sine function we have. More points provide no additional information.

Better Than Nyquist’s Limit

- If clocks are synchronized sender and receiver, we only need one point per period.
- This is because the synchronized starting point counts as one of the two points.

Noisy Channel

- Consider ratio of signal power to noise power.
- Consider noise to be super-imposed signal
- Decibel (dB) = 10 Log (S/N)
- S/N of 10 = 10 dB
- S/N of 100 = 20 dB
- S/N of 1000 = 30 dB

Shannon’s Theorem

- Maximum data rate (bits/second) =

bandwidth (Hz) Log 2 (1 + S/N)

- As before, this only gives us the limit on the data rate imposed by the noise, itself.
- It does not consider the encoding or bandwidth limitations.
- The bandwidth parameter can be confusing. It is there because it governs the effect that the noise has. More bandwidth either dilutes the noise, or gives the data more places to hide, or both.

Shannon’s Theorum

signal

noise

- Increased bandwidth decreases the effects of noise.
- One way to think of this is that the signal has either more frequency space to call
- its own, or the noise gets diluted across the frequency space, or some combination
- of the two.

Higher Frequency = Higher Energy

- frequency =

speed of light (m/s)/wavelength (m)

- Energy (Joules) = frequency * Plank’s constant
- Planck’s constant (Energy in a photon) is 6.626 X 10 –34

Signaling bits on a linkMulti-level Signaling

2-bits per symbol

3-bits per symbol

8

4

7

6

3

5

Levels

Levels

4

2

3

2

1

1

00

11

10

01

00

000

010

101

001

110

Ultimately, what limits the number of bits I can send per symbol?

Introduction to Computer Network

Maximum Capacity/Data Rate

Shannon Capacity:

Bandwidth of link

Signal-to-Noise ratio

- For example:
- Bandwidth of telephone link from telephone to a typical home is approx 3300Hz – 300Hz = 3kHz
- Signal-to-noise ratio is approx 30dB = 10log10(S/N)
- Therefore, C = 3000*log2(1001) ~= 30kb/s

Optical fiber has a higher capacity because the bandwidth, B, of a fiber is much greater than for wire; and it is less susceptible to noise, N.

Introduction to Computer Network

Sampling Result (Nyquist)

- Suppose a signal s(t) has a bandwidth B.
- Sampling Result: Suppose we sample it (accurately) every T seconds.
- If T≤ 1/2B then it is possible to reconstruct the s(t) correctly
- Only one signal with bandwidth B has these sample points
- There are multiple signals with these sample points for signals with bandwidth greater than B
- Increasing the bandwidth results in a richer signal space
- No noise allowed in the sampling result

Introduction to Computer Network

- Unshielded Twisted Pair (UTP)

» Two copper wires twisted - avoid antenna effect

» Grouped into cables: multiple pairs with common sheath

» Cat 3 (voice grade) versus Cat 5 for data

» 100 Mbps up to 100 m, 1 Mbps up to a few km

» Cost: ~ 10cents/foot

- Coax cables.

» One connector is placed inside the other connector

» Holds the signal in place and keeps out noise

» Gigabit up to a km

Introduction to Computer Network

Introduction to Computer Network

- High frequency electromagnetic waves (>1GHz)

q Line of sight terrestrial transmissions and for communications via satellites.

q Some atmospheric interference occurs but reliable transmission can be obtained over distances up to 50 Km.

q Microwaves is absorbed by rain and does not penetrate obstacles.

Introduction to Computer Network

Fiber Types

- Multimode fiber.
- 62.5 or 50 micron core carries multiple “modes”
- used at 1.3 microns, usually LED source
- subject to mode dispersion: different propagation modes travel at different speeds, depending on where source reflects bounces within cable – different paths are different lengths
- Mode dispersion can be combated with a graded refraction index. Cable has variable refraction index to squeeze things back together.
- typical limit: 1 Gbps at 100m
- Single mode
- Narrow cable so that it holds only “one beam” of light
- 8 micron core carries a single mode
- used at 1.3 or 1.55 microns, usually laser diode source
- typical limit: 1 Gbps at 10 km or more
- still subject to chromatic dispersion

q Thin thread of glass or plastic

q Lightweight.

q Fibers act as wave-guides for light which is usually

produced by lasers.

q Visible light has frequency around 5*10 15 Hz,

which ensures an extremely high bandwidth.

q The raw materials are cheap.

q Immune to electrical interference.

q Difficult to join and tap.

q Security advantages

Introduction to Computer Network

Leased Lines

- Dedicated link from Telephone Companies
- DS1 24 digital voice of 64Kbps
- DS3 28 DS1
- STS stands for Synch. Transfer signal

Introduction to Computer Network

Last-Mile Links

- Connect from home to network service providers
- xDSl (Digital Subscriber line), runs on local loop on telephone line. ADSL, VDSL
- CATV- Cabel TV, BW of 6 MHZ, is asymmetric.

Introduction to Computer Network

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