Computer Networks An Open Source Approach

Computer NetworksAn Open Source Approach Chapter 2: Physical Layer Chapter 2: Physical Layer 1

Content 2.1 General Issues 2.2 Medium 2.3 Information Coding and Baseband Transmission 2.4 Digital Modulation and Multiplexing 2.5 Advanced Topics 2.6 Summary Chapter 2: Physical Layer 2

The physical (PHY) layer • The bottommost layer of the OSI model or the TCP/ IP model in computer networks • The only layer that interacts with transmission media • Transmission medium • A material substance that can propagate energy waves called signals from a sender to a receiver • The free space can also be considered a transmission medium for electromagnetic waves 3

Note: OSI Network Architecture 4

Physical layer converts (coding & modulation) digital data into an appropriate signal waveformSignal is transmitted over transmission media • The transmission medium can only carry signals instead of data • The information source from the link layer is of digital data • The physical layer must convert the digital data into an appropriate signal waveform • In modern digital communications, such conversion is a two-step process (coding & modulation) • It first applies information coding to the digital data for data compression and protection • Then modulates the coded data into signalsthat are appropriate for transmission over the communication medium • In analog communication only the process of modulation is used 6

To enable high-speed transmissions • The physical layer needs to decide which coding or modulation technique to use based on the properties of the medium • A wired medium is more reliable • The physical layer focuses solely on improving its throughput and utilization • A wireless medium is less reliable and exposed to the public • The physical layer has to cope with noise and interference and prevent the data from being corrupted (in addition to improving the throughput and utilization) 7

Multiple channels could exist on a medium • A channel between a transmitter and a receiver can be physical or logical • In wired networks, a physical channel is a transmission path traversing through cables • In wireless networks, a physical channel is a band of frequencies in the spectra of electromagnetic waves • A logical channel is a sub-channel where the transmission medium is partitioned by various division methods such as • Time-division • Frequency-division • Code-division • Spatial-division 8

Multiplexing is a kind of technique used to better utilize a medium • Time-Division Multiplexing (TDM) • Frequency-Division Multiplexing (FDM) • Code-Division Multiplexing (CDM) • Space-Division Multiplexing (SDM) 9

Time-Division Multiplexing (TDM) • Two or more bit streams or signals are transferred apparently simultaneously as sub-channels in one communication channel, but are physically taking turns on the channel • The time domain is divided into several recurrent time slots of fixed length, one for each sub-channel 10

Frequency-Division Multiplexing (FDM) • The total bandwidth available in a communication medium is divided into a series of non-overlapping frequency sub-bands, each of which is used to carry a separate signal • This allows a single transmission medium such as a cable or optical fiber to be shared by many signals 11

TDM + FDM 12

Code-Division Multiplexing (CDM) • Each channel transmits its bits as a coded channel-specific sequence of pulses • This coded transmission typically is accomplished by transmitting a unique time-dependent series of short pulses, which are placed within chip times • All channels, each with a different code, can be transmitted on the same fiber and asynchronously demultiplxed 13

TDMA / FDMA / CDMA 14

Spatial-Division Multiplexing (SDM) • A method by which metallic, radio, or optical transmission media are physically separated by insulation, waveguides [導波管], or space in order to maintain channel separations • Within each physically distinct channel, multiple channels can be derived through frequency, time, or wavelength division multiplexing 15

2.1 General Issues • Data from the link layer must be converted into digital signals or analog signals for digital transmission • The transmission and reception flows undergo several conversions in the physical layer • The need for line coding and digital modulation • To further improve the channel utilization, we need techniques such as multiplexing and multiple accesses to enable multiple users to access the same channel • In response to channel impairments, especially in the wireless media, several compensation measures are needed 16

Data and Signal: Analog or Digital • Data • Digital data • Discrete value of data for storage or communication in computer networks • Analog data • Continuous value of data such as sound or image • Signal • Digital signal • Discrete-time signals containing digital information (discrete-time and discrete-value) • Analog signal • Continuous-time signals containing analog information (continuous time and continuous-value) Chapter 2: Physical Layer 4

Digital data and signalsare more robust to noise because • Can be regenerated by regenerative repeaters • Can be protected from corruption by error correcting codes • Analog data • Represented in the form of analog signals are easily affected by noise • Often converted to digital data in the form of a bit stream • Later, they are transformed into signals for transmission • Thus, digital data are used in computer networks to represent analog sources such as images, voices, audio, and video 19

In computer networks, bit streams, or messages, move from one machine to another across network connections through the transmission media • The transmission media convey the energy of signals along a physical path • Cables for electrical signals • Fibers for optical signals • Free space for electromagnetic signals • The physical layer plays the role of convertingdigital data into either digital or analog signals suitable for specific transmission media 20

Analog Data and Signal • Analog signal • A continuous-time signal that contains analog information generated by an analog source, such as a sound or an image • It is often of continuous value (continuous time and continuous-value) • Example of analog communication • Vocal-auditory [聲樂聽覺] communications system • Analog signals can be sampled and quantized into digital signals for storage and communication 21

Sampled Signal (Discrete Signal) ‑ Discrete Time, Continuous Values The continuous signal is represented with a green colored line while the discrete samples are indicated by the blue vertical lines. 22

Quantized Signal‑ Continuous Time, Discrete Values 23

Digital Signal (Sampled, Quantized)‑ Discrete Time, Discrete Values 24

Digital Data and Signal • Digital data take on discrete values such as zeros and ones in computers • They can be transformed into digital signals and transmitted directly for a short distance • Alternatively, they can modulate carriers (periodic analog signals) so that the modulated signals can be transmitted over a long distance • A digital signal can be derived from an analog signal by sampling at discrete times and by quantizing into discrete values • Analog signal [sampling] → discrete-time signal [quantizing] → digital signal • If a waveform has only two levels to represent binary states “0” and “1”, it is a binary digital signal that represents a bit stream 25

Sampling • Sampling is a process that picks up samples at discrete times from a continuous time signal • Each sampled value is held constant within the sampling period, example • a continuous-time signalx(t) • where t is a variable defined on the entire real line of continuous time • can be sampled into a discrete-time signal • whose sampled values at the sample time instants can be represented by a numeric sequence or a discrete-time functionx[n], where n is a discrete variable taking values from the set of integers to represent the discrete time 26

Quantization • Quantization • A process for mapping a range of values to a discrete finite set of numbers or values • Such a mapping process is usually performed by the use of analog to digital converters (ADC) • A quantized signal can be of continuous time but with discrete values • Quantization introduces quantization error , or quantization noise 27

Reconstruction • An interpolation process that recovers the original continuous time signal from the sampled discrete-time signal • To perfectly reconstruct the original signal from a sequence of samples • It needs to sample at a rate that is equal to or higher than twice the highest frequency of the original signal • Nyquist-Shannon sampling theorem 28

Nyquist Theorem vs. Shannon Theorem • A communication channel can be noiseless or noisy • If the channel is considered noiseless, its max data rate is subject to the Nyquist theorem • If noisy, the max data rate is subject to the Shannon theorem • What is the sampling rate for a signal to be accurately reconstructed? • What is the max data rate when information is transmitted over a noiseless channel? 29

Nyquist Theorem What is the sampling rate for a signal to be accurately reconstructed? • To perfectly reconstruct the original signal from a sequence of samples • It needs to sample at a rate that is equal to or higher than twice the highest frequency of the original signal • It must sample at least twice as fast as the bandwidth of the signal • Nyquist sampling theoremfs≧ 2 x fmax • fs: the sampling rate • fmax: a limited bandwidth signal has a maximum frequency Chapter 2: Physical Layer 10

What is the max data rate when information is transmitted over a noiseless channel? • Nyquist theorem • Max data rate for noiseless channel = 2 B log2 L • B: bandwidth (Hz) • L: # states used by a signal encoding method to represent symbols • Example: if a noiseless phone line of 3kHz and one-bit signal encoding (two states) is used, what is the max data rate when a voice is delivered over the phone? • 2 x 3k x log2 2 = 6 kbps Chapter 2: Physical Layer 10

Shannon Theorem • In practice, channels are not noiseless but have many unwanted noises • Thermal noise • Inter-modulation noise • Crosstalk noise • Impulse noise • Shannon theorem: If a signal with a signal-to-noise ratio (SNR, S/N) is transmitted over a noisy channelMax data rate =B log2 (1+S/N) • B: bandwidth • S: signal • N: noise Chapter 2: Physical Layer 11

Shannon theorem is also called Shannon’s limit • This limit is irrelevant to the encoding method, but it is related to SNR • Example: considering a noisy phone of 3kHz, what is the maximum data rate if the SNR (S/N) is 30dB? • 3k x log2 (1+1000) = 29.9 kbps Chapter 2: Physical Layer 11

Note: Signal-to-Noise Ratio (SNR or S/N) • The ratio of the power in a signal to the power contained in the noise that is present at a particular point in the transmission • Typically measured at a receiver • Represented in decibels 34

Note: Decibel 35

Periodic and Aperiodic Signals • Analog vs. digital signal • Analog signal • Continuous time and continuous-value • Digital signal • Discrete-time and discrete-value • Periodic vs. aperiodic signal • Periodic signal • Repeats itself after a certain amount of time • Aperiodic signal • Does not repeat 37

Both analog and digital signals can be either periodic or aperiodic • For example, a sound signal of a human voice is an aperiodic analog signal; a digital clock signal is a periodic digital signal • Other than the time-domain characterization of signals, an alternative approach can be made in the frequency-domain based on the Fourier theory 38

Note: Fourier Transform • Fourier transform is a mathematical transform with many applications in physics and engineering • It transforms a mathematical function of time, f(t), into a new function, F, whose argument is frequency with units of cycles or radians per second • F is known as the Fourier transform and/or the frequency spectrum of the function f • Fourier transform is a reversible operation • i.e., given the function F, one can determine the original function, f • f and F are also respectively known as time domain and frequency domain representations of the same "event" 39

Periodic signal • A signal is said to be periodic if it has a line spectrum consisting of possibly infinite discrete frequencies • A line spectrum is a spectrum in which energy is concentrated at particular wavelengths 42

Spectra of Periodic Analog Signals • Discrete frequencies 100kHz and 400kHz are used to represent two periodic analog signals with different amplitudes Chapter 2: Physical Layer 5

Aperiodic signal • A signal is said to be aperiodic if it has a continuous spectrum with possibly infinite support 44

Spectra of Aperiodic Analog Signals • An aperiodicband-limited analog signal • Band-limited signal • A signal is said to be band-limited if it has finite support; say it is properly contained in the frequency band from f1 to f2 Chapter 2: Physical Layer 6

Spectra of Digital Signals • According to the Fourier theory • A periodic digital signal has a line spectrum that is obtained by multiplying the sinc spectrum by a periodic line spectrum consisting of a discrete frequency pulse train • A aperiodic digital signal has a continuous spectrum that is obtained by multiplying the sinc spectrum by a periodic continuous spectrum ranging from zero to infinite 46

Note: sinc Function • In mathematics and engineering, the sinc function, denoted by sinc(x), has two slightly different definitions • In mathematics, the historical unnormalized sinc function is defined by sinc(x) = sin(x) / x • In digital signal processing and information theory, the normalized sinc function is commonly defined by sinc(x) = sin(∏x) / ∏x 47

A digital signal can be represented by a weighted combination of sinusoidal, sine and cosine, signals with different frequencies, amplitudes, and phases(t) = (4/π) × (sin(2πft) + (1/3)sin(2π(3f)t)) 49

Spectra of Periodic Digital Signals Chapter 2: Physical Layer 7

Computer Networks An Open Source Approach