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## Physical Layer

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**Physical Layer**• Overview of physical layer • Channel limitation • Modulation/demodulation**Representation of Information**• Digital representation • Information that occurs naturally in digital form • data files or image files • Analog information: be digitized • Voice • Music • Video • Most communications networks are digital!**Source Coding**• Networks are handling streams of 0’s and 1’ • Source Encoding: compression, according to statistics of 0’s and 1’s, map blocks of bits to more regular “shorter” blocks! Get rid of redundancy • Source Decoding: inverse of source encoding**Channel Coding**• Channel Encoding: According to channel conditions, add redundancy for more efficient transmission, interleaving may be used too. • Channel decoding: the inverse • Observation: source encoding attempts to eliminate “useless information”, while channel encoding add “useful information”, both deal with redundancies!**Modulation/Demodulation**• Modulation: maps blocks of bits to well-defined waveforms or symbols (a set of signals for better transmission), then shifts transmission to the carrier frequency band (the band you have right to transmit) • Demodulation: the inverse of modulation • Demodulation vs. Detection: Detection is to recover the modulated signal from the “distorted noisy” received signals**Physical Components**• Transmitter • Receiver • Transmission media • Guided: cable, twisted pair, fiber • Unguided: wireless (radio, infrared)**Signal Types**• Basic form: A signal is a time function • Continuous signal: varying continuously with time, e.g., speech • Discrete signal: varying at discrete time instant or keeping constant value in certain time interval, e.g., Morse code, flash lights • Periodic signal: Pattern repeated over time • Aperiodic signal: Pattern not repeated over time, e.g., speech**Information Carriers**• s(t) = A sin (2pft+ ) * Amplitude: A * Frequency: f --- f=1/T, T---period * Phase: , angle (2pft+ )**Frequency Domain Concept**• Signal is usually made up of many frequencies • Components are sine waves • Can be shown (Fourier analysis) that any signal is made up of component sine waves • Can plot frequency domain functions • Time domain representation is equivalent to frequency domain representation: they contain the same information! • Frequency domain representation is easier for design**Received Signals**• Any receiver can only receive signals in certain frequency range (channel concept), corresponding to finite number of terms in the Fourier series approximation: • physically: finite number of harmonics • mathematically: finite number of terms • Transmitted signal design: allocate as many terms as possible in the intended receiver’s receiving range (most of power is limited in the intended receiving band)**Spectrum & Bandwidth**• Spectrum: the range of frequencies contained in a signal • Absolute bandwidth: width of spectrum • Effective bandwidth: just BW, Narrow band of frequencies containing most of the energy • 3 dB BW • Percentage BW: percentage power in the band • DC Component: Component of zero frequency**Data Rate and Bandwidth**• Any transmission system has a limited band of frequencies • This limits the data rate that can be carried • The greater the BW, the higher the data rate • Channel capacity (later)**Analog vs Digital**• Analog: Continuous values within some interval, the transmitted signal has actual meaning, e.g., AM and FM radio • Digital: Digital=DSP+Analog, raw digital bits are processed and mapped to well-known signal set for better transmission, the final transmitted signal is still analog! You could not “hear” though!**Analog Transmission**• Analog signal transmitted without regard to content • Attenuated over distance • Use amplifiers to boost signal, equalizers may be used to mitigate the noise • Also amplifies noise**Digital Transmission**• Concerned with content • Digital repeaters used: repeater receives signal, extracts bit pattern and retransmits the bit pattern! • Attenuation is overcome and distortion is not propagated!**Advantages of Digital Transmission**• Digital technology: low cost, can use low power • Long distance transmission: use digital repeaters • Capacity utilization: get rid of useless information and add useful redundancy for data protection • Security & privacy: encryption • Integration: treat analog and digital data similarly**Channel Impairments**• Attenuation and attenuation distortion: signal power attenuates with distance • Delay distortion: velocity of a signal through a guided medium varies with frequency, multipath in wireless environments • Thermal noise • Co-channel Interference: wireless • Impulse noise (powerline communications)**Channel Capacity**• Data rate is limited by channel bandwidth and channel environment (impairments) • Data rate, in bits per second, is the number of bits transmitted successfully per second! Should not count the redundancy added against channel impairments! • It represents how fast bits can be transmitted reliably over a given medium**Factors Affecting Data Rate**• Transmitted power (energy) • Distance between transmitter and receiver • Noise level (including interference level) • Bandwidth**Nyquist Capacity**• Nyquist Rate: 2B (baud), where B is the BW of a signal • Sampling Theorem: Any signal whose BW is B can be completely recovered by the sampled data at rate 2B samples per second • Nyquist Capacity Theorem: For a noiseless channel with BW B, if the M level signaling is used, the maximum transmission rate over the channel is C = 2B log2( M) • Digital Comm: symbol rate (baud) vs. bit rate**Shannon Capacity**• All channels are noisy! • 1948 paper by Claude Shannon: “A mathematical theory of communications” “The mathematical theory of communications” • Signal-to-noise ratio: SNR=signal power/noise power (watt)**Shannon Capacity (cont)**• Shannon Capacity Theorem: For a noisy channel of BW B with signal-to-noise ratio (SNR), the maximum transmission rate is C = B log2 (1+SNR) • Capacity increases as BW or signal power increases: Shout as you can! • Some exercise: B=3400Hz, SNR=40dB • C=44.8 kbps**Shannon Capacity (cont)**• Shannon Theorem does not give any way to reach that capacity • Current transmission schemes transmit much lower rate than Shannon capacity • Turbo codes: iterative coding schemes using feedback information for transmission and detection • Sailing towards Shannon capacity!**Modulation/Demodulation**• Line coding: representation of binary bits without carrier (baseband coding) • Modulation/demodulation: representation of digital bits with carrier (broadband coding) • Analog to Digital Coding**Line Coding**• Unipolar: all signal elements have same sign • Polar: one logic state represented by positive voltage the other by negative voltage • Data rate: rate of transmitted data (bps) • Bit period: time taken for transmitter to emit the bit, the duration or length of a bit • Modulation rate: rate at which the signal level changes, measured in baud (symbols per sec)**Schemes**• Non-return to Zero-Level (NRZ-L) • Non-return to Zero Inverted (NRZI) • Bipolar-AMI • Pseudo-ternary • Manchester • Differential Manchester**Nonreturn to Zero-Level (NRZ-L)**• Two different voltages for 0 and 1 bits • Voltage constant during bit interval • no transition, i.e. no return to zero voltage • e.g., Absence of voltage for zero, constant positive voltage for one (Unipolar NRZ) • More often, negative voltage for one value and positive for the other---NRZ-L (Polar NRZ)**Nonreturn to Zero Inverted**• Nonreturn to zero inverted on ones • Constant voltage pulse for duration of bit • Data encoded as presence or absence of signal transition at beginning of bit time • 1: Transition (low to high or high to low) • 0: No transition • An example of differential encoding**Differential Encoding**• Data represented by changes rather than levels • More reliable detection of transition rather than level • In complex transmission layouts it is easy to lose sense of polarity**Multilevel Binary**• Use more than two levels • Bipolar-AMI • 0: no line signal • 1: positive or negative pulse • pulses for 1’s alternate in polarity • No loss of sync if a long string of ones (zeros still a problem) • No net dc component • Lower bandwidth • Easy error detection**Pseudo-ternary**• 1: absence of line signal • 0: alternating positive and negative • No advantage or disadvantage over bipolar-AMI Change for 1’s No signal No signal Change for 0’s**Biphase**• Manchester • Transition in middle of each bit period • Transition serves as clock and data • 1: low to high, 0: high to low • Used by IEEE 802.3 (Ethernet) • Differential Manchester • Midbit transition is clocking only • 0: transition at start of a bit period • 1: no transition at start of a bit period • Used by IEEE 802.5 (Token Ring)**Spectra**• Used for the selection of line codes in conjunction with the channel characteristics: design the system so that most power is concentrated in the allowed range Figure 3.26**Modulation Schemes (Binary)**• Public telephone system • 300Hz to 3400Hz • Use modem (modulator-demodulator) • Amplitude Shift Keying (ASK) • Frequency Shift Keying (FSK) • Phase Shift Keying (PSK)**Binary ASK,FSK, PSK**Bit-stream ASK FSK PSK**Digital Modulation**• Binary keying schemes are simple, but not efficient! • Digital modulation uses multiple symbols (waveforms) to improve the efficiency • Information bearers: - Amplitude - Frequency - Phase • Mapping: a block of bits to a waveform**QPSK**• Quadrature Phase Shift Keying**2-D signal**Bk Ak 4 “levels”/ pulse 2 bits / pulse 2W bits per second Signal Constellation • QPSK and QAM Bk 2-D signal Ak 16 “levels”/ pulse 4 bits / pulse 4W bits per second Figure 3.33**QAM**• Quadrature Amplitude Modulation (QAM)