02 - Physical Layer

ucla | CS 118 | 2024-10-01 16:55

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Table of Contents

• Signal Modulation
• Physical Layer
  • Bot Sublayer: Signal Transmission Limits
    • Fourier Analysis
    • Nyquist Limit
    • Shannon Limit
    • Nyquist-Shannon Sampling Thm
  • Top Sublayer: Clock Recovery
    • Manchester encoding
    • Receiver code
  • Broadband Coding
  • Middle Sublayer: Media
    • Twisted Pair Coax
    • Baseband Coax (Ethernet)
    • Fiber Optic
    • Wireless
    • 802.11b (a/c?)
    • Media summary

Signal Modulation

Modem

• Modulation and demodulation of digital signal to analog to digital

Physical Layer

• possibly faulty, single hop, bit-pipe that connects 1 sender to possibly Many receivers; e.g., morse code:

• Constraints at every sublayer

Bot Sublayer: Signal Transmission Limits

• transmission done on light: 0=low,1=high

• distortion is inevitable so:

Fourier Analysis

• we can describe a channel by plotting the amplitude and phase of a signal $S$ over all frequencies s.t. a wave of frequency $\mathcal{f}$ is scaled by fixed $a(\mathcal{f})$ (amplitude) and shifted by fixed $p(\mathcal{f})$ (phase)
• to then find the original signal, we write $S$ as a sum of sine waves with diff frequencies using the amplitude and phase response to guage the difference and add the scaled sine waves to the fourier

• EE - range of signal freqs; CS - speed of cable modem in bits/s

• higher bandwidth = higher fidelity (easier to distinguish high and low) = better bit recovery

• thus, lower bandwidth means more sluggish response as channels can’t infer signals past a certain frequency
• most common noise is white noise - uniformly distributed across all freqs and normally distributed within a specific freq

Nyquist Limit

• Given a bandwidth for an amplitude response:

• we can send signals without intersymbol interference (ISI) up to a rate of 2xBandwidth / second

• this is the limit of sending symbols not bits (baud rate)

Shannon Limit

• speed of transmission depends on noise and bandwidth

• see that we can send multiple bits over a single wave:

• Thus baud rate for $L$ signal levels is = $\log L\times 2B$

• noise messes with the amplitudes, so we set Shannon bounds

• Shannon bound

Nyquist-Shannon Sampling Thm

https://youtu.be/Jv5FU8oUWEY?si=Y2GXnNIvty9OEfAa

• Due to aliasing from too low of a sampling frequency, we may only capture the orginal signal accuratley if the sampling frequency $f_s>2\cdot f_{max}$ is greater than twice the max frequency of the original signal
• this is why audio recorders record at 44.1 kHz (a little more than twice the max frequency humans can hear)

• larger bandwidth = better recovery

Top Sublayer: Clock Recovery

• b/c clocks drift, we hve initial training bits. to anti-alias, we need transitions in clock voltage

• we need signal transitions bw multiple clock cycles of the same signal to know that the clock has ticked

• we add start and stop bits

• asynchronous tranmision of bits over signal don’t require robust start and stop, usually jusst 1-2 trailing stop bits
• synch. transmission needs better clock tolerance -> sophisticated coding, ususally of the form:
• synch. does this to reduce receiver clock startup overhead (knowing when to start the receiver clock is expensive which iss a blocker to assynch transmission, instead long leading and trailing bits wrapping the message)

Manchester encoding

• encodes the transition of the signal/data itself, e.g. hi->lo : 1, lo->hi : 0
• this helps with getting the phase matching easier - with asyc you have 1 transition to sync sender and receiver clock, but with manchester you have a preamble of transitioons of form 010101…11

• solves clock recovery problem but 50% efficient as it encodes 1/2 bit per transition

Receiver code

• usually use phase locked loops to speed up or slow receiver clock to lock in phase

Broadband Coding

• baseband coding uses binary energy levels, e.g. light or voltage
• broadband modules the data/information on a carrier wave at some frequency
• modulation can be Frequency Shift Keying (FSK) - high freq = 1, low freq = 0; or Amplitude Shift Keying (ASK), or QAM (mix), or similar e.g. Phase Shift Keying (PSK)
• TODO: three levers of modulation - FDMA, TDMA, CDMA
• TODO: Signal Multiplexing - Time Division Mux (TDM), Freq Div Mux (FDM)

Middle Sublayer: Media

• hardware tech to best convert digital to analog signal

  • important to consider due to hardware limitations on bandwidth, etc.

Twisted Pair Coax

• twisted pair today

Baseband Coax (Ethernet)

• baseband coax today:

Fiber Optic

• unidirectional

• visible light disperse through reflections in glass due to different wavelengths traveling at diff speeds -> sol: monochromatic light (lasers)

Wireless

• requires spectrum allocation - trying to allocate like a spatial resource does not work as spectrum is time and power shared -> whitespace comms
• radiowave - cheap, good bandwidth, avoids ROW, long diistance (100km), issues with raiin
• satellite - avoids ROW, good bandwidth, world wide distance, expensive, large latency
  • LEO - orbit at varying speeds, cell
  • geostationary much farther = higher latency, but regionally stationary

• types of wireless protocols (not including 5G)

802.11b (a/c?)

• AP configured with SSID, with channel number 1 to 11. non overlapping channels, e.g. 1,6,11 can be used to triple bandwidth -> ssends beacon w/ SSID payload
• each mobiile/client scans all 11 channels looking for SSID beaacons
• issues with hidden terminal problem - mobile A and B can communicate to AP, but not between themselves

Media summary