Data and Computer Communications Chapter 3 – Data Transmission

OSI Layers

TransmissionTerminology Transmission Terminology  Data transmission occurs between a transmitter & receiver via some medium  Guided medium E.g. twisted pair, coaxial cable, optical fiber E.g. twisted pair, coaxial cable, optical fiber  Unguided / wireless medium E.g. air, water, vacuum E.g. air, water, vacuum

TransmissionTerminology Transmission Terminology  Direct link no intermediate devices no intermediate devices  Point-to-point direct link direct link only 2 devices share link only 2 devices share link  Multi-point more than two devices share the link more than two devices share the link

TransmissionTerminology Transmission Terminology  Simplex one direction one direction E.g. televisionE.g. television  Half duplex either direction, but only one way at a time either direction, but only one way at a time E.g. police radioE.g. police radio  Full duplex both directions at the same time both directions at the same time E.g. telephoneE.g. telephone

Frequency, Spectrum and Bandwidth  Time domain concepts Analog signal Analog signal Varies in a smooth way over timeVaries in a smooth way over time Digital signal Digital signal Maintains a constant level then changes to another constant levelMaintains a constant level then changes to another constant level Periodic signal Periodic signal Pattern repeated over timePattern repeated over time Aperiodic signal Aperiodic signal Pattern not repeated over timePattern not repeated over time

Analog & Digital Signals

Periodic Signals Signal is periodic if and only if: s(t + T) = s(t), -∞ < t < +∞ T is the period of the signal

Sine Wave  Peak amplitude (A) Maximum strength of signal Maximum strength of signal Volts Volts  Frequency (f) Rate of change of signal Rate of change of signal Hertz (Hz) or cycles per second Hertz (Hz) or cycles per second Period = time for one repetition (T) Period = time for one repetition (T) T = 1/f T = 1/f  Phase (  ) Relative position in time Relative position in time

Varying Sine Waves s(t) = A sin(2  ft +  )

Wavelength ( )  Distance occupied by one cycle  Distance between two points of corresponding phase of two consecutive cycles  Assuming signal velocity v, we have = vT  Or equivalently, f = v  Especially when v=c  c = 3*10 8 ms -1 (speed of light in free space)

Frequency Domain Concepts  Signals are made up of many frequencies  Components are sine waves  Fourier analysis can show that any signal is made up of component sine waves  Can plot frequency domain functions

Addition of Frequency Components (T=1/f)  Figure (c) represents sum of signals with frequencies f and 3f     

Frequency Domain Representations  Frequency domain function of Fig. (c)  Frequency domain function of single square pulse    < <

Spectrum & Bandwidth  Spectrum Range of frequencies contained in signal Range of frequencies contained in signal  Absolute bandwidth Width of spectrum Width of spectrum  Effective bandwidth Often just bandwidth Often just bandwidth Narrow band of frequencies containing most energy Narrow band of frequencies containing most energy  DC Component Component of zero frequency 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  Square has infinite components and hence bandwidth  But most energy is in first few components  Limited bandwidth increases distortion  There is a direct relationship between data rate & bandwidth

Data Rate Calculation  Case 1 Bandwidth 4MHz, use the sine wave of Fig. 3-7 (a) Bandwidth 4MHz, use the sine wave of Fig. 3-7 (a) 4MHz = 5f – f  f = 1MHz, 4MHz = 5f – f  f = 1MHz, the period of fundamental frequency  1/f = = 1us. One wave takes two data bits the period of fundamental frequency  1/f = = 1us. One wave takes two data bits Data rate = 2 Mbps Data rate = 2 Mbps  Case 2 Bandwidth 8MHz, use the sine wave of Fig. 3-7 (a) Bandwidth 8MHz, use the sine wave of Fig. 3-7 (a) 8MHz = 5f – f  f = 2MHz 8MHz = 5f – f  f = 2MHz Data rate = 4 Mbps Data rate = 4 Mbps  Case 3 Bandwidth 4MHz, use the sine wave of Fig. 3-4 (c) Bandwidth 4MHz, use the sine wave of Fig. 3-4 (c) 4MHz = 3f – f  f = 2MHz Data rate = 4 Mbps 4MHz = 3f – f  f = 2MHz Data rate = 4 Mbps

Data Rate vs. Bandwidth  Bandwidth ↑ Data rate ↑ (compare case 1 & 2) Data rate ↑ (compare case 1 & 2) Same signal quality Same signal quality  Same bandwidth Higher signal quality  lower data rate Higher signal quality  lower data rate Compare case 1 & 3 Compare case 1 & 3  Same data rate Bandwidth ↑  better signal quality Bandwidth ↑  better signal quality Compare case 2 & 3 Compare case 2 & 3

Square Wave  Frequency components of the square wave with amplitudes A and –A can be expressed as:    < <  The waveform has an infinite number of frequency components and hence an infinite bandwidth.  Peak amplitude of the kth frequency component, kf, is only 1/k; most of the energy is in first few freq. components.  Limiting waveform to the first few freq. components generates a waveform reasonably close to that of the original square wave.

Square Wave: Freq. Components

Bit time = T / 2

Effect of Bandwidth on a Digital Signal

Transmission Impairments  Signal received may differ from signal transmitted causing: Analog - degradation of signal quality Analog - degradation of signal quality Digital - bit errors Digital - bit errors  Most significant impairments are Attenuation and attenuation distortion Attenuation and attenuation distortion Delay distortion Delay distortion Noise Noise

Attenuation  Where signal strength falls off with distance  Depends on medium  Received signal strength must be: Strong enough to be detected Strong enough to be detected Sufficiently higher than noise to receive without error Sufficiently higher than noise to receive without error  So increase strength using amplifiers/repeaters  Is also an increasing function of frequency  So equalize attenuation across band of frequencies used E.g. using loading coils or amplifiers E.g. using loading coils or amplifiers

Delay Distortion  Only occurs in guided media  Propagation velocity varies with frequency  Hence various frequency components arrive at different times  Particularly critical for digital data  Since parts of one bit spill over into others  Causing inter-symbol interference

Noise  Additional signals inserted between transmitter and receiver  Thermal due to thermal agitation of electrons due to thermal agitation of electrons uniformly distributed uniformly distributed white noise white noise N= kTB, k = Boltzman’s constant (1.38*10^-21), T – temperature, B - Bandwidth In decibel watts – take log  Intermodulation signals that are the sum and difference of original frequencies sharing a medium signals that are the sum and difference of original frequencies sharing a medium

Noise  Given a receiver with an effective noise temperature of 294K and a 10-MHz bandwidth, the thermal noise level at the receiver output is N = log(294) + 10log(10 7 )  Intermodulation signals that are the sum and difference of original frequencies sharing a medium signals that are the sum and difference of original frequencies sharing a medium

Noise  Crosstalk A signal from one line is picked up by another A signal from one line is picked up by another  Impulse Irregular pulses or spikes Irregular pulses or spikes E.g. external electromagnetic interferenceE.g. external electromagnetic interference Short duration Short duration High amplitude High amplitude A minor annoyance for analog signals A minor annoyance for analog signals But a major source of error in digital data But a major source of error in digital data A noise spike could corrupt many bitsA noise spike could corrupt many bits

Analog and Digital Data Transmission  Data Entities that convey meaning Entities that convey meaning  Signals & signaling Electric or electromagnetic representations of data, physically propagates along medium Electric or electromagnetic representations of data, physically propagates along medium  Transmission Communication of data by propagation and processing of signals Communication of data by propagation and processing of signals

Acoustic Spectrum (Analog)

Audio Signals  Freq. range 20Hz-20kHz (speech 100Hz-7kHz)  Easily converted into electromagnetic signals  Varying volume converted to varying voltage  Can limit frequency range for voice channel to Hz

Video Signals  USA lines per frame, at frames per sec have 525 lines but 42 lost during vertical retrace have 525 lines but 42 lost during vertical retrace  525 lines x 30 scans = lines per sec 63.5  s per line 63.5  s per line 11  s for retrace, so 52.5  s per video line 11  s for retrace, so 52.5  s per video line  Max frequency if line alternates black and white  Horizontal resolution is about 450 lines giving 225 cycles of wave in 52.5  s  Max frequency of 4.2MHz

Digital Data  As generated by computers etc.  Has two dc components  Bandwidth depends on data rate

Analog Signals

Digital Signals

Advantages & Disadvantages of Digital Signals  Cheaper  Less susceptible to noise  But greater attenuation  Digital now preferred choice

Channel Capacity  Max. possible data rate on a communication channel  Is a function of Data rate - in bits per second Data rate - in bits per second Bandwidth - in cycles per second or Hertz Bandwidth - in cycles per second or Hertz Noise - on communication link Noise - on communication link Error rate - of corrupted bits Error rate - of corrupted bits  Limitations due to physical properties  Want most efficient use of capacity

Nyquist Bandwidth  Consider noise free channels  If rate of signal transmission is 2B then can carry signal with frequencies no greater than B i.e. given bandwidth B, highest signal rate is 2B i.e. given bandwidth B, highest signal rate is 2B  For binary signals, 2B bps needs bandwidth B Hz  Can increase rate by using M signal levels  Nyquist Formula is: C = 2B log 2 M  So increase rate by increasing signals At cost of receiver complexity At cost of receiver complexity Limited by noise & other impairments Limited by noise & other impairments

Shannon Capacity Formula  Consider relation of data rate, noise & error rate Faster data rate shortens each bit so bursts of noise affect more bits Faster data rate shortens each bit so bursts of noise affect more bits Given noise level, higher rates mean higher errors Given noise level, higher rates mean higher errors  Shannon developed formula relating these to signal to noise ratio (in decibels)  SNR db = 10 log 10 (signal/noise)  Capacity C=B log 2 (1+SNR) Theoretical maximum capacity Theoretical maximum capacity Gets lower in practice Gets lower in practice

Problem  Suppose the spectrum is between 3Mhz and 4 MHz and SNR db = 24. Calculate channel capacity using Shannon and Nyquist.

Summary  Looked at data transmission issues  Frequency, spectrum & bandwidth  Analog vs digital signals  Transmission impairments