300952
Wireless and Mobile Networks
Lecture 2. Transmission Fundamentals
Lecture objectives
• Understand basic concepts of signals for conveying information
• Differentiate and characterize analog and digital data transmission
• Identify the different factors that affect the capacity of a communication channel
• Understand the concept of multiplexing
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SIGNALS
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• Function of time
Electromagnetic Signal
• Can also be expressed as a function of frequency – Signal consists of components of different frequencies
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Time-Domain Concepts (1)
• Analog signal: signal intensity varies in a smooth fashion over time
– No breaks or discontinuities in the signal
• Digital signal: signal intensity maintains a constant level for some
period of time and then changes to another constant level
• Periodic signal: analog or digital signal pattern that repeats over time
s(t +T) = s(t) -∞ < t < +∞ • where T is the period of the signal
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Analog and Digital Waveforms
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Time-Domain Concepts (2)
• Aperiodic signal: analog or digital signal pattern that doesn't repeat over time
• Peak amplitude (A): maximum value or strength of the signal over time; typically measured in volts
• Frequency (f): rate, in cycles per second, or Hertz (Hz) at which the signal repeats
• Period (T): amount of time it takes for one repetition of the signal – T = 1/f
• Phase (φ): measure of the relative position in time within a single period of a signal
• Wavelength (λ): distance occupied by a single cycle of the signal
– Or, the distance between two points of corresponding phase of two consecutive cycles
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Examples of Periodic Signals
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Sine Wave Parameters
• General sine wave
– s(t)=Asin(2πft+φ)
• Next slide shows the effect of varying each of the three parameters
– (a) A = 1, f = 1 Hz, φ = 0; thus T = 1 s
– (b) Reduced peak amplitude; A=0.5
– (c) Increased frequency; f = 2, thus T = 1⁄2
– (d) Phase shift; φ = π/4 radians (45 degrees)
• Note:2πradians=360°=1period
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s(t) = A sin (2πft + φ)
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Addition of frequency Components(T = 1/f)
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Frequency-Domain Concepts (1)
• Fundamental frequency: when all frequency components of a signal are integer multiples of one frequency, it’s referred to as the fundamental frequency
• Spectrum: range of frequencies that a signal contains
• Absolute bandwidth: width of the spectrum of a signal
• Effective bandwidth (or just bandwidth): narrow band of frequencies that most of the signal’s energy is contained in
– The greater the bandwidth (in Hz), the higher the information-carrying capacity (in bps)
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Frequency-Domain Concepts (2)
• Any electromagnetic signal can be shown to consist of a collection of periodic analog signals (sine waves) at different amplitudes, frequencies, and phases
• The period of the total signal is equal to the period of the fundamental frequency
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Frequency Components of Square Wave
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Relationship between Data Rate and Bandwidth
• The greater the bandwidth, the higher the information-carrying capacity
• Conclusions
– Any digital waveform will have infinite bandwidth
– BUT the transmission system will limit the bandwidth that can be transmitted
– AND, for any given medium, the greater the bandwidth transmitted, the greater
the cost
– HOWEVER, limiting the bandwidth creates distortions
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ANALOG AND DIGITAL DATA TRANSMISSION
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Data Communication Terms
• Data: entities that convey meaning, or information
• Signals: electric or electromagnetic representations of data
• Transmission: communication of data by the propagation and processing of signals
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• Analog – Video – Audio
• Digital – Text
– Integers
Examples of Analog and Digital Data
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Analog Signals
• A continuously varying electromagnetic wave that may be propagated over a variety of media, depending on frequency
• Examples of media:
– Copper wire media (twisted pair and coaxial cable)
– Fiber optic cable
– Atmosphere or space propagation
• Analog signals can propagate analog and digital data
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Digital Signals
• A sequence of voltage pulses that may be transmitted over a copper wire medium
• Generally cheaper than analog signaling
• Lesssusceptibletonoiseinterference
• Suffer more from attenuation
• Digital signals can propagate analog and digital data
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Analog Transmission
• Transmit analog signals without regard to content
• Attenuation limits length of transmission link
• Cascaded amplifiers boost signal’s energy for longer distances but cause distortion
– Analog data can tolerate distortion – Introduces errors in digital data
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Digital Transmission
• Concerned with the content of the signal
• Attenuation endangers integrity of data
• Digital Signal
– Repeaters achieve greater distance
– Repeaters recover the signal and retransmit
• Analogsignalcarryingdigitaldata
– Retransmission device recovers the digital data from analog signal – Generates new, clean analog signal
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Attenuation of Digital Signals
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CHANNEL CAPACITY
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About Channel Capacity
• Impairments, such as noise, limit data rate that can be achieved
• For digital data, to what extent do impairments limit data rate?
• Channel Capacity: the maximum rate at which data can be transmitted over a given communication path, or channel, under given conditions
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Effect of Noise on Digital Signal
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Concepts Related to Channel Capacity
• Data rate: rate at which data can be communicated (bps)
• Bandwidth: the bandwidth of the transmitted signal as constrained by the transmitter and the nature of the transmission medium (Hertz)
• Noise: average level of noise over the communications path
• Error rate: rate at which errors occur
– Error = transmit 1 and receive 0; transmit 0 and receive 1
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Nyquist Bandwidth
• For binary signals (two voltage levels) – C = 2B
• Withmultilevelsignaling
– C = 2B log2 M
• M = number of discrete signal or voltage levels
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Signal-to-Noise Ratio
• Ratio of the power in a signal to the power contained in the noise that’s present at a particular point in the transmission
• Typically measured at a receiver
• Signal-to-noise ratio (SNR, or S/N)
(SNR) =10log
dB 10
• A high SNR means a high-quality signal, low number of required intermediate repeaters
• SNR sets upper bound on achievable data rate
signal power noise power
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Shannon Capacity Formula
• Equation:
• Represents theoretical maximum that can be achieved
• In practice, only much lower rates achieved – Formula assumes white noise (thermal noise)
– Impulse noise is not accounted for
– Attenuation distortion or delay distortion not accounted for
C = B l o g 2 (1 + S N R )
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Example of Nyquist and Shannon Formulations
• Spectrum of a channel between 3 MHz and 4 MHz ; SNRdB = 24 dB
B = 4 MHz − 3 MHz = 1 MHz SNRdB =24dB=10log10(SNR) SNR = 251
• UsingShannon’sformula
• logb(xy) = logbx + logby.
• logb(x/y) = logbx - logby.
• logb(xn) = n logbx.
• logbx = logax / logab
•𝑌=𝑙𝑜𝑔𝑎𝑥→ 𝑥=𝑎𝑦
C = 1 0 6 l o g (1 + 2 5 1) 1 0 6 8 = 8 M b p s 2
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Example of Nyquist and Shannon Formulations
• How many signaling levels are required? C = 2Blog2M
8106 =2(106)log M 2
4=log2 M M =16
Note: If M is a fraction, round up, as we cannot have a fraction of a signal. Ex.: if M = 31.7 then 32 signaling levels are required
•𝑌=𝑙𝑜𝑔𝑎𝑥→ 𝑥=𝑎𝑦
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MULTIPLEXING
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Multiplexing (1)
• Capacity of transmission medium usually exceeds capacity required for transmission of a single signal
• Multiplexing - carrying multiple signals on a single medium – More efficient use of transmission medium
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Multiplexing (2)
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Reasons for Widespread Use of Multiplexing
• Cost per kbps of transmission facility declines with an increase in the data rate
• Cost of transmission and receiving equipment declines with increased data rate
• Mostindividualdatacommunicatingdevicesrequirerelativelymodest data rate support
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Multiplexing Techniques
• Frequency-divisionmultiplexing(FDM)
– Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal
• Time-divisionmultiplexing(TDM)
– Takes advantage of the fact that the achievable bit rate of the medium exceeds the required data rate of a digital signal
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Sources for this lecture
Cory Beard, William Stallings. Wireless Communication Networks and Systems, 1st edition. Pearson Higher Education, 2016
(Chapter 2)
All material copyright 2016
Cory Beard and William Stallings, All rights reserved
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