Electrical Communication System: Block Diagram Information Source Input Transducer Input electric signal Transmitter Transmitted signal Noise and signals from other sources Channel Destination Output Transducer Output electric signal Receiver Received signal Electrical Communication System Information Source voice, audio, video, digital data, etc. Input Transducer translates information into electric signal, e.g., microphone Output Transducer reverts to the original information format, e.g., loudspeaker MSIT 411 1
Electrical Communication System: Block Diagram (continued) Information Source Input Transducer Input electric signal Transmitter Transmitted signal Noise and signals from other sources Channel Destination Output Transducer Output electric signal Receiver Received signal Electrical Communication System Transmitter modulation, filtering, encoding, transmitting (prepare the proper format for the channel) Receiver filtering, amplifying, demodulating, decoding, etc. Channel transmission medium such as twisted pair, coax, fiber, air, etc. Notes: 1. In a two-way communication system, both the transmitter and the receiver are integrated (transceiver) 2. The channel may be shared MSIT 411 2
Waveform: Signal as a function of time Waveform = voltage fluctuation in time: the signal is a function of time (information is represented by voltage variation) Analog Waveform examples: voice, audio, video a(t) (volts) t (second) (Baseband) Digital Waveform examples: data, MPEG video, MP3 music Examples: your weight, your portfolio value, temperature reading in Chicago, patient s heartbeat as displayed on a monitor d(t) (volt) t (second) MSIT 411 3
Sine Waves s(t) = A sin (2πf t) (volt) A T 0 T t (second) A: Amplitude in volts T: Period or Cycle in seconds f = 1/T: Frequency in cycles/second or Hertz (Hz) s(t) = A sin (2πf t) = A sin (ωt), where ω = 2πf radians/sec = angular velocity MSIT 411 4
Signal Power s(t) = A sin (2πf t) (volt) A T 0 T t (second) Instantaneous energy in a signal = s(t) 2 (measured in Joules) Power is energy per unit time, measured in Watts (Joules per second). Average power of a sine wave: = A 2 /2 MSIT 411 5
Sine Wave Example: Household AC 110-Volt AC source: s(t) = 156 sin (2π(60) t) (volt) 156 1/60 0 1/60 t (second) A = Amplitude = 156 Volts, f = Frequency = 60 Hz Average power = 156 2 /2 = 12,168 watts Same average power (or close) with constant 110 Volts ( DC equivalent) MSIT 411 6
Sine Wave Animation http://www.rkm.com.au/animations/animation-sinewave.html MSIT 411 7
Sine Waves with Different Amplitudes and Frequencies High- and low-frequency sine waves A B t Freq. = f B Freq. = f A Noteworthy: In this example, the higher-frequency sine wave (in blue) has a smaller amplitude than the low-frequency sine wave (in green) MSIT 411 8
Sinusoidal Signal Electromagnetic wave s(t) = A sin (2 π f t + θ) Amplitude A=1 Time delay = 12, Phase shift θ = 12/50 cycle = 86.4 degrees s(t) Period= 50 sec, frequency f = 1/50 cycle/sec Time t (seconds)
Sinusoids with Different Phases (same amplitude and same frequencies) 150.00 100 sin(2pi 1000000 t) 100 sin(2pi 1000000 t +2pi/3) 100 sin(2pi 1000000 t - 2pi/3) 100.00 50.00 0.00-50.00-100.00-150.00 t=0 t=1 µs t=2 µs t=3 µs t=4 µs t=5 µs t=6 µs s 1 (t) = 100 sin (2π 10 6 t) Phase = 0 s 2 (t) = 100 sin (2π 10 6 t + 2π/3) Phase = 120 s 3 (t) = 100 sin (2π 10 6 t - 2π/3) Phase = - 120 Note: s 1 (t) + s 2 (t) + s 3 (t) = 0 Phase represents relative timing position between sinusoids. It becomes an important parameter when there are more than one sinusoid involved, which is typically the case in communication systems MSIT 411 10
Two Signal Paths s 1 (t) s 2 (t) Received signal r(t) = s 1 (t) + s 2 (t) Suppose s 1 (t) = sin 2πf t. Then s 2 (t) = h s 1 (t - τ) = h sin 2πf (t - τ) attenuation (e.g., h could be ½) delay (e.g., τ could be 1 microsec.)
Sinusoid Addition (Constructive) s 1 (t) r(t) + = s 2 (t) Adding two sinusoids with the same frequency gives another sinusoid with the same frequency!
Sinusoid Addition (Destructive) s 1 (t) r(t) s 2 (t) + = Signal is faded.
Sine Wave: General Expression Mathematical representation of a sine wave: s(t) = A sin (2π f 0 t + φ) where π φ π is the phase angle of the sine wave In summary, a sine wave is characterized by three parameters: A: amplitude strength, power = A 2 /2 (Watt) f 0 : frequency rate of voltage oscillation in time φ: phase - relative timing position (meaningful only when there are two or more sine waves involved) Importance of sine waves in electrical communication systems: They are the fundamental components ( genes ) of any signal, analog or digital: voice, audio, video, data, They are used as carriers in most communication channels for transmission of information-bearing signals MSIT 411 14
The Frequency Domain The frequency concept originated from sine waves frequency-domain interpretation of the time function s(t) = A sin (2πf 0 t +φ): It has an amplitude A (strength parameter) and a phase φ (timing parameter) at frequency f 0. These are illustrated by the amplitude spectrum and phase spectrum, respectively Example: s(t) = 5 sin (2π(4000)t - 160 ): S(f) amplitude spectrum Arg[S(f)] phase spectrum 4000 f 5-90 f 4000-160 P s (f) power spectrum 12.5 We shall deal mainly with amplitude spectrum 4000 MSIT 411 15
Sine Waves and Their Spectra A High- and low-frequency sine waves B t Freq. = f B Freq. = f A Line (Amplitude) Spectra A B f A f B f MSIT 411 16
Signal Spectrum: Frequency Profile of a Signal Example: A 3-tone signal x(t) = 20sin(2π1000t 90 ) +10sin(2π 2000t + 0 ) +5sin(2π 4000t 160 ) 1. x(t) has an amplitude 20 and phase -90 at frequency f =1000 Hz 2. x(t) has an amplitude 10 and phase 0 at frequency f =2000 Hz 3. x(t) has an amplitude 5 and phase -160 at frequency f =4000 Hz Hence, the above signal can be depicted in the frequency domain as a function of frequency X(f) called signal spectrum amplitude spectrum (magnitude) phase spectrum (angle) X(f) Arg[X(f)] 20 1000 2000 4000 f (Hz) 1000 2000 4000 f (Hz) -90-160 In this example, the spectrum has three spectral lines MSIT 411 17
Signal Spectrum and Bandwidth Generally, any signal, whether it comes from voice, audio, video, or data, is made up of sine waves whose frequencies span a range. The size of the frequency range is called signal bandwidth. The collection of amplitudes for all of the sine waves constitute the signal spectrum. Analog Signal: voice, audio, video Time domain: Waveform a(t) t Fourier Transform Frequency domain: Spectrum A(f) Shape arbitrarily drawn f Digital Signal: PCM, data, MPEG video d(t) Pulse Rate = r (baud) t Fourier Transform Signal Bandwidth (B Hz) Voice ~ 3 khz HQ Audio ~ 15 khz Video ~ 6 MHz D(f) Shape arbitrarily drawn Signal Bandwidth B: proportional to r B = k r, k being a positive constant MSIT 411 18 f
Pulse Width vs. Bandwidth signal pulse Narrowband Power bandwidth = 1/T T time frequency signal pulse Wideband Power bandwidth = 1/T T time frequency 19
Linear Filtering of a Signal X(f) Input signal spectrum (A collection of sine waves within a band of frequencies) Channel or Filter Frequency Response: H(f) Y(f) = H(f) X(f) Output signal spectrum (A collection of sine waves within a band of frequencies) Frequency Response of a channel or filter: H(f) Passband: frequency range within which the frequency response is at or near its maximum (width = channel bandwidth) H(f) Ideal Practical Stopband: frequency range within which the frequency response is at or near zero Transition band: frequency range between passband and stopband (the smaller, the better) Transition band Stopband Channel bandwidth Passband Transition band Stopband f To avoid/limit distortion: Channel Bandwidth Signal Bandwidth (Size and location) MSIT 411 20
Linear Filtering of a Signal X(f) H(f) Y(f) = H(f) X(f) Note: the function multiplier H(f) creates the filtering effect Output Y(f) 0 if H(f) 0 whatever the value of X(f) Y(f) X(f) if H(f) 1 Ideally, H(f) = constant, for f in the passband and H(f) = 0 for all other f Lowpass channel or filter Bandpass channel or filter H(f) Ideal H(f) Ideal Practical f Practical Channel bandwidth Channel bandwidth f Passband Transition band Stopband Transition band Stopband Passband Transition band Stopband MSIT 411 21
Power Loss (Attenuation) and Signal-to-Noise Ratio Transmitted Signal Power P T Channel Received Signal Power P R Input Signal Power P i Power Loss L P T / P R > 1 Power Gain G P R / P T < 1 Repeater/ Amplifier Output Signal Power P o Decibel Convention G db 10 log G db L db 10 log L db Power Gain G P o / P i > 1 Power Loss L P i / P o < 1 Remarks: Attenuation and delay are unavoidable when a signal travels over any communication channel, wired or wireless. Attenuation and delay increase with distance Attenuation and delay are not distortions as long as they are uniform across all the frequencies within the signal spectrum MSIT 411 22
Power Examples Example 1. Consider the following two-hop communication channel with a repeater in between. Find the received signal power following the receiver amplifier. Source P T =10W Hop A Repeater Hop B LA = 30 db Receiver Amplifier G 1 = 20 db L B = 30 db G 2 = 20 db Destination P R =? Solution L = 30 db 20 db + 30 db 20 db = 20 db L = 20 db L = 100 P R = P T /100 = 0.1 W Example 2. A transmitting node on a coax link uses P T = 0.5 W. The coax attenuation is rated at 1 db per 10m. If the receiver node has a receiver sensitivity (i.e., minimum received power required) of 5 µw, what is the maximum length of the link between the two nodes? Solution At the maximum length, the received power is 5 µw which translates to a power loss of L = 0.5W/5µW = 10 5 (largest loss that can be tolerated) L = 10 log 10 L = 50 db Range x (1 db/10m) = 50 db Range = 500 meters MSIT 411 23
Power Gain/Loss: Wired Channels Transmitted Signal Power P T Channel Twisted pair, cable Received Signal Power P R P r (db) P T slope = G db per meter 0 Distance d
Power Gain/Loss: Free Space distance d reference distance d 0 =1 Reference power at reference distance d 0 Path loss exponent=2 In db: P r = P 0 (db) 20 log (d) P r (db) P 0 = G t G r (λ/4π) 2 antenna gains wavelength 0 P 0 slope = -20 db per decade log (d)
Wavelength λ (meters) = c (speed of light) / frequency Wavelength >> size of object è signal penetrates object. Wavelength << size of object è signal is absorbed and/or reflected by object. The antenna size should a fraction of a wavelength (say ¼ to ½).
Indoor Propagation Measurements Ceiling Hypothetical large indoor environment Normalized received power vs. distance
Indoor Propagation Measurements Ceiling Hypothetical large indoor environment Large-scale variation (average over many wavelengths) Normalized received power vs. distance
Indoor Propagation Measurements Ceiling Hypothetical large indoor environment Small-scale variations (over fractions of a wavelength) Normalized received power vs. distance
Power Attenuation: Urban Environment distance d reference distance d 0 =1 Reference power at reference distance d 0 Path loss exponent In db: P r = P 0 (db) 10 n log (d) P 0 slope (n=2) = -20 db per decade P r (db) slope = -40 (n=4) log (d) 0
Large-Scale Path Loss (Scatter Plot) Average Received Power (dbm) Distance (meters, log scale)
Attenuation: Wireless vs. Wired Unshielded Twisted Pair Path loss ~ 13 db / 100 m or 130 db / 1 km Increases linearly with distance Requires repeaters for long distances 1 GHz Radio (free space) Path loss ~ 30 db for the first meter + 20 db / decade 70 db / 100 meters (2 decades) 90 db / 1 km (3 decades) 130 db / 100 km! Increases as log (distance) Repeaters are infeasible for satellites Short distance à Wired has less path loss. Large distance à Wireless has less path loss.
Noise and Signal-to-Noise Ratio Noise is present throughout any communication system transmitter, transmission medium, receiver Dominant noise: receiver noise, because it does not attenuate with the signal The bandwidth of white noise covers the entire frequency range occupied by the communication signal Statistical noise model: Additive White Gaussian Noise (AWGN) White Noise Spectrum + Signal Spectrum N 0 Watt/Hz Signal (power) spectrum Area = P S (Watts) Noise (power) spectrum Power spectrum: shows power (instead of amplitude) as a function of frequency f (Hz) Signal band (B Hz) A receiver filter typically removes out-of-band noise and interference. The bandwidth of this filter should be at least the bandwidth of the transmitted signal. The noise within the signal band are thus retained. Reception quality is determined by the Signal-to-Noise Ratio (SNR) after filtering: S/N Signal Power P S / Noise Power P N (after filtering, usually in db) where P N N 0 B, N 0 Noise Power Spectral Density in Watt/Hz (readily measurable) B Filter Bandwidth in Hz (usually assumed to be the Signal bandwidth) Can an ampliflier improve the SNR? No, it would boost both the signal and the noise. MSIT 411 33
Physical versus Allocated Channel Bandwidth Physical Channel Bandwidth: passband of a linear channel frequency range of a physical channel (e.g., a fiber link, coax, twisted pair, wireless link) with acceptable power attenuation Allocated Channel Bandwidth: a portion of the physical channel bandwidth designated for a particular communication Example: twisted-pair telephone line excellent mediocre Mediocre or poor (uneven and varies) POTS DSL Upstream Up to 384 kbps DSL Downstream Up to 7 Mbps Typically high attenuation 4k 30k 138k 1.1 M f (Hz) ISDN DSL Plain Old Telephone Service (POTS for voice) uses 0 to 4 khz, DSL uses bandwidth above 4 khz. The DSL band is sub-partitioned into 4-kHz slices. Slices with acceptable attenuation carry data; the data rate is proportional to the spectral quality. The overall DSL data rate is the sum rate over all slices. MSIT 411 34
Cable and Fiber 2.1 US Cable Spectrum Cable Channels Upstream FM Cable Data 2-6 5 45 84 120 Cable Channels 14-22 Cable Channels 7-13 Channel N: (78+6N) MHz to (84 + 6N) MHz Cable Channels 23 and up one or more of these can be used for Downstream Cable Data and/or digital TV 174 216 750 f (MHz) Fiber 850 nm ~ 0.8 db/km (Cheaper HW - GaAs) 1300 nm ~ 0.2 0.4 db/km 1550 nm ~ 0.2 0.3 db/km Each offers 25-30 THz spectrum MSIT 411 35
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Useful for wireless telecommunications 37
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The higher the frequency, the more bandwidth is available, but the worse the channel characteristics VLF LF MF HF, VHF, UHF, Satellite (including cellular, PCS) ISM1: 902MHz 928 MHz ISM2: 2.4-2.4835 GHz Satellite ISM3: 5.735 GHz 5.86 GHz 10 4 10 8 4 10 9 10 10 Penetration Loss, multipath fading, rain effect as frequency f (Hz) 39
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beachfront property : Between ~ 700 and 900 MHz 41
Cellular/PCS Spectrum Allocation (1993) Wavelengths too long; propagates too far 802.11b/g (WiFi), 2.4 GHz 802.11a 5.2 GHz 42
db and dbm db is a ratio of two powers: We say that power P 1 is x db stronger than power P 2 if x = 10 log (P 1 /P 2 ), where log is base 10. Example: P 1 is 3 db more than P 2 if P 1 /P 2 2. dbm is power relative to a milliwatt (1 mw = 0.001 W): P in dbm = 10 log (P/0.001) Example: 1 mw = 10 log 1 = 0 dbm
Cellular Signal Strength Measurements drive test plots
Link Budget How much transmit power is required to achieve a target received power? dbs add: Target received power (dbm) + path loss (db) + other losses (components) (db) - antenna gains (db) Total power needed at transmitter (dbm)
Example Transmitter What is the required Transmit power? wireless channel 40 db attenuation Receiver Received power must be > -30 dbm Recall that dbm measures the signal power relative to 1 mw (milliwatt) = 0.001 Watt. To convert from S Watts to dbm, use S (dbm) = 10 log (S / 0.001) Transmitted power (dbm) = -30 + 40 = 10 dbm = 10 mw What if the received signal-to-noise ratio must be 5 db, and the noise power is -45 dbm?
Distortion and Countermeasures Linear Distortion Uneven attenuation within signal bandwidth Unequal delays within signal bandwidth X(f) Channel w/ Linear Distortion H c (f) Equalizer H eq (f) Y(f) = H c (f) H eq (f) X(f) constant attenuation within signal bandwidth H(f) Example: Assume that the frequency range of X(f) is from 0 to 12 khz 0 0.03 4 k 0.02 8 k 0.01 12 k f H c (f) H eq (f) = constant H eq (f) 0.03 0.03 0.03 0 1 4 k 1.5 8 k 3 12 k f 0 4 k 8 k 12 k f MSIT 411 47
Distortion and Countermeasures Non-linear Distortion Uneven gain or attenuation with respect to input signal strength (power) (Practical connection: audio amplifier distortion when volume is tuned too high) Nonlinear distortion cannot be equalized and thus must be avoided Nonlinear distortion is one of the main reasons why signal power has to be constrained in communication systems and networks. Slope = power gain P R or P o Ideal amplifier (constant gain) P R or P o Practical amplifier/channel Saturation Ideal channel (constant loss) P T or P i Linear Range P T or P i MSIT 411 48
Companding A technique used to deal with nonlinear distortion in telephone systems S i S Non-linear Compress x S y S Expand o Channel S x a S y S o S i a S x S y The compressor ensures that signal entering the channel within the linear operating range of the channel The expander is the inverse function of the compressor and thus restores the original signal strength contrast µ-law Compressor (North America) y = log (1+ µx)/log(1+µ), where µ is degree of compression, is used in North America telephone systems. Soft voices actually get amplified while strong voices are suppressed. A-law Compressor (Europe) y = Ax/[1 + ln A] for 0 x 1/A = (1 + ln Ax)/(1+ ln A) for 1/A x 1 MSIT 411 49