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CS647: Advanced Topics in Wireless Networks Basics of Wireless Transmission Part II Drs. Baruch Awerbuch & Amitabh Mishra Computer Science Department Johns Hopkins University CS 647 2.1 Antenna Gain For a circular reflector antenna G = η ( π D / λ )2 η = net efficiency (depends on the electric field distribution over the antenna aperture, losses such as ohmic heating , typically 0.55) D = diameter, thus, G = η (π D f /c )2, c = λ f (c is speed of light) Example: Antenna with diameter = 2 m, frequency = 6 GHz, wavelength = 0.05 m G = 39.4 dB Frequency = 14 GHz, same diameter, wavelength = 0.021 m G = 46.9 dB * Higher the frequency, higher the gain for the same size antenna CS 647 2.2 Path Loss (Free-space) Definition of path loss LP : Pt LP = , Pr Path Loss in Free-space: 2 2 Lf =(4π d/λ) = (4π f cd/c ) LPF (dB) = 32.45+ 20log10 fc (MHz) + 20log10 d(km), where fc is the carrier frequency This shows greater the fc, more is the loss. CS 647 2.3 Example of Path Loss (Free-space) Path Loss in Free-space 130 120 fc=150MHz (dB) f f =200MHz 110 c f =400MHz 100 c fc=800MHz 90 fc=1000MHz 80 Path Loss L fc=1500MHz 70 0 5 10 15 20 25 30 Distance d (km) CS 647 2.4 Land Propagation The received signal power: G G P P = t r t r L L is the propagation loss in the channel, i.e., L = LP LS LF Fast fading Slow fading (Shadowing) Path loss CS 647 2.5 Propagation Loss Fast Fading (Short-term fading) Slow Fading (Long-term fading) Signal Strength (dB) Path Loss Distance CS 647 2.6 Path Loss (Land Propagation) Simplest Formula: -α Lp = A d where A and α: propagation constants d : distance between transmitter and receiver α : value of 3 ~ 4 in typical urban area CS 647 2.7 Path Loss (Urban, Suburban and Open areas) Urban area: LPU (dB) = 69.55 + 26.16log10 fc (MHz) −13.82log10 hb (m) −α [hm (m)] + []44.9 − 6.55log10 hb (m) log10 d(km) where []1.1log10 fc (MHz) − 0.7 hm (m) −[1.56log10 fc (MHz) − 0.8], for l arge city 2 α []hm (m) = 8.29[]log10 1.54hm (m) −1.1, for fc ≤ 200MHz , for small & medium city 2 3.2[]log10 11.75hm (m) − 4.97, for fc ≥ 400MHz Suburban area: 2 fc (MHz) LPS (dB) = LPU (dB) − 2log10 − 5.4 28 Open area: 2 LPO (dB) = LPU (dB) − 4.78[log10 fc (MHz)] +18.33log10 fc (MHz) − 40.94 CS 647 2.8 Path Loss Path loss in decreasing order: Urban area (large city) Urban area (medium and small city) Suburban area Open area CS 647 2.9 Example of Path Loss (Urban Area: Large City) Path Loss in Urban Area in Large City 180 fc=200MHz 170 fc=400MHz (dB) 160 f =800MHz pu c 150 fc=1000MHz 140 fc=1500MHz f =150MHz 130 c 120 Path Loss L 110 100 0102030 Distance d (km) CS 647 2.10 Example of Path Loss (Urban Area: Medium and Small Cities) Path Loss in Urban Area for Small & Medium Cities 180 170 fc=150MHz 160 fc=200MHz 150 fc=400MHz 140 fc=800MHz 130 fc=1000MHz 120 fc=1500MHz Path Loss Lpu (dB) 110 100 0102030 Distance d (km) CS 647 2.11 Example of Path Loss (Suburban Area) Path Loss in Suburban Area 170 160 fc=150MHz 150 fc=200MHz 140 fc=400MHz 130 fc=800MHz 120 fc=1000MHz 110 fc=1500MHz Path Loss Lps (dB) 100 90 0 5 10 15 20 25 30 Distance d (km) CS 647 2.12 Example of Path Loss (Open Area) Path Loss in Open Area 150 140 fc=150MHz po 130 fc=200MHz fc=400MHz 120 fc=800MHz 110 fc=1000MHz 100 fc=1500MHz Path Loss L (dB) 90 80 0 51015 20 25 30 Distance d (km) CS 647 2.13 Slow Fading The long-term variation in the mean level is known as slow fading (shadowing or log-normal fading). This fading caused by shadowing. Log-normal distribution: - The pdf of the received signal level is given in decibels by 2 ()MM− − 1 2 pM()= e 2σ 2πσ where M is the true received signal level m in decibels, i.e., M=10log10m, M is the area average signal level, i.e., the mean of M, σ is the standard deviation in decibels CS 647 2.14 Log-normal Distribution 2σ p(M) M M The pdf of the received signal level CS 647 2.15 Fast Fading The signal from the transmitter may be reflected from objects such as hills, buildings, or vehicles. When MS far from BS, the envelope distribution of received signal is Rayleigh distribution. The pdf is r 2 − r 2 p()r = e 2σ , r > 0 σ 2 where σ is the standard deviation and r is the envelope of fading signal. z Middle value rm of envelope signal within sample range to be satisfied by P(r ≤ rm) =0.5. z We have rm = 1.777σ CS 647 2.16 Rayleigh Distribution P(r) 1.0 0.8 σ=1 0.6 0.4 σ=2 σ=3 0.2 r 0 2 4 6 8 10 The pdf of the envelope variation CS 647 2.17 Fast Fading (Continued) When MS is close to BS, the envelope distribution of received signal is Rician distribution. The pdf is r2 +α2 − r 2σ 2 rα p()r = e I0 , r ≥0 σ 2 σ where σ is the standard deviation, I0(x) is the zero-order Bessel function of the first kind, α is the amplitude of the direct signal CS 647 2.18 Rician Distribution α= 0 (Rayleigh) α = 1 0.6 α = 2 0.5 α = 3 0.4 0.3 σ = 1 Pdf p(r) 0.2 0.1 0 0 2 4 6 8 r r The pdf of the envelope variation CS 647 2.19 Characteristics of Instantaneous Amplitude Level Crossing Rate: Average number of times per second that the signal envelope crosses the level in positive going direction. Fading Rate: Number of times signal envelope crosses middle value in positive going direction per unit time. Depth of Fading: Ratio of mean square value and minimum value of fading signal. Fading Duration: Time for which signal is below given threshold. CS 647 2.20 Doppler Shift Doppler Effect: When a wave source and a receiver are moving towards each other, the frequency of the received signal will not be the same as the source. When they are moving toward each other, the frequency of the received signal is higher than the source. When they are opposing each other, the frequency decreases. Thus, the frequency of the received signal is fR = fC − fD where fC is the frequency of source carrier, & fD is the Doppler frequency. Doppler Shift in frequency: Moving MS v speed v f D = cos θ λ θ where v is the moving speed, Signal λ is the wavelength of carrier. CS 647 2.21 Delay Spread When a signal propagates from a transmitter to a receiver, signal suffers one or more reflections. This forces signal to follow different paths. Each path has different path length, so the time of arrival for each path is different. This effect which spreads out the signal is called “Delay Spread”. CS 647 2.22 Moving Speed Effect V1 V2 V3 V4 Signal strength Time CS 647 2.23 Delay Spread The signals from close by reflectors The signals from intermediate reflectors The signals from far away reflectors Signal Strength Delay CS 647 2.24 Intersymbol Interference (ISI) Caused by time delayed multipath signals Has impact on burst error rate of channel Second multipath is delayed and is received during next symbol For low bit-error-rate (BER) 1 R < 2τd R (digital transmission rate) limited by delay spread τd. CS 647 2.25 Intersymbol Interference (ISI) Transmission 1 1 signal Time 0 Received signal (short delay) Time Propagation time Delayed signals Received signal (long Time delay) CS 647 2.26 Coherence Bandwidth Coherence bandwidth Bc: Represents correlation between 2 fading signal envelopes at frequencies f1 and f2. Is a function of delay spread. Two frequencies that are larger than coherence bandwidth fade independently. Concept useful in diversity reception z Multiple copies of same message are sent using different frequencies. CS 647 2.27 Cochannel Interference Cells having the same frequency interfere with each other. rd is the desired signal ru is the interfering undesired signal β is the protection ratio for which rd ≤βru (so that the signals interfere the least) If P(rd ≤βru ) is the probability that rd ≤βru , Cochannel probability Pco = P(rd ≤βru ) CS 647 2.28 Multiplexing Multiplexing in 4 dimensions channels ki space (s ) i k1 k2 k3 k4 k5 k6 time (t) frequency (f) c code (c) t c t Goal: multiple use s 1 f of a shared medium s 2 f c Important: guard spaces needed! t s 3 f CS 647 2.29 Frequency multiplex Separation of the whole spectrum into smaller frequency bands A channel gets a certain band of the spectrum for the whole time Advantages: no dynamic coordination necessary k1 k2 k3 k4 k5 k6 works also for analog signals c f Disadvantages: waste of bandwidth if the traffic is distributed unevenly inflexible guard spaces t CS 647 2.30 Time multiplex A channel gets the whole spectrum for a certain amount of time Advantages: only one carrier in the medium at any time throughput high even k1 k2 k3 k4 k5 k6 for many users c Disadvantages: f precise synchronization necessary t CS 647 2.31 Time and frequency multiplex Combination of both methods A channel gets a certain frequency band for a certain amount of time Example: GSM Advantages: better protection against tapping k1 k2 k3 k4 k5 k6 protection against frequency selective interference c higher data rates compared to f code multiplex but: precise coordination required t CS 647 2.32 Code multiplex Each channel has a unique code k1 k2 k3 k4 k5 k6 All channels use the same spectrum at the same time c Advantages: bandwidth efficient no coordination and synchronization necessary good protection against interference and tapping f Disadvantages: lower user data rates more complex signal regeneration Implemented using spread spectrum t technology CS 647 2.33 Modulation Digital modulation digital data is translated into an analog signal (baseband) ASK, FSK, PSK - main focus in this chapter differences in spectral efficiency, power efficiency, robustness Analog modulation shifts center frequency of baseband signal up to the radio carrier Motivation
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