midterm review - stanford university · midterm review midterm only covers material from lectures...
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![Page 1: Midterm Review - Stanford University · Midterm Review Midterm only covers material from lectures and HWs l Overview of Wireless Systems: lNothing from Chapter 1 is on the MT l Signal](https://reader030.vdocuments.site/reader030/viewer/2022040116/5ed3443ce720782dc856e462/html5/thumbnails/1.jpg)
Midterm ReviewMidterm only covers material from lectures and HWs
l Overview of Wireless Systems:l Nothing from Chapter 1 is on the MT
l Signal Propagation and Channel Modelsl Chapter 2.1-2.4, 2.6-2.10
l Modulation and Performance Metricsl Chapter 3.1,3.2.1-3.2.2, 3.3
l Fundamental Capacity Limitsl Chapter 4
l Impact of Channel on Performance l Chapter 6
l Diversity Techniquesl Chapter 7.1,7.2.1-7.2.2,7.2.4,7.3.1,7.4.1
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Future Wireless Networks
Wireless Internet accessNth generation CellularWireless Ad Hoc NetworksSensor Networks Wireless EntertainmentSmart Homes/SpacesAutomated HighwaysAll this and more…
Ubiquitous Communication Among People and Devices
•Hard Delay/Energy Constraints•Hard Rate Requirements
Not on MT
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Design Challenges
l Wireless channels are a difficult and capacity-limited broadcast communications medium
l Traffic patterns, user locations, and network conditions are constantly changing
l Applications are heterogeneous with hard constraints that must be met by the network
l Energy, delay, and rate constraints change design principles across all layers of the protocol stack
Not on MT
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Current/Futre Wireless Systems
l Current Systemsl 4G Cellular Systemsl 802.11b/a/n/ac Wireless LANsl Satellite Systemsl Paging Systemsl Bluetoothl Zigbee radios
l Emerging Systems (Can cover in bonus lecture)l Ad hoc/mesh wireless networksl Cognitive radio networksl Wireless sensor networksl Energy-harvesting radiosl Distributed control networksl Communications/SP in Health, Bio-medicine, and Neuroscience
Not on MT
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Signal Propagationl Path Loss
l Free space, 2-path,…l Simplified model
l Shadowingl dB value is Gaussianl Find path loss exponent and
shadow STD by curve fitting
l Multipathl Ray tracingl Statistical model
d
Pr/Pt
d=vt
82,0 ££úûù
êëé= g
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ddKPP tr
![Page 6: Midterm Review - Stanford University · Midterm Review Midterm only covers material from lectures and HWs l Overview of Wireless Systems: lNothing from Chapter 1 is on the MT l Signal](https://reader030.vdocuments.site/reader030/viewer/2022040116/5ed3443ce720782dc856e462/html5/thumbnails/6.jpg)
Outage Probabilityand Cell Coverage Area
l Path loss: circular cellsl Path loss+shadowing: amoeba cells
l Tradeoff between coverage and interference
l Outage probabilityl Probability received power below given minimum
l Cell coverage areal % of cell locations at desired powerl Increases as shadowing variance decreasesl Large % indicates interference to other cells
rP
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Statistical Multipath Model
l Random # of multipath components, each with varying amplitude, phase, doppler, and delay
l Leads to time-varying channel impulse response
l Narrowband channell No signal distortion, just a complex amplitude gainl Signal amplitude varies randomly (Rayleigh, Ricean, Nakagami).l 2nd order statistics (Bessel function), Average fade duration
))(()(),(1
)( tettc n
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![Page 8: Midterm Review - Stanford University · Midterm Review Midterm only covers material from lectures and HWs l Overview of Wireless Systems: lNothing from Chapter 1 is on the MT l Signal](https://reader030.vdocuments.site/reader030/viewer/2022040116/5ed3443ce720782dc856e462/html5/thumbnails/8.jpg)
Wideband Channelsl Individual multipath components resolvablel True when time difference between
components exceeds signal bandwidth
l Scattering function
l Yields delay spread/coherence BW (st~1/Bc)l Yields Doppler spread/coherence time (Bd~1/Tc)
uB/1>>Dt
t1tD 2tDWideband
t
r
s(t,r)=FDt[Ac(t,Dt)] Delay Power Spectrum
Doppler Power Spectrum
f
cu BB >>
Ac(f)0 Bc
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Capacity of Flat Fading Channelsl Channel Capacity
l Maximum data rate that can be transmitted over a channel with arbitrarily small error
l Capacity of AWGN Channel: Blog2[1+g] bpsl g=Pr/(N0B) is the receiver SNR
l Capacity of Flat-Fading Channelsl Nothing known: capacity typically zerol Fading Statistics Known (few results)l Fading Known at RX (average capacity)
( ) )1(log)(1log 20
2 gggg +£+= ò¥
BdpBC
![Page 10: Midterm Review - Stanford University · Midterm Review Midterm only covers material from lectures and HWs l Overview of Wireless Systems: lNothing from Chapter 1 is on the MT l Signal](https://reader030.vdocuments.site/reader030/viewer/2022040116/5ed3443ce720782dc856e462/html5/thumbnails/10.jpg)
l Capacity in Flat-Fading: g known at TX/RX
l Optimal Rate and Power Adaptation
l The instantaneous power/rate only depend on p(g) through g0
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Waterfilling
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Channel Inversion
l Fading inverted to maintain constant SNR
l Simplifies design (fixed rate)
l Greatly reduces capacityl Capacity is zero in Rayleigh fading
l Truncated inversionl Invert channel above cutoff fade depthl Constant SNR (fixed rate) above cutoffl Cutoff greatly increases capacity
● Close to optimal
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Frequency Selective Fading Channels
l For time-invariant channels, capacity achieved by water-filling in frequency
l Capacity of time-varying channel unknownl Approximate by dividing into subbands
l Each subband has width Bc
l Independent fading in each subbandl Capacity is the sum of subband capacities
Bc fP
1/|H(f)|2
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Linear Modulation in AWGN: MPSK and MQAM
l ML detection induces decision regionsl Example: 8PSK
l Ps depends onl # of nearest neighborsl Minimum distance dmin (depends on gs)l Approximate expression
( )sMMs QP gba»
dmin
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Linear Modulation in Fading
l In fading gs and therefore Ps randoml Metrics: outage, average Ps , combined
outage and average.
Ps
Ps(target)
Outage
Ps
Ts
Ts
sssss dpPP ggg )()(ò=
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Moment Generating Function Approach
l Simplifies average Ps calculation
l Uses alternate Q function representation
l Ps reduces to MGF of gs distribution
l Closed form or simple numerical calculation for general fading distributions
l Fading greatly increases average Ps .
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Doppler Effects
l High doppler causes channel phase to decorrelate between symbols
l Leads to an irreducible error floor for differential modulationl Increasing power does not reduce error
l Error floor depends on fDTb as
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l Delay spread exceeding a symbol time causes ISI (self interference).
l ISI leads to irreducible error floor: l Increasing signal power increases ISI power
l ISI imposes data rate constraint: Ts>>Tm (Rs<<Bc)
Delay Spread (ISI) Effects
0 Tm
1
3
4
5
2
Ts
Delay Tm
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Diversityl Send bits over independent fading paths
l Combine paths to mitigate fading effects.
l Independent fading pathsl Space, time, frequency, polarization diversity.
l Combining techniquesl Selection combining (SC)l Maximal ratio combining (MRC)
l Can have diversity at TX or RXl In TX diversity, weights constrained by TX power
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Selection Combiningl Selects the path with the highest gainl Combiner SNR is the maximum of the branch
SNRs.
l CDF easy to obtain (Pip(gi<gthr)), pdf found by differentiating the CDF
l Pout obtained from CDF. Average Ps typically found numerically
l Diminishing returns with number of antennas.l Can get up to about 20 dB of gain.
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MRC and its Performancel With MRC, gS=Sgi for branch SNRs gi
l Optimal technique to maximize output SNRl Yields 20-40 dB performance gainsl Distribution of gS hard to obtain
l Standard average BER calculation
l Hard to obtain in closed forml Integral often diverges
l MGF Approach:
l TX diversity gain with CSI same as RX diversity
ò ò òò SSSS == MMbbb dddpppPdpPP gggggggggg ...)(...)()()(...)()( 21**2*1s s s
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Main Pointsl Wireless channels introduce path-loss, shadowing
and multipath fadingl Shadowing introduced outagel Flat-fading causes large power fluctuationsl ISI causes self-interference
l Performance of digital communications in wireless channels randoml Characterized by outage probability and average
probability of error in flat-fadingl Characterized by irreducible error floors in ISI/Doppler
l Need mechanisms to compensate for multipathl Diversity compensates for effects of flat fading.