1. Wireless Communications: Lecture 2 Professor Andrea Goldsmith
Short Course:
Wireless Communications: Lecture 2
Professor Andrea Goldsmith
UCSD
March 22-23
La Jolla, ca

2. Course Outline Overview of Wireless Communications
Path Loss, Shadowing, and WB/NB Fading
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems
Lecture 1
Lecture 2

3. Lecture 1 Summary

4. Future Wireless Networks
Ubiquitous Communication Among People and Devices
Wireless Internet access
Nth generation Cellular
Wireless Ad Hoc Networks
Sensor Networks
Wireless Entertainment
Smart Homes/Spaces
Automated Highways
All this and more…
Hard Delay/Energy Constraints
Hard Rate Requirements

5. Signal Propagation
Path Loss
Shadowing
Multipath d
Pr/Pt
d=vt

6. Statistical Multipath Model
Random # of multipath components, each with varying amplitude, phase, doppler, and delay
Narrowband channel
Signal amplitude varies randomly (complex Gaussian).
2nd order statistics (Bessel function), Fade duration, etc.
Wideband channel
Characterized by channel scattering function (Bc,Bd)

7. Capacity of Flat Fading Channels
Three cases
Fading statistics known
Fade value known at receiver
Fade value known at receiver and transmitter
Optimal Adaptation
Vary rate and power relative to channel
Optimal power adaptation is water-filling
Exceeds AWGN channel capacity at low SNRs
Suboptimal techniques come close to capacity

8. Modulation Considerations
Want high rates, high spectral efficiency, high power efficiency, robust to channel, cheap.
Linear Modulation (MPAM,MPSK,MQAM)
Information encoded in amplitude/phase
More spectrally efficient than nonlinear
Easier to adapt.
Issues: differential encoding, pulse shaping, bit mapping.
Nonlinear modulation (FSK)
Information encoded in frequency
More robust to channel and amplifier nonlinearities

9. Linear Modulation in AWGN
ML detection induces decision regions
Example: 8PSK
Ps depends on
# of nearest neighbors
Minimum distance dmin (depends on gs)
Approximate expression
dmin

10. Linear Modulation in Fading
In fading gs and therefore Ps random
Metrics: outage, average Ps , combined outage and average. Ts Ps
Outage
Ps(target) Ps Ts

11. ISI Effects
Delay spread exceeding a symbol time causes ISI (self interference).
ISI leads to irreducible error floor
Increasing signal power increases ISI power
Without compensation, requires Ts>>Tm
Severe constraint on data rate (Rs<<Bc) 1 2 3 4 5 Tm Ts

12. Main Takeaway
Narrowband wireless channel characterized by random flat-fading (Bu<<Bc)
Wideband wireless channel characterized by random frequency-selective fading (ISI)
Need to combat flat and frequency-selective fading
Focus of this section of short course

13. Course Outline Overview of Wireless Communications
Path Loss, Shadowing, and Fading Models
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems

14. Adaptive Modulation Change modulation relative to fading
Parameters to adapt:
Constellation size
Transmit power
Instantaneous BER
Symbol time
Coding rate/scheme
Optimization criterion:
Maximize throughput
Minimize average power
Minimize average BER
Only 1-2 degrees of freedom needed for good performance

15. Variable-Rate Variable-Power MQAM
Uncoded
Data Bits
Delay
Point
Selector
M(g)-QAM
Modulator
Power: P(g)
To Channel
g(t)
log2 M(g) Bits
One of the
M(g) Points
BSPK
4-QAM
16-QAM
Goal: Optimize P(g) and M(g) to maximize R=Elog[M(g)]

16. Optimization Formulation
Adaptive MQAM: Rate for fixed BER
Rate and Power Optimization
Same maximization as for capacity, except for K=-1.5/ln(5BER).

17. Optimal Adaptive Schemegk g
Power Adaptation
Spectral Efficiency g
Equals capacity with effective power loss K=-1.5/ln(5BER).

18. Spectral Efficiency Can reduce gap by superimposing a trellis code K2
K=-1.5/ln(5BER)
Can reduce gap by superimposing a trellis code

19. Constellation Restriction
Restrict MD(g) to {M0=0,…,MN}.
Let M(g)=g/gK*, where gK* is later optimized.
Set MD(g) to maxj Mj: Mj  M(g).
Region boundaries are gj=MjgK*, j=0,…,N
Power control maintains target BER M3
M(g)=g/gK*
MD(g) M3 M2 M2 M1 M1
Outage g0
g1=M1gK* g2 g3 g

20. Power Adaptation and Average Rate
Fixed BER within each region
Es/N0=(Mj-1)/K
Channel inversion within a region
Requires power increase when increasing M(g)
Average Rate

21. Efficiency in Rayleigh Fading
Spectral Efficiency (bps/Hz)
Average SNR (dB)

22. Constellation RestrictionM3
M(g)=g/gK*
MD(g) M3 M2 M2 M1 M1
Outage g0
g1=M1gK* g2 g3 g
Power adaptation:
Average rate:

23. Efficiency in Rayleigh Fading
Spectral Efficiency (bps/Hz)
Average SNR (dB)

24. Practical Constraints
Constellation updates: fade region duration
Error floor from estimation error
Estimation error at RX can cause error in absence of noise (e.g. for MQAM)
Estimation error at TX causes mismatch of adaptive power and rate to actual channel
Error floor from delay: let r(t,t)=g(t-t)/g(t).
Feedback delay causes mismatch of adaptive power and rate to actual channel

25. Detailed Formulas Error floor from delay: let =g[i]/g[i-id].
Error floor from estimation error ()
Joint distribution p(,) depends on estimation: hard to obtain. For PSAM the envelope is bi-variate Rayleigh
Error floor from delay: let =g[i]/g[i-id].
p(|) known for Nakagami fading ^ ^

26. Main Points
Adaptive modulation leverages fast fading to improve performance (throughput, BER, etc.)
Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K.
Comes within 5-6 dB of capacity
Discretizing the constellation size results in negligible performance loss.
Constellations cannot be updated faster than 10s to 100s of symbol times: OK for most dopplers.

27. Course Outline Overview of Wireless Communications
Path Loss, Shadowing, and WB/NB Fading
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems

28. Introduction to Diversity
Basic Idea
Send same bits over independent fading paths
Independent fading paths obtained by time, space, frequency, or polarization diversity
Combine paths to mitigate fading effects Tb t
Multiple paths unlikely to fade simultaneously

29. Combining Techniques Selection Combining Maximal Ratio Combining
Fading path with highest gain used
Maximal Ratio Combining
All paths cophased and summed with optimal weighting to maximize combiner output SNR
Equal Gain Combining
All paths cophased and summed with equal weighting
Array/Diversity gain
Array gain is from noise averaging (AWGN and fading)
Diversity gain is change in BER slope (fading)

30. Selection Combining Analysis and Performance
Selection Combining (SC)
Combiner SNR is the maximum of the branch SNRs.
CDF easy to obtain, pdf found by differentiating.
Diminishing returns with number of antennas.
Can get up to about 20 dB of gain.
Outage
Probability

31. MRC and its Performance
With MRC, gS=gi for branch SNRs gi
Optimal technique to maximize output SNR
Yields dB performance gains
Distribution of gS hard to obtain
Standard average BER calculation
Recall
Integral hard to obtain in closed form and often diverges

32. g depends on modulation (a,b)
MGF Approach
Use alternate form of Q function
Define the MGF of gi as
Laplace transform of distribution
Often simple closed form expressions
Rearranging order of integration, we get
g depends on modulation (a,b)

33. EGC and Transmit Diversity
EGQ simpler than MRC
Harder to analyze
Performance about 1 dB worse than MRC
Transmit diversity
With channel knowledge, similar to receiver diversity, same array/diversity gain
Without channel knowledge, can obtain diversity gain through Alamouti scheme: works over 2 consecutive symbols

34. Main Points
Diversity typically entails some penalty in terms of rate, bandwidth, complexity, or size.
Techniques trade complexity for performance.
MRC yields dB gain, SC around 20 dB.
Analysis of MRC simplified using MGF approach
EGC easier to implement than MRC: hard to analyze.
Performance about 1 dB worse than MRC
Transmit diversity can obtain diversity gain even without channel information at transmitter.

35. Course Outline Overview of Wireless Communications
Path Loss, Shadowing, and Fading Models
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems

36. MIMO Systems and their Decomposition
MIMO (multiple-input multiple-output) systems have multiple transmit and receive antennas
Decompose channel through transmit precoding (x=Vx) and receiver shaping (y=UHy)
Leads to RHmin(Mt,Mr) independent channels with gain si (ith singular value of H) and AWGN
Independent channels lead to simple capacity analysis and modulation/demodulation design ~ ~ ~
y=Hx+n
y=S x+n
H=USVH ~ ~ ~
yi=six+ni ~ ~

37. Capacity of MIMO Systems
Depends on what is known at TX and RX and if channel is static or fading
For static channel with perfect CSI at TX and RX, power water-filling over space is optimal:
In fading waterfill over space (based on short-term power constraint) or space-time (long-term constraint)
Without transmitter channel knowledge, capacity metric is based on an outage probability
Pout is the probability that the channel capacity given the channel realization is below the transmission rate.

38. Beamforming Scalar codes with transmit precoding y=uHHvx+uHn
Transforms system into a SISO system with diversity.
Array and diversity gain
Greatly simplifies encoding and decoding.
Channel indicates the best direction to beamform
Need “sufficient” knowledge for optimality of beamforming

39. Optimality of Beamforming
Mean Information
Covariance Information

40. Diversity vs. Multiplexing
Use antennas for multiplexing or diversity
Diversity/Multiplexing tradeoffs (Zheng/Tse)
Error Prone
Best use
depends
on the
application
Low Pe

41. How should antennas be used?
Use antennas for multiplexing:
Use antennas for diversity
High-Rate
Quantizer
ST Code
High Rate
Decoder
Error Prone
Low Pe
Low-Rate
Quantizer
ST Code
High
Diversity
Decoder
Depends on end-to-end metric: Solve by optimizing app. metric

42. MIMO Receiver Design Optimal Receiver: Decision-Feedback receiver
Maximum likelihood: finds input symbol most likely to have resulted in received vector
Exponentially complex # of streams and constellation size
Decision-Feedback receiver
Uses triangular decomposition of channel matrix
Allows sequential detection of symbol at each received antenna, subtracting out previously detected symbols
Sphere Decoder:
Only considers possibilities within a sphere of received symbol.
Space-Time Processing: Encode/decode over time & space

43. Other MIMO Design Issues
Space-time coding:
Map symbols to both space and time via space-time block and convolutional codes.
For OFDM systems, codes are also mapped over frequency tones.
Adaptive techniques:
Fast and accurate channel estimation
Adapt the use of transmit/receive antennas
Adapting modulation and coding.
Limited feedback:
Partial CSI introduces interference in parallel decomp: can use interference cancellation at RX
TX codebook design for quantized channel

44. Main Points
MIMO systems exploit multiple antennas at both TX and RX for capacity and/or diversity gain
With TX and RX channel knowledge, channel decomposes into independent channels
Linear capacity increase with number of TX/RX antennas
With TX/RX channel knowledge, capacity vs. outage is the capacity metric
Beamforming provides diversity gain in direction of dominent channel eigenvectors
Fundamental tradeoff between capacity increase and diversity gain: optimization depends on application

45. Main Points MIMO RX design trades complexity for performance
ML detector optimal; exponentially complex
DF receivers prone to error propagation
Sphere decoders allow performance tradeoff via radius
Space-time processing (i.e. coding) used in most systems
Adaptation requires fast/accurate channel estimation
Limited feedback introduces interference between streams: requires codebook design

46. ISI Countermeasures Equalization Multicarrier Modulation
Signal processing at receiver to eliminate ISI, must balance ISI removal with noise enhancement
Can be very complex at high data rates, and performs poorly in fast-changing channels
Not that common in state-of-the-art wireless systems
Multicarrier Modulation
Break data stream into lower-rate substreams modulated onto narrowband flat-fading subchannels
Spread spectrum
Superimpose a fast (wideband) spreading sequence on top of data sequence, allows resolution for combining or attenuation of multipath components.

47. Course Outline Overview of Wireless Communications
Path Loss, Shadowing, and Fading Models
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems

48. Multicarrier Modulation
R/N bps
QAM
Modulator x
cos(2pf0t)
cos(2pfNt) S
R bps
Serial To
Parallel
Converter
R/N bps
QAM
Modulator
Breaks data into N substreams
Substream modulated onto separate carriers
Substream bandwidth is B/N for B total bandwidth
B/N<Bc implies flat fading on each subcarrier (no ISI)

49. Overlapping Substreams
Can have completely separate subchannels
Required passband bandwidth is B.
OFDM overlaps substreams
Substreams (symbol time TN) separated in RX
Minimum substream separation is BN/(1+b).
Total required bandwidth is B/2 (for TN=1/BN)
B/N f0
fN-1

50. Fading Across Subcarriers
Leads to different BERS
Compensation techniques
Frequency equalization (noise enhancement)
Precoding
Coding across subcarriers
Adaptive loading (power and rate)

51. FFT Implementation of OFDM
Use IFFT at TX to modulate symbols on each subcarrier
Cyclic prefix makes linear convolution of channel circular, so no interference between FFT blocks in RX processing
Reverse structure (with FFT) at receiver x
cos(2pfct)
R bps
QAM
Modulator
Serial To
Parallel
Converter
IFFT X0
XN-1 x0
xN-1
Add cyclic
prefix and
To Serial
Convert
D/A TX x
cos(2pfct)
R bps
QAM
Modulator
FFT Y0
YN-1 y0
yN-1
Remove
cyclic
prefix and
Serial to
Parallel
Convert
A/D
LPF
To Serial RX

52. OFDM Design Issues Timing/frequency offset:
Impacts subcarrier orthogonality; self-interference
Peak-to-Average Power Ratio (PAPR)
Adding subcarrier signals creates large signal peaks
Different fading across subcarriers
Same mitigation techniques as in MCM: Precoding to invert fading, coding across subcarriers, and adaptative loading over time most common
MIMO/OFDM
Apply OFDM across each spatial dimension
Can adapt across space, time, and frequency

53. Main Points OFDM efficiently implemented using FFTs
ISI can be mitigated through equalization, multicarrier modulation (MCM) or spread spectrum
Today, equalizers often too complex or can’t track channel.
MCM splits channel into NB flat fading subchannels
Fading across subcarriers degrades performance.
Compensate through coding or adaptation
OFDM efficiently implemented using FFTs
OFDM challenges are PAPR, timing and frequency offset, and fading across subcarriers

54. Course Outline Overview of Wireless Communications
Path Loss, Shadowing, and WB/NB Fading
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems

55. Introduction to Spread Spectrum
Modulation that increases signal BW
Mitigates or coherently combines ISI
Mitigates narrowband interference/jamming
Hides signal below noise (DSSS) or makes it hard to track (FH)
Also used as a multiple access technique
Two types
Frequency Hopping:
Narrowband signal hopped over wide bandwidth
Direction Sequence:
Modulated signal multiplied by faster chip sequence

56. Direct Sequence Spread Spectrum
Bit sequence modulated by chip sequence
Spreads bandwidth by large factor (K)
Despread by multiplying by sc(t) again (sc(t)=1)
Mitigates ISI and narrowband interference
S(f)
s(t)
sc(t)
Sc(f)
S(f)*Sc(f)
1/Tb
1/Tc Tc
Tb=KTc 2

57. ISI and Interference Rejection
Narrowband Interference Rejection (1/K)
Multipath Rejection (Autocorrelation r(t))
S(f)
I(f)
S(f)*Sc(f)
Info. Signal
Receiver Input
Despread Signal
I(f)*Sc(f)
aS(f)
S(f)
S(f)*Sc(f)[ad(t)+b(t-t)]
brS’(f)
Info. Signal
Receiver Input
Despread Signal

58. Pseudorandom Sequences
Autocorrelation determines ISI rejection
Ideally equals delta function
Maximal Linear Codes
No DC component
Large period (2n-1)Tc
Linear autocorrelation
Recorrelates every period
Short code for acquisition, longer for transmission
In SS receiver, autocorrelation taken over Tb
Poor cross correlation (bad for MAC) 1 -1
2n-1 Tc
-Tc

59. Synchronization
Adjusts delay of sc(t-t) to hit peak value of autocorrelation.
Typically synchronize to LOS component
Complicated by noise, interference, and MP
Synchronization offset of Dt leads to signal attenuation by r(Dt) 1 -1
2n-1 Tc
-Tc
r(Dt) Dt

60. RAKE Receiver Multibranch receiver
Branches synchronized to different MP components
These components can be coherently combined
Use SC, MRC, or EGC x
Demod
y(t)
sc(t) ^ dk
Diversity
Combiner x
Demod
sc(t-iTc) x
Demod
sc(t-NTc)

61. Main Points In DSSS, bit sequence modulated by chip sequence
Spreads bandwidth by large factor (K)
Despread by multiplying by sc(t) again (sc(t)=1)
Mitigates ISI and narrowband interference
ISI mitigation a function of code autocorrelation
Must synchronize to incoming signal
RAKE receiver used to combine multiple paths
S(f)
s(t)
sc(t)
Sc(f)
S(f)*Sc(f)
1/Tb
1/Tc Tc
Tb=KTc 2