Transcript Wireless Communications Research Overview

EE359 – Lecture 8 Outline

Capacity of Flat-Fading Channels
 Fading Known at TX and RX
 Optimal Rate and Power Adaptation
 Channel Inversion with Fixed Rate

Capacity of Freq.-Selective Fading Channels

Digital Modulation Review
 Geometric Signal Representation
 Passband Modulation Tradeoffs
 Linear Modulation Analysis
Review of Last Lecture

Multipath Intensity Profile

Doppler Power Spectrum

Capacity of Flat-Fading Channels
 Theoretical Upper Bound on Data Rate
 Unknown Fading: Worst Case Capacity
 Fading
Statistics Known: Capacity Hard to Find
 Fading Known at Receiver Only

C   B log 2 1    p( )d  B log 2 (1   )
0
Fading Known at
Transmitter and Receiver

For fixed transmit power, same as with
only receiver knowledge of fading

Transmit power S() can also be adapted

Leads to optimization problem
max
C
S ( ) : E[ S ( )]  S

 S ( ) 
0 B log 2 1  S  p( )d
Optimal Adaptive Scheme

S ( )  

S  0
1
0

Waterfilling
Power Adaptation
1

1

 0
else
Capacity

 
R
  log 2   p( )d .
B 0
0 
0
1

0

Channel Inversion

Fading inverted to maintain constant SNR

Simplifies design (fixed rate)

Greatly reduces capacity
 Capacity

is zero in Rayleigh fading
Truncated inversion
 Invert channel above cutoff fade depth
 Constant SNR (fixed rate) above cutoff
 Cutoff greatly increases capacity

Close to optimal
Frequency Selective
Fading Channels
For TI channels, capacity achieved by
water-filling in frequency
 Capacity of time-varying channel unknown
 Approximate by dividing into subbands

 Each
subband has width Bc (like MCM).
 Independent fading in each subband
 Capacity is the sum of subband capacities
1/|H(f)|2
P
Bc
f
Review of Digital Modulation:
Geometric Signal Representation

Transmit symbol mi{m1,…mM}
 Want
to minimize Pe=p(decode mj|mi sent)

mi corresponds to signal si(t), 0tT

Represent via orthonormal basis functions:
 si(t) characterized by vector si=(si1, si2,…, siN)
s3
s2
 Vector space analysis
s1
N
si (t )   sij j (t )
j 1
s4
d
s8
s5
s6
s7
Decision Regions and
Error Probability

ML receiver decodes si closest to x
Signal Constellation
s3
 Assign decision regions:
s2
s1
 Zi=(x:|x-si|<|x-sj| all j)
Z3 Z2
x
Z1
Z4
s
 xZim=m
4
i
^
Z8
Z5
 Pe based on noise distribution s
s8
Z
Z
7
5
6
2
s6
s7 d
Ps  ( M 1)Q d min
/( 2 N 0 )
min


Passband Modulation Tradeoffs

Want high rates, high spectral efficiency, high power
efficiency, robust to channel, cheap.
Our focus

Linear Modulation (MPAM,MPSK,MQAM)




Information encoded in amplitude/phase
More spectrally efficient than nonlinear
Issues: differential encoding, pulse shaping, bit mapping.
Nonlinear modulation (FSK)




Information encoded in frequency
Continuous phase (CPFSK) special case of FM
Bandwidth determined by Carson’s rule (pulse shaping)
More robust to channel and amplifier nonlinearities
Linear Modulation

Bits encoded in carrier amplitude or phase
s(t )   an g (t  nTs ) cos( 2f c t )   bn g (t  nTs ) sin( 2f c t )
n
n
 Pulse shape g(t) typically Nyquist
 Signal constellation defined by (an,bn) pairs
 Can be differentially encoded
 M values for (an,bn)log2 M bits per symbol

Ps depends on
 Minimum distance dmin (depends on s)
 # of nearest neighbors aM
 Approximate expression:
P a Q
s
M

M s

Main Points

Capacity with TX/RX knowledge: variable-rate
variable-power transmission (water filling) optimal


Almost same capacity as with RX knowledge only
This result may not carry over to practical schemes

Channel inversion practical, but should truncate

Capacity of ISI channel obtained by breaking
channel into subbands (similar to OFDM)

Linear modulation more spectrally efficient but less
robust than nonlinear modulation


Pe depends on constellation minimum distance
Pe in AWGN approximated by

Ps  a M Q  M  s
