Coding

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Multiuser Diversity in Delay-Limited Cellular
Systems
Ralf R. Müller ralf_at_iet.ntnu.no Department of
Electronics Telecommunications Norwegian
University of Science Technology, Trondheim
Giuseppe Caire Raymond Knopp caire,knopp_at_eurec
om.fr Institut Eurècom Sophia-Antipolis, France
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Disclaimer

• This is NOT a talk on fair scheduling of users.

Here

• Fairness is not enough.
• Each user has to get their message
  instantaneously with probability
  going to 1.

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Ergodic vs. Delay-Limited Capacity
Two extreme cases of fading channels

1. The channel changes very often within a single
   codeword.
2. The channel is constant within a single codeword.

Ergodic capacity
Delay-Limited capacity
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Delay-Limited Capacity for a Single User
Let the fading d be known at both transmitter and
receiver, AWGN channel with energy per symbol E
and noise density N0
if E d-2 exists, C gt 0
and f (d) d-2.
C 0 for Rayleigh fading.
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Delay-Limited Capacity for Many Users
The result is given as a multi-dimensional
optimization problem in
Stephen V. Hanly, David N.C. TseMultiaccess
fading channels. Part II Delay-limited
capacitiesIEEE Trans. Inform. Theory, vol.
44, no. 7, pp. 2816 - 2831, Nov. 1998.  
Can we obtain a gain by multiuser diversity
without any drawback in quality of service, e.g.
no additional delay?
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Gaussian Multiple-Access Channel without Fading





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Dual Representation of GMAC without Fading



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Transmit Power vs. Receive Power

Rescaling of axis in power region
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Transmit Power vs. Receive Power

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GMAC with Fading
Let the attenuations be random from codeword to
codeword.
if E d-2 exists, C gt 0
C 0 for Rayleigh fading.
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Single User vs. Infinite Users
Single User
Infinite Users
for all rates
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Signal Attenuation

• Path Loss di2 ri-4
• no shadowing no Rayleigh fading

r3
r1
r2
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Delay-Limited Capacity for Path Loss
spec. efficiency bits/sec/Hz
inf. orth. users
infinite users
single user
dB
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• There is a gain by multiuser diversity without
  any drawback in quality of service,

if E d-2 exists.
Without constraints to orthogonal separation of
users, the gain is greater.
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Multiuser Diversity Frequency Diversity
Let each user have M parallel channels.
For Rayleigh fading, DL-capacity is positive if M
gt 1.
Theorem 1 Subject to some technical conditions
on the rates and the fading, each user uses only
that channel of theirs which has the best
propagation conditions, as the number of users
approaches infinity.
Remark 1 Theorem 1 does not hold for a finite
number of users, in general.
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Multiuser Diversity Frequency Diversity
d maxd1 d2 dM
Corollary 1 Subject to some technical conditions
on the rates and the fading, frequency diversity
only re-shapes the fading distribution, as the
number of users approaches infinity.
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Signal Attenuation

• Path Loss di2 ri -4
• 2nd order
• frequency
• diversity
• no shadowing

Rayleigh fading
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Delay-Limited Capacity
without Rayleigh fading
with Rayleigh fading
orthogonal limit
single user
spec. efficiency bits/sec/Hz
channel capacity
The mean fading changes as well.
dB

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Uplink vs. Downlink
Theorem 2 Thanks to multiple-access broadcast
duality on Gaussian channels, all results for
multiple-access channels and transmit power, also
hold for the Gaussian broadcast channel.
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Cellular Systems
Cellular systems are interference limited. You
want to minimize interference into other cells
instead of transmit power.
Corollary 2 Subject to some technical conditions
on the rates and the fading, minimizing
interference power onto base stations of other
cells instead of transmit power is equivalent to
re-shaping the fading distribution as the number
of users approaches infinity.
Open question Does MAC broadcast duality apply
here?
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Cellular Systems (contd)
Consider a linear cellular system w.l.o.g. You
want to minimize interference into other cells
instead of transmit power.
Reuse factor 2
Large number of users makes interference
symmetric.
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Delay-Limited Capacity of Cellular System
Spectral effciency can be doubled.
reuse 2
spec. efficiency bits/sec/Hz
capacity
reuse 3
reuse 4
reuse 2
reuse 3
reuse 4
single user
path loss exponent
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Coming Soon ...

• Hexagonal cells ... Rayleigh fading

Just one more thing
path loss exponent 2
with
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