Decentralized Power Control for Random Access with Multi-User Detection

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• Decentralized Power Control for Random Access
  with Multi-User Detection

Chongbin Xu, Peng Wang, Sammy Chan, and Li Ping
Department of Electronic Engineering City
University of Hong Kong December 27, 2012
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• Reference
• C. Xu, Li Ping, P. Wang, S. Chan, and X. Lin,
  Decentralized Power Control for Random Access
  with Successive Interference Cancellation to
  appear in IEEE JSAC.

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Overview

• Background and Motivation
• Decentralized Power Control
• Two-User AWGN Channel
• K-User AWGN Channel
• K-User Fading Channel
• Conclusions and Future Work

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Overview

• Background and Motivation
• Decentralized Power Control
• Two-User AWGN Channel
• K-User AWGN Channel
• K-User Fading Channel
• Conclusions and Future Work

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Cognitive Radio with Multiple Primary Users
Consider a cognitive radio with multiple users.
The secondary users can transmit only when the
primary users are silent. The secondary users
access the channel opportunistically whenever a
spectrum hole is detected.
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System Characteristics

1. There is usually no time to establish centralized
   control such as TDMA.
2. Thus random access is necessary.
3. If the spectrum holes are scarce, the secondary
   users may accumulate many un-transmitted packets.
   Thus is highly probable that each user has a
   packet to transmit whenever a spectrum hole is
   detected.
4. This is equivalent to the system with packet
   arrival rate l?1.

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Collision and Throughput
In random-access systems, a collision will occur
if k users transmit their packets
simultaneously. Conventionally, the packets
involved in a collision are assumed to be
unrecoverable. The system throughout is limited
by collision probability.
When kl 1 and k?8, the maximum throughput is
36.8 due to high collision probability
Performance of conventional slotted ALOHA
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How to improve the random
access performance?
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Multi-Packet Reception (MPR)
In many situations, it is possible to recover
some or all packets from a collision. This
phenomenon is captured by the multi-packet
reception (MPR) model. Early work on MPR model
is focused on low-rate CDMA-type applications
12. Both 1 and 2 allow multi-user
detection (MUD). However, they are based on the
traditional ALOHA with only one non-zero
transmission power level. The work in 3 allows
multi-level transmission power but it is limited
to single user detection (SUD) only.
1 S. Ghez, S. Verdu, and S. Schwartz,
Stability properties of slotted ALOHA with
multipacket reception capability, IEEE Trans.
Autom. Control, vol. 33, no. 7, pp. 640-649, Jul.
1988. 2 L. Tong and V. Naware, Signal
processing in random access, IEEE Signal
Process. Mag., vol. 21, no.5, pp. 29-39. Sep.
2004. 3 Y. Leung, Mean power consumption of
artificial power capture in wireless networks,
IEEE Trans. Commun., vol. 45, no. 8, pp. 957-964,
Aug. 1997.
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Performance of MPR in Fading Channel
channel multi-level
aware a SUD
b
The channel aware technique assume only a single
non-zero transmission power level. The
multi-level SUD technique is limited to SUD only.

standard slotted ALOHA
R 1 bit/symbol
a M. H. Ngo, V. Krishnamurthy, and L. Tong,
Optimal channel-aware ALOHA protocol for random
access in WLANs with multi-packet reception and
decentralized channel state information, IEEE
Trans. Signal Process., vol. 56, no. 6, pp.
2575-2588, Jun. 2008. b Y. Leung, Mean power
consumption of artificial power capture in
wireless networks, IEEE Trans. Commun., vol. 45,
no. 8, pp. 957-964, Aug. 1997.
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Serial Interference Cancellation
Multi-user detection (MUD) has the potential to
solve the problem by serial interference
cancellation (SIC) 45. In this case, the
signals of the users that have been correctly
detected are subtracted from the received signal,
and there is no interference to the
others. Assume that the signals of users 1, 2, ,
k-1 have been correctly detected and subtracted
from the received signal. Then the SINR of user k
is given by
from remaining interfering users.
4 T. M. Cover and J. A. Thomas, Elements of
Information Theory, New York Wiley, 2006. 5 D.
Tse and P. Viswanath, Fundamentals of Wireless
Communications, Cambridge Cambridge University
Press, 2005.
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Power Requirement for SIC
The following is an illustration of the power
requirement for a two-user SIC system. We can
recover both packets during an collision.
transmission power
user 1 decoded first
user 2 decoded second
user 1 user 2
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Power Control and Feasible Region
Power control is crucial for MUD. We refer to the
closure of power profiles that can support
reliable transmissions of all users as feasible
power region. The following is an example of the
feasible region for a two-user system with R 1
bit/symbol, ideal coding and SIC.
e1e 2 is the worst-case situation.
E1 (2R 1)N0 E2 (2R 1)(E1 N0)
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Feasible Region
E1 (2R 1)N0 E2 (2R 1)(E1 N0)
When Rgt1, equal power line is not in the feasible
region. If centralized power control is possible,
we can allocate the two users with power inside
the feasible region. In particular, the power
pair (E1, E2) or (E2, E1) leads to the minimum
information theoretic sum-power. However, how to
allocate powers without centralized control?
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Objectives

• We aim to improve the throughput of random-access
  systems by allowing MUD at the receiver and
  decentralize power control at the transmitters.
• We will limit our discussions to the simple
  slotted ALOHA systems. It is expected that the
  results can be extended to systems with more
  sophisticated random access protocols such as
  CSMA.
• We will discuss the decentralized power control
  problems in two-user AWGN channel, K-User AWGN
  channel, and K-User fading Channel.

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Overview

• Background and Motivation
• Decentralized Power Control
• Two-User AWGN Channel
• K-User AWGN Channel
• K-User Fading Channel
• Conclusions and Future Work

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Problem Formulation
To improve the performance by optimizing the
power distribution f(e).
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Discrete Power Levels
We define a discrete set En with 0 E0 lt E1 lt
En lt , where En is the minimum power level
that guarantees successful decoding of one user
when the interference power level from the other
user is En1.
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Theorem 1
The support of the optimal distribution is a
subset of the discrete set En.
This theorem greatly simplifies the optimization
problem.
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Optimization Problem

• Based on Theorem 1, the design problem can be
  formulated as follows.

p0
Notes (1) p0 is the probability that a user
does not transmit. (2) pn2 is the probability
that both users using the same powers, and so
transmission will fail.
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Proof of Theorem 1

• Any transmit power E' ? (E0, E1) is unnecessary
  since E1 is the minimum power for reliable
  transmission without interference.

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Proof of Theorem 1 (Continued)

• Provided that the probability of (E0, E1) is
  zero, any E'? (E1, E2) is also unnecessary since
  E2 is the minimum power for reliable transmission
  when the interfering packet has power E1.

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Proof of Theorem 1 (Continued)

• The above reasoning is generalized to show that
  E'? (En, En1) is unnecessary for any n.

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Example Packet Throughput Comparison
Packet throughput T of a 2-user AWGN channel with
ideal coding. R 1 bit/symbol
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Overview

• Background and Motivation
• Decentralized Power Control
• Two-User AWGN Channel
• K-User AWGN Channel
• K-User Fading Channel
• Conclusions and Future Work

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K-User Systems
To optimize the power distribution in a K-user
system, we need to analyze the general K-user
feasible region, which is a tedious issue and we
will not pursuit it further. Instead, we will
discuss a simple and sub-optimal solution. We
refer to a collision involving k (2 k K)
users as a type-k collision. For the sub-optimal
solution, we will only consider type-2
collisions. In this sub-optimal solution, the
system throughput is given by T T1 T2, where
T1 is the throughput related to transmissions
without collisions and T2 the throughout related
to type-2 collisions.
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Throughput Calculation
Denote by pn the probability of transmission
power taking value En. We calculated T1 and T2 as
follows. For convenience, we assume full load for
all users. The discussions can be extended to the
general loading case. T1 is the throughput
related to transmissions without collisions,
calculated by T2 the throughout related to
type-2 collisions, calculated by Thus, we have

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Throughput Optimization
Repeat
To optimize the throughput of the proposed
scheme, we discretize the value of p0, and solve
the following optimization problem for each
discretized p0.
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Example Performance Comparison
Performance in a 3-user system with ideal coding.
R 1 bit/symbol.
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Example Performance Comparison
Performance comparison among various schemes in
AWGN channels with ideal coding and different K.
R 1 bit/symbol.
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Overview

• Background and Motivation
• Decentralized Power Control
• Two-User AWGN Channel
• K-User AWGN Channel
• K-User Fading Channel
• Conclusions and Future Work

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Fading Channels
Consider a K-user system with fading. The
received signal is given by
where the channel gains of all users,
gk, are assumed to be independent and
identically distributed. Assume that each user k
knows its instantaneous channel gain gk. Our aim
is to optimize the conditional distributions
fT(eTg), with eT the transmit power, such that
the system throughput is maximized. The basic
assumption above is that each user knows its own
channel gain. This can be accomplished in
different ways. A possible general solution is
that the receiver will transmit a beacon signal,
which will be used by the transmitters for
channel estimation.
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Channel-Aware ALOHA
As a reference, a channel-aware ALOHA scheme is
proposed in 6 based on the following special
form of fT(eTg), where
ET is a predetermined power value and p(g) the
transmission probability when the channel gain is
g. In the following, we will show that the
system throughput can be significantly enhanced
by jointly optimizing the transmission power
levels and the related transmission
probabilities.
6 M. H. Ngo, V. Krishnamurthy, and L. Tong,
Optimal channel-aware ALOHA protocol for random
access in WLANs with multi-packet reception and
decentralized channel state information, IEEE
Trans. Signal Process., vol. 56, no. 6, pp.
2575-2588, Jun. 2008.
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Support in Fading Channels
Given g, the support of the optimal conditional
transmit power distribution fT(eTg) is a subset
of E0/g, E1/g, E2/g, ... Let y(g) be the PDF
of g. The received power distribution fR(eR) is
given by With pn available, the throughput
can be calculated similarly as in AWGN channels.
We next discuss the optimization of pn(g)
based on the discretization of g.
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Throughput Optimization in Fading Channels
We discretize the value of g according to M1
thresholds g(m)m 1,, M1 and assume that
the received power distributions when g ? g(m),
g(m1)) are the same, i.e., pn(g) pn(m) for
g(m) g lt g(m1). We optimize pn(m) to
maximize the system throughput.
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Example Performance Comparison
Performance comparison among various schemes in
fading channels with ideal coding and different
K. R 1 bit/symbol.
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MUD for Practically Coded Systems

• We have focused on ideal coding and assume
  successive interference cancellation (SIC) for
  MUD in the previous discussions.
• We now consider practically coded systems, where
  IDMA is a simple scheme for MUD with relatively
  low receiver complexity.

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MUD Feasible Region with LDPC Coding
The following is the feasible region of a (3, 6)
regular LDPC coded systems with iterative
receiver for BER 10-5. Please note the
followings. 1) When powers for both users are
low, near equal powers are not feasible. 2) When
powers for both users are high, equal powers are
feasible.
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Analysis of the Optimal Support
In this case, the support of the optimal power
distribution f() is a subset of E0, E1, , En,
, EQ (for a feasible region with monotonically
increasing boundary function).
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Example LDPC Coding
Performance comparison among various schemes in
fading channels with LDPC coding and different K.
R 1 bit/symbol
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Overview

• Background and Motivation
• Decentralized Power Control
• Two-User AWGN Channel
• K-User AWGN Channel
• K-User Fading Channel
• Conclusions and Future Work

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Conclusions

• We have developed a decentralized power control
  scheme for random access systems with MUD.
• We proved that the support of the optimal power
  distribution f is discrete. Based on this
  finding, we designed f. Numerical results
  demonstrate that significant performance gain can
  be obtained by the proposed scheme.
• We have limited our focus to slotted ALOHA-type
  random access schemes. It is expected that the
  results can be extended to systems with more
  sophisticated random access protocols such as
  CSMA.

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Q A
Thank you!
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Introduction Decentralized Power Control

• We study the decentralized power control for
  ALOHA-type random access scheme with MUD.

d() is the Dirac delta function
Example f1(2) f2(2) f (2) 0.5d (e) 0.5d
(e E1)
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Merging of Probabilities

• For given f, we define a new distribution fn
  constructed as follows.

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Proof of Theorem 1

• The distribution pair (fn1, fn) has a better
  performance than (fn, fn), ?n.
• a sample of fn1 can be equivalently obtained
  through the following steps
• Step 1 Draw a power value e1 according to fn
• Step 2 If En lt e1 lt En1, reduce e1 to En
  otherwise, keep e1 unchanged.
• Denote by white circles Ai power pairs drawn
  from (fn, fn) while black circles Ai'
  represent those after the power change in Step 2,
  which are also samples drawn from (f n1,
  fn).

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Example SUD based Optimization
We also consider optimizing the power
distribution for systems with SUD (denoted by
ML-SUD for multiple-level transmission and SUD).
The conventional slotted ALOHA can be regarded
as a special case of ML-SUD, where the
distribution is optimized over two levels E0 0
and E1 only.
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Optimization Problem

• Based on Theorem 1, the design problem can be
  formulated as follows.

Notes (1) p0 is the probability that a user
does not transmit. (2) pn2 is the probability
that both users using the same powers, and so
transmission will fail.
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Proof of Theorem 1
The power change leads to the following three
possibilities. a) A1 fails while A1' succeeds.
Such events result in increased throughput b)
A2 succeeds while A2' fails. Such events cannot
happen as fn(e2) 0, ?e2?(En1, En) c) In all
other situations, both power pairs fail or
succeed simultaneously.
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Example Power Constraint
System throughput of a four-user Rayleigh fading
channel with ideal coding under different power
constraints. R 1 bit/symbol.
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Example Power Distributions
The received power distributions of the ML-SIC
scheme in the previous figure.
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K-Users Slotted ALOHA Systems
Denote by pi the probability of transmission
power taking value Ei. We calculated T1 and T2 as
follows. T1 is the throughput related to
transmissions without collisions. T2 the
throughout related to type-2 collisions.
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Optimization for Type-2 Collisions
Repeat
To optimize the throughput of the proposed
scheme, we discretize the value of p0, and solve
the following optimization problem for each
discretized p0.
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MUD Feasible Region with LDPC Coding
The feasible region of a (3, 6) regular LDPC
coded systems with iterative receiver.
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Example LDPC Coding
Performance comparison among various schemes in
fading channels with LDPC coding and iterative
receiver.
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Power Requirement for SIC
With SIC, its possible to recover two or more
packets involved in a collision even for
high-rate transmissions. For example, if the SINR
threshold for successful detection is given by
SINRth, the following transmit power profile can
lead to successful detection of all users for MUD.
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