Downlink Channel Assignment
and Power Control for
Cognitive Radio Networks
Anh Tuan Hoang, Member, IEEE
Ying-Chang Liang, Senior Member, IEEE
Institute for Infocomm Research (I2R),
Singapore
IEEE Transactions on
Wireless Communications 2008
1
Outline






Introduction
Problem Definition
Channel/Power Allocation with Global
Knowledge of Active CPEs
Channel/Power Allocation with Local
Knowledge of Active CPEs
Results
Conclusions
2
Cognitive Radio Networks

The concept of opportunistic spectrum access allows
secondary cognitive radio networks to opportunistically
exploit the under-utilized spectrum



The overall spectrum utilization can be improved
Transmission from cognitive nodes can cause harmful
interference to primary users of the spectrum
Two important design criteria for cognitive radio
networks


maximize the spectrum utilization
minimize interference caused to primary users
3
Environment

We consider a cognitive radio network that consists of
multiple cells




Within each cell, there is a base station (BS) supporting a set of
customer premise equipments (CPEs)
Each CPE can be either active or idle and a BS needs exactly one
channel to support each active CPE
The spectrum of interest is divided into a set of multiple
orthogonal channels using FDMA
We assume that the channel usage pattern of the PUs is
fairly static over time

cognitive radio network can carry out primary-user detection and
thereby avoiding interfering with PU’s operation
4
Goal and Constraints

The objective is to maximize the number of active CPEs
that can be supported, subject to the following conditions:


R1: The total amount of interference caused by all cognitive
transmissions to each PU must not exceed a predefined threshold.
R2: For each supported CPE, the received signal to interference
plus noise ratio (SINR) must be above a predefined threshold
5
System Model

Model



K channels
M primary users (PUs)
N CPEs across B cells



BS needs exactly one channel to support each active CPE
only consider downlink scenario (BSs to CPEs)
CPE is active with probability pa
6
Notations
7
Operational Requirements (1)

SINR requirement for CPEs

For a given channel c, the SINR at CPE i can be calculated by

No is the noise

is the total interference caused by all primary transmissions on
channel c to CPE i
For reliable transmission toward CPE i


can be the minimum SINR required to achieve a certain bit
error rate (BER) performance at each CPE
8
Operational Requirements (2)

Protecting Primary Users

For each PU, the total interference from all
opportunistic transmissions does not exceed a
predefined threshold ζ
9
Joint Channel Assignment and
Power Control Schemes (1)

Let A be an N × K channel assignment matrix where

Let P be an N × K power control matrix where
10
Joint Channel Assignment and
Power Control Schemes (2)
11
Feasibility Check (1)

Feasibility

There exists a vector of positive transmit power levels
such that



all the SINR constraints of the m CPEs are met
the interference caused to PUs operating on channel c does
not exceed the acceptable threshold
Because each BS can support at most one CPE on each
given channel, we must have m CPEs i1, i2, ..., im
associated with different BSs
12
Feasibility Check (2)

Define an m × 1 vector Uc and an m × m matrix Fc

The SINR constraints of m CPEs i1, i2, ..., im can be written compactly
as
where I is the m × m identity matrix

(
c
ii
 ( No   
c
i
c
i
N
G p
No   
c
i
G P
j 1, j  i
c
ij
c
j

p 
c
i
N
G P )
j 1, j  i
c
ii
G
c
ij

c
j
p 
c
i
N
G P
j 1, j  i
c
ii
G
c
ij
c
j

 ( N o   ic )
Giic
)
13
Feasibility Check (3)


From the Perron-Frobenious theorem ([8], [11], [27],
[28]), (7) has a positive component-wise solution Pc if
and only if the maximum eigenvalue of Fc is less than one
The Pareto-optimal transmit power vector is
[ 8 ] J. Zander, “Performance of optimum transmitter power control in cellular radio systems,”
IEEE Trans. Veh. Technol. 1992.
[11] D. Mitra, “An asynchronous distributed algorithm for power control in cellular radio
systems,” in Proc. 4th WINLAB Workshop on Third Generation Wireless Information
Networks, Rutgers University, New Brunswick, NJ, Oct. 1993.
[27] F. R. Gantmacher, The Theory of Matrices. Chelsea Publishing Company, 1959.
[28] E. Seneta, Non-Negative Matrices. New York: John Wiley & Sons, 1973.
14
Two-step Feasibility Check
Algorithm

Step 1


Check if the maximum eigenvalue of Fc defined in (6) is less than
one.
 If not, the assignment is not feasible
 otherwise, continue at Step 2
Step 2


Using (8), calculate the Pareto-optimal transmit power vector Pc∗
check if Pc∗ satisfies the constraints for protecting PUs in (3) and
the maximum power constraints, i.e. Pc∗ ≤ Pmax
 If yes, conclude that the assignment is feasible and Pc∗ is the
power vector to use
 Otherwise, the assignment is not feasible
15
Channel/Power Allocation with Global
Knowledge of Active CPEs (1)


Without loss of generality, we assume that all N CPEs in
the network are active
The problem of maximizing the number of CPEs served
can be formulated as the following mixed-integer linear
programming (MILP)
16
Channel/Power Allocation with Global
Knowledge of Active CPEs (2)
17
Dynamic Interference Graph
Allocation (DIGA) (1)

Construct interference graphs


Vertex i represents CPE i
Two vertices i and j will be connected by an edge if and only if
CPE i and j cannot be simultaneously supported on channel c


employ the Two-Step Feasibility Check to determine the existence of
an edge between a pair of vertices
Procedure


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start with no CPEs being assigned any channel
allocate a channel to one CPE at a time, until either all CPEs are
served, or there is no more feasible assignment
At each step, construct an interference graph that represents the
interference between pairs of unserved CPEs

This interference graph must also take into account the aggregated
interference caused by transmissions that have been allocated
channels in previous steps
18
Dynamic Interference Graph
Allocation (DIGA) (2)

At each step, given the prior channel allocation matrix A,
for each unserved CPE i, we calculate its degree
corresponding to channel c as follows



D(i, c, A)= ∞ if it is not feasible to assign channel c to CPE i
while supporting all prior assignments
 The feasibility can be checked using the two-step procedure
If it is feasible to assign channel c to CPE i, then D(i, c, A) is the
total number of unserved CPEs that can not be assigned channel
c anymore when this channel is assigned to CPE i
The algorithm then picks a CPE-channel pair [i∗, c∗] that
minimizes D(i, c, A) and assigns channel c∗ to CPE i∗
19
Dynamic Interference Graph
Allocation (DIGA) (3)
20
Other Algorithms

Power Control Scheduling Algorithm (PCSA) [18]




An interference graph is first constructed
The problem is then converted into the problem of finding a
maximum independent set of the interference graph
The interference graph cannot account for the aggregated
interference effect, a clean-up step is needed at the end to
remove some links and make the set feasible
Minimum Incremental Power Allocation (MIPA) [19]

Allocate subchannels to interfering links so that their rate
requirements are met while the total transmit power is
minimized
[18] A. Behzad and I. Rubin, “Multiple access protocol for power-controlled wireless access
nets,” IEEE Trans. Mobile Comput., vol. 3, no. 4, pp.307–316, Oct.-Dec. 2004
[19] G. Kulkarni, S. Adlakha, and M. Srivastava, “Subcarrier allocation and bit loading
algorithms for OFDMA-based wireless networks,” IEEE Trans. Mobile Comput 2005.
21
Channel/Power Allocation with Local
Knowledge of Active CPEs


Assume a centralized power controller to
coordinate transmit powers of all BSs to protect
PUs
Two-Phase Resource Allocation (TPRA) scheme

Phase 1 - Global Allocation


channels and transmit powers are allocated to BSs so that
the interference caused to each PU is below a tolerable
threshold
at the same time, we aim to cover as many CPEs as possible

do not care whether a CPE is active or idle
22
Phase 1 - Global Allocation (1)

Intuition for allocation decision making



A BS that is near any PU receiving on channel c should transmit
at low power to reduce interference
A BS faraway from all PUs receiving on channel c can transmit
at higher power
The K channels are processed one at a time

For channel c, define

denotes the channel gain from base station b to primary user
p on channel c
23
Phase 1 - Global Allocation (2)

Allocation procedure

Sort the base stations in the ascending order of


The BSs will be processed one at a time in this order
For base station bn, determine a particular CPE in that
bn should cover



Given the set
of CPEs being covered by
base stations
Let
be the set of all CPEs i in the cell of bn such that
is feasible on channel c
Then in is the CPE that has the weakest channel gain from
bn
24
Phase 1 - Global Allocation (3)

After processing all BSs, using (8), determine the
transmit power to serve each of these CPEs


i.e.
Finally, based on
coverage matrix C

, determine the N × K
where C(i, c)=1 means CPE i can be served by the
corresponding BS on channel c
25
Phase 2 - Local Allocation (1)

Based on the coverage matrix C obtained in Phase 1,
channel allocation can be carried out within each cell,
independent to what happens in the rest


First, determine all active CPEs in the cell
Next, form a bipartite graph
 represent the set of active CPEs as a set of vertices which are
connected to another set of vertices representing the available
channels


an edge exists between CPE i and channel c if and only if C(i, c)=1
Maximizing the number of active CPEs served is equivalent to
maximizing the number of disjoint edges in the newly-formed
bipartite graph
 This is the maximal bipartite matching problem
26
Phase 2 - Local Allocation (2)
27
Phase 2 - Local Allocation (3)

Berge’s Theorem: A matching is maximum if and only if
there is no more augmenting path



Step 1: Start with the empty match
 For a particular match, if an edge is in the corresponding set of
disjoint edges, then we say the edge is occupied, otherwise, the
edge is free
Step 2: Find an augmenting path for the current match
 The edges within the path must alternate between occupied and
free
 The path must start and end with free edges
 If there is no augmenting path, the current match is maximal
Step 3: Flip the augmenting path found in Step 2
 Change free edges to occupied and occupied edges to free to get a
better matching
 After flipping, the number of matches will be increased by 1
28
 Go back to Step 2
Simulation Environment

Square area: 1000× 1000 m2



Total number of




divided into B adjacent cells, B =4 or 9
a BS is deployed at the center of each cell
CPEs: N = 100
 active with probability pa = 0.1 or 0.2
PUs: M = 5 ~ 20
Channels: K = 8
Power



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maximum transmit power of BS: Pmax =50 mW
noise: No = −100 dBm
required SINR for each CPE: 15 dB
maximum tolerable interference for each PU: −110 dBm
29
Performance of Different Schemes
with Global Knowledge (1)
4 BS
pa = 0.1
pa = 0.2
30
Performance of Different Schemes
with Global Knowledge (2)
9 BS
pa = 0.1
pa = 0.2
31
Percentage of CPEs being
Covered
32
Performance of Different Schemes
with Local Knowledge
4 BS
pa = 0.1
pa = 0.2
33
Conclusions

A control framework is formulated to protect primary
users from excessive interference and to guarantee
reliable communications for cognitive nodes

Global knowledge of active subscribers is available



formulate the optimization problem as a mixed-integer linear
programming
propose a suboptimal allocation scheme based on a dynamic
interference graph
Only local knowledge of active subscribers is available

propose a scalable two-phase channel/power allocation scheme
that achieves good performance
34