Distributed power and admission control

Distributed Admission and Power Control forCognitive Radios in Spectrum Underlay Networks John George Wireless Intelligent Networks Center WINC Nile University, Cairo, Egypt john.tadrous

Distributed Admission and Power Control for

Cognitive Radios in Spectrum Underlay Networks

John George

Wireless Intelligent Networks

Center (WINC) Nile University, Cairo, Egypt

john.tadrous@nileu.edu.eg

Ahmed Sultan

Wireless Intelligent Networks Center (WINC) Nile University, Cairo, Egypt asultan@nileuniversity.edu.eg

Mohammed Nafie

Wireless Intelligent Networks Center (WINC) Nile University, Cairo, Egypt mnafie@nileuniversity.edu.eg

Abstract—In this paper we investigate admission control and power

allocation for cognitive radios in an underlay network We consider the

problem of maximizing the number of supported secondary links under

their minimum QoS requirements without violating the maximum

toler-able interference on primary receivers in a cellular network An optimal

solution to our problem is shown in previous works to be NP-hard We

propose an efficient distributed algorithm with reasonable complexity that

provides results close to the optimum solution without requiring neither

a large amount of signaling nor a wide range of information about the

system parameters Our algorithm is compared with previously proposed

algorithms to demonstrate its relative efficiency.1

I INTRODUCTION

Recent studies by the FCC show that the current utilization

of some spectrum bands is as low as 15% [1] On the other

hand, it is commonly believed that there is a crisis of spectrum

availability at frequencies that can be economically used for

wireless communications via fixed spectrum allocation This

misconception is strengthened by a look at the FCC frequency

chart [2] that indicates multiple allocations over all of the

frequency bands In other words, there is fierce competition

for the use of spectra, especially in the bands below 3 GHz

while in the same time most of these bands suffer from

underutilization Therefore, there is an increasing interest in

developing new efficient techniques for spectrum management

and sharing as in [3] which consequently motivates the concept

of cognitive radios [4] and dynamic spectrum access

Cognitive radios are frequency agile devices that can sense

the spectrum, identify vacant frequency chunks in licensed

bands, and make use of them as long as no harmful

interfer-ence is produced on primary users Moreover, cognitive radios

have to evacuate these frequency chunks upon the arrival of

primary users or when the interference produced by cognitive

radios on primary users exceeds certain limit A challenging

question arises as how to provide Quality of Service (QoS)

for cognitive radios while preventing them from violating the

maximum tolerable interference on primary receivers at the

same time

The operation of cognitive radios in dynamic spectrum

access environment is divided into two paradigms, spectrum

overlay and spectrum underlay [5] In spectrum overlay,

cog-nitive radios are allowed only to access the spectrum chunks

1 This work was partially supported by the Egyptian National

Telecommu-nications Regulatory Authority

that are completely empty of any primary operation In this case, cognitive radios have to sense the spectrum first to ensure that there is a vacant spectrum chunk to be accessed by them

In spectrum underlay systems, cognitive radios are allowed

to share underutilized frequency bands besides the primary users, such that they do not violate the interference temperature declared by primary receivers Hence interference constraints are placed on cognitive radios in the spectrum underlay model

A lot of work has been done to solve the problem of admission control and power allocation for cognitive radios with QoS and interference constraints [6]-[9]

In [6], a centralized user removal algorithm based on tree-pruning technique was proposed, the proposed algorithm leads

to optimal supported set of secondary links but with extensive computations Moreover, a distributed game theoretic approach based on sequential play was introduced, but the sequential play converges to local optimal solutions In [7], a distributed algorithm was introduced that aims at minimization of the total transmit power by primary and secondary links However, the primary users were allowed to increase their transmission power without bounds In order to maximize the number of admitted secondary links under QoS and interference con-straints, the authors of [8] developed two centralized removal

algorithms namely I-SMIRA and I-SMART(R) However, the

removal criteria in both algorithms require the knowledge of instantaneous channel gains between system nodes to be kept

at a central controller which is practically difficult In [9], joint admission control and rate/power allocation for secondary links was investigated while only mean channel gains are available However, the authors do not show how far their algorithm from the optimal solution

In this paper we propose a distributed dynamic algorithm for admission and power allocation for cognitive radios that aims

at maximizing the number of admitted secondary links with their target QoS, without violating the interference constraints allowable by primary receivers in an underlay network Our proposed algorithm can be implemented by secondary users alone without the need of a dedicated controller Moreover, the secondary users do not have to keep track of the instantaneous channel gains of the whole system if they can measure their own signal-to-interference-and-noise-ratio (SINR) locally The algorithm is performed online by the secondary links so that it

Fig 1 7-cell system model

can account for any dynamic changes of the system parameters

in an adequate time (like interference constraints on primary

receivers, number of secondary links currently in the system,

variation of channel conditions, etc.) Our simulations show

that the proposed algorithm for admission of secondary links

yields results that are close to the NP-hard optimum solution,

but with reduced complexity

The rest of this paper is organized as follows The system

model is described in Section II We formulate the admission

control and power allocation problem in Section III Our

proposed solution and related implementation issues are given

in Section IV Section V presents the numerical results Our

work is concluded in Section VI

II SYSTEMMODEL

We consider a spectrum underlay model where secondary

users can share the same frequency band with primary users In

this model we focus on the uplink transmission from primary

users toward their base stations (BS), whereas secondary users

are communicating with each other in an ad-hoc fashion

The decisions for admission and power control for secondary

links are applied in a distributed manner in which only one

secondary link is allowed to take a decision about its transmit

power at a time, while other secondary links remain in their

previous states That is, decisions are taken in a round robin

fashion (RR) A system with seven cells is shown in Fig 1

A Primary Network Model:

Our system model is very close to those in [8] and [9] so we

use almost the same notations for the system description For

the given system model there are M cells of primary network,

each cell has one BS in its center Each cell j has K j , j =

1, 2, · · · , M, primary users transmitting in the uplink direction.

The SINR of the primary link i is measured at BS j as follows:

μ (p) j = P G (p) P r

(1 + f)(K j − 1)P r + η j + N0, j = 1, 2, · · · , M

(1)

where, P G (p) = B/R is the processing gain in case that

primary transmitters are employing spread spectrum technique,

B and R are the primary system bandwidth and transmission

rate respectively, f is the other-cell interference factor, and N0

is the background noise power We assume that the received

power, P r , from a primary transmitter to BS j is fixed at this

BS The transmitted power from a primary user i to its BS j

is given by,

g j,i (u) , i = 1, 2, · · · , K j (2)

where, g (u) j,i is the uplink channel gain between the primary

transmitter i and its intended BS j The interference, η j,

produced by secondary transmitters on BS j is,

N



i=1

g j,i (p) P i , j = 1, 2, · · · , M (3)

Where N is the number of secondary transmitters, P i is the

transmission power of transmitter of secondary link i, and g (p) j,i

is the channel gain from the transmitter of secondary link i to primary BS j.

B Secondary Network Model:

We assume that there are N secondary link pairs, each

com-prising a transmitter and one intended receiver The secondary links are distributed uniformly over the primary network area

of coverage and are communicating in an ad-hoc mode We denote the interference produced by all primary transmitters

on the secondary link i by N i

K



j=1

g (su) i,j P j (u) , i = 1, 2, · · · , N (4)

where K =M j=1 K jis the total number of primary

transmit-ters in the system, and g (su) i,j is the channel gain from primary

transmitter j to the receiver of secondary link i Thus, the SINR at the secondary link i is

μ i = P G i

g i,i (s) P i

N

j=1,j=i g i,j (s) P j + N i + N0

, i = 1, 2, · · · , N

(5)

where P G i = B

R i is the processing gain of secondary link i,

R i is the transmission rate of secondary link i and g j,i (s)is the

channel gain between the transmitter of secondary link j to the receiver of secondary link i In underlay models, spread

spectrum techniques are sometimes applied by secondary links

so that their transmission power can be regarded as noise

at primary receivers [5] However, our proposed algorithm is applicable to any system where users share the same operating band, i.e., spread spectrum techniques are not necessary

III PROBLEMFORMULATION

The admission control and power allocation technique should admit and allocate power for a set of secondary links that fulfills the following conditions First, the interference

produced by secondary links on primary receivers should not

violate a certain limit The SINR of any primary transmitter

is required to be higher than certain threshold γ (p), i.e,

μ (p) j ≥ γ (p) , j = 1, 2, · · · , M (6) Inequality (6) can be rewritten as,

(1 + f)(K j − 1)P r + η j + N0 ≥ γ (p) (7)

Therefore,

I j

The interference constraints can then be written as,

η j ≤ I j , j = 1, 2, · · · , M (9)

where I j is the maximum tolerable interference by primary

receiver (BS) j in order to keep the constraint of (6) satisfied.

Second, since SINR reflects the amount of QoS gained

by each secondary link, the SINR at the receiver of each

secondary link i is required to be greater than a certain target

SINR That is,

μ i ≥ γ i , i = 1, 2, · · · , N (10)

where γ i is the target SINR for secondary link i Note that

each secondary link cannot increase its transmission power

beyond a certain level,

i , i = 1, 2, · · · , N (11) The set of the admitted secondary links is called the active

set and denoted by ℵ Our problem can be defined as the

following optimization problem,

maximize |ℵ|

subject to η j ≤ I j , j = 1, 2, · · · , M

μ i ≥ γ i , i = 1, 2, · · · , N

i , i = 1, 2, · · · , N

(12)

where |ℵ| denotes the cardinality of the active set This

optimization problem is proved in [8] to be NP-hard when

all of the requesting secondary links cannot be supported to

operate concurrently under the given constraints

IV ONLINEDISTRIBUTEDALGORITHM

A Distributed Power Control:

Most of the relevant proposals use the distributed

con-strained power control (DCPC) algorithm [10] as an efficient

power control algorithm for spectrum underlay models

[6]-[8],[11] In fact, DCPC can be applied distributively or in

a central controller that has complete knowledge of all

in-stantaneous channel gains and QoS requirements of all users

The DCPC algorithm aims at allocating power to links such

that the required SINR for each secondary link is achieved

at the minimum possible transmission power, provided that

all links can be supported at their QoS requirements DCPC

iteratively allocates power to secondary link i synchronously

or asynchronously with other links according to the following formula,

P i (t + Δt) = min



P i max , P i (t)γ i

μ i (t)

, i = 1, 2, , N (13)

where, P i (t) is the power of secondary link i at interval t, and P i (t + Δt) is the power of the secondary link i at the

next time interval As proved in [10] the power updates of all of secondary links will converge to a fixed power vector

P(s), regardless of the values of the initial powers Each

element in P(s) denotes the steady state power of one of

the secondary transmitters If the fixed power vector P(s) is

found to contain any elements with value P max, then that means the current set of links cannot be supported at its QoS

requirements Alternatively, if P(s) does not contain any P max

value, then it means the current set of requesting links can be supported at exactly their target QoS requirements Note that, the fixed power vector does not include any information about the interference on primary BSs

B Generic Description of the Algorithm

Our algorithm uses asynchronous DCPC, specifically the power updates are performed in a round robin fashion (RR-DCPC), asynchronous DCPC converges to a fixed power vector faster than synchronous DCPC [11] We divide the current set of requesting secondary links into two sets: the first one is called the active set that contains all the links with transmission power greater than 0, and denoted by ℵ.

Whereas the second set is called the inactive set that contains all the links with transmission power set to 0, and denoted

algorithm as follows, 1) The secondary links start with certain initial power

vec-tor Pinit = (P init

Pmax, and all of them are kept in the active set ℵ

while the set  is initially empty, i.e  = {} and

ℵ = {1, 2, · · · , N}.

2) In a round robin (RR) fashion one secondary link updates its transmission power according to a formula that resembles (13), that is,

P j (LN+j) = min

(14)

where L is an integer and j is the current link performing its power update and the term LN + j is the index

of the current power update, while other secondary links maintain their transmission power unchanged Sec-ondary links are assumed to perform the power updates based on the local measurements of their SINR i.e., they are not required to keep track of channel gains

3) The power updates of step 2 will continue till one of the following three events occurs:

a) Event 1: The system with the active set ℵ

con-verges to a fixed power vector P(s), that does not violate any of constraints in (12) with the secondary links inℵ admitted.

b) Event 2: During the power updates the interference

constraint on a primary BS is violated Conse-quently, the BS broadcasts a warning signal that

it has interference larger than the tolerable level

c) Event 3: When a secondary link j is updating its

transmission power according to (14), it finds that

P j (LN +j) = P max

j implying that this link would

not reach it’s target QoS

4) The system should handle the occurrence of any of

events 2 or 3 efficiently and continues from step 2 until

convergence at event 1 with the admitted links being in

setℵ.

Our distributed algorithm should take an action once any

violation of constraints is detected by either of events 2

or 3 even if RR-DCPC has not completely converged as it

might be not efficient to wait for the convergence of

RR-DCPC while interference constraints on primary receivers are

being violated Hence, after any violation of constraints we

deactivate one secondary link as will be described below

Upon the detection of the infeasibility of the current inactive

set (after the convergence of the DCPC), [8] and [11] proposed

removal of at least one link at a time followed by DCPC

again The efficiency of this kind of handling the infeasibility

events basically depends on the removal criterion used and

the number of links removed at a time Removal criteria

like those in I-SMIRA and I-SMART(R) require information

about all of system parameters be kept at a central controller

e.g., instantaneous channel gains between all nodes, QoS

requirements of secondary links, current allowable level of

interference on primary BSs

Instead, we suggest use of a simple criterion for selecting

one secondary link to be deactivated (to join the set ).

However, the secondary links in are not completely removed

from the system, i.e., they can be reactivated Reactivating

links from the set  can compensate the inefficiency of the

selection criterion by allowing different sets of requesting

secondary links to check the possibility of being admitted

Since it is proved in [10] that the asynchronous power

updates like those used in (14) always converge to a fixed

power vector regardless of the values of the initial power

vector, then fixed power vector P(s) violating (9) or (10)

must violate it had the power vector started with another

initialization Consequently, we can conclude the following

fact:

secondary link in set cannot be activated if it will result

in an active set ℵ that was infeasible before.

Although, the infeasibility of the active set ℵ is checked

after the convergence of the DCPC, we take the occurrence

of either of events 2 or 3 as an indicator for its infeasibility

in order to quickly remove any possible violation of (9) The following two steps are performed to handle events2 or 3:

1) Selecting one secondary link to join : We use a

simple criterion to select a secondary link for joining the set  in order to decrease the amount of signaling

exchanged among secondary links After the power

update of secondary transmitter j, if events 2 or 3 occur, link j is the link to join the set  That is, the user

joining set is the one whose power update is followed

by a constraint violation

2) Re-activating a secondary link: For the link j to be

deactivated and join the set , it should first check the

possibility of replacing a link i, where i ∈ , such that

results in an active set that was not tested before, link

the link j cannot replace any of the inactive links in

 (because the resulting active set, with i and without

j, was estimated before as infeasible), link j joins the

inactive set without activating any of the inactive links Hence, the size of is then incremented by 1 while the

size ofℵ is then reduced by 1.

D Implementation Issues :

For our algorithm to be distributed, a control channel should exist so that the secondary links can exchange control informa-tion (about the recent inactive set and interference constraint violation) during execution of the proposed algorithm

Each secondary link should keep the last version of the current inactive set Upon each join process the link that is

supposed to join should inform the other links that it would

leave the active set, and which secondary link, if any, would

be re-activated Each link would then update its version of

accordingly

There is no need for the secondary links to know the max-imum tolerable interference on primary receivers nor what is the current value of interference they produce on each receiver Instead, the primary BS broadcasts a warning signal over the control channel if the interference produced by secondary links exceeds the tolerable allowable level The secondary links do not have to keep track of channel gains between themselves and primary receivers Once a warning signal from a primary

BS is heard, the secondary link that performed the last power update has to join the set.

As mentioned in the previous subsection, when a secondary

link j joins the set , it first checks the possibilities of

replacing any inactive link i, where i ∈ , producing a new

active set ℵ This, of course, requires the availability of the

history of either the active or inactive sets progression Since our proposed algorithm is distributed, it is enough for each

secondary link to keep a list of only the past inactive sets in

which it was included, in addition to the current inactive set

Thus, if j finds that a new inactive set is produced when it replaces i in , i joins ℵ and j joins  If several members

qualified one If all possible replacements are to produce an

active set previously estimated to be infeasible, then j joins

 and the size of  expands by one All secondary links then

clear their stored histories and keep only the current  We

preferred keeping the history of progression of inactive sets

instead of the active sets at each secondary link, because the

inactive set is initially empty and then grows one by one, that

in turn would facilitate the search process rather than searching

in history of previous active sets

Sometimes when the network conditions are severe with

large number of requesting secondary links, the number of

removed secondary links is large, which in turn may result

in a large history of inactive sets maintained by secondary

links As a result the join process might consume much time in

searching as well as memory for storing previous inactive sets

For this reason, we propose a simple technique for handling

join processes This technique states that, instead of

main-taining a list of previous inactive sets in which a secondary

link was included at that secondary link, each secondary link

would maintain a vector of size N with components set to

zero, then after each replacement between any two secondary

links i and j each link of them will set the vector component

corresponding to the other link to 1 However, if a link j is

supposed to join the inactive set  j will first check if it

could replace any link i in  or not via the components of its

maintained vector A replacement occurs only if j finds the

component of index i in the vector of j is zero Moreover, for

the case in which the inactive set size is increased by 1 then all

secondary links should clear their maintained vectors (setting

their components to zeros) The simulation results showed that

both ways (using lists of previous inactive sets, or vectors with

1 or 0 components) produce almost same number of admitted

secondary links

Finally, the proposed algorithm is assumed to converge

within a time period over which the system is stationary

We are currently investigating the effects of mobility of users

and variations of their arrivals and departures so that they are

accounted for in our future work

V SIMULATIONRESULTS

In this section we present simulation results for of our

proposed algorithm In order to compare the performance

of the algorithm with that in [8], we use the same system

model and parameters Primary users are communicating with

a single BS in the uplink direction The secondary transmitters

are located in an area of size2000m × 2000m with BS of the

primary network located at the center The receiving node of

each secondary link is placed randomly in a1000m × 1000m

square with its transmitting node at the center

The channel gain between any transmitter j and receiver

i,j , where d i,j is

the corresponding distance, β i,jis a random Gaussian variable

with zero mean and a standard deviation of 6 dB to account for

shadowing effects, and K0= 103is a factor that includes some

system parameters such as antenna gain and carrier frequency

The total noise and interference at the receiving node of

Fig 2 Simulation Model

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Target SINR dB

Optimum

Proposed with lists Proposed with 1/0 vectors

Fig 3 Outage probability vs target SINR of secondary links.I = 5(Ni+

N0) and N = 7

all secondary links is N i + N0 = 10−10 W, the maximum

transmission power on secondary links is P i max = 0.1 W, the bandwidth is B = 5.12 MHz, and the minimum transmission rate on secondary links is R i= 64 kbps For each simulation run, the locations of secondary links are generated randomly Fig 3 gives the outage probability calculated as the ratio

of the average number of removed links after convergence to the average number of requesting links, versus target SINR of secondary links We do averaging over 1000 simulation runs

using N = 7 and a maximum tolerable interference at the

primary receiver, I, equal to 5(N i + N0)

We can see from the figure that the proposed algorithm pro-duces outage probability that is close to the optimum solution obtained by exhaustive search for the smallest possible set of removed links This is the same for both cases of the secondary links storing the past inactive sets or storing a vector tracking replacements

Fig 4 shows the number of admitted secondary links versus the number of requesting secondary links for the proposed algorithm and the optimal algorithm The result shows that the number of admitted secondary links is close to the optimum

admitted number This figure is produced for I = 5(N i + N0) and SINR=15dB

To simulate the complexity of our proposed algorithm,

we take the number of comparisons in our proposed second

5 6 7 8 9 10 11 12 13 14 15 4

5 6 7 8 9 10

11

Number of requesting links

Optimum Using lists Using 1/0 vectors

Fig 4 Number of admitted secondary links vs number of requesting

secondary links.I = 5(Ni + N0 ) and SINR=15dB

0 5 10 15 20 25 30 0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Number of requesting secondary links

Using 1/0 vectors I−SMIRA

Fig 5 Average number of basic operations vs number of requesting links

I = 5(Ni + N0 ) and SINR=15 dB

storage scheme (where secondary links maintain vectors of 1

or 0 components) as a measure of basic operations We run the

algorithm for different number of requesting secondary links

At each run we calculate the number of performed

compar-isons and average the results over 100 simulations Moreover,

we run I-SMIRA algorithm under the same simulation setup

and estimated the number of basic operations performed by it

as R−1

i=0 (N − i)2, where R is the number of removed links

by I-SMIRA Note that the complexity of I-SMIRA is reported

to be O (N2) [8],[11] Afterwards, we plot the average number

of basic operations of both algorithms in Fig 5

It is clear from the figure that the proposed second storage

scheme has a smaller number of basic operations

(compar-isons) than I-SMIRA The basic operation of I-SMIRA can be

considered as an addition or multiplication operation Here,

we note that the first storage scheme (where secondary links

maintain lists of previous inactive sets that they were included

in) requires large number of comparisons in searching for

previously formed inactive sets Wee can see from the results

of Figs 3,4,5, the second storage technique is more efficient

than both I-SMIRA and our first proposed technique in terms

of complexity and outage probability

VI CONCLUSION

We address the problem of admission control and power allocation for cognitive radios in spectrum underlay networks Our design objective is to maximize the number of admitted secondary links under their QoS requirements without violat-ing the interference temperature on primary receivers Since

an optimal solution to our problem is proved to be NP-hard,

we propose a suboptimal distributed algorithm Our algorithm,

in contrast with previous works, allows the removed links to

be re-activated to compensate for the non optimality of the used simple removal criterion In order to maintain reduced complexity, we use a simple criterion to control the number

of reactivation of inactive secondary links

Our distributed algorithm is supposed to be applied online based on local information in each secondary link and small amount of signaling that could be exchanged over a control channel Simulation results show that the proposed algorithm produces close results to the optimum solution with reasonable complexity

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VI CONCLUSION

We address the problem of admission control and power allocation