a two-step resource allocation algorithm in multicarrier based cognitive radio systems

A Two-Step Resource Allocation Algorithm in Multicarrier Based Cognitive Radio Systems Musbah Shaat and Faouzi Bader Centre Tecnol`ogic de Telecomunicacions de Catalunya CTTC Parc Medite

A Two-Step Resource Allocation Algorithm in Multicarrier Based Cognitive Radio Systems

Musbah Shaat and Faouzi Bader

Centre Tecnol`ogic de Telecomunicacions de Catalunya (CTTC) Parc Mediterrani de la Tecnolog´ıa, Av Carl Friedrich Gauss 7, 08860 , Castelldefels-Barcelona, Spain

Phone: +34 93 6452911, Fax: +34 93 6452900 Email:{musbah.shaat,faouzi.bader}@cttc.es

Abstract— This paper presents a two-step downlink resource

allocation algorithm for multicarrier based cognitive radio

sys-tems The algorithm allocates the subcarriers to the users in the

first step In the second step, the power is allocated to these

subcarriers in order to maximize the downlink capacity of the

system without causing excessive interference to the primary

user The performance of the proposed algorithm is investigated

using computer simulations to prove that it achieves near optimal

performance and it is better than other existing algorithms.

Moreover, the throughput of Orthogonal frequency division

mul-tiplexing (OFDM) and filter bank multicarrier system (FBMC)

based cognitive radio systems are compared to show the efficiency

of using FBMC in future cognitive radio systems.

Index Terms- Cognitive Radio; OFDM; FBMC; Power

Alloca-tion; resource management.

I INTRODUCTION

Cognitive Radio (CR) was first introduced by Mitola [1] as a

radio that can change its parameters based on interaction with

the environment in which it operates According to Federal

Communications Commission (FCC) [2], temporal and

geo-graphical variation in the utilization of the assigned spectrum

range from 15% to 85% which means that assigning frequency

bands to specific users or service providers exclusively doesn’t

guarantee that the bands are being used efficiently all the time

The CR technology aims to increase the spectrum utilization

by allowing a group of unlicensed users [referred to as

secondary users (SU’s)] to use the licensed frequency channels

(spectrum holes) without causing a harmful interference to the

licensed users [referred to as primary users (PU’s)] and thus

implement efficient reuse of the licensed channels

Multicarrier communication systems have been considered

as an appropriate candidate for CR systems due to its flexibility

in allocating different resources among different users as well

as its ability to fill the spectrum holes left by the PU’s

[3] In [4], the mutual interference between PU and SU was

studied The mutual interference depends on the transmitted

power as well as the spectral distance between PU and SU

Orthogonal frequency division multiplexing (OFDM) based

CR system suffers from high interference to the PU’s due to

large sidelobes of its filter frequency response The insertion

of the cyclic prefix (CP) in each OFDM symbol decreases the

system capacity The filter bank multicarrier system (FBMC)

doesn’t require any CP extension and can overcome the

spectral leakage problem by minimizing the sidelobes of each subcarrier and therefore lead to high efficiency (in terms of spectrum and interference) [5] [6]

The problem of resource allocation for conventional (non-cognitive) multicarrier systems has been widely studied (e.g [7]–[10] and references therein) All of the classical algorithms that was proposed to solve the problem in conventional multi-carrier systems cannot be applied to the CR systems due to the existence of the two different types of users (PU’s and SU’s) where the interference introduced to the PU’s by the SU’s should be taken into consideration In [11], the authors pro-posed an optimal and two suboptimal power loading schemes using the Lagrange formulation to maximize the downlink capacity of the CR system while keeping the interference in-duced to only one PU below a pre-specified threshold without the consideration of the total power constraint P.Wang et al in [12] proposed an iterative partitioned single user waterfilling algorithm The algorithm aims to maximize the capacity of the CR system under the total power constraint with the consideration of the per subcarrier power constraint caused by the PU’s interference limit The mutual interference between the SU and PU was not considered In [13], an algorithm called

RC algorithm was presented for multiuser resource allocation

in OFDM based CR systems This algorithm uses a greedy approach for subcarrier and power allocations by successively assign bits, one at time, based on minimum SU power and minimum interference to PU considerations The algorithm has

a high computational complexity and a limited performance with comparison to the optimal solution

In this paper, a two-step multiuser resource allocation algorithm in multicarrier based CR systems in downlink is proposed In the first step, the subchannels are assigned to users and then in the second step, the powers are allocated

to the different subcarriers in order to maximize the downlink capacity of the CR system under both the interference and power constraints The efficiency of the proposed algorithm will be investigated in OFDM and FBMC based CR systems The rest of this paper is organized as follow: Section II gives the system model and formulates the problem The subcarrier

to user assignment is described in Section III In Section IV, the power allocation algorithm is presented Numerical results are given in Section V while Section VI concludes the paper

(CBS) base station

Secondary User (SU)

(SU)

Primary User (PU)

(PU)

Fig 1 Cognitive Radio Network

II SYSTEMMODEL ANDPROBLEMFORMULATION

In this paper, the downlink scenario will be considered

As shown in Fig 1, the CR system coexist with the PU’s

radio in the same geographical location The cognitive base

station (CBS) transmits to its SU’s and causes interference to

the PU’s Moreover, the PU’s base station interferes with the

SU’s The CR system’s frequency spectrum is divided into N

subcarriers each having a Δf bandwidth The side by side

frequency distribution of the PU and SU’s will be assumed

(see Fig 2) The frequency band B has been occupied by

the PU (active PU band) while the other band represent the

CR band (non-active PU band) It’s assumed that the CR

system can use the non-active PU bands provided that the total

interference introduced to the PU band does not exceed I th

where I th = T th B denotes the maximum interference power

that can be tolerated by the P U and T th is the interference

temperature limit for the PU

Assume that Φiis the power spectrum density (PSD) of the

i thsubcarrier The expression of the PSD depends on the used

multicarrier technique If an OFDM based CR is assumed, the

PSD of the i th subcarrier can be written as [4]

Φi (f) = P i T s

sin πfT

s

πf T s

2

(1)

where P i is the total transmit power emitted by the i th

subcarrier and T s is the symbol duration If FBMC based CR

system is assumed, the PSD of the i thsubcarrier can be written

as

Φi (f) = P i |H i (f)|2 (2) where |H i (f)| is the frequency response of the prototype

filter with coefficients h [n] with n = 0, · · · , W − 1 , where

W = KN and K is the length of each polyphase components

(overlapping factor) Assuming that the prototype coefficients

have even symmetry around the KN

2

th coefficient, and the first coefficient is zero [5], we get

|H i (f)| = h [W /2] + 2

W

2−1



n=1

(3)

The interference introduced by the i thsubcarrier to PU band,

I i (d i , P i ) , is the integration of the PSD of the i thsubcarrier

across the PU band, B , and can be expressed as [4]

I i (d i , P i) =

di+B l/2

|g i |2Φi (f) df = P iΩi (4)

1 2 ……… N Frerquency

PU band

f

CR band

Fig 2 Frequency distribution of the primary and cognitive bands

where d i is the spectral distance between the i th subcarrier and the PU band Ωi denotes the interference factor of the i th

subcarrier

The interference power introduced by the PU signal into the

band of the i thsubcarrier is [4]

J i (d i , P P U) =

di+Δf /2

di−Δf /2

|y i |2ψ l

e jω

where ψ

e jω

is the power spectrum density of the P U signal and y i is the channel gain between the i th subcarrier and PU signal

It will be assumed that all the instantaneous fading gains are perfectly known at the CBS and there is no inter-carrier

interference (ICI) Let v i,m to be a subcarrier allocation

indicator, i.e v i,m = 1 if and only if the subcarrier is

allocated to m th user It is assumed that each subcarrier can

be used for transmission to at most one user at any given time Our objective is to maximize the total capacity of the

CR system subject to the instantaneous interference introduced

to the PU’s and total transmit power constraint Therefore, the optimization problem can be formulated as follows

P1 : max

P i

M m=1

N i=1

υ i,mlog2

1 + P i,m |h i,m |2

σ2i



Subject to

υ i,m ∈ {0, 1} , ∀i, m

M m=1

υ i,m ≤ 1, ∀i

M m=1

N i=1

υ i,m P i,m ≤ P T

P i ≥ 0, ∀i ∈ {1, 2, · · · , N}

M m=1

N i=1

υ i,m P iΩi ≤ I th

(6)

where h i,m is the i th subcarrier fading gain from the CBS

to the m th SU P i,m is the transmit power across the i th subcarrier σ2i = σ2

variance of the additive white Gaussian noise (AWGN) and

J i is the interference introduced by the PU band into the

i th subcarrier and can be evaluated using (5) N denotes the total number of subcarriers, while I thdenotes the interference

threshold prescribed by the PU P T is the total power budget

and M is the number of SU’s.

III SUBCARRIER TOUSERASSIGNMENT(FIRSTSTEP)

The optimization problem P 1 is a combinatorial

optimiza-tion problem and its complexity grows exponentially with the

Algorithm 1 Subcarriers to User Allocation

Initialization:

Setυ i,m = 0 ∀i, m

Subcarrier Allocation:

fori = 1 to N do

m ∗= arg max

m {h i,m }; υ i,m ∗ = 1

end for

input size In order to reduce the computational complexity,

the problem is solved in two steps where in the first step, the

subcarriers are assigned to the users and then the power is

allocated for these subcarriers in the second step Once the

subcarriers are allocated to the users, the multiuser system

can be viewed virtually as a single user multicarrier system

Generalizing the proof given in [7] to consider the CR system,

it can be easily shown that the maximum data rate in downlink

can be obtained if the subcarriers are assigned to the user who

has the best channel gain for that subcarrier as described in

Algorithm 1

IV PROPOSEDALGORITHM FORPOWERALLOCATION

(SECONDSTEP)

By applying the Algorithm 1, the values of the channel

indicators υ i,m are determined where v i,m = 1 if and only if

the subcarrier is allocated to m thuser, and hence for notation

simplicity, single user notation can be used The different

channel gains can be determined form the subcarrier allocation

step as follows

h i=

M



m=1

N



i=1

and hence problem P 1 can be reformulated as follows

P2 : max

P i

N i=1

log2

1 + P i |h i |2

σ2i



Subject to

N

i=1

P iΩi ≤ I th N

i=1

P i ≤ P T; P i ≥ 0

(8)

The problem P 2 is a convex optimization problem The

Lagrangian can be written as

G = − N

i=1

log2

1 + P i ∗ |h i |2

σ i2



+ α

N

i=1

P i ∗Ωi − I th



+β

N

i=1

P i ∗ − P T



− N

i=1

P i ∗ μ i

(9)

where α, μ i , i ∈ {1, 2, , N}, and β are the Lagrange

multipliers The Karush-Kuhn-Tucker (KKT) conditions can

be written as follows

P i ∗ ≥ 0; α ≥ 0; β ≥ 0; μ i ≥ 0; μ i P i ∗= 0

α

N

i=1

P i ∗Ωi − I th



= 0

β

N

i=1

P i ∗ − P T



= 0

∂G

σ2

| hi |2+P ∗ i

+ αΩ i + β − μ i= 0

(10)

and also the solution should satisfy the total power and interference constraints Rearranging the last condition in (10)

we get

αΩi + β − μ i − σ2

Since P i ∗ ≥ 0, we get σ2

αΩ i +β−μ i If |h σ2

i |2 < αΩ1

i +β , then μ i = 0 and hence P ∗

|h i |2 Moreover, if

σ2

|h i |2 > αΩ1

i +β , from (11) we get αΩ i +β−μ1 i ≥ σ2

|h i |2 > αΩ1

i +β and since μ i P i ∗ = 0 and μ i ≥ 0, we get that P ∗

Therefore, the optimal solution can be written as follows

P i ∗=

1

αΩi + β −

σ2

|h i |2

+

(12)

where [x]+ = max (0, x) Solving for the more than one

Lagrangian multiplier is computational complex These mul-tipliers can be found numerically using ellipsoid or interior point method with a polynomial time complexityON3

[14] The high computational complexity makes the optimal solution unsuitable for practical application and hence a low complexity algorithm will be proposed

If the interference constraints are ignored in P 2, the

solu-tion of the problem will follow the well known waterfilling interpretation On the other side, if the total power constraint

is ignored, the Lagrangian of the problem can be written as

G = −

i∈N l

log2

1 + P i  |h i |2

σ i2



+α  i∈N l

P i Ωi − I th

 (13)

where α  is the Lagrange multiplier Equating ∂G ∂P  

i to zero, we get

P i =

1

α Ωi − σ2

|h i |2

+

(14)

The value of α  can be calculated by substituting (14) into

i∈N

P i Ωi = I th to get

I th+

i∈N

Ωi σ i2

|h i |2

(15)

It is obvious that if the summation of the allocated power under only the interference constraints is lower than or equal the available total power budget, i.e N

i=1

P i  ≤ P T, then (14)-(15) will be the optimal solution for the optimization problem

Updated Pmax Set A

Initial Pi Updated Pi

Subcarriers

Power

PU Band (CR allocates zero power in these subcarriers)

Fig 3 An Example of the SU’s allocated power using PI-Algorithm

P2 In most of the cases, the total power budget is quite

lower than this summation and hence the Power Interference

(PI) constrained algorithm, referred to as PI-Algorithm, is

proposed to allocate the power under both the total power

and interference constraints

In order to solve the optimization problem P 2, we can start

by assuming that the maximum power that can be allocated

for a given subcarrier P M ax

i is determined according to the interference constraints only by using (14)-(15) for every

subcarriers i ∈ N By such an assumption, we can guarantee

that the interference introduced to the PU band will be under

the pre-specified threshold Once the maximum power P i M ax

is determined, the total power constraint is tested If the total

power constraint is satisfied, then the solution has been found

and equal to the maximum power that can be allocated to each

subcarrier, i.e P i ∗ = P M ax

i Otherwise, the available power budget should be distributed among the subcarriers giving that

the power allocated to each subcarrier is lower than or equal to

the maximum power P M ax

i This can be done optimally by ap-plying successive conventional waterfillings on the subcarriers

Given the initial waterfilling solution, the channels that violate

the maximum power P M ax

i are determined and upper bounded

with P M ax

i The total power budget is reduced by subtracting

the power assigned so far At the next step, the algorithm

proceeds to successive waterfilling over the subcarriers that

not violated the maximum power P i M ax in the last step This

procedures is repeated until the allocated power P i W.F doesn’t

violate the maximum power P i M axin any of the subcarriers in

the new iteration Once the power allocated to each subcarriers

is determined, the total interference induced to the PU is

evaluated According to the left interference, the maximum

power that can be allocated to each subcarrier is relaxed and

the successive waterfillings are performed again to get the final

solution The final power allocation vector P i ∗ is satisfying

approximately the interference constraint with equality as well

as guaranteing that the total power used is equal to P T A

graphical description of this algorithm can be found in Fig 3

while the algorithm steps are described in Algorithm 2

The computational complexity of Step 1 in the proposed

Algorithm (Algorithm 2) is O (N log N) Steps 2 and 4 of

the algorithm execute the successive waterfillings which has

Algorithm 2 Power Allocation Algorithm

• Let N = {1, 2, · · · , N} to be the set of all the CR available subcarriers and P i ∗ to be the solution of the optimization problem

• Step 1

1) Find the power allocation vector P i  according to interference constraint only using equations (14)-(15) and make it to be the maximum power that

can be allocated to each subcarrier P i M ax = P 

i 2) If N

i=1

P M ax

i ≤ P T, then the solution is found and

hence P i ∗ = P M ax

i , else continue

• Step 2 Find the power allocation vector P i W.F using the iterative waterfilling under the constraints of total power,

P T, and the maximum power that can be allocated to

each subcarrier, P M ax

• Step 3 Find the set of subcarriers A ⊂ N (See Fig 3)

in which P W.F

i and evaluate the left available

interference I Lef t = I th −

i∈N

P W.F

• Step 4 Update P M ax

i by applying equations (14)-(15) on the subcarriers in the set A only under the interference

constraint I th  = I Lef t+

i∈A

P W.F

i Ωi and execute the

iterative waterfilling again under the P T and updated

P M ax

i constraints

a complexity of O (N log N + ηN) where η ≤ N is the

number of the iterations Step 3 has a complexity of O (1).

Hence, The overall complexity of the algorithm is lower thanO (N log N + ηN) + O (1) The value of η is estimated via simulation with an average value η = 2.953 and never exceeds five, i.e η ∈ [0, 5] Comparing to the computational

complexity of the optimal solution , ON3

, the proposed algorithm has much lower computational complexity specially

when the number of the subcarriers N increased.

V SIMULATIONRESULTS

The simulation are performed under the scenario given in

Fig 2 A multicarrier system of 10 SU’s and N = 128 subcar-riers is assumed The value of T s , Δf and P T are assumed to

be 4μ second , 0.3125 MHz and 1 watt respectively AWGN

of variance 10−6 is assumed Without loss of generality, the interference induced by PU’s to the SU’s band is assumed

to be negligible The channel gains h and g are outcomes of

independent, identically distributed (i.i.d) Rayleigh distributed random variables (rv’s) with mean equal to ”1” and assumed

to be perfectly known at the CBS OFDM and FBMC based cognitive radio systems are evaluated The OFDM system is

assumed to have a 6.67% of its symbol time as cyclic prefix.

For FBMC system, the prototype coefficients are assumed to

be equal to PHYDYAS coefficients with overlapping factor

K = 4 [15] The optimal solution is implemented using the interior point method The efficiency of the proposed two-step

algorithm is compared with the RC Algorithm proposed in

0 0.2 0.4 0.6 0.8 1 1.2

10

11

12

13

14

15

Interference Threshold (Watt)

RC Pt=1W Two Step Pt=1W Optimal Pt=2W

RC Pt=2W Two Step Pt=2W

Fig 4 Mean throughput vs interference constraints for OFDM based CR.

11

12

13

14

15

16

17

18

Total power (Watt)

Optimal=5e−6W

RC Ith=5e−6W Two Step Ith=5e−6W Optimal=10e−6W

RC Ith=10e−6W Two Step Ith=10e−6W

Fig 5 Mean throughput vs total power constraints for OFDM based CR.

[13] which allocate the subcarriers and bits considering the

relative importance between the power needed to transmit and

the interference induced to the PU band For fair comparison,

the same bit mapping used in [13] is considered as follow

b i =

 log2 1 + P i ∗ |h i |2

σ2



(16)

where b i denotes the maximum number of bits in the symbol

transmitted in the i thsubcarrier and. denoted the floor

func-tion All the results have been averaged over 100 iterations

A OFDM Based CR System

The achievable capacities versus the interference constraint

of the OFDM based CR system using the optimal, two-step

and RC algorithm are plotted in Fig 4 with P T = 1 and

P T = 2 watts It can be noted that the capacity achieved using

two-step algorithm is very close to that achieved using the

11 11.5 12 12.5 13 13.5 14 14.5 15 15.5

Interference Threshold (Watt)

Optimal Pt=1W

RC Pt=1W Two Step Pt=1W Optimal Pt=2W

RC Pt=2W Two Step Pt=2W

Fig 6 Mean throughput vs interference constraints for FBMC based CR.

11 12 13 14 15 16 17 18

Total power (Watt)

Optimal=5e−6W

RC Ith=5e−6W Two Step Ith=5e−6W Optimal=10e−6W

RC Ith=10e−6W Two Step Ith=10e−6W

Fig 7 Mean throughput vs total power constraints for FBMC based CR.

optimal algorithm with a good reduction in the computational complexity Moreover, the proposed algorithm outperform the

RC algorithm As the allowed interference increase, the total throughput increase The same observation can be seen in Fig 5 which plots the average throughputs of the different

algorithms versus different total power constraints with I th=

5μ and I th = 10μ watts It can be noticed that the throughputs

increased as the total power increased When the total power exceeds a certain value, the throughputs become constant regardless of the increase in total power This is because with such a given interference constraint, the system reach to the maximum total power that can be used to keep the interference

to the primary user below the prescribed threshold

B FBMC Based CR System

The filter bank multicarrier system (FBMC) can overcome the spectral leakage problem by minimizing the sidelobes of

each subcarrier Fig 6 and Fig 7 plot the average throughput

for FBMC based CR system using different algorithms versus

different interference constraint with P T = 1 and P T = 2

watts and different total power constraints with I th = 5μ

and I th = 10μ watts, respectively The proposed two-step

algorithm approaches the optimal solution and outperform the

RC algorithm Comparing with the OFDM based CR system

in Fig 4 and 5, the throughput of FBMC system is higher

than that of OFDM because the sidelobes in FBMC PSD is

smaller than that in OFDM and also the inserted CP in OFDM

based CR systems reduces the total throughput of the system

It can be noticed also that the interference condition introduce

a small restriction on the overall average throughputs in FBMC

based CR systems which is not the case in OFDM based

CR systems These results are contributing to recommend the

using of the FBMC as a candidate for a physical layer in the

future CR system

VI CONCLUSION

A two-step subcarrier and power allocation algorithm in

multiuser multicarrier based cognitive radio system is

pro-posed In the first step, the subcarriers are allocated to the

users based on their channel quality In the second step, the

available power budget is distributed among the subcarriers

using the proposed PI-Algorithm which is an iterative power

allocation algorithm aims to maximize the downlink total

capacity of multicarrier based CR systems under both total

power and maximum allowable interference induced to

pri-mary user constraints The proposed two-step algorithm solves

the problem efficiently and achieves approximately the same

optimal capacity with a good reduction in the computational

complexity The proposed algorithm outperformed the RC

algorithm that uses a greedy approach for the subcarrier and

power allocation Simulation results prove that the FBMC

based CR systems have more capacity than OFDM based ones

The obtained results contribute in recommending the use of

FBMC physical layer in the future cognitive radio systems

Developing a resource allocation algorithm that consider the

fairness among different users as well as their quality of

service (QoS) will be the guideline of our future research work

towards better radio resource management

This work was partially supported by the European

ICT-2008-211887 project PHYDYAS and Generalitat de Catalunya under

grant 2009-SGR-940

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