Resource allocation in OFDM-based cognitive radionetworks with multiple AF relays

Shashika Biyanwilage, Upul Gunawardana and Ranjith LiyanapathiranaSchool of Computing, Engineering and Mathematics

University of Western Sydney, Penrith, NSW 2751, Australia

{shashika, upul, ranjith}@ieee.org

Abstract—This paper investigates the relay selection and powerallocation problems in OFDM-based cognitive radio networkswith multiple amplify-and-forward relays. The objective is tomaximize the total instantaneous capacity of the cognitive radionetwork while maintaining the interference introduced to theprimary network below a given threshold and also maintainingthe total transmit power below the individual power limitations atcognitive radio transmitters. The joint optimization problem is amixed binary integer problem which is NP-hard. Thus, we dividethe joint optimization problem into two subproblems, and solvethe resource allocation problem suboptimally. Two suboptimalresource allocation methods are proposed and their performanceis compared with the joint optimal resource allocation. Resultsshow that near optimal performance can be obtained with lesscomplex suboptimal approaches.

I. INTRODUCTION

The cognitive radio (CR) concept [1] has been proposed to

improve the spectrum utilization by allowing secondary users

(SUs) to cooperatively transmit on the unutilized frequency

bands left by licensed users/primary users (PUs). SUs should

use these available frequency bands without causing harmful

interference to the PUs. OFDM has been identified as a

candidate for realizing the CR concept due to its flexibility

for spectrum allocation [2],[3]. For situations where there is

a weak channel between the CR source and CR destination,

reliable communication can be achieved by introducing a set

of cooperative relays between the source and destination [4].

Using system resources such as intermediate CR relays, data

can be transmitted using relatively low power and possibly

with lower interference to the PUs.

Resource allocation is a key research area in coopera-

tive wireless communication. The system resources: relays,

subcarriers and transmit power, are adaptively allocated to

meet the varying channel conditions and to improve the

system performance. The performance improvement can be

throughput maximization, outage probability minimization

and/or bit-error-rate (BER) minimization. Resource allocation

in non-cognitive, OFDM-based cooperative relay networks

has been widely studied in the recent literature ([5], [6], [7]

and references therein). Unlike in non-cognitive networks, in

CR networks the resource allocation should be performed to

maximize the system performance without causing harmful

interference to the PUs.

In OFDM-based CR systems, SUs can cause interference

to PUs operating in the adjacent frequency bands and vice-

a-versa. The work in [8] and [9] present subcarrier power

allocation schemes for OFDM-based CR networks to maxi-

mize the capacity while maintaining the interference below

a predefined threshold. In [10], authors investigate uplink

resource allocation schemes in OFDMA-based CR networks

and propose a subcarrier and power allocation scheme under

the interference temperature constraints to maximize the total

throughput of the CR uplink transmission. The work in [11]

presents resource allocation schemes for multiuser cognitive

OFDM networks to maximize the capacity under individual

interference constraints at each PU.

In recent years, there has been a significant interest on re-

source allocation in OFDM-based CR relay networks. In [12],

Shaat and Bader study joint optimization of relay selection,

subcarrier pairing and power allocation in OFDM-based CR

networks with multiple decode-and-forward (DF) relays. The

authors derive an asymptotically optimal solution using dual-

decomposition method and also they propose a suboptimal

algorithm with less complexity. The work in [13] presents

suboptimal relay selection and power allocation schemes for

OFDM-based CR systems with multiple DF relays. Subcar-

rier power allocation in OFDM-based CR networks with an

amplify-and-forward (AF) relay is studied in [14], without

considering diversity. Here, only the interference constraint

has been considered. An AF relay assisted CR network with

diversity is studied in [15] and the authors propose optimal

power allocation schemes under peak and average interference

constraints.

In this paper, we study joint optimization of relay selection

and power allocation in multiple AF relay assisted OFDM-

based CR networks. There are two key contributions in this pa-

per compared to the work in [14] and [15]. Firstly, we consider

a general system model with multiple PU bands and multiple

CR relays. Secondly, we consider that the CR transmitters

have a maximum transmit power limitation. Thus the resource

allocation problem is subjected to both interference and trans-

mit power constraints. We propose less complex suboptimal

resource allocation schemes to maximize the instantaneous

capacity, and the performance of the proposed methods is

compared with the optimal resource allocation, which jointly

optimizes the relay selection and power allocation with high

computational complexity.

The remainder of this paper is organized as follows: In

Section II, we describe the system and the channel model.

978-1-4799-5255-7/14/$31.00 ©2014 IEEE

Then in Section III, we formulate the joint resource allocation

problem to maximize the instantaneous capacity, and propose

two suboptimal resource allocation methods. Section IV il-

lustrates the performance of the proposed methods through

computer simulations and compares the results with joint

optimal resource alocation. Finally we conclude the paper in

Section V.

II. SYSTEM MODEL

We consider a scenario where a two-hop OFDM-based CR

system co-exists with a PU system as shown in Fig. 1. There

are L PUs in the vicinity of the CR system and K AF relays

to assist the communication between the CR source (s) and

CR destination (d). We assume that the spectrum sensing has

been performed and the source and the relays have the full

knowledge of the frequency bands available for transmission.

Further it is assumed that the direct link between the source

and the destination is blocked by an obstacle and does not

exist. For the simplicity of presentation, let k denote the kth

relay: k ∈ [1 : K], and l denote the lth PU: l ∈ [1 : L].

Fig. 1. Multi-relay assisted CR system model

We consider frequency selective multipath fading channels,

defined in the time domain by,

hmn,j(t) =M∑j=0

hnδ(t− jT ) (1)

where hmn,j is the complex amplitude of the path between

node m and n (m ∈ {s, k} andn ∈ {k, d, l}). M is the num-

ber of channel taps. We assume that all the channel taps are

subjected to Rayleigh fading and path loss. The number of

subcarriers in the OFDM system is taken as N . The frequency

response of the channel Hmn is given by the N -point Fast

Fourier Transform (FFT) of the channel impulse response. The

channel gain Gmn represents the effect due to both the path

loss and the fading gain. Then,

Gmn =√ε d−α

mn Hmn (2)

where dmn is the distance between the nodes m and n, ε is a

constant that depends on the antenna design and α is the path

loss exponent [16]. ε and α are assumed to be the same for

all the channels under consideration. Then, Gsk,i and Gkd,i

represent the instantaneous channel gains of the ith subcarrier

between source to kth relay and kth relay to destination

respectively. Gsl,i and Gkl,i denote the instantaneous channel

gains between the source to the lth PU and kth relay to the

lth PU, respectively. We assume that the resource allocation

decisions are made at the CR source and the knowledge of

instantaneous CSI, Gsk and Gkd, is available at the time of

decision making. Further it is assumed that the CR network

has perfect knowledge of the instantaneous channel state

information Gsl and Gkl between itself and the PU system.

In the frequency domain, a side-by-side access model is

considered as shown in Fig. 2 [8]. There are L PU bands

with the lth PU having a bandwidth of Bl. The remaining

unused spectrum is divided into N subcarriers each having a

bandwidth of Δf . There are two types of interferences in an

Fig. 2. Spectrum allocation (general model)

OFDM-based CR system: interference introduced by the PU

transmitter to the CR receiver, and the interference introduced

by the CR transmitter to the PU receiver. The interference

introduced by the PU’s signal can be expressed as [17],

Jlm,i = |Gml,i|2∫ di,l+

Δf2

di,l−Δf2

Υ(ejw) dw, (3)

where Υ(ejw) is the power spectral density of the PU signal

and Gml,i is the channel gain of the ith subcarrier between the

lth PU transmitter and the mth CR receiver. di,l is the spectral

distance between the ith subcarrier and the lth PU band.

Similarly, the interference introduced by the CR transmission

can be expressed as [17],

Iml,i = Pi |Gml,i|2 Ts

∫ di,l+Bl/2

di,l−Bl/2

(sin (πfTs)

πfTs

)2

df, (4)

where Pi is the transmit power of the ith subcarrier, Ts is the

symbol duration, and Bl is the lth PU bandwidth. Gml,i is

the channel gain of the ith subcarrier between the mth CR

transmitter and lth PU receiver.

It is assumed that the CR relays support only half duplex

operations and two orthogonal time slots are used for source to

relay communication and relay to destination communication.

In the first time slot, the source sends data to the kth relay,

with power Psk,i on the ith subcarrier. Then in the second time

slot, the kth relay amplifies the signal by a factor of βk,i using

power Pkd,i on the same subcarrier and transmits the amplified

signal to the destination. Following a similar approach as in

[5], βk,i can be expressed as,

βk,i =

√Pkd,i

| Gsk,i |2 Psk,i + σ2k +

∑Ll=1 Jlk,i

, (5)

where, σ2k is the noise variance at the kth relay and Jlk,i is

the interference introduced by the lth PU to the kth relay. If

the destination receives the signal from the relay during the

second time slot, the signal-to-noise ratio (SNR) Γk,i of the

ith subcarrier can be expressed as,

Γk,i =Psk,i | Gkd,iβk,iGsk,i |2

σ2d +

∑Ll=1 Jld,i + (σ2

k +∑L

l=1 Jlk,i) | βk,iGkd,i |2,

=Psk,iγsk,iPkd,iγkd,i

1 + Psk,iγsk,i + Pkd,iγkd,i, (6)

where, γsk,i =|Gsk,i|2

σ2k+

∑Ll=1 Jlk,i

and γkd,i =|Gkd,i|2

σ2d+

∑Ll=1 Jld,i

are

the instantaneous channel-to-noise ratios (CNRs) at the kth

relay and destination, respectively. σ2d is the noise variance

at the destination and Jld,i is the interference introduced by

the lth PU to the destination. Following [8], we assume that

the CR receivers can perfectly estimate the interferences Jlk,iand Jld,i. Given the end-to-end signal-to-noise ratio Γk,i, the

instantaneous mutual information of one subcarrier can be

expressed as,

Rk,i(Psk,i, Pkd,i) =1

2log2(1 + Γk,i) b/s/Hz (7)

III. PROBLEM FORMULATION AND PROPOSED METHODS

Our objective is to determine the relay selection and sub-

carrier power allocation to maximize the total instantaneous

capacity of the CR system while the total transmit power

and interference introduced to the PUs do not exceed the

given thresholds. Let ρk,i = {0, 1} be the relay selection

decision. The total interference introduced by the CR source

transmission can be expressed as,

Isp =

L∑l=1

K∑k=1

N∑i=1

ρk,i |Gsl,i|2 Psk,i Ωl,i (8)

where, Ωl,i = Ts

∫ di,l+Bl/2

di,l−Bl/2

(sin (πfTs)

πfTs

)2

df . Similarly the

interference introduced by the CR relay transmission can be

given as,

Irp =

L∑l=1

K∑k=1

N∑i=1

ρk,i |Gkl,i|2 Pkd,i Ωl,i. (9)

Then the power allocation problem can be stated as follows:

Maximize

N∑i=1

K∑k=1

ρk,iRk,i (Psk,i, Pkd,i) (10)

subject to,∑Ni=1

∑Kk=1 ρk,iPsk,i ≤ PS∑Ni=1 ρk,iPkd,i ≤ PK , ∀k

Isp ≤ IthIrp ≤ Ith∑K

k=1 ρk,i = 1, ∀iρk,i ∈ {0, 1}, ∀k, i

Psk,i ≥ 0, ∀k, iPkd,i ≥ 0, ∀k, i

(11)

where, PS and PK are the source and the kth relay power

budgets, respectively. Ith is the maximum permissible inter-

ference to the PUs.

The optimization problem given in (10) subject to the

constraints in (11) is a mixed binary integer programming

problem and is NP-hard. Hence, it is difficult to find an

analytical solution for the joint optimal relay selection and

power allocation. As shown in [6] and [12], an asymptot-

ically optimum solution can be obtained using the dual-

decomposition method but with a much higher computational

complexity. Thus, we simplify the problem by dividing it into

two subproblems: relay selection and power allocation, and

solve the original resource allocation problem suboptimally,

but with less complexity.

A. Simplified Relay Selection

In this section we find the subcarrier-relay assignment

for a fixed transmit power allocation. It is assumed that all

subcarriers generate the same amount of interference (i.e.,

Ith/N ) to the PUs during source and relay transmissions. Let

P ints,i and P int

k,i be the source and kth relay transmit powers of

ith subcarrier, that is required to generate Ith/N interference.

Then we can express,

P ints,i =

Ith/N∑Ll=1 |Gsl,i|2 Ωl,i

(12)

and

P intk,i =

Ith/N∑Ll=1 |Gkl,i|2 Ωl,i

, (13)

respectively. In this simplified relay selection method, for

each subcarrier, we select the relay which gives the highest

capacity. For the fixed source and relay transmit powers given

in (12) and (13), we calculate the instantaneous capacity

Rk,i(Pints,i , P

intk,i ) =

12 log2

(1 +

P ints,i γsk,iP

intk,i γkd,i

1+P ints,i γsk,i+P int

k,i γkd,i

)for all

the subcarrier-relay pairs, and for each subcarrier select the

relay which gives the maximum capacity. i.e,

ρk,i =

{1, if argmax

kRk,i(P

ints,i , P

intk,i ) ;

0, otherwise.(14)

The computational complexity of this simplified relay se-

lection is O(KN).

B. Optimal Power Allocation

We use an alternate, separate optimization of source and

relay power allocation. The alternate optimization of source

and relay transmit power is widely used with AF relays, and it

is proved to converge to the optimal solution using only a few

iterations [5]. We initialize the source transmit power such that

both the interference constraint and the power constraint are

satisfied. We start with this initial source power allocation, and

optimize the relay transmit power such that the total capacity

is maximized. Then for this optimized relay power allocation,

the subcarrier transmit power at the source is optimized. These

two steps are alternately carried out such that the output of the

previous optimization is the input to the next optimization until

convergence has been achieved.

1) Relay Power Optimization: For a given subcarrier-relay

assignment and source power allocation, the relay power

optimization problem can be stated as follows:

Maximize

K∑k=1

N∑i=1

ρk,i Rk,i (Psk,i, Pkd,i) (15)

subject to, ∑Ni=1 ρk,iPkd,i ≤ PK , ∀ k∑L

l=1

∑Kk=1

∑Ni=1 ρk,i |Gkl,i|2 Pkd,i Ωl,i ≤ Ith

Pkd,i ≥ 0, ∀ k, i(16)

This is a Convex optimization problem and, can be solved us-

ing Karush-Kuhn-Tucker (KKT) conditions [18]. The solution

for the optimal relay transmit power P ∗kd,i can be obtained as,

P ∗kd,i =ρk,iγkd,i

[Psk,iγsk,i

2

(√1 + [·]− 1

)− 1

]+

[·] =2γkd,i

ln(2)Psk,i γsk,i (υk + μ∑L

l=1 |Gkl,i|2 Ωl,i),

(17)

where, the constants υk and μ are non-negative Lagrange

parameters which are selected such that the sum power

constraints and the sum interference constraint in (16) are

satisfied.

2) Source Power Optimization: For a given relay power

allocation we can express the source power optimization

problem as follows:

Maximize

N∑i=1

ρk,iRk,i (Psk,i, Pkd,i) (18)

subject to, ∑Ni=1

∑Kk=1 ρk,iPsk,i ≤ PS∑L

l=1

∑Kk=1

∑Ni=1 ρk,i |Gsl,i|2 Psk,i Ωl,i ≤ Ith

Psk,i ≥ 0, ∀ k, i(19)

Again, this is a Convex optimization problem and the

solution for the optimal source transmit power P ∗sk,i can be

obtained as,

P ∗sk,i =ρk,iγsk,i

[Pkd,iγkd,i

2

(√1 + [·]

)− 1

]+

[·] =2γsk,i

ln(2)Pkd,i γkd,i (δ + λ∑L

l=1 |Gsl,i|2 Ωl,i)

(20)

where, δ and λ are non-negative Lagrange parameters that

should be chosen such that the sum power constraint and the

sum interference constraint in (19) are satisfied.

The two optimization problems given in (15)-(16) and (18)-

(19) can be solved numerically using interior-point method

with a complexity of O(N3) [18].

C. Resource Allocation Method A

For a fixed source and relay power allocation we find the

subcarrier-relay assignment as described in Section III-A. For

this subcarrier-relay assignment we allocate source and relay

transmit powers in an optimal manner as described in Section

III-B. Numerical results show that this suboptimal resource

allocation method achieves near optimal performance in many

situations.

D. Resource Allocation Method B

The optimal power allocation described in Section III-B is

still computationally intensive since it is required to solve for

multiple Lagrange multipliers during each iteration. Thus, here

we use a simplified power allocation method which allocates

transmit power in a way such that both interference and

power constraints are satisfied. The capacity maximization is

not considered. We first find the subcarrier-relay assignment

as described in Section III-A. Let Ps,i and Pk,i be the ith

subcarrier transmit power at the source and the kth relay,

respectively. We assume all the subcarriers generate the same

amount of interference and assign subcarrier transmit powers

such that each subcarrier generates Ith/N interference. Since

this power allocation might violate the maximum transmit

power constraint we allocate the source transmit power as,

Ps,i =

{P ints,i , if

∑Ni=1 P

ints,i ≤ PS ;

min(P ints,i ,

PS

N

), otherwise.

(21)

Similarly at each relay, the relay power is allocated among the

respective subcarriers (subcarriers with ρk,i = 1) as,

Pk,i =

{P intk,i , if

∑i∈Dk

P intk,i ≤ PK ;

min(P intk,i ,

PK

nk

), otherwise.

(22)

where, Dk is the set of subcarriers relayed by the kth relay,

and nk is the number of subcarriers in set Dk. P ints,i and P int

k,i

are as defined in (12) and (13), respectively.

E. Joint Optimal Resource Allocation

With joint optimal resource allocation, all possible

subcarrier-relay assignments are considered, and for each

subcarrier-relay assignment the power is allocated in an op-

timal manner as described in Section III-B. Then the relay

selection and power allocation which results in the maximum

capacity is chosen as the optimal solution. The complexity of

the optimal method is O(KN N3).

IV. SIMULATION RESULTS

We simulate a multi-relay assisted OFDM-based CR system

with L = 2 PUs. The PUs are located at (0, 0) and (1800, 0).The CR source and the CR destination are located at (400, 0)and (1400, 0), respectively. Fig. 3 illustrates the PU and CR

distribution. The CR relays are assumed to be uniformly

distributed within a circular area with a radius r = 100m.

The center of the relay cluster is located between the source

and the destination, dsr (m) away from the source.

Fig. 3. PU and CR distribution

In order to obtain the results with the joint optimal resource

allocation method, number of subcarriers in the OFDM system

is taken as N = 6. The joint optimal resource allocation

involves higher computational complexity for large number

of subcarriers and relays. Further it requires much higher

simulation run time. Thus, the number of subcarriers is limited

to N = 6. The spectrum allocation is as shown in Fig. 4

which is adapted from [13]. The values of Δf , B1, and B2

are 0.3125MHz, 1MHz, and 2MHz, respectively [19]. The

noise variances at the relays and the destination are set to

σ2k = σ2

d = 4.14× 10−16 W. The values of interferences Jlk,iand Jld,i are taken as 1 × 10−17 W. Ts is chosen to be 4μs.

For all evaluations we consider frequency selective Rayleigh

fading channels with M = 2 multipath taps and unit fading

power. The path loss exponent α is fixed at 4. PS and PK are

set to be 20 dBm.

Fig. 4. Spectrum allocation (Simulation)

Fig. 5 illustrates the capacity variation with the interference

threshold for the proposed resource allocation methods. The

number of relays is taken as 3, and the distance from the CR

source to the relay cluster is fixed to be 300m. We have also

plotted the capacity obtained with the joint optimal resource

allocation. It can be observed that the Resource AllocationMethod B has relatively poor performance than the ResourceAllocation Method A. The performance degradation can be

compensated by a simple power allocation strategy used in

the Resource Allocation Method B. Further, the ResourceAllocation Method A shows near optimal performance at low

interference thresholds. It can be observed that at low Ithvalues capacity increases with interference. But at higher

Ith values maximum transmit power becomes the limiting

constraint and capacity saturates with increase in Ith.

Fig. 5. Capacity vs interference threshold, K = 3, dsr = 300m

In Fig. 6, we compare the capacity variation of different

resource allocation methods with varying number of relays.

The interference threshold is fixed at Ith = 5×10−15 W. Ac-

cordingly, as the number of relays increases, the performance

of the Resource Allocation Method A degrades as compared

to the joint optimal resource allocation.

In Fig. 7, the capacity versus relay location is plotted for

different resource allocation schemes with K = 3 relays and

Ith = 5 × 10−15 W. For the given PU and SU distribution,

the maximum capacity is achieved when the relay cluster is

located dsr = 300m away from the source. Also the ResourceAllocation Method A achieves close to optimal performance

when the relay cluster is located close to the source or the

destination.

V. CONCLUSION

In this paper, we have investigated the relay selection

and power allocation problem in OFDM-based CR systems

with multiple AF relays. The resource allocation problem is

formulated to maximize the total instantaneous capacity of the

CR system. Both individual power constraints and interference

constraints have been taken into consideration. The joint

optimization problem is a mixed binary integer programming

problem and hence, it is hard to find an analytical solution.

Thus, two suboptimal resource allocation methods, ResourceAllocation Method A and Resource Allocation Method B,

are proposed in this paper. We first perform relay selection

Fig. 6. Capacity vs number of relays, Ith = 5× 10−15 W, dsr = 300m

Fig. 7. Capacity vs relay location, K = 3, Ith = 5× 10−15 W

suboptimally, assuming fixed power allocation at the source

and relays. For this relay selection, the Resource AllocationMethod A allocates subcarrier transmit power in an optimal

manner and the Resource Allocation Method B allocates trans-

mit power in a suboptimal manner. Results confirm that the

proposed Resource Allocation Method A achieves near optimal

performance with much less computational complexity than

the joint optimal resource allocation.

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