OFDMA-Based Cognitive Radio Networks With Relaying Capability Sakineh Golrezaei-Khuzani and Masoumeh Nasiri-Kenari Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran. email:
[email protected] , email:
[email protected]
Abstract In this paper, a novel OFDMA-based cognitive cooperative relaying scheme is proposed in which cognitive users assist primary users by relaying their information. Both primary users (PU) and cognitive users (CR) communicate to a common base station (BS). Based on the received feedback, cognitive users relay data of primary users. Two different schemes of relay assignment and power allocation are considered. Probability of error of primary user and outage probabilities of both primary and cognitive users are investigated. Our analyses show substantial improvements in the probability of error and outage probability of primary user while the outage probability of the cognitive user does not change significantly. We also perform several simulations to corroborate our theoretical results.
Index Terms cooperation, cognitive radio, OFDMA, outage probability, probability of error.
I. I NTRODUCTION Diversity has been shown to be one of powerful techniques to combat fading in wireless channel. Cooperation in which antennas of different users are shared can provide antenna diversity and substantial performance improvement [1]- [2]. Cooperative diversity can be classified in two basic strategies; amplify and forward (AF) and decode and forward (DF). In AF scheme, relay amplifies the received signal while in DF scheme, relay demodulates received signal before
retransmission. These strategies can be adaptive. Two adaptive strategies including incremental and selection relaying are proposed in [1]. In incremental relaying [1], cooperation takes place based on feedback from a central node and when it is necessary. Thus, only data of unsuccessful subcarriers are relayed. In selection relaying [1], if the channel gain between source and relay lies above a threshold, the relay retransmits the information of source. Recently, due to scarcity of radio spectrum and highly inefficient resource utilization of fixed (licensed) spectrum allocation, cognitive radio has gained wide attentions. Cognitive radio brings better spectrum utilization by allowing unlicensed (cognitive) users to utilize licensed band when they would not introduce any interference to licensed users. Cognitive users must detect spectrum holes unoccupied by primary users and adjust their transmission parameters [8]. Orthogonal Frequency Division Multiple Access (OFDMA) is widely considered as a potential multiple access technology of cognitive radio because of its highly flexible spectrum allocation. [3]- [4] propose different algorithms for resource allocation in OFDMA-based cognitive systems. On the other hand, cooperative techniques can be used in OFDMA-based systems. In [5], two cooperative protocols are considered for OFDMA networks and their corresponding capacities are investigated. Adaptive resource allocation techniques in OFDMA-based relaying system are studied in [6]. Most of the previous works, on using cooperation in OFDMA-based system, investigate resource allocation, but there are not much studies on different relay assignment schemes. [9] combines the benefit of cognitive radio and cooperative transmission. The authors consider a scenario with one primary user and one cognitive user in which the cognitive user acts as a transparent relay for the primary user, and they investigate the system performance from MAC layer view. In this paper, we investigate a more complex scenario from physical layer aspect and study the effect of cooperation on the primary user in term of outage probability and probability of error and on the cognitive user in term of outage probability. In [10], the probability of error performance analysis is investigated for simple DF strategy when there is only one relay. We investigate the probability of error for selection relaying in DF strategy when the relay is chosen among some cognitive users based on different selection rules. To this end, we consider a new OFDMA-based cognitive cooperative relaying network. In the network considered, both the primary user and cognitive user communicate to a common 2
Base-Station (BS). Cognitive users try not to interfere with primary users and also to improve the performance of primary users by relaying their information. The system consists of multiple clusters, where each cluster contains one primary user and a number of cognitive users close to the primary user. Cognitive users of each cluster relay data of the primary user when it is necessary using orthogonal channel. The orthogonality is guaranteed by assigning non-overlapping time slots to relay and primary users [14]- [15]. In the proposed system, the combination of selection and incremental relaying is employed, while in previous works, these relaying schemes are considered and investigated separately. We consider two different relay assignment schemes. In the first scheme, for each subcarrier of the primary user that exposes outage one cognitive user is selected as a relay. The selected user is chosen among the cognitive users that are capable of decoding the subcarrier (selection relaying) and that has highest CR-BS channel gain power [7]. In the second scheme, for all of the subcarriers which experience outage, one cognitive user is selected as a relay. This cognitive user is chosen in a way that the average received SNR due to all unsuccessful subcarriers at BS is maximized. In both schemes, selection DF strategy is used where a relay must first decode data and if data has been correctly decoded, the relay retransmits data. The way that the cognitive users allocate power to relaying primary user’s data can affect the primary and cognitive users performance. Two different power allocations are considered. While in the first scheme, the total power dedicated to the relaying unsuccessful subcarriers of the PU is fixed, in the second scheme, the power allocated to relaying each subcarrier is fixed. We assume that data of users is not jointly encoded across subcarriers. So, the outage probability and probability of error are investigated for each subcarrier. Furthermore, we characterize the cognitive user performance by the outage probability. Simulation results are provided to validate our proposed schemes and support our theoretical analysis. The organization of this paper is as follows. Section II describes the system model. While Section III presents the outage probability and probability of error of the primary user for the first relay assignment scheme, Section IV investigates the analysis for the second relay assignment scheme. In Section V, we analyze the cognitive user performance. In Section VII, some numerical results are presented. Finally, we conclude the paper in Section VIII. 3
II. S YSTEM MODEL AND PROBLEM FORMULATION We consider an OFDMA-based multiple cluster system with one base station, one PU in each cluster and multiple fixed cognitive users [12], see Fig. 1. The subcarriers assigned to each cluster is non-overlapping. Moreover, different clusters are separated based on their geographical proximity, thus, we, well, neglect the effect of inter-cluster interference. All users including the primary and cognitive users have their own data and want to transmit their data to BS (uplink). Full channel state information (CSI) is assumed to be available to BS. For each cluster according to the channel magnitude response, from available subcarriers, BS selects several subcarriers with the highest channel gain for each PU 1 and the remaining subcarriers will be assigned to cognitive users. For each cluster, the communication takes place in two time slots. In the first time slot, both the PU and cognitive users send their own data to the BS using their own allocated subcarriers. In this time slot, in addition to BS, cognitive users receive data of the PU. A central node, which can be the BS, based on the information received, makes decision about which cognitive users to be selected as the relay for the subcarrier(s) of the PU that expose outage in this time slot (incremental relaying), and it informs the selected cognitive users. The information consists of CR-BS channel gains of the cognitive users that are able to decode the unsuccessful subcarriers of the PU. In the second time slot, the PU remains silent. However, cognitive users can send their data using their own subcarriers and they also have opportunity to use the subcarriers of the PU which don’t need to be relayed. Based on the feedback received, the selected relays forward the data of unsuccessful subcarriers of the PU to the BS using the same subcarriers. Received signals of k th subcarrier of the PU at BS and at ith cognitive user (CRi ) in the first time slot are
p yPk U,BS = Pk hkP U,BS XPk U + ZPk U,BS p yPk U,CRi = Pk hkP U,CRi XPk U + ZPk U,CRi
k ∈ L,
(1)
k ∈ L.
(2)
Where Pk and XPk U are the transmitted power and information symbol of k th subcarrier, and 1
The number of subcarriers allocated to each PU depends on the throughput demand of the PU
4
ZPk U,BS is additive white Gaussian noise with variance N0 . L is the set of subcarriers occupied by the PU. hka,b represents the Channel gain at subcarrier k between node a and node b, which for different a and b is assumed to be zero-mean, independent, circularly symmetric complex −α Gaussian random variables with variances Ra,b , where Ra,b is the distance between node a and
node b and α is the propagation loss factor. We have incorporated path loss effects but neglected shadowing. This model can facilitate to investigate the system with various geographic settings. For simplicity, the transmitted power of the PU is assumed to be equal for all subcarriers, i.e.,Pk = P . Symbols of each subcarrier which are not received successfully in BS will be retransmitted by one of the cognitive users in the second time slot. Received signal of k th subcarrier at BS in the second time slot is given by
k yr(k),BS =
p k k Prk hkr(k),BS Xr(k) + Zr(k),BS
k ∈ J,
(3)
k where r(k) is the relay of subcarrier k, Prk is the transmitted power of the relay, Xr(k) denotes k symbol of subcarrier k transmitted by the relay, and Zr(k),BS is additive white Gaussian noise.
J is the subset of L consisting of all subcarriers of the PU that their transmissions fail in the first time slot. As stated before, relay assignment schemes are centralized in which one central node has ability to choose the relays based on information received. This central node can be the BS or a central cognitive user. In addition to relay assignment responsibility, the central node makes decision about resource allocations. Thus, to reduce the overhead at BS, it is better to have a central cognitive user for each cluster 2 .Two different relay assignment schemes are investigated. In the first scheme, among all cognitive users that can decode data of subcarrier k, the best cognitive user is selected as the relay [7]:
r(k) = CRi
2
2
max
∈Dk (P U )
|hkCRi ,BS | .
(4)
The signaling transmissions take place in orthogonal channels, which results in reduction of available bandwidth. However,
for a slow fading channel, relays do not change often, which leads to minimal overhead.
5
Where Dk (P U ) is the set of cognitive users that can decode information of the PU at subcarrier k. If the received SNR of subcarrier k by a cognitive user falls below a specific value, it is assumed that the cognitive user can not decode subcarrier k. In the second scheme, only one relay is selected for all unsuccessful subcarriers. This relay is selected in a way to maximize the average received SNR at BS; the details will be given later. In both assignment schemes, according to selection relaying policy, if the selected relay can decode data of the primary user, it retransmits the data. We apply two different power allocations schemes. In the first scheme, the total power advocated to cooperation is fixed, and as a result the outage probability of one subcarrier will be dependent on other subcarrier conditions in the first time slot. In the second power allocation scheme, the allocated power to each subcarrier is fixed.
III. T HE FIRST RELAY SELECTION SCHEME In this section, we characterize the performance of the first relay assignment scheme.
A. Outage probability When the maximum average mutual information in subcarrier k is below a target rate, outage will be declared. Assuming an independent and identically distributed zero-mean, circularly symmetric complex Gaussian input, the maximum average mutual information between the primary user and BS at subcarrier k under cooperative and direct transmissions respectively are [2]:
k
k ICO
2
|hr(k),BS | |hkP U,BS |2 1 + Prk ), = log2 (1 + P 2 N0 N0 |hkP U,BS |2 1 I k = log2 (1 + P ). 2 N0
(5) (6)
where the parameters are as defined in (1)-(3). 1) Fixed total power for relaying: In this case, the allocated power and outage probability of one subcarrier depend on the number of subcarriers that require relaying. Thus, the final outage 6
probability of each subcarrier k is
k Pout =
l X
P r[j unsuccessful subcarriers including subcarrier k]×
j=1
P r[subcarrier k exposes outage after cooperation|j unsuccessful subcarriers including subcarrier k] =
l X
k (j). Pj,l × Pout
(7)
j=1
Where j is the number of unsuccessful subcarriers in the first time slot, .i.e., |J|, Pj,l denotes the probability that j subcarriers including subcarrier k expose outage in the first time slot and need k relay, Pout (j) is the outage probability of subcarrier k conditioned on j, and l is the number of
subcarriers that have been allocated to the PU, i.e., |L|. When the mutual information of the PU at subcarrier k in the first time slot is below the desired rate, i.e., R: |hkP U,BS |2 1 log2 (1 + P ) < R, 2 N0
(8)
data of this subcarrier needs to be relayed. Due to exponential probability density function (PDF) of |hkP U,BS |2 , the outage probability in direct transmission in the first time slot is computed as C |hkP U,BS |2 1 − 1 ) < R] = 1 − e ηP U,BS . Pout = P r[ log2 (1 + P 2 N0
Where C = 22R − 1, and ηa,b = Pa
−α Ra,b N0
(9)
is the average received SNR at receiver b when transmitter
a allocates power Pa to the subcarrier. By assuming that the subcarriers are independent, Pj,l in (7) is easily computed: Pj,l =
l−1 1 j 1 l−j (Pout ) (1 − Pout ) . j−1
(10)
Since subcarrier k exposes outage in the first time slot, if non of the cognitive users can decode the data of the subcarrier k, this subcarrier experiences outage after cooperation as well. k Thus, Pout (j) can be expressed as [2]:
k Pout (j) = PN D +
X
k Pout (j|Dk (P U ))P r[Dk (P U )],
Dk (P U )|Dk (P U )6=∅
7
(11)
k where Dk (P U ) is defined in (4), P r[Dk (P U )] is the probability of set Dk (P U ), Pout (j|Dk (P U ))
is the outage probability of subcarrier k conditioned on Dk (P U ) when subcarrier k along with j − 1 other subcarriers expose outage, and PN D is the probability that non of the cognitive users can decode the data of the PU in subcarrier k. When data of j subcarriers needs to be relayed, the power
PR j
is allocated to each subcarrier, where PR is the total power dedicated for relaying.
Then, from (4) and (5), the outage probability easily is given by
|hkP U,BS |2 1 PR |hkCRi ,BS |2 k (j|Dk (P U )) = P r[ log2 (1 + P Pout + max ) < R]. 2 N0 N0 CRi ∈Dk (P U ) j | {z } | {z } Y
(12)
X
From (8) and (9) and by assuming independent channel gains for different cognitive users, the PDF of Y and the CDF of X in (12) are easily computed:
fY |Y T2 ] =
FT2 (x)fT1 (x)dx
α α α 1 − e−xRCRm ,BS RCR e−xRCRi ,BS dx. i ,BS
Y
(24)
CRm ∈Dk (P U ),CRm 6=CRi
For obtaining the probability of error, first we must derive the PDF of the instantaneous SN R. By using the maximum-ratio combing (MRC) at BS, from (4) and (5), instantaneous SN R at subcarrier k conditioned on j, is given by
SN Rjk = P
|hkP U,BS |2 PR |hkCRi ,BS |2 + max . N0 N0 CRi ∈Dk (P U ) j
(25)
From the definitions of X and Y in (12) and using the PDF of Y and the CDF of X in (13)-(14), we obtain: R Cf Y |Y
