2011 International Conference on Advanced Technologies for Communications (ATC 2011)
Incremental Cooperative Diversity for Wireless Networks under Opportunistic Spectrum Access Vo Nguyen Quoc Bao
Nguyen Tuan Duc
Hoang Dinh Chien
Telecom. Dept. Posts and Telecom. Inst. of Tech., Vietnam Email:
[email protected]
School of EE Ho Chi Minh Internaltional Uni. Email:
[email protected]
Telecom. Dept. Ho Chi Minh City Uni. of Tech. Email:
[email protected]
Abstract—This paper analyzes the performance of incremental cooperative networks under opportunistic spectrum access where the best relay opportunistically borrows spectrum allocated to a primary user to help the source transmission if the direct link is below a given threshold. Specially, we provide the system outage probability and bit error probability derived in closed-form expression over Rayleigh fading channels. Theoretical analysis and computer simulation are in good agreement showing that the proposed system always outperforms direct transmission and full diversity gain cannot be achieved under opportunistic spectrum access.
I. I NTRODUCTION Since the legendary work by Mitola was published twelve years ago [1] introducing cognitive radio (CR), this concept has subsequently been widely studied for the improvement of spectrum exploitation [2]. In particular, cognitive radio can solve the spectrum congestion problem due to exclusive assignment of frequency spectrum in radio communications by allowing secondary users (SUs) to intelligently identify unused spectrum bands (originally allocated to primary users) and then adaptively use them. Recent studies have shown that cooperative technique can be used in cognitive wireless systems to mitigate interference and to improve spectrum efficiency [3]–[7]. Besides, it is able to provide spatial diversity in cognitive relay networks, where secondary users (SU) can act as relaying nodes for the transmission of primary networks or secondary networks. However, as reported in [8]–[10], full diversity is not achieved when the spectrum acquisition is not always guaranteed in cognitive wireless relay networks using either the well-known repetitionbased relaying scheme [11], [12] or selection cooperation [13]–[15]. In this context, this paper proposes a multinode incremental relaying scheme operating under opportunistic spectrum access. The idea is motivated by [8] and [16] where the secondary destination will request the help from the best cognitive relay if the direct link between the secondary source and the secondary destination does not satisfy the network quality of services (QoS). The proposed scheme is useful for cognitive ad-hoc systems where CR promises to improve the network spectrum-utilization efficiency and to reduce the load for relaying nodes as compared to conventional cooperative networks.
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The main contribution of this paper is therefore to provide closed-form expression of outage probability and bit error probability for spectrum-sensing opportunistic incremental networks over independent but non-identically distributed (i.n.d.) Rayleigh channels. The advantage of the resulting formulas is to avoid the need for lengthy and time-consuming Monte Carlo simulation. Moreover, to the best of authors’ knowledge, the expressions derived in this paper are new and not reported in the literature so far. The rest of this paper is organized as follows. In section II, we introduce the model under study and describe the proposed protocol. Section IV shows the formulas allowing for evaluation of the outage probability, the average BER of the system. In Section IV, we contrast the simulations and the results yielded by theory. Finally, the paper is closed in section V. II. S YSTEM M ODEL We consider the general configuration of cognitive incremental relaying networks where the data transmission of the secondary source-destination pairs is possibly helped by N secondary relay nodes. Each secondary node is equipped with a single antenna and that all the secondary nodes are halfduplex and, thus, cannot simultaneously transmit and receive. The data transmission in the network takes place two phases: broadcast phase and incremental phase. In the broadcast phase, the secondary source transmits its information, which is received by the destination and the relays, thanks to broadcast nature of wireless channels. At the end of the first time slot, the destination checks the signal quality of the direct link between the source and the destination. If it is greater than a predetermined threshold (γth ), the destination will broadcast a feedback message indicating the successful reception at the destination to the source and all relays. Having received such the message, the source will make use of the following time slot to send a new signal while the relays will not perform any transmission, i.e. still keep idle. Otherwise, a ”failure” message is sent to request the help of the best opportunistic relay in the second time slot, named as the incremental phase. Different from standard cooperative incremental relaying networks [16], [17], each incremental phase typically consists of two essential sub-phases: 1) a spectrum sensing sub-phase, in which cognitive relaying nodes attempt to detect available spectrum holes; and 2) a data transmission sub-phase, in which the
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best relay among available ones amplifies and then forwards the received signals towards the secondary destination [14], [15]. Without any a priori knowledge of primary signals, as in [8]–[10], [18], all secondary relaying nodes perform energy detection - the simplest spectrum sensing technique - to detect currently unused bands [19], [20]. It simply treats primary signals as noise and decides on the presence or absence of the primary signal based on the energy of the observed signal. However, in practice, the relay nodes may not always be able to acquire spectrum holes resulting in the fact that such relays cannot always involve in cooperative transmission. In Rayleigh fading channels, the average probability of detection for each potential relay is reported in [20, eq. (9)]. It is assumed that every channel between the secondary nodes experiences slow, flat, Rayleigh fading. Due to Rayleigh fading, the channel powers denoted by |hSD |2 , |hSRk |2 and |hRk D |2 are independent and exponential random variables whose means are λ0 , λ1,k and λ2,k , respectively. Let us define 2 2 2 γ0 = P1 |hSD | , γ1,k = P1 |hSRk | , and γ2,k = P2 |hRk D | as the instantaneous SNRs for the links S → D, S → Rk , and Rk → D, respectively, where P1 and P2 are the corresponding average transmit signal-to-noise (SNRs) for the source and the relays. It is assumed that the receivers at the destination and relays have perfect channel state information but no transmitter channel state information is available at the source and relays. III. P ERFORMANCE A NALYSIS In this section, we focus on the derivation of a closed-form expression for the outage probability and the bit error rate of the considered system. To achieve our goal, we first develop the PDF of the instantaneous SNRs in transmission phase, which then is used for the derivation. A. Outage Probability The outage probability is an important quality of service (QoS) measure, which is defined as the probability that the end-to-end instantaneous SNR is below the predetermined threshold. Mathematically, the outage probability can be derived as follows: Pr(O)
=
Pr{γ0 ≤ γth } Pr{O|γ0 ≤ γth } + Pr{γ0 > γth } Pr{O|γ0 ≤ γth }
=
Pr{γ0 ≤ γth } Pr{O|γ0 ≤ γth }.
=0
(1)
In contrast to conventional incremental cooperative networks, the number of relays involved in the incremental phase is not fixed, i.e. varying according to the result of the spectrum sensing sub-phase. With opportunistic relaying, only the best relay among relays successful in obtaining spectrum forwards the received data toward the destination as per the rule of amplify-and-forward (AF). Denoting R as the set of potential relays, it is obvious that its cardinality, K = |R|, is a random variable taking values from 0 to N . For each K, N = N !(NK!−K)! possible subsets of size K. Thus, there are K
applying the law of total probability [21], the conditional outage probability, Pr{O|γ0 ≤ γth }, can be re-written as Pr{O|γ0 ≤ γth }
N K Pr(R = {Rn1 , · · · , RnK }) . (2) = K=0 n1 ,...,nK =1 ×Pr(O|R = {Rn1 , · · · , RnK }∩γ0 ≤ γth ) n1
