Secondary Outage Analysis of AmplifyandForward Cognitive Relays with Direct Link and Primary Interference
Abstract
The use of cognitive relays is an emerging and promising solution to overcome the problem of spectrum underutilization while achieving the spatial diversity. In this paper, we perform an outage analysis of the secondary system with amplifyandforward relays in a spectrum sharing scenario, where a secondary transmitter communicates with a secondary destination over a direct link as well as the best relay. Specifically, under the peak power constraint, we derive a closedform expression of the secondary outage probability provided that the primary outage probability remains below a predefined value. We also take into account the effect of primary interference on the secondary outage performance. Finally, we validate the analysis by simulation results.
Amplifyandforward relays, cognitive radio, outage probability, spectrum sharing.
1 Introduction
1.1 Relays in Cognitive Radio
In future wireless networks, cognitive radio [1] is an exciting solution to overcome the inefficient use of spectrum as it allows spectrum sharing between the licensed user (primary user) and the unlicensed user (secondary user). In a spectrum sharing scenario [2, 3], a secondary user (SU) may share the spectrum with the primary user (PU), provided that SU does not violate the interference constraint at the PU receiverwhich prompts SU to limit its transmit power to satisfy the interference constraint.
The use of relays for secondary communication in cognitive radio, at the same time, offers better reliability and improved coverage for SU’s transmission [4, 5, 6, 7, 8]. In addition, the cognitive relays provide increased spatial diversity compared to only direct link transmission. However, the secondary system with relays, in spectrum sharing, faces particularly following two challenges that hinder its performance:

Limitations on its transmit power to satisfy the interference constraint at PU receiver.

Harmful interference from primary transmissions.
Among various relaying protocols, amplifyandforward (AF) and decodeandforward (DF) are the most popular due to their low complexity. In AF relaying, a relay amplifies the signal received from the secondary transmitter and forwards it to the secondary destination [9, 10], whereas in DF relaying, the relay decodes the received signal and forwards it to the secondary destination [11, 6].
1.2 Contributions and Related Work
1) Contributions: We perform an analysis for the outage probability of a secondary system with AF relaying, provided that the outage probability of PU remains below a predefined thresholdwe characterize the interference to PU as its outage probability. We couple the primary outage constraint with the peak power constraint. We then choose the best relay that maximizes the endtoend signaltointerference noise ratio (SINR), and derive a closedform expression for the secondary outage probability considering the interference from the primary transmission. We assume the presence of the direct link between the secondary transmitter and the secondary destination, and use the maximum ratio combining (MRC) to combine two copies of signalone via direct link and second via the best relayat the secondary destination.
2) Related Work: In [6, 12], authors derive a closedform expression of the secondary outage probability with the direct link and primary interference under PU’s outage probability constraint. In [13], authors consider a spectrum sharing scenario, where a single AF relay assists the secondary direct link communication, and the signals at the secondary destination are combined by selection combining; but the PU interference is ignored. In [14], authors study the effect of PU’s interference on secondary outage probability for AF relays in absence of the direct link, while [15] uses similar setup like [14] for DF relays. Authors in [16, 17] study a secondary system with DF relays under direct link and primary interference with the interference power constraint at PU. The references [4, 18] consider the direct secondary link along with DF relays and calculate the secondary outage probability. However, they ignore the effect of PU’s interference on the secondary transmission.
2 System Model
Consider a cognitive radio network consisting of a primary transmitter (PT), a primary destination (PD), a secondary transmitter (ST), a secondary destination (SD), and AF secondary relays (SR), as shown in Fig. 1. The ST communicates with SD via the direct link as well as th AF relay ( 1, 2, , ). The relays operate in a halfduplex mode. The communication between ST and SD happens over two time slots, each of second duration. In the first time slot, ST transmits the signal with power to SD over the direct link, and to secondary relays; while in the second time slot, the best relay amplifies the received signal and forwards it to SD with power . At SD, two received signal copiesfirst via direct link and second via the best relayare combined by the maximum ratio combining. Relay selection can be employed by a centralized entity, such as the secondary source or a secondary networkmanager or in a distributed manner using timers [19]. We consider the peak power constraint on transmit powers of ST and th secondary relay. In addition, the constraint that the primary outage probability should be below a predefined value regulates the transmit powers of ST and th secondary relay. Denote the powers of ST and th secondary relay, when they are regulated by the primary outage constraint alone, by and , respectively. Then, combining both above constraints, the maximum allowable powers for ST and th secondary relay become
(1) 
and
(2) 
respectively. The channel between a transmitter and a receiver is a Rayleigh fading channel with its channel gain denoted by . Therefore, the channel power gain is exponentially distributed with the mean channel power gain . Thus, we can write the probability density function (PDF) and cumulative distribution function (CDF) of as
(3) 
(4) 
respectively, where represents the exponential function. We consider that the channels are independent of each other, experience blockfading, and remain constant for two slots of the secondary communication, i.e., for second, as in [4, 6, 7].
3 Maximum Average Allowable Transmit Power for Secondary Transmitter and Relays
We use the primary outage probability to characterize the quality of service (QoS) of primary transmissions. The outage probability of the primary user should be below a certain value , given the interference from the secondary transmitter and relay. For a constant primary transmit power , we can calculate the primary outage probability as
(5) 
where is the primary user’s desired data rate, is additive white Gaussian noise (AWGN) power at all receivers, and is the transmit power of ST. The term represents the received SINR at PD. In (5), at the maximum allowed average power for ST, i.e., when = , the weak inequality becomes equality. Thus, from (5), conditioned on , we can write
(6) 
where . Thus, we can write (6) as
(7) 
Taking expectation with respect to , we obtain
(8) 
Rearranging the terms and using (6), we find the maximum secondary transmit power under alone primary outage constraint as
(9) 
where . After combining with the peak power constraint, the maximum average allowable transmit power for the secondary transmitter can be given by (1). Similar to (9), the transmit power of th secondary relay regulated alone by the primary outage constraint can be readily found as
(10) 
After combining with the peak power constraint, the maximum average allowable transmit power for relay can be given by (2).
4 Derivation of Secondary Outage Probability
The AF relays cooperate opportunistically, where the relay with the largest endtoend SINR at the secondary destination is selected to forward the received signal in the second time slot. Thus, after receiving the signal from both time slots, SD combines them using MRC technique. The endtoend SINR is given by [20, 21]
(11) 
where is the set of relays given as , , , and denote SINR at the th relay, and SINR at SD due to direct transmission and relaying respectively, which are given by
(12) 
(13) 
(14) 
For analytical tractability, we use the upper bound given in (11), which is tight in medium to high SINR range [20, 21]. We can obtain and from (1) and (2). The secondary outage occurs when the instantaneous SINR of the secondary transmission falls below the designated threshold, . Thus, we can write the secondary outage probability as
(15) 
where with is the desired secondary data rate. From (11), we can see that, , , and () contain a common term , that makes them dependent. Thus, conditioning on and denoting , we can write
Now, we have
(17)  
We also have
(18)  
where (18) results from the independence of and , given . For ease of presentation and without compromising the insight into analysis, we assume that mean channel gains of ST are the same for all relays and so is for SD, PT, and PD channels. Thus, we have . Next, given , we compute as
(20) 
We also compute as
(21) 
(22) 
Hence, PDF of is given by
(23) 
From (LABEL:eq:main), we have
(24) 
Hence, the outage probability can be expressed as
(25) 
where is the expectation operator on and
(26) 
(27) 
(28) 
We use the following results in (29) and (30) to derive the integrations : When is an exponential random variable with mean , we have
(29) 
(30) 
with . Using (29), we compute as
(31) 
To compute , we write it as
(32) 
where
and
To compute and , we use the following notations for convenience of presentation:
(35) 
Thus, we can write
(36) 
For and , we have and we can write (36) in terms of the exponential integral as shown later in this section. Using the substitution, and denoting , we write
(37) 
Using the partial fraction expansion, we have
(38) 
Thus, we can write
(39)  
(40)  
(41) 