# Resource Allocation and Outage Analysis for An Adaptive Cognitive Two-Way Relay Network

## Abstract

In this paper, an adaptive two-way relay cooperation scheme is studied for multiple-relay cognitive radio networks to improve the performance of secondary transmissions. The power allocation and relay selection schemes are derived to minimize the secondary outage probability where only statistical channel information is needed. Exact closed-form expressions for secondary outage probability are derived under a constraint on the quality of service of primary transmissions in terms of the required primary outage probability. To better understand the impact of primary user interference on secondary transmissions, we further investigate the asymptotic behaviors of the secondary relay network including power allocation and outage probability, when the primary signal-to-noise ratio goes to infinity. Simulation results are provided to illustrate the performance of the proposed schemes.

Two-way relay, cognitive radio networks, outage probability, power allocation, relay selection.

## 1 Introduction

\IEEEPARstartCognitive radio techniques enable secondary users (SUs) to access the frequency bands originally licensed to primary users (PUs) while ensuring that the quality of service (QoS) of primary transmissions is not affected, which can improve spectral efficiency significantly [1]. However, the SUs often operate with constrained transmit power to guarantee the QoS of PUs in terms of interference temperature, thus limiting the throughput and coverage of the secondary system. To combat this problem, cooperative diversity systems involving scattering relay networks have recently been researched to exploit the spatial diversity gain and to enhance the secondary channel performance [2], [3]. It has also been shown that cooperative diversity with relay selection can achieve the same diversity-multiplexing tradeoff as achieved by the traditional cooperation protocols where all relays are involved in forwarding the signals from source nodes [4], [5].

The conventional one-way relay scheme suffers from a loss in spectral efficiency because of half-duplex transmission [6]. To circumvent this disadvantage, a two-way relay system was proposed in [7]. A two-way relay system has two transmission phases. During the first phase, two secondary transceivers (STs) simultaneously broadcast their signals. After successfully receiving the combined signals, the relay node forwards the signals to the two STs during the second phase. Since there are two different relaying paths, the total spectral efficiency of a two-way relay system can be doubled compared with a conventional one-way relay system. Two protocols for two-way relay networks, commonly known as decode-and-forward (DF) and amplify-and-forward (AF) relaying, were proposed in [7]. Based on these, several cooperative diversity schemes for two-way relay networks with relay selection have been proposed [8, 9, 10, 11]. Note that all the aforementioned works studied non-cognitive radio networks. However, in practical cognitive radio systems, PUs and SUs can simultaneously transmit signals by sharing the same spectrum resources. As a result, the relays and secondary receivers inevitably suffer interference from PUs. From the viewpoint of SUs, these interferences come in the form of co-channel interference (CCI) and it is important to analyze their effect on system performance.

### 1.1 Related Work

So far, the literature that studies outage performance and resource allocation in cognitive two-way relaying networks with CCI is relatively scarce. Interference was considered only during the second transmission phase in [12], where exact outage probability was obtained while ignoring the noise at the receivers. In [13], the exact outage probability was derived under a cognitive two-way relay network setting. However, the system outage event was defined as having either one of the two STs in outage, which simplifies the derivation but does not represent system outage correctly. In [14], a max-min strategy over instantaneous achievable channel rates was employed to address relay selection and power allocation for cognitive two-way AF relaying networks. The CCI from the PUs was modeled as Gaussian noise, which does not characterize the practical cognitive radio communication appropriately. Relay selection and power allocation schemes in cognitive two-way DF relaying network were studied for the first time to maximize the achieved sum rate in [15]. However, the CCI was considered at primary nodes whereas the interference resulting from primary transmission in secondary receivers was not considered. In [16], the power allocation problem in the cognitive two-way relay network with amplify-and-forward strategy was studied and the secondary sum rate was maximized whereas the optimization problem dealt with the terminal side without any control on relay parameters. Instantaneous secrecy rate was maximized in [17] for relay selection, which is the same as maximizing signal-to-noise ratio (SNR). Besides the inappropriate system modeling of CCI, the resource allocation schemes in the aforementioned works lead to the maximization of the instantaneous SNR. These resulting resource allocation schemes require perfect knowledge of instantaneous channel state information (CSI) between the nodes in the cognitive network. In fact, it is highly computationally complex and also sometimes impossible to accurately learn the knowledge of instantaneous CSI in the network. Moreover, in the cognitive radio network setting, the knowledge of instantaneous CSI for the primary interference transmitted from the primary network to the secondary network is required if those schemes are to be implemented, which is extremely difficult if there are no pilot symbols specifically designed for the secondary nodes in the primary signal. Therefore, optimal power allocation for outage probability minimization comes into consideration in such a scenario, which only requires the knowledge of statistical CSI [18, 19, 20].

### 1.2 Main Contributions

In this paper, we investigate an adaptive cooperative diversity scheme in cognitive two-way relay networks using the DF protocol, where mutual interference between PUs and SUs is considered. The STs broadcast their signals to the relays and to each other through the direct link during the first phase. During the second phase, if the relays can decode the signals received during the first phase, the best relay is chosen to forward the signals to the STs; otherwise, the STs adaptively repeat the same transmission to each other through the direct link as during the first phase. Then, the STs combine the two copies of the received signals after the two transmission phases.

The main contributions of this paper are as follows:

1) We explore the adaptive use of the direct link and the relay link to achieve higher system performance in cognitive DF two-way relaying networks. Our analysis can also be used for the scenario where only relay link is available.

2) For the first time, a power allocation scheme for STs and the relays is developed that minimizes the secondary outage probability under a QoS constraint from the primary network, requiring no instantaneous CSI of the transmission links.

3) The optimal relay selection approach for this two-way system is also provided to minimize outage probability, which requires only statistical CSI. To the best of our knowledge, this is the first work to study the resource allocation problem using statistical CSI information for the proposed general framework. An exact closed-form expression for the secondary outage probability is also derived in this paper. Asymptotic behavior of the secondary system is analyzed given that the primary user SNR goes to infinity.

The rest of the paper is organized as follows: we give the system model in Section II. Section III provides the outage analysis of the relaying network. Based on the outage analysis, we address the power allocation and relay selection problems in Section IV. We analyze the asymptotic behavior of the system in Section V. Numerical simulation results and conclusion are given in Section VI and Section VII.

## 2 Proposed Adaptive Cooperation Scheme

### 2.1 System Model

Consider a general spectrum-sharing cognitive two-way relaying network as shown in Fig. 1. In the primary network, a primary transmitter sends data to a primary destination . Meanwhile, in the secondary relay network, STs and exchange information with each other. Secondary relays , are available to assist secondary data transmissions using the DF protocol. We assume that the channel link from to undergoes Rayleigh fading with instantaneous coefficient . Therefore, the channel gain is exponentially distributed with mean . We also assume reciprocity of all the channels and zero-mean additive white Gaussian noise (AWGN) with variance at each receiver.

During the first phase, STs and simultaneously broadcast their signals to the relay and to the corresponding receiver, i.e., , . By employing multiple antennas and self-interference cancelation (SIC), the STs can send and receive at the same time [21]. Thus, considering coexistence of primary transmission, the received signal at the primary receiver can be expressed as

(1) |

where , and are the transmit powers of , and respectively, , and denote the unit-mean-energy symbols transmitted respectively by , and , and is the AWGN. The QoS of primary transmissions is quantified by the outage probability in this paper. The primary QoS guarantee is represented by the inequality that the outage probability of primary transmission does not exceed a predefined outage probability threshold , which is expressed as

(2) |

where with being the primary data rate. We calculate and write the primary QoS guarantee during the first phase as

(3) |

where , and denote the transmit SNR at the primary transmitter, and STs and , respectively. In order to ensure (2.1), we adopt the static power allocation scheme to guarantee the QoS for primary transmission. First we rewrite (2.1) and find the constraint in terms of the power of the STs and which is denoted by where

(4) |

and .

### 2.2 Proposed Adaptive Cooperation with Relay Selection

In this subsection, we focus on the adaptive relay cooperation scheme with relay selection. During the first phase, some relays may successfully decode the received signals, among which the best relay is chosen to forward the data to STs. First of all, the received signal during the first phase at is represented as

(5) |

where is the zero-mean AWGN with variance . For convenience, we denote to be the set of all the relays and those relays that are able to successfully decode the received signals constitute a set . Therefore, is a dynamic relay set that depends on the decoding status of the relays. Note that the relay set determines whether a direct transmission between STs is needed or not. If it is not needed, the relay set determines the feasible relay that can be chosen to forward the signal.

During the second phase, if is empty, i.e., , STs and will repeat the transmission of the original signals to each other through the direct link. In this case, with SIC and signal combination using maximum ratio combining (MRC) method, the SINR at each ST can be respectively expressed as

(6) | |||

(7) |

Otherwise, if is not empty, where , the relay chosen within will transmit its decoded data stream to the two STs. Finally, STs combine the two copies of the received signals using SIC and MRC methods. Therefore, the respective SINR is given as

(8) | |||

(9) |

where is the transmit power of , and and are the ratios of total transmit power at for the transmission of original signals from and to and , respectively.

## 3 Outage Performance Analysis

In this section, we give the analysis of the outage probability of the proposed adaptive relay cooperation scheme. The exact results of secondary outage probability are derived. Based on the results, we shall provide the resource allocation schemes.

We first study the outage in the relay nodes as defined in (10). According to the achievable rate region as discussed in [22, 12], the event of each failing to decode the received signals and resulting in outage is denoted as and can be expressed as

(10) |

where , , with and being the data rates at STs and , respectively, and are correlated and represent the signal-to-interference-plus-noise ratio (SINR) at with respect to signals from and respectively.

###### Proposition 1

The outage probability of each relay is given as

(11) |

where , , and .

See Appendix 9.

As we can see from the proposition, the outage probability is dependent on the transmit powers of the networks, data rates, and the statistical conditions of the channels linked to the relay . Note that only the relays that are not in outage can be chosen to forward the signals to the STs. Depending on the channel coefficient , the outage probability takes different forms of expressions. Thus, further analysis in this paper that is based on is conducted in a case-by-case fashion.

Now we study the outage behavior of secondary system under the condition that the relay node is chosen and can successfully forward the signals to the STs and . Specifically, if forwards the signals as the relay, the secondary system is in outage if at least one of the two STs can not successfully decode the received signal. Let denote the corresponding outage event.

(12) |

where and are defined in (8) and (9), respectively. The STs are in outage if they can not receive and decode the signals as is implied by (12).

###### Proposition 2

In the high SNR regime, i.e., when , the probability that the STs are in outage is given as

(13) |

where and

See Appendix 10.

The probability characterizes the outage property of the secondary system when the relay node is chosen to forward the signals to the STs. From the expressions of and , we observe that the choice of relay has an influence on the secondary system outage performance by the following means: the forward power ratios and , transmit power of the relay , and the channel conditions of the links between the relay and the transceivers and .

Here, we provide the exact probability that the secondary system is in outage.

With (1), the probability of the case can be simply given as

(14) |

and the outage probability of the secondary network given this case is expressed as

(15) |

Similarly, the occurrence probability of the case is

(16) |

where is the complementary set to . Based on (29), we can also derive the conditional secondary outage probability in this case as

(17) |

with where and The PDFs and are given in Appendix 11. Then, taking account of various integral intervals and binomial expansion, we derive the expression of as in (18).

(18) |

where is the non-empty subset of with elements.

## 4 Power Allocation and Relay Selection

In the following, we optimize the outage performance of the secondary receivers in the relay network to address the problems of power allocation and relay selection. In the context of power allocation for the DF relaying network, we have to determine the powers of STs and , represented by and , power of the relay , represented by , and the power ratio for transmission of different data streams at the relay, represented by and .

Next, we determine the power allocation for the STs, i.e., and . First, note that the quality of the direct link between the STs may be severely affected due to long distance. This also partially constitutes the reason to employ relays since the links between the STs and the relays are relatively of much higher quality as well as providing diversity. To effectively make use of the relay channel diversity to enhance system performance, we maximize the minimum probability that the link between the STs and a relay is connected, while and satisfy constraint , which can be expressed as

(24) |

where

Recalling (1), we give the optimal power allocation of to minimize while satisfying the constraint .

Let represent the corresponding with respect to . We provide the integrated power allocation strategy of in the following lemma.

###### Lemma 1

The optimal power allocation to minimize is given by

(25) |

where

with and {proof} See Appendix 12.

Then, let us look at the allocation schemes at the relay, i.e., the power allocation for the relay node and relay selection. We give the power of the relay, i.e., in the following lemma.

###### Lemma 2

The optimal transmit power of the chosen best relay is given by

(26) |

See Appendix 13.

During the second phase, the selected relay forwards the combined data streams to the STs with power ratios and . Here, we address the relay selection and provide the power allocation for optimal and to minimize overall secondary system outage probability. Note that when is chosen for relaying, the secondary outage probability is , which is hereby to be minimized.

###### Lemma 3

The optimal power ratios of and are given by

(27) |

and

(28) |

where .

See Appendix 14.

Therefore, these three lemmas constitute the power allocation scheme including all the transmission powers of the secondary nodes. Note that the derived optimal also apply in the case where there is no direct link between the STs.

We substitute the derived optimal and back into . The relay selection scheme selects such that the system outage probability , given that is selected, is minimized, which can be written as

(29) |

It indicates that the proposed relay selection criterion considers the statistical instead of instantaneous CSI of the primary and secondary networks. The benefit of this criterion is prominent since the instantaneous CSI of the networks is typically difficult to obtain. However, the statistical CSI of the primary and secondary networks are much easier for the relays to obtain. Thus, in the particular settings of cognitive relay networks, it is highly desired that power allocation and relay selection request only statistical channel conditions. Note that both centralized and distributed relay selection algorithms can be developed using the proposed relay selection criterion. Specifically, for a centralized relay selection algorithm, an additional node is needed to maintain a table, which consists of relays and the corresponding statistical CSI. The selection and the related management are completed within this node. For a distributed relay selection algorithm, each relay maintains a timer which is assigned an initial value inversely proportional to min. Therefore, the best relay exhausts its timer the earliest compared with the other relays, and then broadcasts a control packet to notify other relays [23].

## 5 Asymptotic Behavior Analysis

In a cognitive radio setting, the primary users are licensed to access the channel with QoS guarantee, and the power of primary transmitter is rather high, comparing to secondary transmit power and interference. In order to have a better understanding of the impact of primary interference on secondary network performance, we analyze the asymptotic behaviors of the derived power allocation and the secondary outage probability when the primary SNR approaches infinity.

First, let us look at the asymptotic behavior of the power allocation. To make it compact and consistent, the power allocation scheme is expressed with respect to SNRs as well.

When , we have Let represent the corresponding asymptotic with respect to the . We provide the integrated asymptotic power allocation strategy of in the following corollary.

###### Corollary 1

The optimal power allocation when is given by

(30) |

with , where and

See Appendix 15.

###### Corollary 2

The optimal power allocation for the relay