# Energy-efficient buffer-aided optimal relay selection scheme with power adaptation and inter-relay interference cancellation.

AbstractConsidering the tradeoff between energy consumption and outage behavior in buffer-aided relay selection, a novel energy-efficient buffer-aided optimal relay selection scheme with power adaptation and Inter-Relay Interference (IRI) cancellation is proposed. In the proposed scheme, energy consumption minimization is the objective with the consideration of relay buffer state, outage probability and relay power control, in order to eliminate IRI. The proposed scheme selects a pair of optimal relays from multiple candidate relays, denoted as optimal receive relay and optimal transmit relay respectively. Source-relay and relay-destination communications can be performed within a time-slot, which performs as Full-Duplex (FD) relaying. Markov chain model is applied to analyze the evolution of relay buffer states. System steady state outage probability and achievable diversity order are derived respectively. In addition, packet transmission delay and power reduction performance are investigated with a specific analysis. Numerical results show that the proposed scheme outperforms other relay selection schemes in terms of outage behavior with power adaptation and IRI cancellation in the same relay number and buffer size scenario. Compared with Buffer State relay selection method, the proposed scheme reduces transmission delay significantly with the same amount of relays. Average transmit power reduction can be implemented to relays with the increasing of relay number and buffer size, which realizes the tradeoff between energy-efficiency, outage behavior and delay performance in green cooperative communications.

Keywords: Buffer-aided relay selection, power adaptation and Inter-Relay Interference (IRI) cancellation, energy-efficiency, buffer state, outage probability

1. Introduction

With the rapid and radical evolution of information and communication technology, corresponding energy consumption is also growing at a staggering rate. Furthermore, it has been reported that mobile operators are already among the top energy consumers [1]. Reducing energy consumption in wireless communications has attracted increasing attention and green communications has become a major research topic [1]. Recently, a lot of interests have been drawn by the cooperative relaying technique, which enhances the reliability of data transmission and expands the capacity of wireless communication system. The cooperative relaying technique has been proven to be an effective method of enhancing network capacity, reducing users' energy consumption, extending network lifetime and improving system throughput. In [2], the author introduced a new approach using Mobile Edge Computing (MEC) as ad-hoc relay nodes for overload or broken of MEC system, and find out the capacity of ad-hoc relay nodes affects the MEC recovery system throught significantly. These advantages have great significance to the energy-constrained wireless sensor networks. Therefore, energy efficiency has become a hot research topic in cooperative communications [1].

Relay selection and power control are two key technologies in cooperative communications. Communication system performance mainly depends on the selection of relay nodes, while power control is implemented to adjust relay power based on power adaptation criterion in the energy-constrained wireless network, in order to optimize system quality of service, such as throughput, outage probability, etc [3-4]. The earlier works in cooperative communications mainly focus on non-buffer relays, i.e., relays forward data packets immediately when they receive from source node [3-4]. With the implementation of buffer-aided relays, they could decide whether it should transmit or receive data packets based on channel gain in the current time slot, thus system degrees of freedom can be improved and outage probability can be correspondingly reduced [4]. In traditional decode-and-forward based cooperative relaying system, max-min relay selection scheme is proposed in [5], where the best relay selection criterion is based on the maximum signal-to-noise ratio (SNR) criterion. The scheme achieves the optimal performance and ensures a full diversity that equals to the number of relays. In order to improve system performance, each relay equipped with a buffer. Max-max relay selection scheme is proposed in [6], which selects optimal receive and forward relays based on the criterion of best channel qualities between Source-Relay (S-R) and Relay-Destination (R-D) respectively. However, the scheme assumes that the buffer size is neither full nor empty at the relay. Since this assumption is not practical for finite buffers, max-link relay selection policy for cooperative system with finite buffers is investigated [7]. In each time slot, optimal relay can be selected dynamically in accordance with available instantaneous channel quality and buffer state. A buffer state based relay selection scheme for a finite buffer-aided cooperative relaying system is proposed in [8], which selects an optimal relay based on channel quality and buffer state in different time slots.

In the above relay selection schemes, relays are equipped with a buffer. The result show that buffering is a promising solution to cooperative networks that enhances degree of freedom and reduces outage probability. However, energy consumption at relays are rarely considered in these schemes, which may cause dramatically increasing of relay energy with the guarantee of outage behavior and link quality requirement. Traditional cooperative relays are operated at the Half-Duplex (HD) mode in which relays cannot receive or transmit data simultaneously. Hence, it results in half spectral efficiency loss [9]. To eliminate inter-relay interference and minimize system energy consumption per time slot, a Successive Opportunistic Relaying (SOR) selection scheme is proposed in [10]. However, the authors overlooked the relationship between buffer states and channel qualities in the scheme. N. Zlatanov [11] proposed a new relaying protocol employing adaptive link selection. Both delay tolerant and delay-constrained transmission cases are taken into consideration, and the corresponding throughput performances are analyzed respectively. It is also pointed out that buffer-aided half-duplex relaying can outperform ideal full-duplex relaying in terms of throughput performance [12-13]. That is, HD relays with buffers can mimic FD relaying. Outage probability and system latency can be effectively decreased [12]. HD relays with buffers that imitates space FD max-max relay selection (SFD-MMRS) exceeds twice the capacity of the best relay selection (BRS) with HD relays and provides full diversity and large SNR gains [13]. Recent literature [14] proposes opportunistic FD based relay selection and the corresponding optimal power allocation scheme.

This work proposes an energy-efficient buffer-aided optimal relay selection scheme with power adaptation and IRI cancellation in order to solve the tradeoff problem between energy consumption and outage behavior. The main contributions of this paper are summarized as follows:

1) Selecting a pair of optimal relays based on the energy consumption, buffer state and outage probability of the relays, which is denoted as optimal receive relay and optimal transmit relay respectively in the proposed relay selection scheme. The source-relay and relay-destination communications can be performed within a time-slot, which mimics FD relaying.

2) Proposing a theoretical framework for the analysis of the evolution of relay buffer states based on a Markov chain model. Then, the system steady state outage probability and achievable diversity order are derived respectively.

3) Analyzing the average packet transmission delay at source and optimal relays and power reduction. Average transmit power reduction can be realized with the increasing of relay number and buffer size.

Numerical results show that the proposed optimal relay selection scheme outperforms other relay selection schemes mentioned in [8,10]. The outage behavior, average transmit power reduction and average delay performance metrics are uniformly improved.

The rest of this paper is organized as follows. System model is introduced in Section II. Section III provides the specific energy-efficient buffer-aided optimal relay selection scheme. The analysis of energy consumption, outage behavior and system latency are presented in Section IV respectively. Numerical results and performance analysis are shown and discussed in Section V. Finally, conclusions are drawn in Section VI.

2. System Model

System model of energy-efficient buffer-aided relay selection is shown in Fig. 1. We assume that a simple cooperative network consisting of one source S, one destination D and a cluster C with K relays [R.sub.k] [member of]C (1 [less than or equal to] k [less than or equal to] K). The cluster C has a cluster head (CH) which is in charge of handling the broadcasting information in the cluster and selects appropriate relay to participate in cooperative communications. All relays operate in the HD mode and Decode-and-Forward protocol is implemented to forward information [9]. A direct link between the source and the destination does not exist and communication can be established only via relays [11]. Each relay is equipped with a data buffer of size L, where the source information can be stored and decoded at the relay. We use [L.sub.k] (0 [less than or equal to] [L.sub.k] [less than or equal to] L) to denote the number of packets stored in the buffer of the k -th relay [R.sub.k] . [l.sub.ij], (i [member of] {S,[R.sub.1],...,[R.sub.K]}, j [member of] {[R.sub.1],...,[R.sub.K],D}) are denoted the channel link between node i and node j. We use [h.sub.ij] to denote the channel coefficients between node i and node j, and the channel coefficients is assumed to be a circularly symmetric complex Gaussian distributed random variable with zero mean and variance [[OMEGA].sub.ij].

In this system model, time is assumed to be divided into slots with equal length. At each time slot, the CH selects a pair of relays that have the highest channel gain and the lowest energy consumption in accordance with optimal relay selection strategy, namely, the best receive relay [R.sup.*.sub.r] and the best transmit relay [R.sup.*.sub.t]. In one time slot, CH chooses the optimal receive relay ([R.sup.*.sub.r]) from the candidate relays. Source sends data packets to this best receive relay [R.sup.*.sub.r] and stores these packets into its buffer. At the same time slot, CH selects the optimal transmit relay ([R.sup.*.sub.t]) from the candidate relays. The best transmit relay [R.sup.*.sub.t] forwards data packets form its buffer to destination in accordance with "first-in--first-out" rule.

In traditional cooperative systems, relays directly forward data packets from source node [3-4]. In the proposed scheme, each relay has its own buffer that can store data packets, i.e., the buffer-aided relaying [6-8,10]. Therefore, in the proposed cooperative relay selection scheme, CH determines the best receive relay and transmit relay in accordance with channel quality and buffer state in the current time slot. It selects a pair of optimal relays based on energy-efficient buffer-aided optimal relay selection scheme. For example, CH chooses a relay as optimal receive relay [R.sup.*.sub.r] and stores packets from source into its buffer during the first time slot. These data packets will not be forwarded promptly in second time slot. CH will recollect channel quality and relays' buffer state and choose a pair of optimal relays (denoted as the best receive relay [R.sup.*.sub.r] and the best transmit relay [R.sup.*.sub.t]) to complete cooperative transmission. It implements FD relaying and enhances the system spectral efficiency. The retransmission process is based on an Acknowledgement/Negative-Acknowledgement (ACK/NACK) mechanism. If the receivers (either a relay [R.sup.*.sub.r] or the destination D) do not receive a packet successfully, it will send a NACK to the transmitter. Then, the transmitter will retransmit the packets. If the receivers receive a packet successfully, it will send a ACK to the transmitter.

Without loss of generality, before the description of specific relay selection scheme, we make the following assumptions:

1) Each relay equips with a omni-directional antenna whose maximum transmit power is [P.sub.max]. The transmit power level can be adaptively adjusted in the range of [0, [P.sub.max]]. Relay transmits a packet in each time slot, therefore, the maximum energy consumption is denoted as [E.sub.max] = [P.sub.max] [T.sub.s] for a packet transmission.

2) All the channel links are assumed to be Rayleigh flat fading and Additive White Gaussian Noise (AWGN). The channel is assumed to be stationary in one time slot.

3) Channel coefficients ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) are independent identical distribution (i.i.d) from one time slot to another.

4) One relay can only receive or forward a packet in one time slot. Namely, the relay [R.sub.k] receives a data packet, the buffer state can be denoted as [L.sub.k]+1.

5) Noise variance is identical for relay and destination.

3. Energy-efficient buffer-aided optimal relay selection scheme

In this section, we investigate optimal relay selection policy called energy-efficient buffer-aided optimal relay selection. Considering that the buffer-aided HD relaying can achieve ideal FD relaying in terms of throughput performance [12-13] and opportunistic FD based relay selection [14], we proposed an optimal relay selection scheme to select the optimal receive relay and the optimal transmit relay simultaneously in one time slot. It mimics FD relaying. Relay power adaptation and IRI cancellation can be achieved. Hence, system spectral efficiency can be enhanced. The scheme can be divided into the following two steps:

Step 1: At the beginning of each slot, the source broadcasts a pilot sequence and the K relays estimate the (S-[R.sub.k]) channel state information (CSI). We assume the channel gain between source and destination is in deep fading, the D cannot get the (S-D) CSI. Then, the destination sends pilot signals to the relays, which extract the ([R.sub.k]-D) CSI. Relays attains channel gains denoted by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], as well as (S-[R.sub.k]) and ([R.sub.k]-D) channel link states denoted by [l.sub.SR.sub.k] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the current time slot.

Step 2: In this step, the CH is used to collect the channel gains attained in the step 1 of all the links. Any relay that can communicate with the others is selected as the CH. Without loss of generality, we assume that [R.sub.1] is the CH. Thus, CH collects channel qualities and buffer states of each relay at the current time slot. For different values of buffer size [L.sub.k], relay [R.sub.k] has different cases of available links:

1) [L.sub.k] = 0, relay buffer is empty. It can only be used for packet reception.

2) [L.sub.k] = L, relay buffer is full. It can only be used to forward a packet.

3) 0 < [L.sub.k] < L, relay buffer is neither full nor empty. It can be used to receive or forward a packet.

CH collects CSI and divides relay cluster into two sets ([Q.sub.t], [Q.sub.r]) in accordance with adaptive link selection rules (Table 1). Suppose [Q.sub.t] is relay set that is composed of relays forwarding data packets to D while [Q.sub.r] is relay set that is made up of relays receiving data packets from S. In Table 1, we assume that L [greater than or equal to] 2.This assumption is based on the fact: For the relay with buffer size L = 1, if a relay receive a packet, the relay will transmit the packet immediately in order to increase the number of available links of the system in the following time slot. As a result, the benefits of relays equiped with buffer will be reduced.

In Table 1, the term "outage" denotes that the corresponding link is in outage. "successful" means that the link is not in outage. "Silence" denotes that the relay keeps in silence (neither transmits nor receives). "Receive" means that the relay chooses to receive a packet. "Transmit" denotes that the relay chooses to transmit a packet.

In case 4, the link states [l.sub.SR.sub.k],[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are all stay in the "successful" state and the buffer state [L.sub.k] [greater than or equal to] 2, relay [R.sub.k] will decide to transmit a data packet to D. In this case, it is easier for relay to forward the data packets in its buffer to destination, which effectively reduces the packet transmission delay. For case 5 ([L.sub.k] < 2), relay [R.sub.k] will decide to receive a data packet from S. It makes that more links are available to relay. According to the above different cases, there are 4 different scenarios:

(1) [Q.sub.r] [not equal to] [empty set], [Q.sub.t] = [empty set] ([empty set] denotes the empty set), in this scenario, no relay will be selected to transmit a packet and the CH can only choose a relay to receive a packet from source. Denote [L.sub.min] = min([L.sub.k] |[R.sub.k] [member of] [Q.sub.r]), CH first finds out the receive relay set [Q.sub.r1] from the set [Q.sub.r], [Q.sub.r1] = {[L.sub.k] = [L.sub.min] |[R.sub.k] [member of] [Q.sub.r]}. The [Q.sub.r1] denote the set of the relays whose buffer has minimum number of packets. Then, CH choose [R.sup.*.sub.r] that satisfies [l.sub.SR.sup.*.sub.r] 's channel gain maximization and source power minimization from [Q.sub.r1], [R.sup.*.sub.r] = arg min [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If the [R.sup.*.sub.r] receive the packet successfully, and stores a received data packet into this relay's buffer. (2) [Q.sub.r] = [empty set], [Q.sub.t] [not equal to] [empty set], in [L.sub.max] = max([L.sub.k] |[R.sub.k] [member of] [Q.sub.t]), CH first finds out the transmit relay set [Q.sub.t1] from the set [Q.sub.t], [Q.sub.t1] = {[L.sub.k] = [L.sub.max] |[R.sub.k] [member of] [Q.sub.t]}. The [Q.sub.t1] number of packets. Then, the CH choose [R.sup.*.sub.t] that satisfies [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 's channel gain maximization and [R.sup.*.sub.t]'s power minimization from [Q.sub.t1], [R.sup.*.sub], = arg min [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and transmits one data packet that stored in its buffer to the destinatio

(3) [Q.sub.r] [not equal to] [empty set], [Q.sub.t] [not equal to] [empty set], in this scenario, CH select a pair of optimal relays simultaneously. CH first finds out [R.sup.*.sub.r]that satisfies [l.sub.SR.sup.*.sub.r] 's channel gain maximization and source power minimization from [Q.sub.r1]. At the same time, it finds out [R.sup.*.sub.t]that satisfies [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 's channel gain maximization and [R.sup.*.sub.t] 's power minimization from [Q.sub.r1].

(4) [Q.sub.r] [not equal to] [empty set], [Q.sub.t] [not equal to] [empty set], in this scenario, all the available links are in outage, and there is no need to select best relays.

By implementing the energy-efficient buffer-aided optimal relay selection scheme, spatial degree of freedom is increased and system outage probability is reduced. Meanwhile, cooperative relay energy efficiency is guaranteed. In addition, this scheme selects a pair of best relays with energy consumption minimization in accordance with channel quality and relays' buffer state. The proposed scheme reduces the average latency in buffer-aided relaying system, further improves the reliability and reduces transmission energy consumption.

4. Performance analysis of energy-efficient relay selection

4.1 Energy Consumption Analysis

CH selects a pair of optimal relays in accordance with channel quality and each relay's buffer state. The proposed scheme not only guarantees energy efficiency of relays in the current time slot, but also considers buffer states and channel qualities to realize relay power adaptation and IRI cancellation.

Without loss of generality, we make specific analysis of scenario (3) ([Q.sub.r] [not equal to] [empty set], [Q.sub.t] [not equal to] [empty set]), since scenario (1) (2) (4) are the special cases of scenario (3). In scenario (3), source sends a data packet [x.sub.t] in the time-slot t. CH selects the best receive relay via optimal relay selection scheme. At the same time, it also chooses the best transmit relay, which forwards the packets [x.sub.p] (p < t) that are stored in its buffer in the previous time slots p to destination. Therefore, the optimal receive relay [R.sup.*.sub.r] received data packets in the time-slot t can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Destination receives data packets from the best transmit relay [R.sup.*.sub.r], which can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where [P.sub.s] is the source power level and [P.sub.[R.sup.*.sub.t]] is the selected optimal transmit relay power level. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes channel coefficient between the pair of selected optimal relays. Noise N denotes the additive white Gaussian noise with zero mean and variance [[delta].sup.2]. For simplicity, the noise is assumed to be equal at each receiver. Therefore, S [right arrow] [R.sup.*.sub.r] link capacity ([I.sub.SR.sup*.sub.r]) and [R.sup.*.sub.t] [right arrow] D link capacity ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) are expressed as follows respectively

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

It is obvious that the reception signal of optimal receive relay [R.sup.*.sub.r] contains the interference from the optimal transmit relay [R.sup.*.sub.t] which forwards previous packets [x.sub.p] to the destination. Hence, the optimal receive relay that correctly decodes its signal sent from source should satisfy two requirements: (1) The IRI cancellation should be satisfied, that is, interference between the selected optimal relay pairs must be eliminated. (2) Transmission rate at the optimal receive relay is greater than or equal to a fixed target rate [r.sub.0]. For simplicity, we assume that the noise power is identical and has unit variance. Thus, [R.sup.*.sub.r] that separates the interference from [R.sup.*.sub.t] is said to be satisfied the following conditions.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

When the optimal receive relay [R.sup.*.sub.r] separates the interference from the optimal transmit relay [R.sup.*.sub.t], it is said to be met the following requirements.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Substitute (5) into (4), the range of the optimal transmit relay power [P.sub.R.sup*.sub.t] can be rewritten as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Let [Pr.sub.SR.sub.k] represent the outage probability between source and the k -th relay, and the [Pr.sup.th.sub.out] denote the outage probability that the HD relaying system aims to deliver packet at a fixed target rate [r.sub.0] with the fixed power (P). Hence, the optimal receive relay [R.sup.*.sub.r] can be determined by the following optimization problem shown as below. The energy-efficient buffer-aided optimal receive relay selection scheme is considered as the source power control problem, in which source energy consumption minimization is served as objective with the constraints of source-relay outage probability, source-relay link capacity and inter-relay link capacities to eliminate IRI.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

If data rate at the destination is greater or equal to a fixed target rate [r.sub.0], the destination can correctly decode the message sent from the optimal transmit relay. Therefore, for the destination correctly decodes the forwarded message, the range of the optimal transmit relay power level [P.sub.R.sup.*.sub.t] can be expressed as below.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Similarly, the optimal transmit relay [R.sup.*.sub.t] selection strategy can be defined by the following optimization problem shown as below. Just as (6), the energy-efficient buffer-aided optimal transmit relay selection scheme is regarded as the relay power control problem, in which relay energy consumption minimization is served as its objective with the constraints of relay-destination outage probability, relay-destination link capacity and inter-relay link capacities to eliminate IRI.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

Based on the above problem formulation, we can draw conclusions that the best relay pair selection algorithm chooses an optimal receive relay as well as an optimal transmit relay simultaneously. The best receive relay [R.sup.*.sub.r] is the one that has smaller buffer size [L.sub.k], larger channel gain and lower source power level in the receive relay set [Q.sub.r1]. The best transmit relay [R.sup.*.sub.t] is the one that has larger buffer size [L.sub.k], larger channel gain and lower relay power level in the transmit relay set [Q.sub.r1].

We substitute (5) into (4), and let the variance of AWGN (noise power) has unit value [[delta].sup.2] = 1. Then, we can deduce the minimum power level of source and the optimal transmit relay from (4), (5) and (7), which can be written as follows respectively

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

4.2 Outage Behavior Analysis

A. Construction of Markov Chain State Transition Matrix

In this section, we investigate the outage behavior of the proposed energy-efficient buffer-aided optimal relay selection scheme via Markov Chain (MC) model. We use MC states to describe the states of relay buffers, which is the number of data packets [L.sub.k] stored in the buffer of the k -th relay [R.sub.k]. MC state transition matrix indicates the connectivity between relays' buffer states. Assuming the k -th relay buffer stores [L.sub.k] (0[less than or equal to][L.sub.k][less than or equal to] L) data packets that has total L + 1 different state values. As a result, the cluster which consists of K buffer-aided relays have [(L + 1).sup.K] buffer states in total. The n -th buffer state can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

Let A denote the [(L + 1).sup.K] x [(L + 1).sup.K] state transition matrix of MC. More specifically, the entry [A.sub.mn] = Pr([X.sub.t+1] = [s.sub.m]|[X.sub.t]= [s.sub.n]) indicates the transition probability that the state moves from [s.sub.n] at time t to [s.sub.m] at time t + 1. The transition probability [A.sub.mn] depends on the relay buffer status and the set of available links that can successfully transmit one packet. State transition matrix A can be constructed in accordance with the connectivity between different buffer states. A relay can only receive or transmit one data packet in a time slot. Namely, when the relay [R.sub.k] receives a packet, the relay buffer state can be expressed as [L.sub.k]+1.

If the system chooses the available link [l.sub.ij] to complete cooperative transmission in one time slot, however, the buffer state is not changed, which means the outage behavior is occurred in the selected channel link in this time slot. Thus, the outage probability of link [l.sub.ij] [12] can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where [h.sub.ij] is the channel coefficients of link [l.sub.ij], and modeled as a circularly symmetric complex Gaussian distributed random variable with zero mean [|[h.sub.ij]|.sup.2] is a Chi-Square random variable with two degrees of freedom and the probability density function conforms to exponential distribution [15]. The variance of AWGN (noise power) has unit value [[delta].sup.2] =1. Thus, the HD relaying system's link outage probability [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Based on relay buffer states, the channel gains, and the adaptive link selection rules (shown in Table 1), we can obtain the available links [[PSI].sub.n] that connects to buffer state [s.sub.n] (i.e., buffer state moves from [s.sub.n] at time t to [s.sub.m] at time t + 1). Let [[PSI].sub.n.sup.s] denote the selected channel link via optimal relay selection scheme. Due to the fact that channel gains between source and relays are different from channel gains between relays and destination, the transition probability from buffer state [s.sub.n] to [s.sub.m] is also different in each time slot. Hence, the entry of MC state transition matrix [A.sub.mn] can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where the conditional probability notation Pr([s.sub.n] [right arrow][s.sub.m] | [[PSI].sub.n.sup.s]) depends on the proposed energy-efficient buffer-aided optimal relay selection scheme. For those states that are not connected to buffer state [s.sub.n] cannot be arrived from state [s.sub.n] through one step transition, the entry is denoted as [A.sub.mn] = 0. When all the available links are unable to deliver packets, the buffer state remains unchanged. Therefore, we have

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

B. Steady State Distribution of the MC

In the above subsection, we define the MC state transition matrix A with finite buffer size. In this subsection, we analyze the steady state distribution of the MC. The stationary distribution of buffer state which is denoted by MC column vector [pi] is investigated, and the corresponding system stationary performance is explored.

In our system model, due to the fact that all the possible states of the MC may transit from one state to other states and the link outage behavior may occur with outage probability [Pr.sub.ij] > 0. Hence, the MC is irreducible. Based on the fact that the buffer state remains the same when system is in outage, the probability is greater than zero at any buffer state after N transitions. Hence, the constructed MC is non-periodic.

According to [7], as the MC state transition matrix A is irreducible and non-periodic, the steady state distribution of the MC can be obtained as

[pi] = [(A-I + B).sup.-1]b (14)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], I denotes the identity matrix and B is a [(L +1).sup.K] x [(L +1).sup.K] matrix with all elements equal to one.

Just as the definition of outage probability in max-link relay selection scheme in [7], system outage behavior is assumed to be the link outage occurred in the S [right arrow] [R.sub.k] link and [R.sub.k] [right arrow] D link. In this case, no packet is transmitted and buffer state is unchanged. It is said that the outage behavior is occurred. The diagonal elements of the MC state transition matrix A represent there is no changes happened in buffer states, hence, we can calculate the outage probability in accordance with the corresponding steady state probability. Therefore, the system outage probability can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

The K buffer-aided relays with L buffer size have totally [(L + 1).sup.K] buffer states. In these [(L + 1).sup.K] states, [(L - 1).sup.K] states are neither full nor empty. We can divide the [(L + 1).sup.K] buffer states into two independent categories. The first category [F.sub.1] denotes the states in which all the relay buffers are neither full nor empty. The second category [F.sub.2] contains the [(L + 1).sup.K] - [(L - 1).sup.K] buffer states in which at least one relay buffer state is either full or empty. Assume each relay has infinite buffer size (L [right arrow] [infinity]), the limitation of system outage probability can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

Based on the proposed optimal relay selection scheme, we define [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as the transition probability matrices from buffer state category [F.sub.2] to [F.sub.1] and buffer state category [F.sub.1] to [F.sub.2] respectively. Refer to the max-link relay selection scheme [7], the transition probability matrices [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are also defined in this scheme. In the energy-efficient buffer-aided optimal relay selection scheme, relays with empty buffers have the highest priority to be selected as the candidate receive relays while relays with full buffers have the highest priority to be selected as the candidate transmit relays. For the Max-link relay selection scheme, it chooses the optimal relay in accordance with the best channel quality. Therefore, when the buffer size (L [right arrow] [infinity]), we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If the relay buffer size L < 2, it has higher priority to receive a packet, which avoids the relay buffer staying in empty. Therefore, when buffer size (L [right arrow] [infinity]), we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Let [[pi].sub.F.sub.1],[[pi].sub.F.sub.2] represent the stationary probabilities for buffer state categories [F.sub.1] and [F.sub.2] respectively. Similarly, we can define the stationary probabilities [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for buffer state categories [F.sub.1] and [F.sub.2] in the Max-link relay selection scheme. Hence, we have

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

Since the MC state transition matrix A is reversible, it is easily to find that the transition probability matrices [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are also reversible. We can obtain the relationship between transition probability matrices and the stationary probabilities for buffer state categories [F.sub.1] and [F.sub.2] shown as below.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

For the MC stationary probabilities, they satisfy [[pi].sub.F.sub.1] + [[pi].sub.F.sub.2] = 1 and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we apply (18) to find the stationary probabilities for buffer state category [F.sub.1] expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Based on the above analysis, we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] when the buffer size (L [right arrow] [infinity]). Substitute the conditions into (19), we can obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. According to [7], it is pointed out that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Due to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The second part in (16) equals to zero for the transition probability [A.sub.nn] < 1. Hence, for the extreme case with infinite buffer size L [right arrow] [infinity], the outage probability of the proposed optimal relay selection scheme can be simplified as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

According to the previous analysis, it is shown that if buffer size L [right arrow] [infinity] and transmission power L [right arrow] [infinity], for [S.sub.n] [member of] [F.sub.1], there are 2K available links, the stationary outage probability can be further simplified as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

The achievable system diversity order is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

Proof of (22):

We apply (21) into the definition of system diversity order, thus

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The approximation of limitation formula [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is adopted, and we can obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

4.3. Packet Latency Analysis

In general, the traditional cooperative relays are operated in the half-duplex mode. Hence, the packet latency (delay) includes two parts: (1) the transmission delay between S [right arrow] [R.sub.k]; (2) the transmission delay between [R.sub.k] [right arrow] D.

Suppose that the source has M packets to be sent to the destination, each packet requires two time-slots to be forwarded to the destination. According to the proposed energy-efficient buffer-aided optimal relay selection scheme, we choose a pair of optimal relays (the optimal receive relay [R.sup.*.sub.r] and the optimal transmit relay [R.sup.*.sub.t]) within a time-slot to mimic FD relaying. In the proposed scheme, packets can be delivered and forwarded to destination in one time-slot, hence the packet transmission latency can be reduced effectively [13]. If M is large enough, the overall transmission time slot to deliver M packets is approximately M. Therefore, system average throughput is denoted as [eta] = (M/M) = 1.

According to Little's law [16], the average transmission delay [D.sub.S] between source and the k -th relay S [right arrow] [R.sub.k] can be written as

[D.sub.S] =[E[[q.sub.S]]/[[eta].sub.s]] (23)

where E[[q.sub.S]] and [[eta].sub.s] represent the average queuing length and throughput at the source respectively. We assume that the source always has packets to transmit, thus the queuing length at the source depends on the probability that a S [right arrow] [R.sub.k] link is selected. Thus, the average queuing length and throughput at the source can be expressed as follows respectively.

E[[q.sub.S]] = 1-[Pr.sub.S-R] [[eta].sub.s] = [Pr.sub.S-R] (24)

where [Pr.sub.S-R] denotes the probability that CH selects a appropriate relay to deliver a data packet.

Based on the fact that the number of packets received by the relay [R.sub.k] must be equal to these leave the relay. Let [Pr.sub.R-D] denote the probability that CH chooses [R.sub.k] [right arrow] D link to transmit a packet that stored in relay's buffer. Thus, we have [Pr.sub.S-R] = [Pr.sub.R-D].

Different from [8], we assume that [Pr.sub.S-R-D] denotes the probability that CH selects the optimal receive relay [R.sup.*.sub.r] and forward relay [R.sup.*.sub.t] simultaneously, hence, we have

[Pr.sub.out] + [Pr.sub.S-R] + [Pr.sub.R-D]-[Pr.sub.S-R-D] =1 (25)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] represents the probability that the optimal receive and forward relay pairs are selected at buffer state [s.sub.n] with the proposed relay selection scheme.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the selected k -th relay buffer size at buffer state [s.sub.n]. Hence, (24) can be written as

E[[q.sub.S]] =[1+[pr.sub.out]-[pr.sub.S-R-D]/2]

[[eta].sub.s]= [1-[pr.sub.out]+[pr.sub.S-R-D]/2] (27)

Based on the above analysis, the average packet delay [D.sub.S] at source can be expressed as

[D.sub.S] = [1+[pr.sub.out]-[pr.sub.S-R-D]]/[1-[pr.sub.out]+[pr.sub.S-R-D]] (28)

Similarly, we analyze the average packet delay at relays. Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denote the queuing length of the equivalent buffer size at buffer state [S.sub.n]. The average queuing length at relay buffers can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

According to Little's law [16], the average packet delay [D.sub.R] between the k -th relay and destination [R.sub.k] [right arrow] D can be obtained as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)

Different from [8], due to the fact that the proposed scheme selects an optimal receive relay as well as an optimal transmit relay within the same time slot, which operates in FD relaying mode. Therefore, the overall average packet delay is the maximum value of (28) and (30) shown as below.

D = max([D.sub.S], [D.sub.R]) (31)

5. Numerical Results and Discussions

In the above section, we theoretically analyzed the energy consumption, outage probability and average packet latency of the energy-efficient buffer-aided optimal relay selection scheme. In this section, we perform numerical results for the proposed scheme in a simple buffer-aided relaying system scenario with K = 2 relays and buffer size L = 2. According to (10), there are 9 buffer states in this buffer-aided relaying system, which are shown in Table 2. Suppose the MC state transition matrix is [A.sub.9x9]. We can obtain the state transition diagram [8,10] in accordance with the proposed energy-efficient buffer-aided optimal relay selection scheme.

Fig. 2 shows the MC state transition diagram of buffer-aided relaying system with K = 2 and L = 2. According to the proposed optimal relay selection scheme, we can get the MC state transition matrix shown as below.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (32)

Based on the analysis of MC state transition matrix, we obtain system outage performance for the proposed energy-efficient buffer-aided optimal relay selection scheme with different SNR scenarios, which are compared with max-max relay selection [6], max-link relay selection [7], buffer state relay selection [8] and Successive Opportunistic Relaying (SOR) selection [10]. Fig. 3 illustrates the outage behavior of the proposed scheme with other four relay selection schemes for K =2 relays with buffer size L = 2. It is shown that the outage probability decreases as the increase of transmission SNR. The proposed energy-efficient buffer-aided optimal relay selection scheme has the best outage performance, which outperforms buffer state relay selection scheme [8] and SOR selection scheme [10]. The proposed scheme considers the relay buffer states, channel qualities and system energy consumptions simultaneously, and selects a pair of optimal relays to receive and transmit packets within a time slot. In the proposed scheme, the buffer state is neither full nor empty that provides more available links to transmit data packets, which reduces system outage probability significantly.

Fig. 4 and Fig. 5 illustrate the outage behavior of the proposed energy-efficient buffer-aided optimal relay selection scheme with different buffer size and relay numbers. In Fig. 4, it is obvious that the outage probability decreases with the increasing of relay buffer size L for buffer state relay selection [8] and the proposed scheme. The performance indicates that the available links increase with the length of buffer size, consequently system outage probability is reduced. Meanwhile, for the same transmission SNR and buffer size, the proposed scheme outperforms buffer state relay selection scheme. Furthermore, outage performance of the proposed scheme with buffer size L = 3 approaches to outage performance with buffer size L [right arrow] [infinity]. The proposed scheme outperforms buffer state relay selection scheme approximately 5dB SNR in the scenario of outage probability [10.sup.-3]. Fig. 5 shows the outage performance of the proposed scheme with buffer size L = 3 and different relay numbers. It is apparent that the outage probability decreases noticeably with the increasing of relay numbers.

Packet latency performance of different relay selection schemes are presented in Fig. 6. It is shown that the average packet delay decreases with the increasing of transmission SNR for each scheme. The reason is that system outage probability decreases as the transmission SNR increases, hence, in order to successfully deliver data packets, the required time slots are correspondingly reduced, so that the packet latency performance is improved. Packet latency performance of the proposed scheme and other two relay selection schemes (i.e., max-link relay selection scheme [7] and buffer state relay selection scheme [8]) are provided in this figure. It is obvious that the proposed relay selection scheme has the lowest packet delay for relay number K = 2 with buffer size L = 2. According to (31), the proposed optimal relay selection scheme mimics the FD relaying. Packets can be received and forwarded within a time slot. Hence, the average throughput is nearly two times of the common HD relay selection schemes, and the outage performance outperforms other relay selection schemes. System packet latency performance can be improved significantly. Furthermore, it is indicated that the average packet delay increases with relay buffer size L in low SNR region, which is similar to the packet latency performance of buffer state relay selection scheme. However, in high SNR region, the average packet latency is independent of relay buffer size, which is only related with relay numbers K (the average packet latency upper bound approximates to K + 1 if SNR [right arrow] [infinity]). Average packet delay also increases with cooperative relay numbers K.

Fig. 7 shows power reduction of the proposed energy-efficient buffer-aided optimal relay selection scheme with power adaptation and IRI cancellation in different relay number and buffer size scenario. Buffer state relay selection scheme is used as a benchmark [8]. According to (9), the minimum transmit power of the optimal transmit relay is lower than buffer state relay selection scheme [8], which indicates that the proposed scheme is more energy-efficient (larger power reduction). In addition, the power reduction increases with transmission SNR. The reduced power enhances with the increasing of relay numbers for fixed relay buffer size (L = 3), that is, the proposed scheme effectively mitigate IRI with power adaptation. For the same relay numbers (K = 2), the differences of the reduced power are minor with the increasing of relay buffer size. The power reduction approaches to HD buffer-aided relay selection bound, which is coherent with the conclusion drawn in [10].

6. Conclusions

In this paper, an energy-efficient buffer-aided optimal relay selection scheme with power adaptation and IRI cancellation is proposed. Compared with other relay selection schemes such as max-max relay selection based on optimal channel qualities and finite buffer size max-link relay selection scheme, the proposed scheme eliminates IRI via power adaptation, and selects a pair of optimal relays with low energy consumption, high channel gain and optimal buffer state in the same time slot. The selected optimal relays can mimic FD relaying to receive and transmit data packets within a time slot. Energy consumption analysis, outage behavior analysis and packet latency analysis are provided respectively. Numerical results show that, compared with max-max relay selection scheme, max-link relay selection scheme, buffer state relay selection scheme and SOR scheme, the proposed scheme has the best outage performance in the same relay number and buffer size scenario. Compared with buffer state relay selection scheme, the proposed scheme reduces packet transmission delay and power consumption effectively in the case of the same relay numbers. Therefore, the proposed scheme enhances energy-efficiency of buffer-aided relaying in cooperative transmission, which realizes the tradeoff between energy-efficiency, outage behavior and latency performance in green cooperative communications.

Acknowledgment

The authors would like to greatly appreciate anonymous reviewers for their valuable comments and constructive suggestions in helping to improve the quality of this paper. This research work was supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LY15F010008, LY14F010018) and National Natural Science Foundation of China (Grant No. 61102066), and Young Talent Cultivation Project of Zhejiang Association for Science and Technology (Grant No. 2016YCGC009).

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Xiaorong Xu (1), Liang Li (1), Yingbiao Yao (1), Xianyang Jiang (1), Sanqing Hu (2)

(1) College of Telecommunication Engineering, Hangzhou Dianzi University Hangzhou, Zhejiang 310018 - China

(2) Electrical and Computer Engineering Department, Stevens Institute of Technology Hoboken, NJ 07030 - USA

[e-mail: xuxr@hdu.edu.cn]

(*) Corresponding author: Xiaorong Xu

Received May 3, 2016; revised August 1, 2016; accepted August 29, 2016; published November 30, 2016

Xiaorong Xu is with the College of Telecommunication Engineering, Hangzhou Dianzi University (HDU), Hangzhou, China, as associate professor. He received the B. Eng. degree in Communication Engineering and M. Eng. degree in Communication and Information System from HDU, Hangzhou, China, in 2004 and 2007, respectively. He received Ph.D. degree major in Signal and Information Processing from Nanjing University of Posts and Telecommunications (NJUPT), Nanjing, China, in 2010. Previously, from 2011 to 2013, he was working as a postdoctoral researcher in the Institute of Information and Communication Engineering, Zhejiang University (ZJU), Hangzhou, China. During 2013-2014, he served as a research scholar with the Electrical and Computer Engineering Department, Stevens Institute of Technology (SIT), Hoboken, NJ, USA. Currently, he is working as a associate professor in HDU. Dr. Xu's research interests emphasize on energy efficiency in cooperative communications, energy efficiency and PHY security in Cognitive Radios (CR), as well as Compressive Sensing (CS) theory, etc.

Liang Li is with the College of Telecommunication Engineering, Hangzhou Dianzi University (HDU), Hangzhou, China, as postgraduate student. He received the B. Eng. degree in Communication Engineering from HDU, Hangzhou, China, in 2014. Currently, he is working toward his M. Eng. degree in Electronics and Communications Engineering in HDU. His research interests include energy efficiency in cooperative communications and energy efficiency in future green wireless communications, etc.

Yingbiao Yao is with the College of Telecommunication Engineering, Hangzhou Dianzi University (HDU), Hangzhou, China, as associate professor. He received the M. Eng. degree in Communication and Information System from Xi'an Shiyou University, Xi'an, China, in 2003, He received Ph.D. degree major in Communication and Information System from Zhejiang University (ZJU), Hangzhou, China, in 2006. Since 2006, he has been with the College of Telecommunication Engineering, HDU. During 2011-2012, he served as a research scholar with the Electrical and Computer Engineering Department, Rensselaer Polytechnic Institute, Albany, NY, USA. Currently, he is working as a associate professor in HDU. Dr. Yao's research interests emphasize on energy efficiency in WSN and future green wireless communications, Multiprocessor System-on-Chip (MPSoC) and solid state disk (SSD) for embedded system application, etc.

Xianyang Jiang is with the College of Telecommunication Engineering, Hangzhou Dianzi University (HDU), Hangzhou, China. He received his M. Eng. degree in Communication and Information System from Department of Electronic Engineering, Zhengzhou University, Zhengzhou, China, in 2004. He received his Ph.D. degree major in Communication and Information System from Department of Electronic Engineering, Tsinghua University, Beijing, China, in 2009. Since 2009, he has been with the College of Telecommunication Engineering, HDU. From July 2012 to December 2012, he served as a research scholar with the Electrical and Computer Engineering Department, Stevens Institute of Technology (SIT), Hoboken, NJ, USA. Dr. Jiang's research interests include energy efficiency in broadband wireless communications, cooperative communications and Cognitive Radio Networks (CRN), etc.

Sanqing Hu is with the Electrical and Computer Engineering Department, Stevens Institute of Technology (SIT), Hoboken, NJ, USA, as assistant researcher. He received his B. Eng and M. Eng degree in Electrical and Information Engineering from Huazhong University of Science and Technology, Wuhan, China, in 2007 and 2009, respectively. In 2013, He received his Ph. D. degree in Electrical Engineering from Stevens Institute of Technology, Hoboken, NJ, USA. Dr. Hu's research interests emphasize on energy efficiency in cooperative communications, cognitive radio networks, cellular telecommunications, machine learning and data mining in communication applications, etc. Dr. Hu also serves as the journal reviewer for IEEE Transactions on Communications, IEEE Transactions on Wireless Communications, IEEE Transactions on Vehicular Technology, IEEE Communications Letters and several international journals.

Table 1. Adaptive link selection rules Cases Link state [l.sub.SR.sub.k] Case 1 outage Case 2 outage Case 3 successful Case 4 successful Case 5 successful Cases Link state [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Case 1 outage Case 2 successful Case 3 outage Case 4 successful Case 5 successful Cases Buffer state [L.sub.k] Case 1 Case 2 [L.sub.k]>0 Case 3 [L.sub.k]<L Case 4 2[less than or equal to][L.sub.k] Case 5 [L.sub.k]<2 Cases Decision Case 1 Silence Case 2 Transmit Case 3 Receive Case 4 Transmit Case 5 Receive Table 2. Buffer states of relaying system with K = 2 and L = 2 States [S.sub.1] [S.sub.2] [S.sub.3] [S.sub.4] [L.sub.1][L.sub.2] 00 01 02 10 States [S.sub.5] [S.sub.6] [S.sub.7] [S.sub.8] [L.sub.1][L.sub.2] 11 12 20 21 States [S.sub.9] [L.sub.1][L.sub.2] 22

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Author: | Xu, Xiaorong; Li, Liang; Yao, Yingbiao; Jiang, Xianyang; Hu, Sanqing |
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Publication: | KSII Transactions on Internet and Information Systems |

Article Type: | Report |

Date: | Nov 1, 2016 |

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