Time switching based, outage‐constrained, energy harvesting and energy‐efficient cooperative radio communication policy

Funding information OPERA research grant (FR/SCM/160714/EEEI/) from Birla Institute of Technology & Science (BITS) Pilani, Pilani campus, India Abstract In this work, the authors consider a two-hop cooperative radio communication system that consists of energy harvesting relays. The EH relays harvest energy from its received radio frequency signal. The EH relay nodes adopt the time-switching protocol for simultaneous EH and information processing. For the system model, the authors propose an energyefficient, outage-constrained relaying policy. In it, the EH relay that harvests maximum energy forwards the information to the destination. However, the selected EH relay transmissions are outage-constrained. For the proposed outage-constrained collaborative EH system model, the authors present insightful analysis. Specifically, the authors derive a single integral expression for the expectation of maximum energy harvested over frequencyflat Rayleigh fading and shadowing channel. The authors also present an insightful link outage probability analysis and asymptotic analysis in a useful scaling regime. Besides outage analysis, the authors investigate the proposed policy’s performance in terms of average spectral efficiency and average energy efficiency. To validate the analytical results, the authors conduct numerical simulations. Using the numerical plots, the authors quantify the proposed policy’s link outage and energy efficiency performance gains compared with benchmark policies. The proposed outage-constrained, green cooperative communication policy and its analysis are useful for green collaborative EH systems.


INTRODUCTION AND MOTIVATION
Collaborative (or cooperative) communication technologies use the intermediate cooperating nodes to assist in the data transmission between the source node and the destination node [1]. These collaborative relay nodes are either non-regenerative or regenerative, or both. The non-regenerative relay node plays the role of forwarding its received signals to the destination node without any additional processing such as decoding and encoding [2]. However, the regenerative relay node decodes and re-encodes its received signal before forwarding it to the destination [3]. The relay-aided collaborative communication technique offers enhanced coverage and increased network capacity [4].
However, frequent use of the conventional, battery-equipped relay node to transfer the signal toward the destination This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. IET Communications published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology node decreases its battery life. The limited energy capabilities of batteries keep constraints on applications of wireless systems that employ them. Furthermore, recurrent charging or battery replacements are not very convenient and feasible options for relay nodes in ad hoc wireless networks [5].
The researchers have taken a great deal of interest in the present day to come up with a solution that can resolve the issue of limited battery resources in the relay nodes. One such predominantly accepted remedy by the research community is based on energy harvesting (EH). It is the method of energy storage via ambient resources like wind, solar, or radiofrequency (RF) signals [6]. However, most of the conventional resources like solar or wind are unpredictable and inefficient because of their environmental dependence [7]. Therefore, RF-EH is attractive in collaborative communications because of its controllability and reliability [8].

Relevant literature, comparisons and comments
Several works considered RF signal-based EH using simultaneous wireless information and power transfer (SWIPT) technique in energy harvesting and energy-efficient (green) collaborative wireless systems [9]. Several authors proposed and investigated two main protocols: power-splitting protocol and timeswitching protocol (TSP) [10]. In the TSP, a single antenna with a simple switch selects EH and information decoding tasks over time [11]. This paper considers TSP, given its simplicity and ease of implementation.
SWIPT's capability to concurrently transmit the information signal and power, SWIPT, and associated ideas grew researchers' attention. Several research works are present in the literature on single EH collaborative relay systems and multi-EH collaborative relay systems. The authors in [12] considered an EH collaborative wireless relay system model with a single regenerative relay. In it, the authors derived optimum PSP and TSP coefficients and studied outage probability. In [13,14] also, the authors considered a single-EH collaborative relay assisted system for which they adopted a hybrid policy that combines both TSP and PSP for determining its optimised ratio.
Single EH relay wireless systems are inexpensive and easy to build when compared to the multi-EH collaborative wireless systems and networks. However, the adaptation of multi-EH relays in collaborative systems helps in achieving extended transmission coverage and more reliability. Furthermore, to reduce the complexity of implementation, EH relay selection is a viable solution in multi-EH collaborative relay systems [15]. Apart from that, in a multi-EH collaborative relay system, relay selection mitigates the problem of synchronisation [16] and reduces the EH relay node (EHRN) channel state information (CSI) requirements.
In several works, the authors proposed and investigated different kinds of EH relay selection policies and investigated various physical layer (PHY) performance measures. In [17], the authors proposed two EH relay selection policies, namely, selecting a relay node randomly and selecting based on the distance of the EH multi-relay nodes. In it, for both these relay selection policies, the authors evaluated the outage analysis. The authors in [18] proposed the EH relay model with selective max−max relay selection (S-MMRS). In the S-MMRS policy, relay selection occurs with the knowledge of the best sourcerelay and relay-destination link. In [18], the authors investigated the outage probability of the relay selection policy and compared it with the MMRS policy.
Furthermore, in [19], the authors proposed a non-energy aware relay selection policy. In this work, the EH relay, which has the best relay node to destination node instantaneous channel power gain, is selected to forward the signal to the destination. For such a policy, the authors analysed the outage probability. Further, in [20], the authors proposed a relay selection policy that requires average channel power gains. A partial relay selection policy is proposed in [21]. In this policy, selecting the best EH relay is based on the signal power to noise power ratio (SNR) of the source to relay link. Therefore, the relay with the best SNR of the source node to the relay node link is selected for signal transmission.
There are some more relevant relay selection policies in the literature. In [22], the author proposed the battery-aware relay selection (BARS) policy. In the BARS policy, the relay nodes having harvested energy higher than the specified threshold forms a subset. In this work, the relay node, which delivers maximum end-to-end SNR, is chosen from the subset, which eventually forwards its received signal. Similarly, policy in [23] also adopts a similar approach for relay selection, but a subset of selected relay nodes participate in the relaying process. The authors proposed a minimum self-interference relay selection policy in [24]. In it, the authors considered a full-duplex link with regenerative relay nodes.
Furthermore, two EH relay-assisted collaborative communication system is considered in [25]. For the system model presented in [25], the authors analysed throughput for the following relay selection policy. EH relay node-1 is selected when the probability of SNR of the link between source node to EH relay node-one link is greater than SNR of the link between source node to relay node-2; else, relay node-2 is selected. Furthermore, [26] proposed opportunistic relay selection policy, which uses max{min{Γ sr i , Γ r i d }} (where i ∈ 1, 2, … , L) algorithm for the relay selection. Note that Γ sr i and Γ r i d denote the instantaneous SNR of the source node to i th relay node link and i th relay node to the destination node link, respectively. For such an algorithm, the outage probability is analysed.
Unlike these studies, we propose a novel energy harvesting and energy-efficient (green) collaborative radio system model and outage-constrained relaying policy. The authors in the literature described above did not explore the outage-constrained relaying and investigate its performance in various physical layer measures such as energy efficiency, spectral efficiency, and outage probability.
Comparisons and comments: In [27], the authors employed a relay selection policy that selects the EHRN, which harvests maximum energy. In it, the authors investigated end-to-end link outage analysis in the high SNR regime. However, our system model, communication policy, objectives, and analysis are different and exhaustive. The critical difference lies in the selected EH relay strategy to forward the information. Precisely, the selected maximum EH relay decides to transmit or not based on the channel conditions between itself and the destination. This fundamental change in relaying strategy based on the outage brings more novelty, usefulness, and significance to the policy and its spectral efficiency and energy efficiency analysis.
In [28], the authors also used a similar relay selection policy, that is, the relay that harvests maximum energy forwards the signal to the destination node. However, we propose an energyefficient communication policy that comprises EHRN selection and its second hop transmissions based on channel conditions. Furthermore, the analysis that we present is much more rigorous and comprehensive. In [28], the expression for average maximum energy harvested by relay nodes is derived considering: (i) small scale fading with path loss and (ii) large scale fading with path loss. However, in this paper, we derive an analytical expression for the system model with small scale fading plus shadowing with path loss.
Furthermore, the analytical expression that we derive for the outage probability is in a single integral form. In addition to the outage analysis, we also present average spectral efficiency and average energy efficiency analysis. To gain more insights, we also show insightful asymptotic analysis, which is not present in [28]. Below, we present our specific contributions to the proposed green collaborative system model.

Novelty and contributions
Our proposed policy differs from the policies in the literature in the following ways. Firstly, our policy considers harvested energies that depend on channel conditions in the first hop, and secondly, the outage constrains the selected EH relay transmissions in the second hop. Thus, the novelty in our work fundamentally lies in outage-constrained relaying. In this paper, we consider an EH non-regenerative relay-assisted dual-hop green collaborative wireless system. As in [29], we adopt the TSP that separates two prominent tasks at the EH relay nodes, namely, information processing and energy harvesting. However, in the novel model that we propose, the communication policy is energy efficient due to the energy conservation rule based on outage constraint on the second hop transmissions. Therefore, the analysis for the physical (PHY) layer measures such as spectral efficiency and energy efficiency are non-trivial, useful, and insightful. Our contributions to this work are as follows.

Energy-efficient, dual-hop communication policy:
For the proposed multi-EH, time switching based green collaborative wireless system, we come up with a novel and energy-efficient communication policy. According to this policy, we select the EH relay that harvests maximum energy. The selected EH relay decides to transmit or not to transmit based on the channel conditions. 2. Generalised first-order statistical analysis: Based on random harvested energies, we formulate an order statistics problem. In the problem formulation, we consider a general fading scenario, that is, small scale fading with shadowing and path loss. For it, we derive a single integral expression for an average of the random variable representing the maximum of the random harvested energies. Note that the analysis in [28] is a particular case of the generalised analysis we present in this paper. 3. Link outage probability analysis: We present the link outage probability analysis for the link between the selected EH relay and the destination. Specifically, we derive a single integral expression for the outage probability. In addition to the exact outage analysis, we also develop asymptotic insights in a useful scaling regime. 4. Spectral efficiency performance analysis: Spectral efficiency is an important PHY layer performance measure. We present fading averaged spectral efficiency (FAvSE ) performance analysis of the proposed policy. Specifically, we derive a sin-gle integral expression for the exact FAvSE . Furthermore, we also present an insightful closed-form upper bound for exact FAvSE . We extend the analysis and present asymptotic insights on FAvSE . 5. Energy efficiency performance analysis: Energy efficiency is another critical performance measure of bandwidth efficiency per unit energy consumption. We present fading averaged energy efficiency (FAvEE ) performance analysis of the proposed policy. Specifically, we derive a single integral expression for the exact FAvEE . Furthermore, we also present an insightful closed-form upper bound for exact FAvEE . We extend the analysis and present asymptotic insights on FAvEE . The performance analysis of FAvEE and FAvSE is useful in revealing essential trade offs between these performance measures. 6. Numerical results and performance benchmarking: We numerically evaluate outage probability, average spectral efficiency, average energy efficiency and compare them with two benchmark policies. We present various plots to investigate the proposed policy's performance as a function of the proposed system model parameters. Using these numerical plots, we quantify the proposed green collaborative radio communication policy's performance improvements compared to benchmark policies in the literature. Specifically, we observe that the proposed policy achieves a performance gain of 9.86% in energy efficiency compared to the partial relay selection policy. Furthermore, the performance gain of 56.80% is achieved compared to the random relay selection policy. Table 1 presents the notations that we use in the rest of the paper. We present the rest of the content in the following manner: The green collaborative EH system modelling and protocol and assumptions are presented in Section 2. Section 3 describes performance measures and objectives. Section 4 contains problem formulation and the first-order statistics of the random variable, which represents maximum energy harvested. Section 5 presents outage-constrained relay transmission of the proposed policy. Section 6 presents the link outage analysis with its asymptotic analysis. Analytical results on exact FAvSE and exact FAvEE with its upper bound are derived in Sections 7 and 8. Section 7 and 8 also constitute the asymptotic analysis. Furthermore, while Section 9 contains simulation results, Section 10 presents conclusions and future research directions. Lastly, Appendix/Appendices A presents the derivations of the analytical results.

COLLABORATIVE EH WIRELESS SYSTEM MODEL
Consider the green collaborative wireless system shown in Figure 1. In it, source node S needs to send the information to the destination node D via two-hop statistically independent

Notation Symbol Remarks
Probability of an event P ()  is a probabilistic event.
Cumulative distribution function (CDF) F  (r )  is a continuous random variable.
Complementary cumulative distribution function (CCDF) F c  (r )  is a continuous random variable.
Probability density function (pdf) p  (r )  is a continuous random variable.

Expectation of a random variable E[]
 is a continuous random variable.
Circularly symmetric complex Gaussian random variable distribution  ( Z , 2 Z ) Z is random variable with statistical average Z , and variance 2 Z .

FIGURE 1
Energy harvesting multi-relay assisted, green collaborative system model. In it, for each timeslot, an outage-constrained EH relay node that harvests maximum energy participate in forwarding its received signal to the destination node wireless fading channels. We assume the absence of a direct link between the transmitting source node S and the destination node D. For each timeslot T , the relay that harvests the maximum energy among the L relay nodes is selected to forward its received signal to node D. In the multi-EH system, we consider L RF-EH non-regenerative relay nodes, which are denoted as R 1 , R 2 , … , R L , and d 1 , d 2 , … , d L denotes the distances between the source node and EHRNs, respectively. We also assume that each EHRN has a sufficient energy storage facility, and all the nodes in the system model have a single antenna for half-duplex transmission and reception. Note that only the selected RF EHRN assists the source node in forwarding its data. However, the selected relay transmits or does not transmit based on the channel conditions. Therefore, the communication policy that we propose considers the CSI of both the hops. Furthermore, each EH node harvests RF energy from the incoming source signal and consumes this harvested RF energy to forward its received signal to the destination node [29]. We also assume that the source node and the destination node has sufficient energy resources; that is, there is no power constraint.
Source and the first hop channels: Let P s is the average source transmit power. We assume that the source node is a non-EH node. Further, we assume quasi-static frequency-flat Rayleigh fading channels between source node to EHRNs. Let 1 , 2 , … , L represent the instantaneous channel power gains of S − R n (n = 1, 2, … , L) links, respectively. We assume that the channels are statistically independent [29,30]. However, the channels need not be identical.
In the proposed green collaborative EH model, we consider TSP. Note that implementing TSP leads to a system with perfect synchronisation and reduced complexity [29,31]. We assume that the processing power required for EHRNs is very small and negligible [29,32]. We present details on TSP based transmission policy, EH relay selection, and the second hop outageconstrained transmission in the following sections.
Remarks on model and its extensions: In the EHRNs-assisted collaborative wireless system model, we consider only one sourcedestination pair. However, different system model extensions are indeed possible. For instance, the green collaborative system having multiple source-destination pairs, a green collaborative system having nodes equipped with multiple antennas. For such complex models, the communication protocols would be more complicated because of issues such as synchronisation, resource allocation and channel estimation. To the best of the author's knowledge, design, and performance analysis of the proposed green collaborative wireless system is novel, nontrivial, and insightful.

2.1
Time switching based transmission policy TSP comprises two essential tasks, namely, EH and information transmission. All the EHRNs in the system follow TSP. Figure 2 shows a timeslot of TSP-based communication policy. In it, T denote the timeslot duration, which comprises three sub-timeslots, which are of duration T , is the sub-timeslot for data transmission from source to EHRNs. The second sub-timeslot T is the fraction of time for which EHRN harvest energy from the received RF signal. Lastly, the third subtimeslot T is another data transmission sub-timeslot for the selected EH relay to forward information.
Remarks on sub-timeslot T : Note that the fraction serves as information transmission versus energy harvesting trade-off parameter. The system engineer has to choose carefully. For instance, selecting the value such that an outage probability of about 1% is achievable [33]. It is possible to optimise the green collaborative system with optimum . However, we focus on designing energy-efficient communication policy and its performance analysis for ad hoc EH wireless systems wherein the nodes would have only partial CSI [34].

2.1.1
EH relay node tasks-harvesting and transmission EHRN consists of two subsystems, namely, EH subsystem (EHSS) and information processing subsystem (IPSS). The main task of EHSS is to rectify the received RF signal and to store the energy. The RF-EH circuits are assumed to be highly sensitive. IPSS, on the other hand, manages downconversion of RF-to-baseband signal and baseband signal processing. Note that all the harvested energy by EHRNs in T duration is used to forward the data signal to the destination [29].
Remarks on EHRN and EH process: In this paper, we consider non-regenerative EH relay nodes, given its simplicity and ease of implementation. Therefore, these relays require minimal processing by the IPSS. Further, we assume that the EH relay uses its harvested energy in the sub-timeslot for information transmission within that timeslot T . Note that due to the time-varying fading channel, the energy harvested by an EHRN is random.

EH relay selection and remarks
We propose an energy-efficient or green collaborative communication policy that consists of a simple EH relay selection policy, and, outage-constrained energy conserving relaying policy. While the former reduces the CSI requirement significantly, the latter conserves energy by allowing the selected EHRN to transmit based on channel conditions. We state the EH relay selection policy as follows: Let  1 ,  2 , … ,  L denote the harvested energies by the L EHRNs during the time T . We choose the relay that harvests maximum energy, that is, choose the EHRN R when Remarks on EH relay selection: We note that for each timeslot T , the non-selected EH relay may have some amount of residual energy. We assume that the non-selected EHRN uses its residual energy for low-data transmission to some other destination. Therefore, at the end of each timeslot, all energy storing subsystems of EHRNs will be empty [35].
We use the order statistics approach for ordering the continuous random variables. For the Rayleigh fading model, the harvested energies, which depend on instantaneous channel power gains, are exponentially distributed. Let  n denote the maximum energy harvested by the n th EH relay node. Suppose that k th (n ≠ k) EH relay node also harvest the same amount of energy, denoted by  k . Note that  n and  k represent two continuous random variables. Now, consider the probability of these two relays harvesting equal energy, has area zero [36]. Thus, we conclude that, in probabilistic sense, it is not possible to have two relays harvesting maximum amount of energy. However, it is indeed possible to select a subset of L EH relays as described below.
Extensions-Subset of L EH relays selection: Unlike selecting a single EH relay that harvests maximum energy, it is possible to choose a subset M of L relays (M < L) based on the certain harvested energy threshold. However, the subset of L EH relays selection would cause synchronisation problems in synchronous or coherent green collaborative radio communication systems. In addition to timing and frequency synchronisation challenges, the selection of more EH relays would increase hardware complexity and the burden of acquiring more CSI. Increased CSI requirement would lead to higher pilot overhead and hence more energy consumption. Therefore, subset relays selection is neither spectrally efficient (due to large pilot overhead) nor energy-efficient (due to enhanced transmissions) in green collaborative radio systems. Moreover, the subset EH relays selection based on the threshold is beyond our proposed work scope. The subset EH relays selection, and outageconstrained relaying policy and its performance analysis could be potential future work.
We note that the above relay selection policy uses only instantaneous and partial CSI of the channels between the source and the EHRNs. The proposed relay selection policy is useful in practical ad hoc wireless systems wherein the nodes would have only one hop or partial CSI [34]. We assume that the selected non-regenerative EHRN is always active and has sufficient harvested energy to forward the signal to the destination. Furthermore, to choose the EHRN that harvest maximum energy, in addition to CSI, the knowledge of other parameters such as distances, path loss exponent, harvesting duration, are also essential for computing the harvested energies. We assume that this knowledge is available to the source node.
However, the novelty of the communication policy lies in the energy conserving nature of the relaying policy. In it, the selected relay R forwards its received signal only when the channel power gain between R and destination node is above a specific threshold. Based on fading channel outage, we determine the threshold as a function of outage probability. We now present remarks on the CSI requirements of various nodes below.

Remarks on CSI
The CSI requirements of the proposed green collaborative communication system are as follows: • Source CSI requirement: The source S requires instantaneous CSI of the links between the source node to all the EHRNs. This CSI is useful for determining the strongest EHRN, which forwards the signal to the destination node based on the channel conditions. Therefore, for relay selection, the node S requires partial instantaneous CSI. One approach for CSI acquisition is as follows. The EHRN estimates the CSI between itself and the source node based on known pilot signals and sends the estimated CSI back to the source node by exploiting channel reciprocity. However, this conventional method of channel estimation requires a dedicated battery that does not rely on RF-EH [37]. Alternatively, a more practical solution of CSI acquisition in the energy-constrained network is presented in [38]. In [38], the source node acquires CSI from a one-bit feedback algorithm. In this algorithm, on receiving the information symbol at the relay for EH, it sends a one-bit feedback signal based on the energy level higher than or lower than the previously received information symbol. Further, based on received feedback bit, the channel is estimated using a specific optimisation technique. • EHRN CSI requirement: The EHRNs do not require CSI between themselves and the source. This non-requirement of CSI is because the EHRN acts as a non-regenerative repeater and does not do any additional processing. Therefore, EHRN implementation is relatively simple and practically amenable. However, the selected EH relay requires CSI between itself and the destination link and channel outage parameter to determine the channel state for further transmission. • Destination node CSI requirement: We assume that at the end of the timeslot T , the destination receiver performs maximum likelihood (ML) detection. For decoding, the destination node D requires instantaneous CSI of two fading channels, namely, the CSI between the source to the selected EHRN, and between the selected EH relay node and the destination node. Note that the CSI acquisition process remains the same as adopted by the source node.

PERFORMANCE MEASURES AND OBJECTIVES
The critical physical (PHY) layer performance measures are outage probability, symbol error probability, spectral efficiency, and energy efficiency. Note that each of the PHY layer performance measures is a function of SNR at the destination.
For the proposed green collaborative system model, we consider the following objectives: • Objective I−First order statistics: In the proposed model, the L EHRNs harvest energies probabilistically due to the timevarying nature of the fading channels. Let  1 , … ,  L denote these energies. Therefore, we have L continuous, positive-valued random variables. Our first objective is to obtain an insightful analytical expression for In the analysis, we consider a generalised fading model that accounts for both small scale and large scale fading effects. To account for small scale fading, we assume a frequency-flat Rayleigh fading model. Furthermore, to account for large scale fading effects, we consider the simplified path loss model [33] with shadow fading. • Objective II−Outage probability: We address the problem of determining the outage probability at the destination. Specifically, we obtain an analytical expression for the outage probability. We consider Rayleigh fading with the simplified path loss model for the analysis. Furthermore, we also develop insightful asymptotic outage analysis. • Objective III−Average spectral efficiency: We address the problem of determining the FAvSE at the destination. Specifically, we obtain an analytical expression for FAvSE . Furthermore, we also develop insightful upper bound for it. FAvSE is a vital PHY layer performance measure of wireless systems, which quantifies the efficient usage of the spectrum. In addition to exact analysis and upper bounding, we also develop asymptotic FAvSE analysis. • Objective IV−Average energy efficiency: We address the problem of determining the FAvEE at the destination. Specifically, we obtain an analytical expression for FAvEE . Furthermore, we also develop insightful upper bound for it. FAvEE is a vital PHY layer performance measure of wireless systems, which quantifies the efficient use of the harvested energy and power. In addition to exact analysis and upper bounding, we also develop asymptotic FAvEE analysis.
The performance analysis we develop in the various sections below is non-trivial, novel, and useful to design and develop optimum green collaborative wireless systems and networks. Furthermore, the analytical results that we derive serve as a valuable benchmark for EH collaborative relay systems.

ORDER STATISTICS OF GREEN COLLABORATIVE MODEL
In this section, we consider the first objective and develop an insightful statistical analysis for average maximum harvested energy by EHRNs. The EHRNs harvest energy from the source RF signal transmissions. Therefore, harvested energy is the function of source transmit power and TSP parameters. We assume that and T are the same for all the EHRNs. The path loss effect due to separation between the source and EHRNs is deterministic, and the range for path loss exponent is 2 ≤ ≤ 7, which cover different wireless propagation environments [33]. Furthermore, is the energy conversion efficiency, which is the same for all EHRNs.

4.1
Large scale plus small scale fading model The fading model, which is under consideration, accounts for multi-path fading effects, shadow fading, and path loss. Let Y n ∼  (0, 2 n ). When the generalised fading model is used, the instantaneous energy harvested at a specific EHRN (R n ) is given by where n = 10 Y n 10 , which denotes a log-normal random variable, and n , which denotes an exponential random variable, are statistically independent. Let E[ n ] = n . The average energy harvested at n th relay node R n is given by We state the following result on the statistical average of E[max{ 1 , … ,  L }] for the general fading scenario. Let  max denote the statistical average of the continuous random variable dy.
(4) Suppose the separation between the source node and all the EHRNs be equal, that is d 1 Furthermore, assuming all the mean channel power gain of the source node to EHRNs links are equal, that is, 1  Remark. We can numerically evaluate the above single integral expression. In the absence of shadow fading, we ignore the random variable, which implies Rayleigh fading with the simplified path loss model. On the other hand, in the absence of multipath fading, we have only a large scale fading model. The average maximum harvested energy  max increases with the increase in the number of EH relays. Assuming all other parameters fixed, as the mean channel power gain increases,  max increases, as expected. For L = 1,  1 serves as a lower bound. Thus, we have a trade-off between EH collaborative system complexity and the mean harvested energy  max . We numerically evaluate the  max in Section 9.

OUTAGE-CONSTRAINED RELAY TRANSMISSION
The relay selection policy for the first hop selects the strongest EHRN, which requires partial instantaneous CSI. We now extend the communication policy by considering relay to destination link CSI. If the selected EH relay to destination node channel quality is very poor, the transmitted signal will experience deep fade with high probability. Therefore, in such deep fade scenarios, the selected EHRN should conserve the harvested energy by avoiding transmissions.
We propose the following energy conservation rule based on the link outage defined on instantaneous channel power gain. Mathematically, the selected EH relay sets where  acts as the indicator of the relay transmission, r d is the channel power gain of R − D link and 0 is the threshold for the channel power gain of the R − D link. We call  as the energy conserving parameter of the policy. The expression for 0 is obtained by deriving outage probability, that is, p 0 ≜ P ( r d < 0 ). Therefore, the outage probability is given by Further simplification yields the following expression for threshold.
where r d is the mean channel power gain of R − D link.
Remark. The outage-constrained EH relay transmissions in the second hop serve as an energy conservation strategy. Furthermore, the inclusion of it makes the end-to-end collaborative communication policy novel and energy-efficient. We note that the energy conservation strategy requires CSI of the second hop link. We note that the channel power gain threshold 0 depends on average channel power gain and p 0 . Note that 0 → 0 as p 0 → 0. Thus, the energy-efficient end-to-end green collaborative communication policy considers the channel conditions local to the selected relay.
In the following sections, we consider each of the objectives and present performance analysis of the above proposed green collaborative communication policy.

LINK OUTAGE ANALYSIS
Outage probability is a vital PHY layer performance measure of wireless systems. In the design of wireless systems, an outage probability of 0.01 is a typical target [33]. This section deals with the analysis of outage probability for R −D link, where R is the selected EHRN in the system model. Note that the EH relay selection reduces synchronisation problem and hardware complexity [16]. Furthermore, selecting the relay that harvests maximum energy improves the performance of the system.
Let is a unit energy information symbol. The selected EH relay forwards its received signal to the destination node. We note that EH relays are implementation-friendly and need not consume its harvested energy for additional processing tasks. Note that h r d is the channel gain for the R − D link. Further, we assume statistically independent frequency-flat Rayleigh fading channel model for all the links. Therefore, the signal received at the destination node is given by where n d ∼  (0, 2 d ) is the additive noise component. For the R −D link, the instantaneous SNR is given by where  is the distance between the strongest EHRN and the destination node, |h r d | 2 ≜ r d the instantaneous channel power gain of R −D link, and r d is the corresponding mean channel power gain of the R −D link. Note that r d is exponentially distributed. Furthermore, if Γ th is the threshold SNR at the destination, then P (Γ D < Γ th ) denotes the outage probability for the R −D link [33].
The link outage probability is given by For r d < 0 , Γ D = 0 since  = 0. Therefore, we have where Below, we present an analytical result on the link outage probability.
For the proposed outage-constrained transmission policy, the link outage probability is given by where K 1 (⋅) is the modified Bessel function of second kind and first-order. Proof of the above expression is shown in Appendix A.2.
Remarks: We note that the link outage probability reduces due to the constrained transmissions based on channel conditions. The general analytical expression for the outage probability has a single integral, which we evaluate numerically. Note that the result is valid for Rayleigh fading with the simplified path loss model. In the presence of shadow fading, we observe further degradation in outage performance due to decreased end SNR. We note that, for L = 1, we have an upper bound. As the number of EHRNs L increases, link outage decreases.
We note that a 1% outage probability is a typical target in wireless systems [33]. Therefore, it is reasonable to choose the system design parameters such as threshold and the number of relays optimally to meet the target outage. By using multiple antennas at the source and destination and with beamforming, it is possible to improve outage performance significantly. However, the improvement in outage performance comes with the expense of hardware complexity and accurate CSI requirement.
Remarks on EH subsystem parameter : As mentioned before, in this work, we do not focus on the optimisation of the EH model parameter . However, observing the fact that the outage probability is a function of , one can obtain an estimate of by solving the outage equation numerically.

Asymptotic link outage analysis
Consider the following scaling regime: Let the mean channel power gains and 0 are fixed. The source transmit power P s → ∞. Assume that the EH model parameters such as and T , all distances, path loss exponent, L, and Γ th are all fixed. Furthermore, the relays have sufficiently large energy storage capacity. Let p r −D ,out denote the asymptotic outage probability. In the asymptotic regime, we have As P s → ∞, we have k ≜

AVERAGE SPECTRAL EFFICIENCY ANALYSIS
Considering the energy conserving transmission policy, we analyse two other significant PHY layer performance measures, namely, spectral efficiency and energy efficiency. In this section, we derive analytical expressions for the exact FAvSE , it's upper bound and asymptotic expression of FAvSE in high SNR regime.
For a given bandwidth, FAvSE gives knowledge regarding the capability of achieving the information rate in the green collaborative wireless system. To determine FAvSE , we take the statistical average of instantaneous spectral efficiency with respect to channel fading. Mathematically, FAvSE can be expressed as Note that FAvSE is a function of instantaneous fading SNR, which is given by (11). Below, we state an analytical result on the exact FAvSE . where , E 1 (.) is the exponential integral, and is the instantaneous channel power gain and mean channel power gain of the S − R link, respectively. The proof is relegated in Appendix A.3.

Remarks on exact FAvSE
: Note that the above analytical expression is valid for independent and identically distributed (i.i.d.) channels. For non-identical, statistically independent channels, we get a more complicated analytical result for the exact FAvSE . We also note that further simplification of the single integral expression for FAvSE is not possible. Hence, we evaluate the exact FAvSE numerically. We find that the exact FAvSE depends on various EH model parameters, average channel power gains, number of relays L, and the outage constraint. Furthermore, we see that the exact FAvSE performance improves with the number of EH relays. To gain further insights, we derive an insightful closed-form upper bound for the exact FAvSE .

Upper bound for exact FAvSE
We use Jensen's inequality to derive the upper bound of FAvSE . Applying the inequality, exact FAvSE can be upper bounded as Below, we state the simplified closed-form expression for the upper bound FAvSE .
. The derivation is presented in Appendix A.4.

Remarks on the FAvSE upper bound:
Note that the upper bound is in closed-form. Unlike the exact FAvSE expression, the upper bound has a much simpler form. However,  UB also depends on various EH system parameters and mean channel power gains. We evaluate the accuracy of the upper bound in Section 9. Note that all the system parameters on which the upper bound depends are inside the logarithm. To get explicit dependence on the system model parameters, we present an asymptotic analysis in an interesting scaling regime.

Asymptotic average spectral efficiency analysis
For the proposed green collaborative communication policy, we analyse asymptotic FAvSE in an interesting scaling regime. Let mean channel power gain of all the links be equal and fixed to . Furthermore, the source transmit power P s is assumed to be very large. We also assume, p 0 → 0; therefore, we have 0 = 0. Let  be the asymptotic FAvSE . Below, we present an analytical result for  .
In the scaling regime, the asymptotic FAvSE ( ) is given by The proof of this result is shown in Appendix A.5.
Remarks on asymptotic FAvSE : The asymptotic expression usefulness lies in showing the explicit dependence of the system model parameters. For very large L, that is, as L → ∞, ∑ L m=1 1 m ≈ ∫ L 1 ln t dt = ln L. Therefore, we get  ≈ (log 2 e)ℂ 1 r d ln L. In other words, given the fixed mean channel conditions and the fixed EH model parameters, the asymptotic spectral efficiency ∝ log 2 L.

AVERAGE ENERGY EFFICIENCY ANALYSIS
In this section, we derive analytical results on the exact FAvEE , its upper bound and asymptotic energy efficiency. FAvEE serves as another critical PHY layer performance measure. It provides insights regarding the efficient utilisation of the energy by the proposed wireless system. Energy efficiency () is a closely related performance parameter of spectral efficiency. It is the ratio of spectral efficiency to the total power consumed in the network. FAvEE can be mathematically represented as where P T is the total power consumed in the green collaborative system. Power consumption model: The total power is the sum of three power components. Mathematically, P T is given by where P s is the source transmit power, P r is the relay transmit power and P c is the power consumed by the circuitry. Further, relay transmit power can be expressed as Remarks on exact FAvEE: Note that the above analytical expression is valid for i.i.d. channels. For non-identical, statistically independent fading channels, we get a more complicated analytical result for the exact FAvEE . We note that further simplification of FAvEE expression is not possible. Therefore, we evaluate the exact FAvEE numerically. Similar to the exact FAvSE , the exact FAvEE also depends on various system parameters. However, FAvEE also depends on the power consumption model parameters. We evaluate the performance of FAvEE in Section 9. To gain further insights, we derive an insightful closed-form upper bound for the exact FAvEE .

Closed-form upper bound for FAvEE
To derive closed-form upper bound for the FAvEE , we apply Jensen's inequality on the numerator term of Equation (22). Below, we state the result on closed-form upper bound.
For the proposed policy, the exact FAvEE can be upper bounded as follows: . The Proof is relegated in Appendix A.7.

Remarks on the FAvEE upper bound:
Note that the FAvEE upper bound is in closed-form. Unlike the exact FAvEE expression, the upper bound is simpler and easier to evaluate. We evaluate the accuracy of the FAvEE upper bound in Section 9.
To get more explicit dependence on the system model parameters, we present an asymptotic analysis in an interesting scaling regime.

Asymptotic FAvEE analysis
For the proposed green collaborative communication policy, we analyse asymptotic FAvEE in the scaling regime mentioned before. Let  be the asymptotic FAvEE . Below, we present an analytical result for  .
In the scaling regime, the asymptotic FAvEE is given by The proof is shown in Appendix A.8.

NUMERICAL RESULTS AND INTERPRETATION
In this section, we first numerically evaluate and plot the statistical average  max . Furthermore, we obtain several numerical results to validate the derived analytical expressions for the outage probability, FAvSE , and FAvEE . To verify the mathematical expressions, we perform Monte-Carlo simulations. Before presenting the plots, we briefly explain the simulation methodology.

Simulation methodology and parameters
Initial parameter declaration: Table 2 presents the list of simulation parameters considered for generating plots. Note that we mention simulation specific parameters inside the captions of the simulation results. A summary of the simulation methodology is as follows.
Data symbol generation at the source: We generate 10 5 equally likely real data symbols, which are having unit energy. We assume that the source transmits with fixed power P s .
Fading channel and noise realisations: We generate 10 5 fading channel and noise realisations according to frequency-flat Rayleigh fading and additive white noise model.
Relay EH profile, relay selection policy with energy conservation strategy: Each relay node harvests a certain amount of energy, which is given by  n = channel realisation, we first calculate instantaneous spectral efficiency and energy efficiency. Finally, for the number of channel realisations, we evaluate FAvSE and FAvEE and compare them with that of the benchmark random relay selection policy.

9.2
Impact of mean channel gain on  max Figure 3 plots  max as a function of mean channel power gain for different L. Note that only Rayleigh fading with path loss (absence of shadowing) is considered in the figure. Therefore, the mathematical expression for the average maximum harvested energy becomes  max = ( ). It can be deduced from the mathematical expression, that if the value of L increases, the  max also increase, which can also be observed from the figure. However, this leads to increased system complexity. Further, with the increase in the mean channel power gain of the source to the relay link, the mean harvested energy by the relay nodes also increase because of good channel conditions. Hence,  max increases monotonically as a function of the mean channel power gain. Note that the presence of shadow fading also shows a similar trend. However,  max is affected when the RF signal path undergoes shadowing.

Evaluation of link outage probability
Our primary focus is on average energy efficiency and explicitly show the performance gains achieved by our proposed policy in terms of energy efficiency. However, we also present numerical results on outage probability and spectral efficiency to get more insights. Specifically, to understand the performance trade-off between average energy efficiency and average spectral efficiency. We consider two benchmark policies for comparing numerical results on outage probability, spectral efficiency, and energy efficiency. The two benchmark policies are the partial relay selection policy [21] and random relay selection policy [21,25].
In the partial relay selection policy, the EH relay is selected based on the instantaneous SNRs of links between the source node and the relay nodes. Hence, the relay having maximum instantaneous SNR of source node to itself is selected to forward the signal. Unlike this benchmark policy, our proposed outage constrained, energy-efficient collaborative radio communication policy consists of two parts: (i) EH relay selection based on energy harvested in a particular slot and (ii) outage based relaying to conserve energy in poor channel conditions. On the other hand, in the random EH relay selection policy, the EH relay is selected randomly (independent of channel statistics and energy harvested) to process and forward its received signal to the destination. Our proposed policy differs from the random EH relay selection policy in several ways. Firstly, our policy considers harvested energies that depend on channel conditions, and secondly, the outage constrains the selected EH relay transmissions. Thus, the novelty in our work fundamentally lies in outage-constrained relaying. Below, we present an outage performance plot with benchmarking.
Outage performance benchmarking and comparisons: Figure 4 plots outage probability as a function of source transmit power P s for different L. The figure compares the outage performance of the proposed outage-constrained, green cooperative radio communication policy and the benchmark policies. The initial observation is that, as the source transmit power increases, all the policies' outage probability decreases. This trend is due to the modified Bessel function of the second kind in (15) at high source transmit power. Further, we find that as L increases, the outage probability decreases, as expected. This improvement in outage performance is due to the improved average amount of maximum energy harvested for large L. However, the improved outage performance comes with the higher hardware complexity and processing burden of the green cooperative radio system with many EH relays. Further, since the transmission of the proposed policy is outage constrained, its performance is better than both the benchmark policies. Quantitatively, we observe that the proposed policy perform approximately 1.25 times better in comparison to partial relay selection policy at P s = 10 dB. Lastly, proposed policy perform approximately 2.2 times better in comparison to random relay selection policy at P s = 10 dB.
Remarks: Note that the random EH relay selection policy is insensitive to L because of the following reasons: Since we have assumed i.i.d. channel gains for all links, the random relay selection is insensitive to L. Furthermore, the EH relay selection is independent of the amount of energy harvested in a time slot. However, one can expect the dependency of L on outage probability in non-i.i.d. scenarios due to the chances of selecting the EH relay with higher mean channel power gain.

Numerical results on FAvSE with benchmarking
Performance benchmarking and comparisons: Figure 5 plots FAvSE as a function of source transmit power for the proposed policy and the benchmark policies. The proposed green collaborative radio communication policy is compared with two benchmark policies: partial relay selection policy and random relay selection policy. Since the proposed green collaborative radio communication policy is outage constrained, therefore the performance of proposed policy is analysed for two different outage probability values, that is, p 0 = 0.1 and p 0 = 0.2. We observe that the proposed green collaborative radio communication policy's performance is better than the random relay selection policy for both the p o values. Furthermore, due to the outage constrained relay transmission of the proposed policy, its spectral efficiency performance shows little degradation compared to the partial relay selection policy. However, in the following figure, we show that the proposed green collaborative radio communication policy is more energyefficient than the benchmark policies.
Remarks: Note that the proposed policy is not spectral efficient (though it is energy efficient, shown in the figure 9) in comparison to the partial relay selection policy. However, during the outage, the partial relay selection policy is not reliable and energy-efficient. Furthermore, the throughput, which is a function of link probability error (depends on modulation and coding schemes), will be low in poor channel conditions. Thus, the benchmark policies would consume the precious harvested energy by transmitting signals via the non-reliable, erroneous link between the selected EH relay and the destination. Extensions and applications: To look in a different model and perspective, consider a collaborative EH relays-assisted network with multiple destinations. In such a scenario, we can extend our proposed policy to choose the best (least outage) destination node to transmit the selected EH relay signal. Thus, the proposed green collaborative radio communication policy is readily applicable to more complex green collaborative networks.
Furthermore, consider the proposed green collaborative model with multiple hybrid EH relays, where the relay can partially use the in-built battery in place of harvested energy during outage events. This replacement of pure-EH relays by hybrid EH relays can enhance performance in terms of FAvSE and communication reliability. However, these improvements come at the expense of improved relaying complexity and cost.
Impact of P s on FAvSE : Figure 6 plots FAvSE as a function of source transmit power. It also plots FAvSE upper bound and the random relay selection policy. We observe that as the source transmit power increases, the FAvSE also increases. This trend happens because of the increase in the SNR at the destination led by the increase in source transmit power (can be analysed from Equation (20)). Further, we see that the exact FAvSE and the Monte-Carlo simulations match well. In the figure, we also observe that the upper bound tracks the exact FAvSE well. Furthermore, we see that the proposed policy significantly outperforms the benchmark random relay selection policy.
Remarks on accuracy: The percentage deviation between values obtained from analytical results and simulations depends primarily on the following factors as described below.
i). Approximations: The approximations in analysis lead to more variation between analysis and simulation plots. Since we have not considered any approximations and modelled the proposed system exactly in our simulation, our analytical graphs closely match the simulation graphs. ii). Channel realisations: According to the law of large numbers [39], the accuracy of the performance measure that we numerically evaluate via simulations improves with a large number of channel realisations or samples. Note that we have considered many channel realisations (that is 10 5 ). Therefore, the variation between analysis and simulation plot is significantly less or negligible.
Impact of mean R − D channel power gain on FAvSE : Figure 7 plots FAvSE as a function of the average channel power gain of the R − D link. This figure shows the impact of mean channel power gain on FAvSE , and the upper bound. It also plots the average spectral efficiency of the random relay selection policy. As the average channel power gain increases, the FAvSE (as analysed in Equation (20)) also increases because of the improvement in SNR at the destination. However, the rate of increase in FAvSE is relatively slow due to the performance measure's logarithmic nature.
Further, we see that the exact FAvSE and Monte-Carlo simulations match well. In the figure, we also observe the upper bound tracking the exact FAvSE well. Lastly, we see that the proposed policy outperforms the benchmark relay selection policy by a large margin for all mean channel power gains.
Impact of P s and L on FAvSE: Figure 8 plots FAvSE as a function of the source transmit power P s for different L. This figure shows the impact of P s and L on the exact FAvSE for the proposed policy. As P s increases, the FAvSE also increases, as expected. Furthermore, from the analysis in Section 4.1, we observe that as the source transmit power increases, the  max increases. This improvement in the  max causes the improvement in the SNR at the destination. Thus, we observe the enhanced FAvSE performance in the figure. We also observe that FAvSE increases rather slowly for large L. This gradual improvement in FAvSE as a function of L is due to its dependence logarithmically. Therefore, we need to choose L wisely to trade-off green collaborative radio system complexity and performance.

Numerical results on FAvEE with benchmarking
Performance benchmarking, comparisons, and gains: Figure 9 plots FAvEE as a function of source transmit power for the proposed policy and the benchmark policies. The proposed outage-constrained green collaborative radio communication policy is compared with two benchmark policies: partial relay selection and random relay selection. Note that the proposed policy is analysed for two different outage probability values, that are, p 0 = 0.1 and p 0 = 0.2. Further, we observe that the proposed policy for both the values of p 0 performs better than the benchmark policies. The specific reason for the performance gain is power conservation based on the outage constraint. A performance gain of 9.86% in energy efficiency is achieved by the proposed policy with p 0 = 0.2 in comparison to the partial relay selection policy at P s = 0 dB. Furthermore, the performance gain of 56.80% is achieved compared to the random relay selection policy.
Remarks: Note that, due to the outage-constrained relay transmissions, a substantial performance gain in terms of energy efficiency can be observed by the proposed green collaborative radio communication policy when compared to the benchmark policies. Furthermore, for large scale collaborative multi-hop energy harvesting Internet of Things (IoT), the aggregate energy efficiency gains could be much higher for the proposed policy than the benchmark policies. Impact of P s on FAvEE: Figure 10 shows the impact of increasing the source transmit power P s on FAvEE . The figure also plots the upper bound and the benchmark policy. We see that as P s increases, the FAvEE of the proposed model decreases. This degradation in average energy efficiency is due to increased average total power consumption. The upper bound tracks the exact FAvEE well. Furthermore, we see that the proposed policy significantly outperforms the random relay selection policy.
Impact of mean R − D channel power gain on FAvEE: Figure 11 shows the impact of increasing average channel power gain of R − D link on FAvEE . The Figure also shows the upper bound and the benchmark policy. We see that as average channel power gain increases, the SNR of the signal received at the destination node increases. Therefore, the FAvEE monotonically increases. However, the total average power consumption remains fixed. Note that the exact FAvEE and Monte- Impact of P s and L on FAvEE: Figure 12 shows the exact FAvEE for increasing P s for different L. The FAvEE performance is better for high L at low P s values. This trend continues till a few dBs of P s because of different logarithmic dependence in the numerator and the denominator term, which can be seen in Equation (28). On the other hand, at higher values of P s , FAvEE performance is poor due to increased total average power consumption.
FAvEE − FAvSE trade-off: Figure 13 plots both the average spectral efficiency and the average energy efficiency as functions of the source transmit power. This plot explicitly shows the trade-off between FAvSE and FAvEE . We see that, as P s increases, FAvSE increases, as expected. On the other hand, as P s increases, the system's total average power consumption increases. Therefore, FAvEE decreases.
Remarks: Note that a monotonically decreasing trend (for FAvEE versus FAvSE ) is similar to the behaviour shown in the literature plot [40]. Thus, we validate the spectral efficiency and energy efficiency trade-off. The designer can appropriately adjust the regime to achieve the required spectral efficiency or energy efficiency depending on the system or network requirements.

CONCLUSIONS AND FURTHER RESEARCH
This paper uses a novel outage-constrained, energy harvesting collaborative wireless system that uses multiple time switching based non-regenerative EH relays. In it, the relay nodes harvest energy from its received RF signal. Considering small scale fading and large scale fading with path loss, we developed a firstorder statistical analysis of the maximum harvested energy. To gain more insights, we also evaluated the system performance in terms of outage probability, FAvSE , and FAvEE . Specifically, we derived novel and insightful analytical expressions for exact performance measures and upper bounds. We also presented an insightful asymptotic analysis for these PHY layer performance measures. Based on the numerical results, we found that the relay selection policy outperforms the benchmark policies in terms of FAvEE . We observe that the proposed policy achieves a performance gain of 9.86% in energy efficiency than the partial relay selection policy. Furthermore, the performance gain of 56.80% is achieved compared to the random relay selection policy. The substantial gains achieved by the green collaborative system with relay selection motivate its use in green collaborative and cognitive ad hoc networks. An interesting problem for future work is determining the optimised value of EH duration for the time switching policy based on channel characteristics.
= max Since  max is a non-negative random variable, the average energy harvested can be evaluated from the CCDF.
Using the fact that Q(y) = dy.
Further simplification using the standard integral [41, (3.324.1)] yields the desired expression for outage probability. .
(A14) From the energy conservation rule, we have  = 0 for r d < 0 and  = 1 for r d ≥ 0 . Simplifying further, we get where ℂ 1 = we get the desired single integral expression for FAvSE in Equation (18).

A.4 Proof of Result 2: Closed-from FAvSE upper bound
To determine the expression for upper bound FAvSE , we first obtain the average SNR of R − D link, that is, E[Γ D ]. Therefore, from Equation (11), E[Γ D ] is given by . (A17) Using statistical independence of ,  max , and r d , we have It is easy to show that E[] = 1 − p 0 . From Equation (8) In the scaling regime, as p 0 → 0, we have 0 → 0. Therefore, in the scaling regime, e − 0 r d → 1. Further simplification yields the designed expression for the asymptotic FAvSE .

A.6
Proof of Result 4: Exact FAvEE From Equation (24), the average relay transmit power can be expressed as (A22) By virtue of statistical independence of the random variables, P r can be expressed as (A25) Further, substituting Equations (18) and (A25) in Equation (22) we get (25).