Amplify-forward Research Articles

Time‐switched energy harvesting amplify‐forward relay with direct link: Performance analysis

SummaryA dual‐hop time‐switched (TS) energy harvesting (EH) amplify forward (AF) relay system has been considered, which comprises three nodes: source (S), destination (D), and an energy harvesting relay (R), respectively. Besides the relay link, the proposed architecture has an additional direct link between the source and destination node. For this model, we derive the expressions for system outage probability and throughput. The proposed architecture shows significant performance increments in terms of system outage probability and throughput when compared with a traditional EH relay system having no direct link.

Secrecy Performance by Power Splitting in Cooperative Dual-Hop Relay Wireless Energy Harvesting

In wireless communication systems, for secure communication between a transmitter and receiver over the communication channel, the physical layer security is widely utilized. The paper presents a dual-hop wireless full-duplex relay (FDR) network with a source relay and destination relay between two nodes and listening devices. The relay and source use energy harvesting to gain energy from power beacon. Two cooperative techniques are utilized to investigate the amplify-forward (AF) and decode-forward (DF) secrecy capacity in the energy harvesting power splitting system. It is shown that the secrecy performance of an AF relay is better than the secrecy performance of a DF relay in the given form. At 40-meter distance between the relay and the eavesdropper in an energy harvesting system, the AF relay outperforms the DF relay. The simulation is performed using the Monte-Carlo method in MATLAB.

Performance Analysis of Intelligent Reflecting Surfaces in Multi-Input-Single-Output Indoor Hotspot Environment

The evolution of 5G and beyond is boosting the development of telecommunication technology. In the future communication system, achievable rate and energy efficiency become the main aspects due to highly reliable and low latency requirements. Applying multiple antennas and applying cooperative communication scenarios to the system may enhance the network's performance. Intelligent reflecting surfaces (IRS) and relaying protocols are some examples of cooperative communication applications. IRS is multiple two-dimensional meta-surface elements that can reflect the incoming signal to get the desirable beam-forming based on its phase. While the relay is a device that can be used to enhance the performance of the networks based on its protocols such as amplify forward (AF) and decode forward (DF). Accordingly, this paper studies an IRS supporting MISO transmission and compares it with the relay deployment scenario. As a result, IRS has higher performance compared with any other scenario, and adding more IRS elements may enhance the achievable rate.

Selection Combiner in Time-Varying Amplify Forward Cooperative Communication

This research presents the diversity combining schemes for Multiple Symbol Double Differential Sphere Detection (MSDDSD) in a time-varying amplify-and-forward wireless cooperative communication network. Four diversity combiners, including direct combiner, Maximal Ratio Combiner (MRC), semi MRC and Selection Combiner (SC) are demonstrated and explained in details. A comprehensive error probability and outage probability performance analysis are carried through the flat fading Rayleigh environment for semi MRC and SC. Specifically, error performance analysis is obtained using the PDF for SC detectors. Finally, power allocation expression based on error performance minimization approach is presented for the proposed SC performance optimization. It is observed that the performance analysis matches well with the simulation results. Furthermore, the proposed SC scheme offers better performance among the conventional MRC and direct combiner schemes in the presence of frequency offsets.

End-to-End Performance Analysis of Underwater Optical Wireless Relaying and Routing Techniques Under Location Uncertainty

On the contrary of low speed and high delay acoustic systems, underwater optical wireless communication (UOWC) can deliver a high speed and low latency service at the expense of short communication ranges. Therefore, multihop communication is of utmost importance to extend the range, improve degree of connectivity, and overall performance of underwater optical wireless networks (UOWNs). In this regard, this paper investigates relaying and routing techniques and provides their end-to-end (E2E) performance analysis under the location uncertainty. To achieve robust and reliable links, we first consider adaptive beamwidths and derive the divergence angles under the absence and presence of a pointing-acquisitioning-and-tracking (PAT) mechanism. Thereafter, important E2E performance metrics (e.g., data rate, bit error rate, transmission power, amplifier gain, etc.) are obtained for two potential relaying techniques; decode & forward (DF) and optical amplify & forward (AF). We develop centralized routing schemes for both relaying techniques to optimize E2E rate, bit error rate, and power consumption. Alternatively, a distributed routing protocol, namely Light Path Routing (LiPaR), is proposed by leveraging the range-beamwidth tradeoff of UOWCs. LiPaR is especially shown to be favorable when there is no PAT mechanism and available network information. In order to show the benefits of multihop communications, extensive simulations are conducted to compare different routing and relaying schemes under different network parameters and underwater environments.

Cooperative Hybrid VLC-RF Systems With Spatially Random Terminals

In this paper, a cooperative hybrid visible light communication (VLC)-radio frequency (RF) relay system, which includes a transmitter (S) with a cluster of light emitting diodes (LED) lamps, a relay (R), and a destination (D), is taken into consideration. Moreover, decode-forward (DF) and amplify-forward (AF) schemes are considered at R to aid the data transmissions between S and D. Specially, R is randomly located in the coverage of the LED lamps, D is randomly distributed out of the coverage of the LED lamps. Then, VLC is employed for S-R link, and a traditional RF communication technology is adopted over the R-D link. Considering Nakagami- $m$ fading over the R-D link, and the randomness of the locations of R and D, the statistical characteristics of the received signal-to-noise ratio at D under AF scheme, and the ones at R and D under the DF scheme are characterized, respectively. Subsequently, approximated analytical and asymptotic expressions for the outage probability of the considered system are derived, as well as the approximated expression for the average symbol error rate of M-ary quadrature amplitude modulation scheme under the DF scheme. Finally, simulation and numerical analysis are conducted to verify the correctness of our proposed models.

Multi-objective optimization design for multi-source multicasting MIMO AF relay systems

In this paper, we consider a multi-source multicasting two-hop multi-input multi-output amplify-forward (AF) relay system, where multiple source nodes multicast their own messages to a group of receivers with the cooperation of an AF relay node. In particular, we aim at minimizing the transmission power consumption and the mean-squared error (MSE) of the receiver estimated signal simultaneously. However, the two objectives are coupled and even conflicting. In view of this, a multi-objective optimization (MOO) framework is adopted to achieve the trade-off between the two objectives. The formulated MOO problem (MOOP) takes into account the constraints of the MSE upper bound and the maximum transmission power budget. Since the MOOP is non-convex and hard to tackle, we propose a resource allocation algorithm by exploiting the weighted Tchebycheff approach and the optimal structure of the relay precoding matrix. Simulation results not only demonstrate the effectiveness of the proposed algorithm, but also unveil an important trade-off between the total power consumption and the MSE at receivers.

Effects of threshold based relay selection algorithms on the performance of an IEEE 802.16j mobile multi-hop relay (MMR) WiMAX network

IEEE 802.16j MMR WiMAX network introduces multi-hop relay architecture, which involves cooperative relay stations focusing on increasing the network throughput and coverage. Relay selection algorithms can be used to choose the optimal relay, which help in reducing the computational complexity during the signal processing operation of the wireless network. In this research work, a conventional Amplify-Forward (AF)/Decode-Forward (DF) assisted multi-relay IEEE 802.16j WiMAX network is considered. The effects of relay selection algorithms on the performance metrics such as Symbol Error Rate (SER) and channel capacity are investigated in detail through simulation-based study. Further, the performance of this network utilizing the proposed relay selection algorithms, namely threshold based max_min and threshold based harmonic mean of SNR, are compared with the existing max_min and harmonic mean of SNR based algorithms. Standard diversity combining techniques such as Maximal Ratio Combining (MRC) and Selection Combining (SC) are used for combining the transmitted signal at the receiver. In addition, the impact of relay locations on the performance metrics are explored. It is observed that both the proposed threshold based max_min and threshold based harmonic mean of SNR based relay selection algorithms outperform the max_min and harmonic mean of SNR based algorithms, as both the SER and channel capacity for the considered multi-relay WiMAX network is improved significantly. Further, this extensive study and analysis will be beneficial for the design of MMR WiMAX networks.

TAS-Based Incremental Hybrid Decode–Amplify–Forward Relaying for Physical Layer Security Enhancement

In this paper, a transmit antenna selection (TAS)-based incremental hybrid decode–amplify–forward (IHDAF) scheme is proposed to enhance physical layer security in cooperative relay networks. Specifically, TAS is adopted at the source in order to reduce the feedback overhead. In the proposed TAS-based IHDAF scheme, the network transmits signals to the destination adaptive select direction transmission (DT) mode, AF mode, or DF mode depending on the capacity of the source-relay link and source-relay link. In order to fully examine the benefits of the proposed TAS-based IHDAF scheme, we first derive its secrecy outage probability (SOP) in a closed-form expression. We then conduct asymptotic analysis on the SOP, which reveals the secrecy performance floor of the proposed TAS-based IHDAF scheme when no channel state information is available at the source. Theoretical analysis and simulation results demonstrate that the proposed TAS-based IHDAF scheme outperforms the selective decode-and-forward, the incremental decode-and-forward, and the noncooperative DT schemes in terms of the SOP and effective secrecy throughout, especially when the relay is close to the destination. Furthermore, the proposed TAS-based IHDAF scheme offer a good tradeoff between complexity and performance compared with using all antennas at the source.

Spectral Efficiency and Relay Energy Efficiency of Full-Duplex Relay Channel

Full-duplex relaying has the potential to improve the spectral efficiency (SE) of cooperative communication systems. Due to residual self-interference (RSI), increase of the relay power does not always contribute to SE improvement. To fully utilize full-duplex relaying in cooperative communications, the effect of RSI on the SE achieved by different relay schemes need to be investigated. In this paper, we study bounds on the SE of full-duplex relay channel with decode-forward (DF) relaying, compress-forward (CF) relaying, and amplify-forward (AF) relaying in the presence of RSI. For respective schemes, optimal relay power and the corresponding maximal SE are derived in closed-form. Bounds on the relay energy-efficiency (REE) are presented for different schemes, which are useful for system design under per-node energy efficiency constraint. Based on the SE performance, the conditions of employing full-duplex relay, criteria for selecting relay scheme among DF, CF, and AF schemes, and the conditions of adopting hybrid full-duplex or half-duplex mode are elaborated regarding to RSI strength. In summary, this paper investigates the relationship among SE, REE, and system design by taking into account the effect of RSI for a general class of cooperation schemes.

Sum Secrecy Rate Maximization for Full-Duplex Two-Way Relay Networks Using Alamouti-Based Rank-Two Beamforming

Consider a two-way communication scenario where two single-antenna nodes, operating under full-duplex mode, exchange information to one another through the aid of a (full-duplex) multi-antenna relay, and there is another single-antenna node who intends to eavesdrop. The relay employs artificial noise (AN) to interfere the eavesdropper's channel, and amplify-forward (AF) Alamouti-based rank-two beamforming to establish the two-way communication links of the legitimate nodes. Our problem is to optimize the rank-two beamformer and AN covariance for sum secrecy rate maximization (SSRM). This SSRM problem is nonconvex, and we develop an efficient solution approach using semidefinite relaxation (SDR) and minorization-maximization (MM). We prove that SDR is tight for the SSRM problem and thus introduces no loss. Also, we consider an inexact MM method where an approximately but computationally cheap MM solution update is used in place of the exact update in conventional MM. We show that this inexact MM method guarantees convergence to a stationary solution to the SSRM problem. The effectiveness of our proposed approach is further demonstrated by an energy-harvesting scenario extension, and by extensive simulation results.

Cooperation in 5G Heterogeneous Networking: Relay Scheme Combination and Resource Allocation

In 5G heterogeneous networking, it is promising to integrate different wireless networks to provide higher data rate. This paper models the integrated system as a receiver frequency division relay channel (RFDRC) and studies how to improve the transmission rate by combining decode-forward (DF), compress-forward (CF), and amplify-forward (AF) schemes. First, we establish clear criterions on how to select a relay scheme among DF, CF, and AF schemes and prove that the CF outperforms AF for all possible configurations. Based on the scheme selection criterions, we propose a hybrid DF–CF scheme which takes advantage of both DF and CF schemes in RFDRC. A near-optimal resource allocation is presented for the DF–CF-based system, leading to a new achievable rate for RFDRC. For ease of implementation, we further put forward a hybrid DF–AF scheme and reconsider the joint bandwidth and power allocation. Two suboptimal resource allocation solutions are established. In particular, when source frequency band and relay frequency band have equivalent bandwidth, we show that the proposed hybrid DF–AF scheme can achieve the concave envelope of the maximum between DF rate and AF rate. Numerical results show that the proposed schemes bring significant gains for RFDRC.

Multi-Hop Relaying: An End-to-End Delay Analysis

The impact of multi-hopping schemes on the communication latency in a relay channel is studied. The main aim is to characterize conditions under which such schemes decrease the communication latency given a reliability requirement. Both decode-forward (DF) and amplify-forward (AF) with block coding are considered, and are compared with the point-to-point (P2P) scheme which ignores the relay. Latency expressions for the three schemes are derived, and conditions under which DF and AF reduce latency are obtained for high signal-to-noise ratio ( ${\mathsf{SNR}}$ ). Interestingly, these conditions are more strict when compared to the conditions under which the same multi-hopping schemes achieve higher long-term (information-theoretic) rates than P2P. It turns out that the relation between the source-destination ${\mathsf{SNR}}$ and the harmonic mean of the ${\mathsf{SNR}}$ ’s of the channels to and from the relay dictates whether multi-hopping reduces latency or not.

Power Allocation for a Hybrid Decode–Amplify–Forward Cooperative Communication System With Two Source–Destination Pairs Under Outage Probability Constraint

We develop a two-source–destination-pair cooperative communication scheme that can achieve multiuser diversity and cooperative diversity. In this scheme, we use hybrid decode–amplify–forward (HDAF) protocol to improve system performance. From practical point of view, HDAF protocol performs better than amplify-and-forward and decode-and-forward protocols by combining the merits of both. Meanwhile, we derive a closed-form expression of outage probability associated with HDAF protocol analyzed. Based on outage probability constraint, we investigate optimal power allocation that minimizes the total power. Numerical analysis is used to confirm the accuracy of the derived theory and to examine the performance of our proposed cooperative scheme, particularly as we analyze power savings in using optimal power allocation compared with equal power allocation, which is commonly assumed in previous studies. It is shown that significant power savings can be obtained by using the proposed power optimization method.

Ergodic Capacity Analysis of Full-duplex Mimo Relay Channel using Tracy-Widom Distribution with Processing Delay

We explore a full-duplex technique in wireless communication particularly for relay networks. We consider the relay to operate in full-duplex, which occurs when transmission and reception are conducted in the same channel. We investigate potential benefits of full-duplex technique in relay networks, which uses multiple antennas for transmission and reception combined with the Amplify-Forward (AF) scenario. We study the effects of multiple antennas in terms of relay capacity. We derive an ergodic capacity expression using the Tracy-Widom distribution. Using Singular Value Decomposition (SVD) and perfect Channel State Information (CSI), we investigate these three scenarios: First, we consider the relay to have an antenna larger than that of both source and destination. Second, we consider both relay and destination to have an antenna larger than that of the source. Third, we consider both relay and source to have antenna larger than that of the destination. We show the results that the capacity of the relay with a fullduplex technique is almost twice the capacity of an half-duplex. We show that increasing the number of destination antennas is not help much when one of the source antennas is small. Moreover, the capacity decreases due to a channel hardening effect, when the number of destination antennas is larger than that of the source.

English

To achieve the multiuser diversity and cooperative diversity, a two source destination pair is considered for cooperative communication system. Hybrid Decode Amplify Forward (HDAF) Relaying Protocol improves the system performance by combining the merits of both Amplify Forward (AF) and Decode Forward (DF) protocols is used. The fast and efficient Parallel Shift Water Filling (SPWF) algorithm can minimize the total power, based on the outage probability constraint. In the conventional algorithms, the solution is obtained by an iterative binary searching and Lagrange Multiplier searching process. In contrast, PSWF Algorithm removes the iterative searching process. It executes the PSWF only once, and then directly calculates the final solution with the parallel shift property as an enabling mechanism. Numerical analysis is used to compare the various relaying protocols based on outage probability and Bit Error Rate.

Outage Performance of Hybrid Decode–Amplify–Forward Protocol with the nth Best Relay Selection

In this paper, we consider the Hybrid Decode---Amplify---Forward protocol with the $$n$$ n th best-relay selection scheme. In the best-relay selection scheme, the best relay only forwards the sourc...

Two-Way Amplify–Forward Relaying Using Frequency-Domain Oversampling on Frequency-Selective Fading Channels

Frequency-domain oversampling (FDO) is studied for two-way amplified-and-forward relaying (TWAR) on the frequency-selective fading channel. In the FDO-based scheme, a zero postfix (ZP) is inserted in the transmitted data block, and a fractionally spaced frequency-domain (FSFD) minimum mean-square-error (MMSE) estimate is performed on the received data block. Compared with the conventional MMSE receiver using a cyclic prefix (CP) without FDO, the FSFD -MMSE receiver can extract the frequency diversity on the frequency-selective fading channel. Moreover, a semi-analytical result on the error performance of the FSFD-MMSE receiver is also provided, which matches the simulation result closely. Finally, the robustness of the FDO-based scheme to the time-varying fading and the frequency offset is also studied through simulations.

Broadcast Approaches to the Diamond Channel

The problem of dual-hop transmission from a source to a destination via two parallel full-duplex relays in block Rayleigh fading environment is investigated. All nodes in the network are assumed to be oblivious to their forward channel gains; however, they have perfect information about their backward channel gains. We also assume a stringent decoding delay constraint of one fading block that makes the definition of ergodic (Shannon) capacity meaningless. The focus of this paper is on simple, efficient, and practical relaying schemes to increase the expected-rate at the destination. For this purpose, various combinations of relaying protocols and the broadcast approach (multi-layer coding) are proposed. For the decode-forward (DF) relaying, the maximum finite-layer expected-rate as well as two upper-bounds on the continuous-layer expected-rate are obtained. The main feature of the proposed DF scheme is that the layers being decoded at both relays are added coherently at the destination although each relay has no information about the number of layers being successfully decoded by the other relay. It is proved that the optimal coding scheme is transmitting uncorrelated signals via the relays. Next, the maximum expected-rate of ON/OFF based amplify-forward (AF) relaying is analytically derived. For further performance improvement, a hybrid decode-amplify-forward (DAF) relaying strategy, adopting the broadcast approach at the source and relays, is proposed and its maximum throughput and maximum finite-layer expected-rate are presented. Moreover, the maximum throughput and maximum expected-rate in the compress-forward (CF) relaying adopting the broadcast approach, using optimal quantizers and Wyner-Ziv compression at the relays, are fully derived. All theoretical results are illustrated by numerical simulations. As it turns out from the results, when the ratio of the relay power to the source power is high, the CF relaying outperforms DAF (and hence outperforms both DF and AF relaying); otherwise, DAF scheme is superior.

On Capacity Scaling of Multi-Antenna Multi-Hop Networks: The Significance of the Relaying Strategy in the “Long Network Limit”

The sum-capacity <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$C$</tex></formula> of a static uplink channel with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> single-antenna sources and an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> -antenna destination is known to scale linearly in <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> , if the random channel matrix fulfills the conditions for the Marcenko-Pastur law: if each source transmits at power <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P/n$</tex></formula> , there exists a positive <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$c_{0}$</tex></formula> , such that <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\lim_{n \ura{} \infty}C/n=c_{0}$</tex></formula> almost surely. This paper addresses the question to which extent this result carries over to multi-hop networks. Specifically, an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$L+1$</tex></formula> -hop network with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> non-cooperative source antennas, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> fully cooperative destination antennas, and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L$</tex></formula> relay stages of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n_{\cal R}$</tex></formula> (cooperative or non-cooperative) relay antennas each is considered. Four relaying strategies are assessed based on the interrelationship between two sequences. For each considered strategy <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm XF}$</tex></formula> , there exists a sequence <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(c_{L}^{\rm XF})_{L=0}^{\infty}$</tex> </formula> , such that <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$c_{L}^{\rm XF}=\lim_{n \ura{} \infty}R^{\rm XF}_{L}/n$</tex></formula> almost surely, where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$R^{\rm XF}_{L}$</tex></formula> denotes the supremum of the set of sum-rates that are achievable by the strategy over <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L\!+\!1$</tex> </formula> hops. This sequence depends on the sequence <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(P_{L})_{L=0}^{\infty}$</tex> </formula> , where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$P_{L}$</tex></formula> corresponds to the power of the source stage and each of the relay stages in an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L\!+\!1$</tex></formula> -hop network. Results are summarized as follows: <orderedlist continuation="restarts" numeration="bullet" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <listitem><para>Decode &amp; forward (DF): For <formula formulatype="inline"><tex Notation="TeX">$n_{\cal R}=n$</tex></formula>, <formula formulatype="inline"><tex Notation="TeX">$c^{\rm DF}_{L}$</tex></formula> is constant with respect to <formula formulatype="inline"> <tex Notation="TeX">$L$</tex></formula>, if also <formula formulatype="inline"><tex Notation="TeX">$P_{L}$</tex></formula> is constant with respect to <formula formulatype="inline"> <tex Notation="TeX">$L$</tex></formula>.</para></listitem></orderedlist>