Cooperative relaying techniques have recently received significant interests from both academia and industry due to their ability to provide spatial diversity to address the ever increasing demand for extended network coverage, higher data rates without sacrificing extra power resources, greater mobility and enhanced reliability. This thesis mainly considers two themes. Firstly, in the context of self-powered multiple-input-multiple-output (MIMO) full-duplex (FD) relaying, our research focuses on design and performance analysis of MIMO FD relaying systems in the presence of practical transmission impairments. Namely, the impact of spatial fading correlation, imperfect channel state information (CSI), loopback self-interference (LI), and co-channel interference (CCI) on the system performance are investigated. Secondly, in the context of wirelessly-powered MIMO HD relaying, our research focuses on energy beamforming which is used to maximize the overall harvested energy so as to enable longer-distance wireless power transfer when compared to the single antenna nodes. Namely, in the presence of MIMO relaying systems, hop-by-hop information and energy beamforming is proposed where the transmitted signal is steered along the strongest eigenmode of each hop. The wirelessly powered relay scavenge energy from the source information radio-frequency (RF) signal through energy beamforming, where both the time-switching receiver (TSR) and power-splitting receiver (PSR) are considered, then uses the harvested energy to forward the source message to the destination. Our research focuses on developing a comprehensive analytical framework for deriving new closed-form expressions for the outage probability and ergodic capacity for amplify-and-forward (AF) relaying systems, including simpler tight bounds and asymptotic high signal-to-noise (SNR) ratio analysis. First, the optimization problem for the design of source, relay, and destination precoding and/or decoding weight vectors which maximizes the overall signal-to-interference-plus-noise ratio (SINR) is formulated. Then, in order to get closed-form precoding and decoding weight vectors, a sub-optimal solution based on null space projection designed to completely suppress the LI and/or CCI is proposed, through which a closed-form overall SINR is presented. Simulation results show the exactness and tightness of the proposed exact and bound analytical expressions, respectively.

The demand for mobile wireless network resources is constantly on the rise, pushing for new communication technologies that are able to support unprecedented rates. In this thesis we address the issue by considering advanced interference management techniques to exploit the available resources more efficiently under relaxed channel state information (CSI) assumptions. While the initial studies focus on current half-duplex (HD) technology, we then move on to full-duplex (FD) communication due to its inherent potential to improve spectral efficiency. Work in this thesis is divided into four main parts as follows. In the first part, we focus on the two-cell two-user-per-cell interference broadcast channel (IBC) and consider the use of topological interference management (TIM) to manage inter-cell interference in an alternating connectivity scenario. Within this context we derive novel outer bounds on the achievable degrees of freedom (DoF) for different system configurations, namely, single-input single-output (SISO), multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) systems. Additionally, we propose new transmission schemes based on joint coding across states that exploit global topological information at the transmitter to increase achievable DoF. Results show that when a single state has a probability of occurrence equal to one, the derived bounds are tight with up to a twofold increase in achievable DoF for the best case scenario. Additionally, when all alternating connectivity states are equiprobable: the SISO system gains 11/16 DoF, achieving 96:4% of the derived outer bound; while the MISO/MIMO scenario has a gain of 1/2 DoF, achieving the outer bound itself. In the second part, we consider a general G-cell K-user-per-cell MIMO IBC and analyse the performance of linear interference alignment (IA) under imperfect CSI. Having imperfect channel knowledge impacts the effectiveness of the IA beamformers, and leads to a significant amount of residual leakage interference. Understanding the extent of this impact is a fundamental step towards obtaining a performance characterisation that is more relevant to practical scenarios. The CSI error model used is highly versatile, allowing the error to be treated either as a function of the signal-to-noise ratio (SNR) or as independent of it. Based on this error model, we derive a novel upper bound on the asymptotic mean sum rate loss and quantify the DoF loss due to imperfect CSI. Furthermore, we propose a new version of the maximum signal-to-interference plus noise ratio (Max-SINR) algorithm which takes into account statistical knowledge of the CSI error in order to improve performance over the naive counterpart in the presence of CSI mismatch. In the third part, we shift our attention to FD systems and consider weighted sum rate (WSR) maximisation for multi-user multi-cell networks where FD base-stations (BSs) communicate with HD downlink (DL) and uplink (UL) users. Since WSR problems are non-convex we transform them into weighted minimum mean squared error (WMMSE) ones that are proven to converge. Our analysis is first carried out for perfect CSI and then expanded to cater for imperfect CSI under two types of error models, namely, a norm-bounded error model and a stochastic error model. Additionally, we propose an algorithm that maximises the total DL rate subject to each UL user achieving a desired target rate. Results show that the use of FD BSs provides significant gains in achievable rate over the use of HD BSs, with a gain of 1:92 for the best case scenario under perfect CSI. They also demonstrate the robust performance of the imperfect CSI designs, and confirm that FD outperforms HD even under CSI mismatch conditions. Finally, the fourth part considers the use of linear IA to manage interference in a multi-user multi-cell network with FD BSs and HD users under imperfect CSI. The number of interference links present in such a system is considerably greater than that present in the HD network counterpart; thus, understanding the impact of residual leakage interference on performance is even more important for FD enabled networks. Using the same generalised CSI error model from the second part, we study the performance of IA by characterising the sum rate and DoF losses incurred due to imperfect CSI. Additionally, we propose two novel IA algorithms applicable to this network; the first one is based on minimising the mean squared error (MMSE), while the second is based on Max-SINR. The proposed algorithms exploit statistical knowledge of the CSI error variance in order to improve performance. Moreover, they are shown to be equivalent under certain conditions, even though the MMSE based one has lower computational complexity. Furthermore for the multi-cell case, we also derive the proper condition for IA feasibility.

This diploma thesis deals with wireless doorbell realisation. The doorbell is battery-powered and supports half duplex voice transferring. The general aim is to design system circuitry, PCB and to create microcontroller firmware.

There is growing interest in developing reliable, high performance, underwater acoustic networks (UWANs). However, the acoustic communication channel, with its slow sound propagation, high signal attenuation, and low bandwidth, presents significant challenges to network designers. One advantage offered by the acoustic channel is the ability to form directional communication beams, which improve signal strength and reduce interference. The work presented here describes a novel medium access control protocol for UWANs designated Beam-Enabled Acoustic Link Establishment (BEALE). BEALE addresses the inherent challenges of the acoustic channel by incorporating two techniques: link-level scheduling and dynamic directional beam steering. BEALE neighbors exchange packets based on a link-level schedule negotiated between the two nodes. This scheduling allows nodes to steer transmit and receive beams in the appropriate direction at the appropriate time while minimizing control overhead. Using steered, directional beams increases the gain between sender and receiver, reduces the senders interference with other nodes, and, at the receiver, rejects possible interference from other nodes and noise sources common in the ocean, resulting in increased spatial reuse. The core protocol has been modeled in a UWAN simulator developed specifically for this research. The results demonstrate significant improvement in throughput and packet loss over two benchmark UWAN random access protocols when evaluated over a variety of spatial node topologies and traffic patterns. The core BEALE protocol is further enhanced herein by a Half-Duplex Sliding Window algorithm. The HDX Sliding window is shown through point-to-point simulation to markedly improve bandwidth utilization and error rate in large Bandwidth Delay Product (BDP) situations. Extension of the HDX Sliding Window to more complex multi-flow, two-way and multi-hop cases requires an additional level of communication coordination provided by the BEALE Sliding Window Scheduler presented here. The functional challenges and novel concept of the scheduler are described in detail. The BEALE protocol performance promotes a rich list of potential future research, such as rigorous characterization of the BEALE Sliding Window Scheduler, BEALE accommodation of mobile nodes, conceptual operability of a BEALE-enabled network of a central multi-beam sink node supporting large numbers of simple source nodes, and rate adaptation. / text

In-band full-duplex (FD) communications have been optimistically promoted to improve the spectrum utilization and efficiency. However, the penetration of FD communications to the cellular networks domain is challenging due to the imposed uplink/downlink interference. This thesis presents a tractable framework, based on stochastic geometry, to study FD communications in multi-tier cellular networks. Particularly, we assess the FD communications effect on the network performance and quantify the associated gains. The study proves the vulnerability of the uplink to the downlink interference and shows that the improved FD rate gains harvested in the downlink (up to 97%) comes at the expense of a significant degradation in the uplink rate (up to 94%). Therefore, we propose a novel fine-grained duplexing scheme, denoted as α-duplex scheme, which allows a partial overlap between the uplink and the downlink frequency bands. We derive the required conditions to harvest rate gains from the α-duplex scheme and show its superiority to both the FD and half-duplex (HD) schemes. In particular, we show that the α-duplex scheme provides a simultaneous improvement of 28% for the downlink rate and 56% for the uplink rate. We also show that the amount of the overlap can be optimized based on the network design objective. Moreover, backward compatibility is an essential ingredient for the success of new technologies. In the context of in-band FD communication, FD base stations (BSs) should support HD users' equipment (UEs) without sacrificing the foreseen FD gains. The results show that FD-UEs are not necessarily required to harvest rate gains from FD-BSs. In particular, the results show that adding FD-UEs to FD-BSs offers a maximum of 5% rate gain over FD-BSs and HD-UEs case, which is a marginal gain compared to the burden required to implement FD transceivers at the UEs' side. To this end, we shed light on practical scenarios where HD-UEs operation with FD-BSs outperforms the operation when both the BSs and UEs are FD and we find a closed form expression for the critical value of the self-interference cancellation power required for the FD UEs to outperform HD UEs.

Throughout the evolution of communication networks, users have consistently been demanding additional data and coverage. Future 6G networks seek to enable a seamless cyber-physical world through interconnected and integrated connectivity. Hereafter, to address these challenges and ensure the adaptability of future wireless networks, new technologies emerge. Relaying presents an attractive alternative, as it can be a cost-efficient deployment of highly dense networks, and it can enhance the performance of mobile networks in terms of both coverage and capacity. In addition, to meet the demanding Key Performance Indicators (KPI) of user experience, the relaying can be achieved via a User Equipment (UE) through UE-to-Network relaying as an alternative to conventional small-cell deployment of relay stations. The purpose of this project is to assess the impact of UE-based relaying policies. A comparative analysis is conducted, examining these schemes and a macro-only deployment. The study begins by conducting an analysis of the Third Generation Partnership Project (3GPP) urban macro scenario and then extends to include the real-world deployment scenario in London. Results have validated that UE relaying techniques help improve cell edge capacity and coverage compared to macro-only deployments. User throughput is enhanced up to three times in Downlink (DL) and twelve times in Uplink (UL) in the 3GPP urban macro deployment. While user throughput is improved up to ten times in DL and thirteen times in UL on the London map deployment. / Under utvecklingen av kommunikationsnätverk har användarna konsekvent efterfrågat ytterligare data och täckning. Framtida 6G-nätverk strävar efter att möjliggöra en sömlös cyber-fysisk värld genom sammanlänkad och integrerad anslutning. För att möta dessa utmaningar och säkerställa anpassningsbarheten hos framtida trådlösa nätverk framträder nya teknologier. Reläering utgör ett attraktivt alternativ eftersom det kan vara en kostnadseffektiv implementering av högt täta nätverk och signifikant förbättra prestandan hos mobila nätverk både vad gäller täckning och kapacitet. Dessutom kan reläeringen användas för att möta de utmanande behoven av användarupplevelse genom att användarutrustning (UE) används för reläeringen, vilket utgör ett alternativ till konventionell implementering av småceller för relästationer. Det primära fokuset för detta projekt är att bedöma påverkan av reläeringspolicyn baserad på UE. En jämförande analys genomförs där dessa metoder och enbart makroimplementering undersöks. Inledningsvis utförs studien i en urbant makroscen från Third Generation Partnership Project (3GPP), vilket utgör en grund för att utöka metodologin till en verklig implementeringsscen i London. Resultaten har visat att UE-reläeringstekniker bidrar till att förbättra kapaciteten och täckningen i cellens utkanter jämfört med enbart makroimplementering. Användarnas genomströmning ökar upp till tre gånger i nerlänken (DL) och tolv gånger i upplänken (UL) i 3GPP: s urbana makroimplementering. Samtidigt förbättras användarnas genomströmning upp till tio gånger (DL) och tretton gånger (UL) i Londonkartaimplementationen.

Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP) networks and layered networks. KPP networks can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable. Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes. Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT.

Cooperative wireless communication has received significant attention during recent years due to several reasons. First, since the received power decreases rapidly with distance, the idea of multi-hopping is becoming of particular importance. In multi-hopped communication, the source exploits some intermediate nodes as relays. Then the source sends its message via those relays to the destination. Second, relays can emulate some kind of distributed transmit antennas to form spatial diversity and combat multi-path fading effect of the wireless channel. Parallel Relay Channel is an information theoretical model for a communication system whereby a sender aims to communicate to a receiver with the help of relay nodes. It represents the simplest model for a multi–hop wireless network and a full understanding of the limits of communication over such a channel can potentially shed light on the design of more efficient wireless networks. However, the capacity of the relay channel has been established only for few special cases and little progress has been made toward solving the general case since the early 1980s. In this dissertation, motivated by practical constraints, we study the information theoretical limits of the half-duplex Gaussian Parallel Relay channel , as well as, the transmission strategies for the parallel relay channel with bandwidth mismatch between the first and the second hops. Chapter 2 investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., \emph{Simultaneous} and \emph{Successive} relaying, associated with two possible relay scheduling are proposed. The simultaneous relaying protocol is based on \emph{Broadcast-multiaccess with Common Message (BCM)} scheme. For the successive relaying protocol: (i) a \emph{Non-Cooperative} scheme based on the \emph{Dirty Paper Coding (DPC)}, and (ii) a \emph{Cooperative} scheme based on the \emph{Block Markov Encoding (BME)} are considered. The composite scheme of employing BME in \emph{at most} one relay and DPC in \emph{at least} another one is shown to achieve at least the same rate when compared to the \emph{Cooperative} and \emph{Non-Cooperative} schemes. A \emph{``Simultaneous-Successive Relaying based on Dirty paper coding scheme" (SSRD)} is also proposed. The optimum scheduling of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients, the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity, it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network. Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the Amplify-and-Forward (AF) and the Decode-and-Forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). Recently, a Rematch-and-Forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In chapter 3, we propose a \emph{Combined Amplify-and-Decode Forward (CADF)} scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

Abstract This thesis is devoted to studying two wireless relay network models, namely wireless tandem multiple-input-multiple-output (MIMO) relay networks and wireless two-hop multicast relay networks. Regarding wireless tandem MIMO relay networks, we develop a systematic approach to analyze their fundamental diversity-multiplexing tradeoff (DMT) under the assumption that the relays implement a class of practical full-duplex techniques that enable them to opt for either full-duplex or half-duplex mode. Based on the analysis, we make contribution from the following aspects: First of all, we thoroughly compare the performance of full-duplex and half-duplex mode operations in the framework of wireless tandem relay networks. We find that both full-duplex and half-duplex modes have opportunity to outperform each other. Specifically, for many tandem relay networks, in the low multiplexing gain region, the best relay-mode configuration is to let all the relays operate in half-duplex mode since this relay-mode configuration achieves the best diversity gain in the low multiplexing gain region. However, in the high multiplexing gain region, the best diversity gain is usually achieved by switching some relays to full-duplex mode. Furthermore, we study how residual interference at relays working in full-duplex mode affects the DMT of a tandem network. We find that residual interference not only derogates the performance of full-duplex mode, but also affects the optimal power allocation of the network. Specifically, if residual interference is zero or has a sufficiently low power level, a linear power allocation scheme can achieve the optimal DMT of the network. Otherwise, the optimal DMT is achieved by a nonlinear power allocation scheme. Finally, the DMT analysis illustrates an effective principle to deal with general multi-hop wireless networks, which is to break them down into small scale subnetworks with certain key structures. Then, studying the general multi-hop wireless networks essentially becomes studying those small scale subnetworks and the relationship among them. Regarding wireless two-hop multicast relay networks, we focus on a case study where a single source multicasts to two destinations through the assistance of two relays. We propose and analyze the performance of a partial decode-and-forward protocol for the network, which includes the full decode-and-forward protocol as a special case and achieves a better performance in general. Specifically, we prove that the achievable rate of the partial decode-and-forward protocol can either reach arbitrarily close to the cut-set upper bound of the network or reach within 1 bit/s/Hz to that, asymptotically with respect to the transmit power. We also show that the partial decode-and-forward protocol can achieve the optimal DMT of the network. Then, we discuss the perspective of implementing the partial decode-and-forward strategy to more general multicast relay networks. / Tiivistelmä Tämä opinnäytetyö tutkii kahta langatonta välitysverkkomallia, nimittäin langatonta tandem multiple-input-multiple-output (MIMO) välitysverkkoa ja langatonta monilähetysvälitysverkkoa kahdelle hypylle. Kehitämme systemaattisen lähestymistavan diversiteetti-multipleksointi vaihtokaupan (DMT) analysointiin langattomiin tandem MIMO välitysverkkoihin, olettaen välittäjien käyttävän käytännöllisiä full-duplex lähetystekniikoita, jotka mahdollistavat valinnan joko full-duplex tai half-duplex lähetystilan välillä. Analyysin perusteella kontribuoimme seuraavilla tavoilla: Ensinnäkin, vertailemme perusteellisesti full-duplex sekä half-duplex lähetystiloja langattomissa tandem välitysverkoissa. Huomaamme, että molemmat full-duplex ja half-duplex lähetystilat voivat suoriutua toinen toistaan paremmin. Tarkemmin sanoen, monissa tandem välitysverkoissa silloin kun multipleksoinnin hyöty on alhainen, paras välitystapa on antaa kaikkien välittäjien käyttää half-duplex lähetystilaa, koska silloin saavutetaan paras diversiteettilisäys. Toisaalta, kun multipleksointilisäys on suuri, paras diversiteettilisäys saadaan yleensä asettamalla jotkin välittäjät full-duplex lähetystilaan. Lisäksi, tutkimme kuinka full-duplex lähetystilaa käyttävien välittäjien jäljelle jäävä interferenssi vaikuttaa tandemverkon DMT:aan. Huomaamme, että jäljelle jäävä interferenssi vähentää full-duplex mallin tehokkuutta ja lisäksi vaikuttaa optimaaliseen tehonjakamiseen verkossa. Tarkemmin sanoen, jos jäljelle jäävä interferenssin tehotaso on nolla tai tarpeeksi lähellä sitä, lineaarisella tehojaolla voi saavuttaa verkon optimaalisen DMT:n. Muutoin, optimaalinen DMT saavutetaan epälineaarisella tehojaolla. Lopuksi, DMT analyysi havainnollistaa tehokkaan periaatteen yleisluontoisten monihyppyverkkojen käsittelemiseen, eli verkon jakamisen pienempiin osiin erilaiin avainrakenteisiin. Tämän jälkeen yleisluntoisten langattoimen monihyppyverkkojen tutkiminen tapahtuu tutkimalla näitä pieniä osia ja niiden välisiä vuorovaikutussuhteita. Langattomaan kahden hypyn monilähetysvälitysverkkon osalta keskitymme tapaustutkimukseen, jossa yksi lähettäjä monilähettää kahdelle vastaanottajalle kahden välittäjän avulla. Ehdotamme tälle verkolle osittaista decode-and-forward protokollaa, joka sisältää täyden decode-and-forward protokollan erikoistapauksena ja saavuttaa yleisesti tätä protokollaa paremman tehokkuuden. Tarkemmin sanoen, todistamme että tällä protokollalla siirtonopeus lähetystehon suhteen joko lähenee asymptoottisesti verkon cut-set ylärajaa mielivaltaisen lähelle tai saavuttaa sen 1 bit/s/Hz sisään. Osoitamme myös, että osittainen decode-and-forward protokolla voi saavuttaa verkon optimaalisen DMT:n. Tämän jälkeen, käsittelemme osittaisen decode-and-forward strategian impelentointia yleisluontoisille monilähetysvälitysverkoille.