A new approach to information-theoretic converses is proposed based on Shannon’s original sphere-packing argument. Typical sequence arguments are hardened with decoding sets to include structured codewords. Each decoding set is shown to have a minimum volume of 2nH(Y|X)typical y-sequences in the point-to-point discrete-memoryless channel if the probability of decoding error vanishes. Since a codebook of type p(x) generates at most 2nH(Y)typical y-sequences, the error probability is non-vanishing when R > maxp(x)I(X;Y). Kolmogorov’s zero-one law is applied to prove the error probability also goes to one, unifying the weak and strong converses. In preparation for the capacity of the relay channel, i.i.d codebooks are shown via the zero-one law and a sphere-absorption argument, to exhibit a clustering property where their orbits in the y-space asymptotically coincide or separate into clusters of indistinguishable codewords. The capacity of the relay channel is shown to be ${\max _{p\left({{x_s},{x_r}}\right)}}\min \left\{ {I\left({{X_s},{X_r};{Y_d}}\right),I\left({{X_s};{Y_r}{Y_d}\mid {X_r}}\right) - \delta } \right\}$ where $\delta : = \min \left\{ {{{\left| {I\left({{{\hat Y}_r};{Y_r}\mid {X_r}{Y_d}}\right) - {C_0}} \right|}^ + },I\left({{X_s};{Y_d}\mid {X_r}{Y_r}}\right)} \right\}$, C0:= I(Xr;Yd), and ${\hat Y_r}$ emulates Xsin a virtual source-relay channel.

The decode-forward region is characterized for general multi-source, multi-relay, all-cast channels. This region depends on the sequences of nodes that forward each message, the encoding delays in each sequence, and the messages decoded at each node. The assumption of causality creates necessary conditions on the encoding delays since nodes cannot forward messages they have not decoded. Flow decompositions are introduced to describe these dependencies. Every rate vector in the decode-forward region corresponds to a set of flow decompositions. The conditions derived from causality impose some structure on otherwise arbitrary sets of flow decompositions. Given this structure, there exists an equivalent set of flow decompositions that recovers the same region in a causal manner.

We consider the discrete memoryless symmetric primitive relay channel, where, a source$X$wants to send information to a destination$Y$with the help of a relay$Z$and the relay can communicate to the destination via an error-free digital link of rate$R_{0}$, while$Y$and$Z$are conditionally independent and identically distributed given$X$. We develop two new upper bounds on the capacity of this channel that are tighter than existing bounds, including the celebrated cut-set bound. Our approach significantly deviates from the standard information-theoretic approach for proving upper bounds on the capacity of multi-user channels. We build on the blowing-up lemma to analyze the probabilistic geometric relations between the typical sets of the$n$-letter random variables associated with a reliable code for communicating over this channel. These relations translate to new entropy inequalities between the$n$-letter random variables involved. As an application of our bounds, we study an open question posed by (Cover, 1987), namely, what is the minimum rate$R_{0}^{*}$needed for the$Z$–$Y$link in order for the capacity of the relay channel to be equal to that of the broadcast cut. We consider the special case when the$X$–$Y$and$X$–$Z$links are both binary symmetric channels. Our tighter bounds on the capacity of the relay channel immediately translate to tighter lower bounds for$R_{0}^{*}$. More interestingly, we show that when$p\to 1/2$,$R_{0}^{*}\geq 0.1803$; even though the broadcast channel becomes completely noisy as$p\to 1/2$and its capacity, and therefore the capacity of the relay channel, goes to zero, a strictly positive rate$R_{0}$is required for the relay channel capacity to be equal to the broadcast bound. Existing upper bounds on the capacity of the relay channel, and the cut-set bound in particular, would rather imply$R_{0}^{*}\to 0$, while achievability schemes require$R_{0}^{*}\to 1$. We conjecture that$R_{0}^{*}\to 1$as$p\to 1/2$.

An achievable rate-region for the two-way multiple-relay channel is proposed using decode-forward block Markovian coding. We identify a fundamental tension between the information flow in both directions that leads to an intractable number of decode-forward schemes and achievable rate regions, none of which are universally better than the others. We introduce a new concept in decode-forward coding called ranking, and discover that each of these rate regions are different realizations of a single expression that depends on the rank assignment. This discovery makes it possible to characterize the complete achievable rate region that includes all of the interesting decode-forward schemes and corresponding rate regions.

This paper investigates quality of service (QoS) provisioning for Internet of Things (IoT) in long-term evolution advanced (LTE-A) heterogeneous networks (HetNets) with partial spectrum usage (PSU). In HetNets, the IoT users with ubiquitous mobility support or low-rate services requirement can connect with macrocells (MCells), while femtocells (FCells) with PSU mechanism can be deployed to serve the IoT users requiring high-data-rate transmissions within small coverage. Despite the great potentials of HetNets in supporting various IoT applications, the following challenges exist: 1) how to depict the unplanned random behaviors of the IoT-oriented FCells and cope with the randomness in user QoS provisioning and 2) how to model the interplay of resource allocation (RA) between MCells and FCells under PSU mechanism. In this work, the stochastic geometry (SG) theory is first exploited to statistically analyze how the unplanned random behaviors of the IoT-oriented FCells impact the user performance, considering the user QoS requirements and FCell PSU policy. Particularly, to satisfy the QoS requirements of different IoT user types, the concept of effective bandwidth (EB) is leveraged to provide the users with probabilistic QoS guarantee, and a heuristic algorithm named QA-EB algorithm is proposed to make the EB determination tractable. Then, the interplay of RA between the MCells and FCells is formulated into a two-level Stackelberg game, where the two parties try to maximize their own utilities through optimizing the macro-controlled interference price and the femto-controlled PSU policy. A backward induction method is proposed to achieve the Stackelberg equilibrium. Finally, extensive simulations are conducted to corroborate the derived SINR and ergodic throughput performance of different user types and demonstrate the Stackelberg equilibrium under varying user QoS requirements and spectrum aggregation capabilities.

In this paper, a new MAC protocol for LTE over unlicensed spectrum (LTE-U) is presented that allows friendly co-existence of LTE-U with other unlicensed wireless networks, including Wi-Fi. Specifically, in a time-slotted LTE-U system, LTE- U users can transmit continuously for a period after a successful channel reservation during the spectrum sensing period. Following each LTE transmission period, a certain duration is reserved for asynchronous Wi-Fi transmissions. By adaptively adjusting the periods of LTE transmissions, Wi-Fi transmissions, and spectrum sensing, different levels of Wi-Fi protection can be achieved. Based on the proposed MAC, an analytical model is developed to study the throughput performance of both LTE-U and Wi-Fi, considering the asynchronous transmission nature of Wi-Fi within the time-slotted MAC structure. Impacts of the protocol parameters, i.e., the periods of LTE/Wi-Fi transmissions and spectrum sensing, on the throughput performance of LTE-U and Wi-Fi are also investigated. Extensive simulation results are provided to validate the analysis.

Consider a symmetric primitive relay channel, where, the source X wants to send information to the destination Y with the help of a relay Z, the relay Z can communicate to the destination Y via an error-free digital link of rate R0, and Y, Z are conditionally independent and identically distributed given X. This paper presents two new upper bounds on the capacity of such relay channels, where the first one is a sharpened version of the recently proposed bound by (Xue, 2014), and the second one is novel. These two bounds are shown to be generally tighter than the cut-set bound, and as an example they are numerically evaluated for the case of binary symmetric channels.

We propose an achievable decode-forward rate region for the two-way multi-relay network. The region is the outcome of a carefully mediated attempt, through a so-called “reverse-order” ranking policy, to privilege the disadvantaged nodes in the network over the advantaged. We use the word “advantage” in reference to the ability of a node to recover the decode-forward outer-bound by virtue of its position in the network. The proposed rate-region shows promise in recovering most of a decode-forward outer-bound which, due to a fundamental deadlock problem we identify, is not tight. The rate region itself is derived from (n-2)! individual regions, each corresponding to a unique decode-forward scheme, which geometrically fit together into an intelligible whole. The underlying theory, offset encoding, appears to be well suited for multi-source multi-relay networks with bidirectional information flow.

This paper studies the cooperative transmission scheme and the achievable rate for uplink communications in an LTE-Advanced cellular network with Type II in-band decode-and-forward relay stations. The physical layer uplink transmission is based on single carrier frequency division multiple access (SC-FDMA) with frequency-domain equalization (FDE). Unlike orthogonal frequency division multiple access (OFDMA) where the users achievable rate is the summation of the rates on all allocated subcarriers, achievable rate of SC-FDMA system has a more complex expression because the subcarriers are transmitted sequentially rather than in parallel. With the joint superposition coding for cooperative relaying, we derive the expressions of the achievable rate for both zero-forcing (ZF) equalization and minimum mean square error (MMSE) equalization. Numerical results are given to verify the derived uplink achievable rates.

Carrier Aggregation is considered as a key revolution in Long Term Evolution-Advanced systems to meet the explosively increasing aspiration for high data rates. Unlike extensive simulative evaluations on CA in literature, current theoretical analysis on CA is not convincing due to lack of effective interference modeling. In this paper, we exploit the theory of stochastic geometry to provide tractable statistical interference modeling for downlink CA in LTE-A systems. Our objective is to demonstrate the benefits of CA by comparing the user performance between the legacy LTE users and LTE-A users. Specifically, we first model the distributions of base stations and users into Poisson Point Processes. Then, the user service probability and subchannel usage in each carrier are calculated for LTE and LTE-A users, respectively. The obtained probabilities are applied to derive the user SINR distribution and ergodic rates. To better clarify the impact of system/user parameters on the investigated performance, a special case is presented where the network is interference-limited and the channel fast fading is considered as Rayleigh fading. Finally, simulation results validate our analytical model and demonstrate that LTE-A users can achieve significantly better SINR and ergodic-rate performance than LTE users when the cell is not heavily loaded.

Decode-and-forward (D-F) and compress-and-forward (C-F) are two fundamentally different relay strategies proposed by Cover and El Gamal in 1979. Individually, either of them has been successfully generalized to multirelay channels. In this paper, to allow each relay node the freedom of choosing either of the two strategies, we propose a unified framework, where both the D-F and C-F strategies can be employed simultaneously in the network. It turns out that, to incorporate in full the advantages of both the best known D-F and C-F strategies into a unified framework, the major challenge arises as follows: For the D-F relay nodes to fully utilize the help of the C-F relay nodes, decoding at the D-F relay nodes should not be conducted until all the blocks have been finished; however, in the multilevel D-F strategy, the upstream nodes have to decode prior to the downstream nodes in order to help, which makes simultaneous decoding at all the D-F relay nodes after all the blocks have been finished inapplicable. To tackle this problem, nested blocks combined with backward decoding are used in our framework, so that the D-F relay nodes at different levels can perform backward decoding at different frequencies. As such, the upstream D-F relay nodes can decode before the downstream D-F relay nodes, and the use of backward decoding at each D-F relay node ensures the full exploitation of the help of both the other D-F relay nodes and the C-F relay nodes. The achievable rates under our unified relay framework are found to combine both the best known D-F and C-F achievable rates and include them as special cases. It is also demonstrated through a Gaussian network example that our achievable rates are generally better than the rates obtained with existing unified schemes and with D-F or C-F alone.

This paper considers an LTE-Advanced cooperative cellular network where a Type II relay station (RS) is deployed to enhance the cell-edge throughput and to extend the coverage area. To better exploit the existing resources, the RS and the eNodeB (eNB) transmit in the same channel (In-Band) with decode-and-forward relaying strategy. For such a network, this paper proposes joint Orthogonal Frequency Division Multiplexing (OFDM) subcarrier and power allocation schemes to optimize the downlink multi-user transmission efficiency. Firstly, an optimal power dividing method between eNB and RS is proposed to maximize the achievable rate on each subcarrier. Based on this result, we show that the optimal joint resource allocation scheme for maximizing the overall throughput is to allocate each subcarrier to the user with the best channel quality and to distribute power in a water-filling manner. Since QoS provision is one of the major design objectives in cellular networks, we further formulate a lexicographical optimization problem to maximize the minimum rate of all users while improving the overall throughput. A sufficient condition for optimality is derived. Due to the complexity of searching for the optimal solution, we propose an efficient, low-complexity suboptimal joint resource allocation algorithm, which outperforms the existing suboptimal algorithms that simplify the joint design into separate allocation. Both theoretical and numerical analyses demonstrate that our proposed scheme can drastically improve the fairness as well as the overall throughput.

In this paper, we study the resource allocation in a device-to-device (D2D) communication underlaying green cellular network, where the base station (BS) is powered by sustainable energy. Our objective is to enhance the network sustainability and efficiency by introducing power control and cooperative communication. Specifically, we propose optimal power adaptation schemes to maximize the network efficiency under two practical power constraints. We then take the dynamics of the charging and discharging processes of the energy buffer into consideration to ensure the network sustainability. To this end, the energy buffer is modeled as a G/D/1 queue where the input energy has a general distribution. Power allocation schemes are proposed based on the statistics of the energy buffer to enhance the network efficiency and sustainability. Both theoretical analysis and numerical results demonstrate that our proposed power allocation schemes can improve the network throughput drastically while maintaining the network sustainability at a certain level.

In this paper, we analyze the user accommodation capabilities of LTE-A systems with carrier aggregation for the LTE users and LTE-A users, respectively. The adopted performance metric is equivalent capacity (EC), defined as the maximum number of users allowed in the system given the user QoS requirements. Specifically, both LTE and LTE-A users are divided into heterogeneous user classes with different QoS requirements, traffic characteristics and bandwidth weights. Two bandwidth allocation strategies are studied, i.e., the fixed-weight strategy and the cognitive-weight strategy, where the bandwidth weights of different user classes are prefixed under the former and dynamically changing with the cell load conditions under the latter. For each strategy, closed-form expressions of ECs of different user classes are derived for LTE and LTE-A users, respectively. A net-profit-maximization problem is further formulated to discuss the tradeoff among the bandwidth weights. Extensive simulations are conducted to corroborate our analytical results, and demonstrate an interesting discovery that only a slightly higher spectrum utilization of LTE-A users than LTE users can result in a significant EC gain when the user traffic is bursty. Moreover, the cognitive-weight strategy is shown to outperform considerably the fixed-weight one due to stronger adaptability to the cell load conditions.

In two-way relay channels, two terminal nodes exchange information with the help of a relay node. Designing practical coding schemes for such channels is challenging, especially when messages are encoded into multiple streams and a destination node receives signals from multiple nodes. In this paper, we prove an achievable region for half-duplex three-phase two-way relay channels. Furthermore, we propose low-density parity-check (LDPC) codes for such channels where two source codewords are encoded by systematic LDPC codes at the relay node. To analyze the performance of the codes, discretized density evolution is derived for the joint decoder at terminal nodes. Based on the discretized density evolution, degree distributions are optimized by iterative linear programming in 3 steps. The length of the obtained optimized codes is 26% longer than the theoretic one.

The Long Term Evolution - Advanced (LTE-A) standard is widely accepted for the 4th generation mobile systems to satisfy the explosive growth of high-data-rate demand. Carrier Aggregation (CA) is considered as one of the most momentous techniques adopted in LTE-A standard. Many studies have been done to analyze the performance of LTE-A systems with CA in terms of average user throughput. However, the system-level capacity analysis of LTE-A systems has not been well studied. In this paper, we explore the downlink admission control process in LTE-A systems with CA to compare the capacities between LTE users and LTE-A users, based on the metric - equivalent capacity. Specifically, taking into account the user heterogeneity, the system evolution is modeled as a birth-death process for each user class based on an effective user traffic generation model. A closed-form relationship between the equivalent capacity and system bandwidth is then derived for a single-carrier LTE-A system with the help of binomial-normal approximation. The relationship is further extended to multi-carrier case for both LTE users and LTE-A users. Finally, simulation results are provided to verify our analytical ones, and demonstrate that the equivalent capacity of LTE-A users surpasses that of LTE users significantly.

In the classical compress-and-forward relay scheme developed by Cover and El Gamal, the decoding process operates in a successive way: the destination first decodes the compression of the relay's observation and then decodes the original message of the source. Recently, several modified compress-and-forward relay schemes were proposed, where the destination jointly decodes the compression and the message, instead of successively. Such a modification on the decoding process was motivated by realizing that it is generally easier to decode the compression jointly with the original message, and more importantly, the original message can be decoded even without completely decoding the compression. Thus, joint decoding provides more freedom in choosing the compression at the relay. However, the question remains in these modified compress-and-forward relay schemes-whether this freedom of selecting the compression necessarily improves the achievable rate of the original message. It has been shown by El Gamal and Kim in 2010 that the answer is negative in the single-relay case. In this paper, it is further demonstrated that in the case of multiple relays, there is no improvement on the achievable rate by joint decoding either. More interestingly, it is discovered that any compressions not supporting successive decoding will actually lead to strictly lower achievable rates for the original message. Therefore, to maximize the achievable rate for the original message, the compressions should always be chosen to support successive decoding. Furthermore, it is shown that any compressions not completely decodable even with joint decoding will not provide any contribution to the decoding of the original message. The above phenomenon is also shown to exist under the repetitive encoding framework recently proposed by Lim , which improved the achievable rate in the case of multiple relays. Here, another interesting discovery is that the improvement is not a result of repetitive encoding, but the benefit of delayed decoding after all the blocks have been finished. The same rate is shown to be achievable with the simpler classical encoding process of Cover and El Gamal with a block-by-block backward decoding process.

Recent advances in green energy technologies have boosted the deployment of green wireless communication networks. Unlike traditional energy sources, green energy, e.g., solar, wind, and hydro, etc, is sustainable and eco-friendly in nature. However, the capacity and availability of green energy highly depend on the weather and location, which may lead to violation of users' Quality of Service (QoS) requirements. In this paper, we jointly consider the power allocation and access point (AP) placement problems in green wireless cooperative communication networks. Specifically, the network scenario includes several cooperative users served by an AP. The objective aims at maximizing the overall throughput by jointly allocating transmitting power and deploying the green APs, i.e., APs powered by green energy, subject to the harvested energy constraint. To this end, a closed form power allocation scheme and an AP placement metric are proposed. Our theoretical analysis shows that the overall throughput can be dramatically improved with our proposed scheme. Moreover, extensive simulation results demonstrate that our scheme approaches the optimal solution and significantly outperforms non-cooperative transmission under a variety of network scenarios.

In this paper, we propose a spectrum allocation framework that jointly considers the Quality-of-Service (QoS) provisioning for heterogeneous secondary Real-Time (RT) and Non-Real Time (NRT) users, the spectrum sensing, spectrum access decision, channel allocation, and call admission control in distributed cooperative Cognitive Radio Networks (CRNs). Giving priority to the RT users with QoS requirements in terms of the dropping and blocking probabilities, a number of the identified available channels are allocated to the optimum number of the RT users that can be admitted into the network, while the remaining identified available channels are allocated adaptively to the optimum number of the NRT users considering the spectrum sensing and utilization indispensability. Extensive analytical and simulation results are provided to demonstrate the effectiveness of the proposed QoS-based spectrum resource allocation framework.

Energy efficient transmission and bit allocation schemes are investigated in multi-source single-sink wireless sensor networks (WSN). For transmission in AWGN channels with path loss, this work shows that the overall energy consumption can be saved if each source transmits using its minimum power and cooperates with other sources in TDMA mode. From the source coding perspective, the Slepian-Wolf coding theorem is applied for efficient bit allocation since sources are usually highly correlated in WSN. Combining these two parts, we propose a closed form bit allocation scheme to minimize the overall energy consumption by assigning more bits to the nodes with better channel conditions. Based on this scheme, we further extend the network lifetime through a heuristic algorithm to average the energy consumption among all sensors.

The output distribution of a Gaussian channel, when the rate is above capacity, is investigated. It is shown that there is an asymptotic equipartition property (AEP) of the typical output sequences, independently of the specific codebook used, as long as the codebook is typical according to the standard random codebook generation. This equipartition of the typical output sequences is caused by the mixup of input sequences when there are too many of them, namely, when the rate is above capacity. This discovery may shed some light on the optimal design of the compress-and-forward relay schemes.

The compress-and-forward relay scheme developed by (Cover and El Gamal, 1979) is modified by realizing that it is not necessary for the destination to decode the compressed observation of the relay; and even if the compressed observation is to be decoded, it can be more easily done by joint decoding with the original message, rather than in a successive way. This modification introduces flexibility in choosing the compression rate at the relay, which improves the robustness of the compress-and-forward relay scheme in the application to uncertain networks. Nevertheless, it is also shown that this flexibility is associated with a penalty on the achievable rate, and higher than necessary compression rates will incur suboptimal achievable rates.

In this paper, we propose Low-density Parity-check (LDPC) codes for two-way relay channels, where two sources communicate with each other through a relay. At the relay, a simpler interference cancellation joint decoder decodes for the multiple access phase of two-way relay channels. Then, the relay codeword is encoded from two decoded source codewords with LDPC codes. At source, a sub-optimal belief propagation decoder decodes message from codewords received from the relay, the other source and its own source. Simulation results are given to show that our proposed simpler interference cancellation joint decoder at the relay is only 0.2 dB away from the existing sub-optimal belief propagation joint decoder. The required Eb/No at the source is 1.5 dB less than that of the single user channel with the same bit error rate (BER).

To satisfy the stringent requirement of capacity enhancement in wireless networks, cooperative relaying is envisioned as one of the most effective solutions. In this paper, we study the capacity enhancement problem by way of Relay Stations (RSs) placement to achieve an efficient and scalable design in broadband wireless access networks. To fully exploit the performance benefits of cooperative relaying, we develop an optimization framework to maximize the capacity as well as to meet the minimal traffic demand by each Subscriber Station (SS). In specific, the problem of joint RS placement and bandwidth allocation is formulated into a mixed-integer nonlinear program. We reformulate it into an integer linear program which is solvable by CPLEX. To avoid exponential computation time, a heuristic algorithm is proposed to efficiently solve the formulated problem. Numerical analysis is conducted through case studies to demonstrate the performance gain of cooperative relaying and the comparison between the proposed heuristic algorithm against the optimal solutions.

To satisfy the stringent requirement of capacity enhancement in wireless networks, cooperative relaying is envisioned as one of the most effective solutions. In this paper, we focus on the problem of capacity enhancement by way of relay stations (RSs) placement, which is a critical task of network planning and deployment to achieve an efficient and scalable network design. To fully exploit the performance benefits of cooperative relaying, we develop an optimization framework to maximize the capacity as well as meet the minimal traffic demand for each subscriber station (SS). The problem of joint RS placement and bandwidth allocation is formulated into a mixed integer nonlinear program and solved through a heuristic approach based on genetic algorithm (GA). Moreover, an upper bound on the capacity is derived to assist the estimation of system performance given a network configuration. Numerical results are presented to demonstrate the effectiveness of the solution approach and the performance benefits due to RS placement and optimal bandwidth allocation through cooperative relaying.

For a wireless network withnnodes distributed in an areaA, and withnsource-destination pairs communicating with each other at some common rate, the hierarchical cooperation scheme proposed in (Ozgur, Leveque, and Tse, 2007) is analyzed and optimized by choosing the number of hierarchical stages and the corresponding cluster sizes that maximize the total throughput. It turns out that increasing the number of stages does not necessarily improve the throughput, and the closed-form solutions for the optimization problem can be explicitly obtained. Based on the expression of the maximum achievable throughput, it is found that the hierarchical scheme achieves a scaling with the exponent depending onn. In addition, to apply the hierarchical cooperation scheme to random networks, a clustering algorithm is developed, which divides the whole network into quadrilateral clusters, each with exactly the number of nodes required.

In this paper, the maximum number of simultaneous active transmitters (i.e. user capacity) is obtained in the many user case for fading multiple-access channels in which a minimum rate must be maintained for all active users. The results are presented in the form of scaling laws as the number of transmitters increases and three commonly used fading models, namely, Rayleigh, Rician and Nakagami are considered. It is shown that in all three cases, the user capacity scales double logarithmically with the number of users and differs only by constants depending on the distributions. We also show that the scheduling policy maximizing the number of simultaneous active transmitters can be implemented in a distributed fashion.

In this paper, we extend the results on the maximum number of active users maintaining minimum rate Rmin> 0 in broadcast channels, known for Rayleigh fading to the cases of Rician and Nakagami fading models. Under the assumption of independent Rician fading channels for different receivers, as the total number of receivers n goes to infinity, the maximum number of active receivers is shown to be equal to ln(2P In n)/Rminwith probability approaching one, where P is total transmit power. For broadcast channels with Nakagami fading, the maximum number of active receivers is shown to be equal to ln(omega/mu P In n)/Rminwith probability approaching one, where omega and mu are the Nakagami distribution parameters. A by-product of the results is to also provide a power allocation strategy that maximizes the total throughput subject to the rate constraints.

For a wireless network with n nodes distributed in an area A, with n source-destination pairs communicating with each other at some common rate, the hierarchical cooperation scheme proposed in [A. Ozgur et al., 2007] is studied and optimized by choosing the number of hierarchical stages and the corresponding cluster sizes that maximize the total throughput. It turns out that increasing the number of stages does not necessarily increase the throughput, and the closed-form solutions for the optimization problem can be explicitly obtained. Based on the expression of the maximum achievable throughput, it is found that the hierarchical scheme achieves a scaling with the exponent depending on n.

In this paper, a power allocation scheme is proposed to maximize the number of active terminals in fading multi-user channels in which a minimum rate must be maintained for all active users. It is assumed that receivers and transmitters have perfect channel state information. Both uplink and downlink scenarios are considered and under the assumption of independent Rayleigh fading channels for different terminals, the optimal number of active terminals is asymptotically obtained as the total number of users, n, is large enough. For broadcast channels with successive interference cancellation at receivers and multiple- access channels with joint decoding at the receiver, the maximum number of active terminals is shown to be arbitrarily close to In ( Ptotal/sigma2\ In n) /Rminwith probability approaching one, where Ptotaland Rmindenote total transmit power and the minimum rate respectively, and sigma2represents the noise variance.

Cooperative relaying is one of the most effective techniques in coverage extension and capacity enhancement by virtue of spatial diversity. To fully explore the benefits of adopting relay stations (RSs), a vital issue is the placement of RSs by jointly considering an advanced coding scheme. In this paper, we aim to provide a general framework for solving the minimum cost RS placement problem in 802.16J Mobile Multi-hop Relay (MMR) networks. We first introduce a novel dual-relay architecture, where all the users, i.e., the mobile stations (MSs) and the fixed subscriber stations (SSs), are connected to the BS via two active RSs through decoded-and-forwarding scheme. We will then demonstrate that the most significant advantages of the dual-relay architecture lie in the ability of achieving high throughput for the systems. In addition, the users can be subject to better fault tolerance, robustness, and power saving. We formulate the dual- relay RS placement problem, and solve it through a two-phase algorithm to deal with the NP-hardness. Numerical analysis is conducted to evaluate the performance gain due to cooperative RS placement in the proposed framework, and demonstrate that the proposed approach can lead to a well acceptable solution compared with that by exhaustively searching.

We propose an achievable rate region for the two- way two-relay channel using decode-and-forward block Markovian coding. A previous attempt to obtain an achievable region for this network encountered a fundamental deadlock problem in which each relay needed to decode before the other to enable mutual assistance. In this paper, the deadlock is resolved by introducing an additional constraint that ensures some relay can decode at least one source before the other relay. The resulting achievable region is an extension of existing results for the two- way single-relay channel.

For wireless networks with multiple sources, an omnidirectional relay scheme is developed, where each node can help relay multiple sources in different directions. This is accomplished by the decode-and-forward relay strategy, with each relay binning the multiple messages to be transmitted, in the same spirit of network coding. Specially for the all-source all-cast problem, where each node is an independent source to be transmitted to all the other nodes, this scheme completely eliminates interference in the whole network, and the signal transmitted by any node is used by any other node. For networks with regular topologies, assuming no beamforming is to be performed, this omnidirectional scheme is capable of achieving the maximum achievable rate.

For broadcast channels, a power allocation scheme is proposed to maximize the number of active receivers, for each of which, a minimum rate Rmin> 0 can be achieved. Under the assumption of independent Rayleigh-fading channels for different receivers, as the total number of receivers n goes to infinity, the maximum number of active receivers is shown to be arbitrarily close to ln(Pln n)/Rminwith probability approaching 1, where P is the total transmit power.

To make the WiMAX Point-to-Multi-Point (PMP) systems more competitive and applicable to the future metropolitan area networking scenarios, deploying relay stations (RSs) as defined in IEEE 802.16j has been considered a promising solution that can replace the 802.16e mesh mode for coverage extension and throughput enhancement. In this paper, we are committed to tackle the task of RS placement and relay time allocation in IEEE 802.16j Mobile Multi-hop Relay (MMR) networks, in order to meet the uneven distributed traffic demand of each subscriber station (SS) as well as the thirst for system capacity. By incorporating advanced cooperative relaying technology such as Decode-Forward (D-F) or Compress-Forward (C-F), the task of RS placement and relay time allocation is formulated into an optimization problem, aiming at finding the optimal location of a single RS and the resource allocation for all the SSs. Numerical analysis is conducted through a number of case studies to demonstrate the performance gain by using the proposed approach for relay placement and relay time allocation.

Networks with multiple source–destination pairs, involving possibly multicast, and where there are multiple nodes that can serve as potential relay nodes, are considered. A multisource, multirelay coding scheme is developed. In this scheme, each source's information is sent to its destination nodes via a multirelay route, with the multiple multirelay routes operating concurrently even when they intersect with each other, in the same spirit as code-division multiple access (CDMA). It is found that in the generalization to multiple sources, backward decoding achieves higher rates than sliding-window decoding. The routing structure where a joint backward decoding can be performed is characterized. The achievable rate region is found to combine aspects of both multiple relay and multiple access. Potential applications of this coding scheme to sensor networks are discussed. In particular, the exact capacity for the data downloading problem in sensor networks, where there are multiple sensor sources and one sink or collector node, is established for certain geometries when there is phase fading that is unknown to the transmitter.

A multi-relay scheme is developed for networks with multiple sources. By this scheme, each source is sent to its destination nodes via a multi-relay route, and the multiple multi-relay routes from the multiple sources can operate at the same time even if they intersect with each other, in the same spirit of the code-division multiple-access (CDMA). It is found that in the generalization to multiple sources, the backward decoding achieves higher rates than the sliding-window decoding. The corresponding achievable rate region is characterized. Potential applications of this scheme to sensor networks are discussed, where capacity results in certain scenarios are established

Wireless networks with a minimum inter-node separation distance are studied where the signal attenuation grows in magnitude as 1/ρ/sup δ/ with distance ρ. Two performance measures of wireless networks are analyzed. The transport capacity is the supremum of the total distance-rate products that can be supported by the network. The energy cost of information transport is the infimum of the ratio of the transmission energies used by all the nodes to the number of bit-meters of information thereby transported. If the phases of the attenuations between node pairs are uniformly and independently distributed, it is shown that the expected transport capacity is upper-bounded by a multiple of the total of the transmission powers of all the nodes, whenever δ>2 for two-dimensional networks or δ>5/4 for one-dimensional networks, even if all the nodes have full knowledge of all the phases, i.e., full channel state information. If all nodes have an individual power constraint, the expected transport capacity grows at most linearly in the number of nodes due to the linear growth of the total power. This establishes the best case order of expected transport capacity for these ranges of path-loss exponents since linear scaling is also feasible. If the phases of the attenuations are arbitrary, it is shown that the transport capacity is upper-bounded by a multiple of the total transmission power whenever δ>5/2 for two-dimensional networks or δ>3/2 for one-dimensional networks, even if all the nodes have full channel state information. This shows that there is indeed a positive energy cost which is no less than the reciprocal of the above multiplicative constant. It narrows the transition regime where the behavior is still open, since it is known that when δ<3/2 for two-dimensional networks, or δ<1 for one-dimensional networks, the transport capacity cannot generally be bounded by any multiple of the

For the multiple-level relay channel, an achievable rate formula, and a simple coding scheme to achieve it, are presented. Generally, higher rates can be achieved with this coding scheme in the multiple-level relay case than previously known. For a class of degraded channels, this achievable rate is shown to be the exact capacity. An application of the coding scheme to the allcast problem is also discussed.

We consider networks consisting of nodes with radios, and without any wired infrastructure, thus necessitating all communication to take place only over the shared wireless medium. The main focus of this paper is on the effect of fading in such wireless networks. We examine the attenuation regime where either the medium is absorptive, a situation which generally prevails, or the path loss exponent is greater than 3. We study the transport capacity, defined as the supremum over the set of feasible rate vectors of the distance weighted sum of rates. We consider two assumption sets. Under the first assumption set, which essentially requires only a mild time average type of bound on the fading process, we show that the transport capacity can grow no faster than O(n), where n denotes the number of nodes, even when the channel state information (CSI) is available noncausally at both the transmitters and the receivers. This assumption includes common models of stationary ergodic channels; constant, frequency-selective channels; flat, rapidly varying channels; and flat slowly varying channels. In the second assumption set, which essentially features an independence, time average of expectation, and nonzeroness condition on the fading process, we constructively show how to achieve transport capacity of /spl Omega/(n) even when the CSI is unknown to both the transmitters and the receivers, provided that every node has an appropriately nearby node. This assumption set includes common models of independent and identically distributed (i.i.d.) channels; constant, flat channels; and constant, frequency-selective channels. The transport capacity is achieved by nodes communicating only with neighbors, and using only point-to-point coding. The thrust of these results is that the multihop strategy, toward which much protocol development activity is currently targeted, is appropriate for fading environments. The low attenuation regime is open.

This paper proposes a new coding scheme and proved a new achievable rate formula for the Gaussian case. The scheme is simpler and avoids some inconvenient techniques (e.g., the Slepian-Wolf partitioning), in giving the same achievable rate for the single relay case. More importantly, this new coding scheme is easier to extend to the multiple level relay case, and generally achieves higher rates. Here we present the results for the discrete memoryless case. The paper also goes on to obtain the capacity of some relay channels under fading, which is the first significant capacity result for such channels, and one, which may possibly constitute a breakthrough in the field.

We study the transport capacity of wireless networks with fading, in the high attenuation regime where either the medium is absorptive or the path loss exponent is greater than 3. For a network of n nodes we show that even were the states of all channels to be noncausally known a-priori, the transport capacity is no more than O(n). On the other hand, even when the channels are frequency selective and independent from time to time, G(n) is achievable through a multihop strategy

How much information can be carried over a wireless network with a multiplicity of nodes, and how should the nodes cooperate to transfer information? To study these questions, we formulate a model of wireless networks that particularly takes into account the distances between nodes, and the resulting attenuation of radio signals, and study a performance measure that weights information by the distance over which it is transported. Consider a network with the following features. I) n nodes located on a plane, with minimum separation distance /spl rho//sub min/>0. II) A simplistic model of signal attenuation e/sup -/spl gamma//spl rho////spl rho//sup /spl delta// over a distance /spl rho/, where /spl gamma//spl ges/0 is the absorption constant (usually positive, unless over a vacuum), and /spl delta/>0 is the path loss exponent. III) All receptions subject to additive Gaussian noise of variance /spl sigma//sup 2/. The performance measure we mainly, but not exclusively, study is the transport capacity C/sub T/:=sup/spl Sigma/on/sub /spl lscr/=1//sup m/R/sub /spl lscr///spl middot//spl rho//sub /spl lscr//, where the supremum is taken over m, and vectors (R/sub 1/,R/sub 2/,...,R/sub m/) of feasible rates for m source-destination pairs, and /spl rho//sub /spl lscr// is the distance between the /spl lscr/th source and its destination. It is the supremum distance-weighted sum of rates that the wireless network can deliver. We show that there is a dichotomy between the cases of relatively high and relatively low attenuation. When /spl gamma/>0 or /spl delta/>3, the relatively high attenuation case, the transport capacity is bounded by a constant multiple of the sum of the transmit powers of the nodes in the network. However, when /spl gamma/=0 and /spl delta/<3/2, the low-attenuation case, we show that there exist networks that can provide unbounded transport capacity for fixed total power, yielding zero energy priced communication. Examples show that nodes can profitably cooperate over large distances using coherence and multiuser estimation when the attenuation is low. These results are established by developing a coding scheme and an achievable rate for Gaussian multiple-relay channels, a result that may be of interest in its own right.

We present a network information theory for wireless communications. This theory addresses the following issues: (i) How the amount of information that can be carried over a wireless network scales as the number n of nodes in the network increases. (ii) Obtains bounds on the pre-constant in the scaling law, thus obtaining bounds on network capability as a function of n, the number of nodes in the network. (iii) What, strategies for operating the wireless network give optimal performance up to order.