This paper introduces a dual-function radar-communication (DFRC) system with cognitive radio capability to tackle the spectral scarcity problem in wireless communications. Particularly, a cognitive DFRC system operates on a spectrum owned by a primary system to simultaneously perform data communication and target tracking while maintaining its interference to the primary users (PUs) below a certain threshold. To achieve this, an optimization problem is formulated to jointly design the beamforming vectors for both the radar and communication functions in minimizing the mean square error (MSE) of the beam patterns between the designed and desired waveforms under three constraints: i) the signal-to-interference-plus-noise ratio (SINR) at each data communication user; ii) the perantenna transmit power; and iii) the interference imposed on each PU. The semidefinite relaxation technique is utilized to search for the optimal solution to the optimization problem. The simulation results indicate that our proposed cognitive DFRC approach can effectively protect the PUs while simultaneously perform its communication and radar functions.

This paper proposes a generalized Firefly Algorithm (FA) to solve an optimization framework having objective function and constraints as multivariate functions of independent optimization variables. Four representative examples of how the proposed generalized FA can be adopted to solve downlink beamforming problems are shown for a classic transmit beamforming, cognitive beamforming, reconfigurable-intelligent-surfaces-aided (RIS-aided) transmit beamforming, and RIS-aided wireless power transfer (WPT). Complexity analyzes indicate that in large-antenna regimes the proposed FA approaches require less computational complexity than their corresponding interior point methods (IPMs) do, yet demand a higher complexity than the iterative and the successive convex approximation (SCA) approaches do. Simulation results reveal that the proposed FA attains the same global optimal solution as that of the IPM for an optimization problem in cognitive beamforming. On the other hand, the proposed FA approaches outperform the iterative, IPM and SCA in terms of obtaining better solution for optimization problems, respectively, for a classic transmit beamforming, RIS-aided transmit beamforming and RIS-aided WPT.

This paper studies a non-convex power minimization problem for reconfigurable-intelligent-surfaces-aided communication systems whose constraints are multivariate functions of two independent optimization variables, i.e., active and passive beamforming vectors. A widely adopted alternative optimization (AO) approach approximates the originally non-convex problem by two convex sub-optimization problems where each sub-optimization problem deals with one variable considering the other variable as a constant. The solution for the original problem is obtained by iteratively solving these sub-optimization problems. Although the AO approach converts the original NP-hard optimization problem to two convex sub-problems, the solutions attained by this method may not be the global optimal solution due to the approximation process as well as the inherent non-convexity of the original problem. To overcome the issue, this paper adopts a nature-inspired optimization approach and introduces a novel Firefly algorithm (FA) to simultaneously solve for two independent optimization variables of the originally non-convex optimization problem. Computational complexity analyses are provided for the proposed FA and the AO approaches. Simulation results reveal that the proposed FA approach prevails its AO counterpart in obtaining a better solution for the understudied optimization problem with the same order of computational complexity.

Key update and residence management have been investigated as an effective solution to cope with desynchronization attacks in mobility management entity (MME) handovers. In this paper, we first analyze the impacts of the key update interval (KUI) and MME residence interval (MRI) on handover processes and their secrecy performance in terms of the number of exposed packets (NEP), signaling overhead rate (SOR), and outage probability of vulnerability (OPV). Specifically, the bounds of the derived NEP and SOR not only capture their behaviors at the boundary of the KUI and MRI, but also show the tradeoff between the NEP and SOR. Additionally, through the analysis of the OPV, it is shown that the handover security can be enhanced by shortening the KUI and the desynchronization attacks can be avoided with high-mobility users. The above facts accordingly motivate us to propose a multi-objective optimization (MO) problem to find the optimal KUI and MRI that minimize both the NEP and SOR subject to the constraint on the OPV. To this end, two scalarization techniques are adapted to transform the proposed MO problem into single-objective optimization problems, i.e., an achievement-function method via fractional programming (FP) and a weighted-sum method. Based on the derived bounds on NEP and SOR, the FP approach can be optimally solved via a simple numerical method. For the weighted-sum method, the firefly algorithm (FA) is utilized to find the optimal solution. The results show that both techniques can solve the proposed MO problem with a significantly reduced searching complexity compared to the conventional heuristic iterative search technique.

The pilot contamination problem creates a limitation to the potential benefits of massive multiple input multiple output (MIMO) systems. To mitigate the pilot contamination, in this study, the authors propose a novel channel estimation for massive MIMO systems, using sparse Bayesian learning (SBL) based on a pattern‐coupled hierarchical Gaussian framework. In the proposed technique, the sparsity of each channel coefficient is controlled by its own hyperparameter and the hyperparameters of its immediate neighbours. The simulation results show that the channel coefficients can be estimated more efficiently in contrast to the conventional channel estimators in terms of channel estimation with pilot contamination. Furthermore, they derive the mean square error (MSE) analytical expression for the proposed technique and based on that MSE expression, a pilot design criterion is proposed to design the optimal pilot to improve the estimation accuracy of the proposed algorithm using the Lagrange multiplier optimisation method. Results show that they can reduce the MSE of the SBL estimator by employing the optimal pilot sequence.

Considering simultaneous wireless information and power transfer (SWIPT), we study a multiple-input- single-output (MISO) secrecy channel which consists of a multi-antenna trans- mitter and a cooperative jammer (CJ), multiple multi-antenna energy receivers (ERs), i.e., potential eavesdroppers, and multiple single-antenna co-located receivers (CRs). Both transmitter and CJ send the intend signal with artificial noise (AN) and jamming signal to interfere with the ERs. All receivers (CRs and ERs) adopt a power splitter to decode information and harvest power simultaneously. We exploit AN and CJ to facilitate efficient wireless energy transfer and secure transmission. Our aim is to maximize the minimum harvested energy among all ERs and CRs subject to the total power constraints at the transmitter and CJ while guaranteeing the minimum secrecy rate for each CR above its requirement. By incorporating norm-bounded channel uncertainty model, we propose a joint design of robust secure transmission. The original problem is solved by a two- step approach. In the first step, the proposed problem is reformulated as a sequence of semidefinite programs (SDPs). In the second step, the proposed problem can be handled by one-dimensional search to attain the optimal solution. Simulation results indicate that the performance of the proposed scheme outperforms that of separated AN-aided or CJ-aided scheme.

This paper investigates a wireless powered sensor network (WPSN), where multiple sensor nodes are deployed to monitor certain external environment. A multi-antenna power beacon (PB) provides the power to these sensor nodes during wireless energy transfer (WET) phase, and then the sensor nodes employ the harvested energy to transmit their own monitoring information to one fusion center (FC) during wireless information transfer (WIT) phase. We maximize the system sum throughput of the sensor network considering two different scenarios, i.e., PB and the sensor nodes belong to the same/different service operator(s). For the first scenario, we propose an approach to jointly design the energy beamforming and the energy time allocation which is a convex optimization problem. We further develop a closed- form solution for the proposed sum throughput maximization. For the second scenario, where PB and the sensor nodes belong to the different service operators, we formulate the sum throughput maximization as Stackelberg-game-based and Social welfare schemes, in which we are then able to derive their equilibriums in closed-form solutions. Finally, numerical results are provided to validate the performance of our proposed schemes.

This paper investigates the security at the physical layer in cooperative wireless networks (CWNs) where the data transmission between nodes can be realised via either direct transmission (DT) or relaying transmission (RT) schemes. Inspired by the concept of physical-layer network coding (PNC), a secure PNC-based modify-and-forward (SPMF) is developed to cope with the imperfect shared knowledge of the message modification between relay and destination in the conventional modify-and-forward (MF). In this paper, we first derive the secrecy outage probability (SOP) of the SPMF scheme, which is shown to be a general expression for deriving the SOP of any MF schemes. By comparing the SOPs of various schemes, the usage of the relay is shown to be not always necessary and even causes a poorer performance depending on target secrecy rate and quality of channel links. To this extent, we then propose an opportunistic secure transmission protocol to minimise the SOP of the CWNs. In particular, an optimisation problem is developed in which secrecy rate thresholds (SRTs) are determined to find an optimal scheme among various DT and RT schemes for achieving the lowest SOP. Furthermore, the conditions for the existence of SRTs are derived with respect to various channel conditions to determine if the relay could be relied on in practice.

This paper considers multiple-input multiple-output (MIMO) full-duplex (FD) two-way secrecy systems. Specifically, both multi-antenna FD legitimate nodes exchange their own confidential message in the presence of an eavesdropper. Taking into account the imperfect channel state information (CSI) of the eavesdropper, we formulate a robust sum secrecy rate maximization (RSSRM) problem subject to the outage probability constraint of the achievable sum secrecy rate and the transmit power constraint. Unlike other existing channel uncertainty models, e.g., norm- bounded and Gaussian-distribution, we exploit a moment-based random distributed CSI uncertainty model to recast our formulate RSSRM problem into convex optimization frameworks based on a Markov's inequality and robust conic reformulation, i.e., semidefinite programming (SDP). In addition, difference-of-concave (DC) approximation is employed to iteratively tackle the transmit covariance matrices of these legitimate nodes. Simulation results are provided to validate our proposed FD approaches.

In LTE networks, key update and residence management have been investigated as an effective solution to cope with desynchronization attacks in mobility management entity (MME) handovers. In this paper, we first analyse the impacts of the key update interval (KUI) and MME residence interval (MRI) on the handover performance in terms of the number of exposed packets (NEP) and signaling overhead rate (SOR). By deriving the bounds of the NEP and SOR over the KUI and MRI, it is shown that there exists a tradeoff between the NEP and the SOR, while our aim is to minimise both of them simultaneously. This accordingly motivates us to propose a multiobjective optimisation problem to find the optimal KUI and MRI that minimise both the NEP and SOR. By introducing a relative importance factor between the SOR and NEP along with their derived bounds, we further transform the proposed optimisation problem into a single-objective optimisation problem which can be solved via a simple numerical method. In particular, the results show that a higher accuracy of up to 1 second is achieved with the proposed approach while requiring a lower complexity compared to the conventional approach employing iterative searches.

In this paper, we propose beamforming schemes to simultaneously transmit data to multiple information receivers (IRs) while transfering power wirelessly to multiple energy-harvesting receivers (ERs). Taking into account the imperfection of the instantaneous channel state information, we introduce a probabilistic-constrained optimization problem to minimize the total transmit power while guaranteeing data transmission reliability, secure data transmission, and power transfer reliability. As the proposed optimization problem is non-convex and has an infinite number of constraints, we propose two robust reformulations of the original problem adopting safe-convex-approximation techniques. The derived robust formulations are in semidefinite programming forms, hence, they can be effectively solved by standard convex optimization packages. Simulation results confirm the superiority of the proposed approaches to a baseline scheme in guaranteeing transmission security.

This paper considers an underlay access strategy for coexisting wireless networks where the secondary system utilizes the primary spectrum to serve its users. We focus on the practical cases where there is uncertainty in the estimation of channel state information (CSI). Here the throughput performance of each system is limited by the interference imposed by the other, resulting in conflicting objectives. We first analyze the fundamental tradeoff between the tolerance interference level at the primary system and the total achievable throughput of the secondary users. We then introduce a beamforming design problem as a multiobjective optimization to minimize the interference imposed on each of the primary users while maximizing the intended signal received at every secondary user, taking into account the CSI uncertainty. We then map the proposed optimization problem to a robust counterpart under the maximum CSI estimation error. The robust counterpart is then transformed into a standard convex semi-definite programming. Simulation results confirm the effectiveness of the proposed scheme against various levels of CSI estimation error. We further show that in the proposed approach, the trade-off in the two systems modelled by Pareto frontier can be engineered by adjusting system parameters. For instance, the simulations show that at the primary system interference thresholds of -10 dBm (-5 dBm) by increasing number of antennas from 4 to 12, the secondary system throughput is increased by 3.3 bits/s/channel-use (5.3 bits/s/channel-use).

This paper investigates the security at the physical layer of cooperative relay communications. Inspired by the principle of physical-layer network coding (PNC), we propose a new secure relaying scheme, namely secure PNC-based modify-and-forward (SPMF). In the proposed scheme, the relay node linearly combines the decoded data from the source node with an encrypted key before conveying the mixed data to the destination node. As both the linear PNC operation and encrypted key at the relay are unknown to the eavesdropper, the SPMF scheme provides a double security level in the system. Particularly, taking into account the practical scenario of the imperfect knowledge shared between the relay and destination, the secrecy outage probability (SOP) of the proposed SPMF scheme is analysed and evaluated in comparison with modify-and-forward, cooperative jamming, decode-and- forward and direct transmission schemes. The proposed scheme is shown to achieve a performance improvement of up to 3 dB when compared to the conventional schemes under imperfect knowledge of shared information between the nodes.

The downlink problem of a cloud‐based central station (CCS) to multiple base stations (BSs) in a heterogeneous cloud radio access network (HCRAN) sharing the same time and frequency resources is studied. The authors adopt nonorthogonal multiple access (NOMA) and propose power allocation for the wireless downlink in the HCRAN. Taking into account practical channel modelling with power consumptions at BSs of different cell types (e.g. macrocell, micro‐cell etc.) and backhauling power, they analyse the energy efficiency (EE) of the practical HCRAN utilising NOMA. Simulation results indicate that the proposed NOMA for the HCRAN outperforms the conventional orthogonal frequency division multiple access scheme in terms of providing higher EE of up to four times. Interestingly, the results reveal a fact that the EE of the NOMA varies as a quasi‐concave function. An optimisation problem is accordingly introduced to find the optimal number of BSs that maximises the EE of the HCRAN. It is shown that, with a low power supply at the CCS, a double number of micro BSs can be served providing an improved EE of up to 1.6 times compared with the macro BSs and remote radio heads, while they achieve the same EE performance with high‐power CCS.

We introduce a downlink robust optimization approach that minimizes a combination of total transmit power by a multiple antenna base station (BS) within a cell and the resulting aggregate inter-cell interference (ICI) power on the users of the other cells. This optimization is constrained to assure that a set of signal-to-interference-plus-noise ratio (SINR) targets are met at user terminals with certain outage probabilities. The outages are due to the uncertainties that naturally emerge in the estimation of channel covariance matrices between a BS and its intra-cell local users as well as the other users of the other cells. We model these uncertainties using random matrices, analyze their statistical behavior, and formulate a tractable probabilistic approach to the design of optimal robust downlink beamforming vectors. The proposed approach reformulates the original intractable non-convex problem in a semidefinite programming (SDP) form with linear matrix inequality (LMI) constraints. The resulting SDP formulation is convex and numerically tractable under the standard rank relaxation. We compare the proposed chance-constrained approach against two different robust design schemes as well as the worst-case robustness. The simulation results confirm better power efficiency and higher resilience against channel uncertainties of the proposed approach in realistic scenarios.

In this paper, we propose a robust transmission strategy for multi-cell networks equipped with multiple-antenna base stations (BSs) under universal frequency reuse and in the presence of channel estimation error.We propose a distributed optimization scheme, where each BS individually minimizes a combination of its total transmit power and its resulting overall interference inflicted on the users of the adjacent cells, subject to maintaining a desired quality of service at its local users.We transform the proposed scheme to a robust optimization problem for the worst case of errors and derive a semidefinite programming (SDP) using rank-relaxation.We prove that the derived SDP always yields exact rank-one optimal solutions.This is in contrast to the standard rank-relaxed SDP technique that requires an additionally high computational complexity to approximate the solutions with sufficient accuracies, required for an effective beamforming.A comparison of simulation results show that the proposed transmission strategy can expand the signal-tointerference-plus-noise-ratio operational range with significantly reduced power consumption levels at BSs and perform closely to its centralized counterpart.

In this paper, we study simultaneous data transmission and power transfer for multiple information receivers (IRs) and energy-harvesting receivers (ERs) in cellular networks. We propose an optimization problem to maximize a linear combination of the useful signal power at each IR and total received power at each ER subject to the following three sets of constraints: i) data reliability by maintaining the required level of signal to interference plus noise ratio (SINR) for all IRs; ii) information security by keeping leakage SINR levels of all IRs at every ER below a predefined value, which helps prevent possible eavesdroppers, i.e., ERs, from detecting information aimed for the IRs; and iii) power consumption by guaranteeing that the transmit power at each base station is within its available budget. Using semidefinite relaxation (SDR) technique, we then transform the proposed problem into a convex form. We further prove that the transformed problem always yields rank-one optimal solution. Hence, our approach does not require any computationally expensive randomization procedure, as usually utilized in a typical SDR method, in obtaining optimal solutions. Simulation results indicate that the proposed approach prevails conventional scheme in terms of providing higher IRs' total throughput, higher received power level at each ER and more secure for the transmission of information.

Orthogonal frequency division multiple access and coordinated multipoint transmission/reception are two key techniques employed in LTE-Advanced to provide high-speed connectivity to mobile users regardless of their locations within the cells. The combination of the two techniques in a cellular network with large cells however, results in timing asynchronization. This leads to symbol timing offset (STO) and, thus, degrades users' performance. In this paper, we propose a novel user position aware (UPA) algorithm to tackle the timing offset problem by partitioning the coverage area into different zones based on users' received power requirements. Serving base stations in each zone are assigned such that their distances to a user within the zone are bounded. Hence, the time difference of signals arrived at the user is controlled and, therefore, the effect of STO is mitigated. We analyze the performance of the proposed method by deriving bounds on the STO, and signal-to-interference-plus-noise ratio (SINR) in different zones. Simulation results confirm that the proposed UPA algorithm significantly reduces the STO and improves users' SINR.

In this paper, we introduce a downlink beamforming strategy in a cognitive cell located at the boarder of two adjacent cells of a multicell network to support the local cell-edge users of both cells. The proposed strategy is formulated as an optimization problem to minimize a linear combination of total transmit power of the cognitive base station (BS) and the resulting total interference on the other users located outside of the cognitive cell, so that the signal-to-interference-plus-noise ratio (SINR) targets of the cell-edge users are maintained. In a realistic scenario where CSI may be imperfect, the beamforming design for the cognitive BS based on perfect channel state information (CSI) can easily end up violating the tolerable interference levels of the users falling outside of the cognitive cell. We reformulate the proposed strategy as a robust optimization problem with outage-probability based constraints to account for the imperfection in CSI. Using the S-Procedure, we transform the intractable probabilistic constraints to a computationally tractable set of conservative deterministic constraints. Finally, applying the rank relaxation, we rewrite the resulting problem in semidefinite programming (SDP) form that can be solved using the standard convex optimization packages. The simulation results confirm the effectiveness of the proposed robust scheme in power-efficiently expanding the range of achievable SINR targets for the cell-edge users.

In this paper, we focus on robust design of downlink beamforming vectors for multiple antenna base stations (BSs) in a multi-cell interference network. We formulate a robust optimization problem where an individual BS within a cell designs its beamforming vectors to minimize a combination of its sum-power, used for assuring a desired quality of service at its local users, and its aggregate induced interference on the users of the other cells, to balance inter-cell interference across the multiple cells. The proposed robust formulation uses spherical uncertainty sets to model imperfections in the second-order statistical channel knowledge between the BS and the users. To maintain tractability of the robust solutions, we derive an equivalent semidefinite programming (SDP) formulation that is convex under standard rank relaxation. The numerical results confirm the effectiveness of the proposed algorithm under various sizes of uncertainty set and the fact that the attained robust solutions always satisfy the rank constraint.

This paper addresses the problem of strong intercell interference on cell-edge users in conventional cellular networks by deploying cognitive cells within the vicinity of primary cell borders. The cognitive base stations serve primary cell-edge users within the cognitive cells. In return, the cognitive base stations are rewarded by the same spectrum allocated to the primary base stations to serve secondary users. We propose a strategy that is formulated as an optimization problem for the cognitive cell to minimize the total transmit power of the cognitive base station. This optimization problem is subjected to maintain a controlled level of interference at the primary outer-cell users falling outside of the cognitive cell and to assure required levels of signal-to-noise-plus-interference-ratio (SINR) at all primary cell-edge and secondary users within the cognitive cell. Simulation results confirm that the beamforming scheme in conjunction with the proposed cognitive structure lead to a significant reduction in overall power transmitted in the network.

In this paper, we propose a downlink transmission strategy based on intercell interference pricing and a distributed algorithm that enables each base station (BS) to design locally its own beamforming vectors without relying on downlink channel state information of links from other BSs to the users. This algorithm is the solution to an optimization problem that minimizes a linear combination of data transmission power and the resulting weighted intercell interference with pricing factors at each BS and maintains the required signal-to-interference-plus-noise ratios (SINR) at user terminals. We provide a convergence analysis for the proposed distributed algorithm and derive conditions for its existence. We characterize the impact of the pricing factors in expanding the operational range of SINR targets at user terminals in a power-efficient manner. Simulation results confirm that the proposed algorithm converges to a network-wide equilibrium point by balancing and stabilizing the intercell interference levels and assigning power optimal beamforming vectors to the BSs. The results also show the effectiveness of the proposed algorithm in closely following the performance limits of its centralized coordinated beamforming counterpart.

In this paper, we tackle the problem of intercell-interference in the absence of cooperation amongst base stations (BSs). The problem originates from the simultaneous transmissions of several BSs to their local users within their corresponding cells using the same frequency band. We propose a decentralized downlink beamforming scheme in cellular interference channels so that individual BSs can independently design their own beamforming vectors based on the locally attainable second order statistical channel state information at each BS. In this scheme, while each BS minimizes a combination of its total transmit power and the resulting total interference on the other vulnerable users of the adjacent cells, it assures that certain targeted signal-to-interference-plus-noise ratio (SINR) levels are achieved at its local users. Using the reciprocity of wireless network and the uplink-downlink duality, we develop a fast-converging iterative algorithm for downlink transmissions by distributed BSs. Finally, we derive a feasibility condition for the existence of a unique solution to the proposed optimization problem. This condition can be used to develop a scheduling algorithm for choosing a set of feasible users within each cell. Simulation results confirm the effectiveness of the proposed decentralized algorithm in closely following the performance curve of its centralized counterpart.

In this paper, we study a coordinated beamforming (CBF) scheme for a multi-cell scenario where precoding/beamforming vectors for all coordinating base stations (BSs) are jointly designed in a manner that each BS transmits to its local users. We minimise the total transmit power across coordinating BSs while keeping the signal-to-interference-plus-noise ratio (SINR) at each user above the required level. We formulate the optimisation problem for CBF in a standard semidefinite programming form using instantaneous channel state information. Then, taking into consideration the uncertainty in the estimation of channel covariance matrix, we formulate the CBF problem based on the second order statistical properties of channel so that the robustness of the designed system parameters is guaranteed within a tolerable channel estimation error. We show that, although this robustness comes at the expense of increased overall power, a significant reduction in signaling overhead can be attained with a minor increase in total transmit power at moderately low SINRs.

In this paper, we address the problem of severe performance degradation of cell-edge users in conventional cellular networks via multicell processing with improved spectral efficiency. Using uplink-downlink duality, we propose an iterative multicell beamforming algorithm that minimises the total transmit power within a virtual cell of 3 adjacent sectors of 3 neighbouring BSs. We derive and employ a channel model that includes the angular spread caused by random local scatterers in the vicinity of a user. Simulation results confirm that the proposed algorithm converges fast to the optimal solution.

Implementing a distributed antenna system (DAS) improves system capacity and reduces transmit power. One challenge in a DAS is intercell interference due to simultaneously supporting multiple users with the same carrier frequency. We propose a multicell beamforming (MBF) technique to remove intercell interference amongst coordinated cells within a DAS. As the MBF technique requires circulations of users' data amongst groups of cells, we introduce a user position aware (UPA) MBF algorithm to reduce backhaul burden. Our proposed UPA MBF scheme guarantees a consistent quality of service to users irrespective of their locations within a cell with minimum total transmit power across base stations of a DAS. An effective sum rate formula is also derived to evaluate the backhaul effects on these schemes.

Various facets of cognitive radio technology have been studied in recent years. However, one possibility that is only thus-far marginally investigated is the ability to perform secondary access at the same time, band and location as ongoing primary transmissions through beamforming to secondary users. Clearly one reason why this has not been at the forefront of research is that it could imply a significant interference to primary users. This paper, however, demonstrates that such an approach is not only feasible, but derives an optimisation problem to constrain interference to primary users while keeping the received signal-to- interference-plus-noise ratio at the secondary users to above a threshold to maintain an acceptable level of quality of service, even taking into account positioning errors. It analyses the described concept and shows good performance against effective beam width increases in secondary transmissions, enacted to improve coverage to account for angular positioning error.

This study derives upper bounds on the throughput of the wireless backhaul link within a cluster of inter-connected three base stations (BSs) or a cluster of a controlling BS and three fixed relay stations. The authors propose and analyse the Ring protocol for the former and the Star protocol for the latter using network coding concept. These protocols can be used individually or in an overlaid fashion in a coordinated multi-cell system or in a cellular-distributed-antenna system to exchange information in the backhaul. To avoid the weakest link acting as a bottleneck and determining the backhaul throughput, as a result, the authors derive throughput optimising time sharing factors to compensate for the resulting bit imbalances in the backhaul.