Static spectrum allocation leads to resource wastage and inter-operator spectrum sharing is a possible way to improve spectrum efficiency. In this work, we assume that two cellular network operators agree upon sharing part of their spectrum, which can then be dynamically accessed by either of them in a mutually exclusive way. Our goal is to numerically assess the gain, in terms of cell capacity, due to such orthogonal spectrum sharing. Hence, we propose a centralized algorithm that performs coordinated scheduling, in order to numerically evaluate an upper bound on the achievable sum capacity. The algorithm is centralized and exploits complete information on both networks to perform the optimum allocation. The simulation results illustrate the impact of the multiuser diversity and the asymmetry in the traffic load among the networks on the overall achievable gain.
In this paper, we focus on next-generation cellular networks and discuss physical resources sharing among the operators. This implies cooperative usage of the available radio frequencies and also infrastructure sharing. In particular, we analyze the spectrum sharing gain achievable at different time scales and the main factors impacting on it. Then, we move towards a wider idea of resource sharing and consider a joint spectrum and infrastructure sharing (full sharing). We describe a two-layer resource management architecture that enables operators to reduce costs while still guaranteeing a good service level. The main findings of our investigations are to quantify the effectiveness of resource sharing and open up new perspectives for the operators of next-generation networks.
In this paper pilot aided channel estimation (PACE) for OFDM is addressed. For PACE equidistantly spaced pilot symbols allow to reconstruct the channel response by means of interpolation. The optimum minimum mean squared error (MMSE) estimator performs smoothing and interpolation jointly. To reduce the complexity of the optimum MMSE estimator, we propose to separate the smoothing and interpolation tasks. The separated smoothing and interpolation estimator (SINE) consistsof a MMSE based smoother which only operates at the received pilot symbols, and an interpolator which is independent of the channel statistics. We show that the separated approach gets close to the optimum MMSE, while the complexity is grossly reduced. However, at high SNR an error floor is observed, which is caused by edge effects, i.e. subcarriers near the beginning and end of the band suffer from an increased interpolation error.
The computational complexity of optimum decoding for an orthogonal space-time block code is quantified. Four equivalent techniques of optimum decoding which have the same computational complexity are specified. Modifications to the basic formulation in special cases are calculated and illustrated by means of examples.
The computational complexity of optimum decoding for an orthogonal space-time block code {cal G}_N satisfying {cal G}_N^H{cal G}_N=c(∑_{k=1}^Kos_ko^2)I_N where c is a positive integer is quantified. Four equivalent techniques of optimum decoding which have the same computational complexity are specified. Modifications to the basic formulation in special cases are calculated and illustrated by means of examples. This paper corrects and extends and unifies them with the results from the literature. In addition, a number of results from the literature are extended to the case c>1.
The downlink of multicell orthogonal frequency-division multiple-access (OFDMA) networks is studied, and the adaptive allocation of spectrum, power and rate is addressed. The authors consider networks with adaptive frequency reuse and discrete-level rates. Initially, the joint allocation problem is formulated as a centralised non-linear mixed-integer program (MIP), which is computationally intractable to solve optimally for practical problem sizes. Then, the capability of the receivers is exploited to estimate the subcarrier channel gains and the joint allocation problem is accordingly decomposed into subproblems, each of which is solved by a different base station with linear complexity. In the proposed iterative algorithm, the base stations perform rate and receiver allocation per subcarrier, with concurrent iterations. A filtering method is introduced to further decrease the algorithm complexity. Furthermore, for benchmarking purposes, the authors transform the original non-linear MIP to a linear MIP and find the optimal solution by means of standard branch-and-cut solvers. The merit of the proposed algorithm is demonstrated with numerical comparisons of its performance against the solutions of the linear MIP and the iterative waterfilling algorithm.
We consider the joint allocation of receiver, bit, and power to subcarriers in the downlink of multicell orthogonal frequency-division multiple-access (OFDMA) networks. Assuming that the cells share the entire bandwidth and that the rates are discrete, we formulate the joint allocation problem as a nonlinear mixed integer program (MIP), which however has exponential worst-case complexity. We capitalize on the capability of the receivers to measure the interference-plus-noise on every subcarrier and decompose the joint problem into a set of smaller-scale linear MIPs solved by individual base stations. Accordingly, we propose a distributed algorithm with linear complexity, in which the base stations participate in the problem solution in a round-robin manner. Simulation results demonstrate the effectiveness of the proposed algorithm in comparison with the iterative waterfilling algorithm and the successive optimal solution, by means of standard branch-and-cut solvers, of the individual MIPs.
Physical resource sharing between wireless operators and service providers is necessary in order to support efficient, competitive, and innovative wireless communication markets. By sharing resources, such as spectrum or infrastructure, which are usually exclusively allocated interference is created on the physical layer. Therefore, the economic gains, regulatory overhead, and engineering efforts need to be addressed by a consolidated cross-layer approach. This paper describes briefly the approach taken by the EU FP7 project SAPHYRE.
The paper describes the potential gain by spectrum sharing between cellular operators in terms of network efficiency. The focus of the study is on a specific resource sharing scenario: spectrum sharing between two operators in cellular downlink transmission. If frequency bands are allocated dynamically and exclusively to one operator – a case called orthogonal spectrum sharing – significant gains in terms of achievable throughput (spectrum sharing gains between 50% and 100%) and user satisfaction are reported for asymmetric scenarios at link and system level as well as from two hardware demonstrators. Additionally, if frequency bands are allocated simultaneously to two operators – a case called non-orthogonal spectrum sharing – further gains are reported. In order to achieve these, different enablers from hardware technologies and base station capabilities are required. However, we argue that all requirements are fulfilled in 3GPP and newer mobile standards. Therefore, the results and conclusions of this overview paper encourage to seriously consider the inter-operator spectrum sharing technologies.
We study the nonorthogonal spectrum sharing scenario, in which coexisting transmitters of different operators concurrently utilize the same frequency band. The transmitters (and possibly the receivers) are equipped with multiple antennas. In EU FP7 project SAPHYRE, we propose various transmit beamforming techniques to manage the interference in the physical layer. We show that operating points that are more efficient than orthogonal spectrum sharing can be reached, when the operators cooperatively design their beamforming vectors to minimize the interference.
We consider the problem of finding Pareto-optimal (PO) operating points for the multiple-input single-output (MISO) interference channel when the transmitters have statistical (covariance) channel knowledge. We devise a computationally efficient algorithm, based on semidefinite relaxation, to compute the PO rates and the enabling beamforming vectors. We illustrate the effectiveness of our algorithm by a numerical example.
We consider the two-user multiple-input single-output (MISO) interference channel and the rate region which is achieved when the receivers treat the interference as additive Gaussian noise and the transmitters have perfect channel state information (CSI). We propose a computationally efficient method for calculating the Pareto boundary of the rate region. We show that the problem of finding an arbitrary Pareto-optimal rate pair, along with its enabling beamforming vector pair, can be cast as a sequence of second-order cone programming (SOCP) feasibility problems. The SOCP problems are convex and they are solved very efficiently using standard off-the-shelf (namely, interior-point) algorithms. The number of SOCP problems that must be solved, for the computation of a Pareto-optimal point, grows only logarithmically with the desired accuracy of the solution.
We study the NP-hard problem of scheduling andpower control with quality-of-service (QoS) constraints. We consider a generic wireless network comprising K mutually interfering links and N < K orthogonal time or frequency slots. We formulate the joint resource allocation problem as a constrained optimization problem, specifically, as a mixed integer programming (MIP) problem. This enables us to solve the problem exactly, and relatively efficiently for the vast majority of instances, using off-the-shelf algorithms. We also apply our formulation to the paradigm of cognitive underlay networks.
In recent years, there is growing interest in hybrid fiber-copper access solutions, as in fiber to the basement (FTTB) and fiber to the curb/cabinet (FTTC), combined with advanced vectored transmission modalities. The twisted pair segment in these architectures is in the range of a few hundred meters, thus supporting transmission over up to 30 MHz. In this paper, we assess the capacity potential of these very short loops using full-binder channel measurements collected by France Telecom R&D. Key statistics are provided for both uncoordinated and vectored transmission, and the vectoring benefit is evaluated. The results provide useful bounds for developers and providers alike.
We assess the capacity potential of very short very-high data-rate digital subscriber line loops using full-binder channel measurements collected by France Telecom R&D. Key statistics are provided for both uncoordinated and vectored systems employing coordinated transmitters and coordinated receivers. The vectoring benefit is evaluated under the assumption of transmit precompensation for the elimination of self-far-end crosstalk, and echo cancellation of self-near-end crosstalk. The results provide useful bounds for developers and providers alike.
In recent years, there has been a growing interest in hybrid fiber-copper access solutions, as in fiber to the basement (FTTB) and fiber to the curb/cabinet (FTTC). The twisted pair segment in these architectures is in the range of a few hundred meters, thus supporting transmission over tens of MHz. This paper provides crosstalk models derived from measured data for quad cable, lengths between 75 and 590 meters, and frequencies up to 30MHz. The results indicate that the log-normal statistical model (with a simple parametric law for the frequency-dependent mean) fits well up to 30MHz for both FEXT and NEXT. This extends earlier log-normal statistical modeling and validation results for NEXT over bandwidths in the order of a few MHz. The fitted crosstalk power spectra are useful for modem design and simulation. Insertion loss, phase, and impulse response duration characteristics of the direct channels are also provided.
We consider the problem of transmit beamforming to multiple cochannel multicast groups. Since the direct minimization of transmit power while guaranteeing a prescribed minimum signal to interference plus noise ratio (SINR) at each receiver is nonconvex and NP-hard, we present convex SDP relaxations of this problem and study when such relaxations are tight. Our results show that when the steering vectors for all receivers are of Vandermonde type (such as in the case of a uniform linear array and line-of-sight propagation), a globally optimum solution to the corresponding transmit beamforming problem can be obtained via an equivalent SDP reformulation. We also present various robust formulations for the problem of single-group multicasting, when the steering vectors are only approximately known. Simulation results are presented to illustrate the effectiveness of our SDP relaxations and reformulations.
The problem of transmit beamforming to multiple cochannel multicast groups is considered for the important special case when the channel vectors are Vandermonde. This arises when a uniform linear antenna antenna (ULA) array is used at the transmitter under far-field line-of-sight propagation conditions, as provisioned in 802.16e and related wireless backhaul scenarios. Two design approaches are pursued: (i) minimizing the total transmitted power subject to providing at least a prescribed received signal-to-interference-plus-noise-ratio (SINR) to each intended receiver; and (ii) maximizing the minimum received SINR under a total transmit power budget. Whereas these problems have been recently shown to be NP-hard, in general, it is proven here that for Vandermonde channel vectors, it is possible to recast the optimization in terms of the autocorrelation sequences of the sought beam vectors, yielding an equivalent convex reformulation. This affords efficient optimal solution using modern interior point methods. The optimal beam vectors can then be recovered using spectral factorization. Robust extensions for the case of partial channel state information, where the direction of each receiver is known to lie in an interval, are also developed. Interestingly, these also admit convex reformulation. The various optimal designs are illustrated and contrasted in a suite of pertinent numerical experiments.
The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signal-to-interference-plus-noise ratio (SINR) at each receiver; and a "fair" approach maximizing the overall minimum SINR under a total power budget. The core problem is a multicast generalization of the multiuser downlink beamforming problem; the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of the emerging WiMAX and UMTS-LTE wireless networks. The joint problem also contains single-group multicast beamforming as a special case. The latter (and therefore also the former) is NP-hard. This motivates the pursuit of computationally efficient quasi-optimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient high-quality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Extensive numerical results using both simulated and measured wireless channels are presented to corroborate our main findings.
The problem of transmit beamforming to multiple co-channel multicast groups is considered, from the viewpoint of guaranteing a prescribed minimum signal-to-interference-plus-noise-ratio (SINR) at each receiver. The problem is a multicast generalization of the SINR-constrained multiuser downlink beamforming problem: the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of 802.16 wireless networks. Based on earlier results for a single multicast group, the joint problem is easily shown to be NP-hard, a fact that motivates the pursuit of quasi-optimal computationally efficient solutions. It is shown that Lagrangian relaxation coupled with a randomization / co-channel multicast power control loop yields a computationally efficient high-quality approximate solution. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Carefully designed and extensive simulation results are presented to support the main findings.
The joint power control and base station (BS) assignment problem is considered under Quality-of-Service (QoS) constraints. If a feasible solution exists, the problem can be efficiently solved using existing distributed algorithms. Infeasibility is often encountered in practice, however, which brings up the issue of optimal admission control. The joint problem is NP-hard, yet important for QoS provisioning and bandwidth-efficient operation of existing and emerging cellular and overlay/underlay networks. Recognizing this, there have been several attempts to develop reasonable heuristics for joint admission and power control. This contribution takes a more disciplined approach. The joint problem is first concisely formulated as a constrained optimization problem, whose objective combines the BS assignment, admission, and power control components. The formulation also allows for multicasting. A geometric programming approximation is then developed, which forms the core of a heuristic, yet well-motivated centralized algorithm that generates approximate solutions to the original NP-hard problem. Numerical results against an enumeration baseline illustrate the merits of the approach.
We consider a wireless network comprising a number of cochannel (hence mutually interfering) links. We study the power control problem of maximizing the rate that all links can simultaneously support under a novel setup, where receivers have interference cancelation (IC) capabilities. The problem of allocating the transmitting power is intertwined with determining the links on which receivers can perform IC and the order of cancelations. We provide and prove the theoretical results of the problem complexity and structural properties. For the problem solution, we propose a mixed-integer linear programming framework that enables jointly determining the optimal power and the IC patterns using off-the-shelf algorithms. This allows for the accurate assessment of the potential of IC for power control. Extensive numerical results are presented for performance evaluation, demonstrating the benefit of deploying IC in power control.
We consider a wireless network comprising a number of mutually-interfering links. We study the transmit power control problem that determines the egalitarian signal-to-interference-plus-noise ratio under a novel setup. Namely, we assume that the receivers have multiuser detection capability, which enables decoding and cancellation of the interference, when it is strong enough. Determining the interference terms that can be cancelled is a combinatorial problem, which is intertwined with the power control problem. We propose a mixed-integer linear programming framework that jointly solves these problems optimally, using off-the-shelf algorithms. We illustrate with a simulation result the merit of the novel approach against the conventional one that precludes interference cancellation.
A distributed beamforming algorithm is proposed for the two-user multiple-input single-output (MISO) interference channel (IFC). The algorithm is iterative and uses as bargaining value the interference that each transmitter generates towards the receiver of the other user. It enables cooperation among the transmitters in order to increase both users’ rates by lowering the overall interference. In every iteration, as long as both rates keep on increasing, the transmitters mutually decrease the generated interference. They choose their beamforming vectors distributively, solving the constrained optimization problem of maximizing the useful signal power for a given level of generated interference. The algorithm is equally applicable when the transmitters have either instantaneous or statistical channel state information (CSI). The difference is that the core optimization problem is solved in closed-form for instantaneous CSI, whereas for statistical CSI an efficient solution is found numerically via semidefinite programming. The outcome of the proposed algorithm is approximately Pareto-optimal. Extensive numerical illustrations are provided, comparing the proposed solution to the Nash equilibrium, zero-forcing, Nash bargaining, and maximum sum-rate operating points.
We consider the slow-fading two-user multiple-input single-output (MISO) interference channel. We want to understand which rate points can be achieved, allowing a non-zero outage probability. We do so by defining four different outage rate regions. The definitions differ on whether the rates are declared in outage jointly or individually and whether the transmitters have instantaneous or statistical channel state information (CSI). The focus is on the instantaneous CSI case with individual outage, where we propose a stochastic mapping from the rate point and the channel realization to the beamforming vectors. A major contribution is that we prove that the stochastic component of this mapping is independent of the actual channel realization.
In this paper, we study an achievable rate region of the two-user multiple-input single-output (MISO) interference channel. We find the transmit beamforming vectors that achieve Pareto-optimal points. We do so, by deriving a sufficient condition for Pareto optimality. Given the beamforming vector of one transmitter, this condition enables us to determine the beamforming vector of the other transmitter that forms a Pareto-optimal pair. The latter can be done in closed form by solving a cubic equation. The result is validated against state-of-the-art methods via numerical illustrations.
In this paper, we study an achievable rate region of the two-user multiple-input single-output (MISO) interference channel. We find the transmit beamforming vectors that achieve Pareto-optimal points. We do so, by deriving a sufficient condition for Pareto optimality. Given the beamforming vector of one transmitter, this condition enables us to determine the beamforming vector of the other transmitter that forms a Pareto-optimal pair. The latter can be done in closed form by solving a cubic equation. The result is validated against state-of-the-art methods via numerical illustrations
We study the two-user multiple-input single-output (MISO) Gaussian interference channel where the transmitters have perfect channel state information and employ single-stream beamforming. The receivers are capable of performing successive interference cancellation, so when the interfering signal is strong enough, it can be decoded, treating the desired signal as noise, and subtracted from the received signal, before the desired signal is decoded. We propose efficient methods to compute the Pareto-optimal rate points and corresponding beamforming vector pairs, by maximizing the rate of one link given the rate of the other link. We do so by splitting the original problem into four subproblems corresponding to the combinations of the receivers' decoding strategies-either decode the interference or treat it as additive noise. We utilize recently proposed parameterizations of the optimal beamforming vectors to equivalently reformulate each subproblem as a quasi-concave problem, which we solve very efficiently either analytically or via scalar numerical optimization. The computational complexity of the proposed methods is several orders-of-magnitude less than the complexity of the state-of-the-art methods. We use the proposed methods to illustrate the effect of the strength and spatial correlation of the channels on the shape of the rate region.
We study the two-user multiple-input single-output (MISO) interference channel for the scenario where the transmitters have perfect channel state information and employ single-stream beamforming. We assume that the receivers are able of decoding the data from both transmitters. Hence, the signal from the interfering transmitter might be decoded, treating the desired signal as noise, and subtracted from the received signal. We propose an efficient method for finding the Pareto boundary of the corresponding achievable rate region. This method has a complexity which is constant in the number of transmit antennas.
We consider the two-user multiple-input single output (MISO) interference channel (IFC) and assume that the receivers treat the interference as additive Gaussian noise. We study the rates that can be achieved in a slow-fading scenario, allowing an outage probability. We introduce three definitions for the outage region of the IFC. The definitions differ on whether the rates are declared in outage jointly or individually and whether there is perfect or statistical information about the channels. Even for the broadcast and the multiple-access channels, which are special cases of the IFC, there exist several definitions of the outage rate regions. We provide interpretations of the definitions and compare the corresponding regions via numerical simulations. Also, we discuss methods for finding the regions. This includes a characterization of the beamforming strategies, which are optimal in the sense that achieve rate pairs on the Pareto boundary of the outage rate region.
We study the achievable ergodic rate region of the two-user multiple-input single-output interference channel, under the assumptions that the receivers treat interference as additive Gaussian noise and the transmitters only have statistical channel knowledge. Initially, we provide a closed-form expression for the ergodic rates and derive the Nash-equilibrium and zero-forcing transmit beamforming strategies. Then, we show that combinations of the aforementioned selfish and altruistic, respectively, strategies achieve Pareto-optimal rate pairs.
We consider the downlink of an inter-operator spectrum sharing scenario where two operators share the same piece of spectrum and use it simultaneously. A base station of one operator cooperates with a base station of the other operator in order perform joint user selection and beamforming using a central unit. Optimal scheduling, in the sense of maximizing sum-rate or proportional fairness, is in many cases impractical due to high computational complexity. Therefore, we propose a heuristic algorithm that schedules users based on simple beamforming techniques. Once the users are scheduled, we compute the optimal beamforming vectors for them. This method still performs an exhaustive user search. Therefore, we also propose a greedy user selection scheme. From numerical evaluations, we notice that these schemes perform close to the optimal selection. Also, we use our proposed methods to identify when spectrum sharing provides extra gains over the non-sharing scenario.
We assess the system-level performance of non-orthogonal spectrum sharing achieved via maximum sum-rate (SR), Nash bargaining (NB), and zero-forcing (ZF) transmit beamforming techniques. A look-up table based physical layer abstraction and radio resource management mechanisms (including packet scheduling) are proposed and incorporated in system-level simulations, jointly with other important aspects of network operation. In the simulated scenarios, the results show similar system-level performance of SR (or NB) as ZF in the context of spectrum sharing, when combined with maximum sum-rate (or proportional fair) packet scheduler. Further sensitivity analysis also shows similar behavior of all three beamforming techniques with regard to the impact on system-level performance of neighbor-cell activity level and feedback error. A more important observation from our results is that, under ideal conditions, the performance enhancement of non-orthogonal spectrum sharing over orthogonal spectrum sharing and fixed spectrum assignment is significant.
In this paper, four transmit beamforming (BF) techniques are selected and compared to realize inter-operator spectrum sharing, which is a promising solution for the spectrum shortage problem. The BF techniques include two game-theoretic (GT) algorithms, zero-forcing (ZF) and minimum mean square error (MMSE). After a brief description of the BF techniques in a multiple-input single-output (MISO) system, their computational complexity is analyzed. The effectiveness of these techniques in real radio frequency (RF) signal transmission is verified by implementation on a flexible hardware-in-the-loop (HIL) testbed. First, several important aspects regarding practical implementation are discussed. Afterwards, the HIL measurement results are shown, where considerable sum rate gain can be observed due to spectrum sharing. Finally, the appropriate BF technique can be chosen based on a tradeoff between complexity and performance.
We consider the downlink of a multicell network where neighboring multi-antenna base stations share the spectrum and coordinate their frequency and spatial resource allocation strategies to improve the overall network performance. The objective of the coordination is to maximize the number of users that can be scheduled, meeting their quality-of-service requirements with the minimum total transmit power. The coordinated scheduling and multiuser transmit beamforming problem is combinatorial; we formulate it as a mixed-integer second-order cone program and propose a branch and bound algorithm that yields the optimal solution with relatively low-complexity. The algorithm can be used to motivate or benchmark approximation methods and to numerically evaluate the gains due to spectrum sharing and coordination.
A fundamental aspect in performance engineering of wireless networks is optimizing the set of links that can be concurrently activated to meet given signal-to-interference-and-noise ratio (SINR) thresholds. The solution of this combinatorial problem is the key element in scheduling and cross-layer resource management. In this paper, we assume multiuser decoding receivers, which can cancel strongly interfering signals. As a result, in contrast to classical spatial reuse, links being close to each other are more likely to be active concurrently. Our focus is to gauge the gain of successive interference cancellation (SIC), as well as the simpler, yet instructive, case of parallel interference cancellation (PIC), in the context of optimal link activation. We show that both problems are NP-hard and develop compact integer linear programming formulations that enable to approach global optimality. We provide an extensive numerical performance evaluation, indicating that for low to medium SINR thresholds the improvement is quite substantial, especially with SIC, whereas for high SINR thresholds the improvement diminishes and both schemes perform equally well.