Managing interference in a network of macrocells underlaid with femtocells presents an important, yet challenging problem. A majority of spatial (frequency time) reuse based approaches partition the users based on coloring the interference graph, which is shown to be suboptimal. Some spatial time reuse based approaches schedule the maximal independent sets (MISs) in a cyclic, (weighted) round-robin fashion, which is inefficient for delay-sensitive applications. Our proposed policies schedule the MISs in a non-cyclic fashion, which aim to optimize any given network performance criterion for delay-sensitive applications while fulfilling minimum throughput requirements of the users. Importantly, we do not take the interference graph as given as in existing works; we propose an optimal construction of the interference graph. We prove that under certain conditions, the proposed policy achieves the optimal network performance. For large networks, we propose a low-complexity algorithm for computing the proposed policy. We show that the policy computed achieves a constant competitive ratio (with respect to the optimal network performance), which is independent of the network size, under wide range of deployment scenarios. The policy can be implemented in a decentralized manner by the users. Compared to the existing policies, our proposed policies can achieve improvement of up to 130 in large-scale deployments.
Another method to mitigate interference is to deploy coordinated beam scheduling @cite_28 @cite_22 . In @cite_28 and @cite_22 , the authors schedule a subset of beams to maximize the total reward associated with the scheduled subset, where the reward per beam reflects the channel quality and traffic. The first difference from our work is that the proposed approach schedules a fixed subset of beams and leaves the other UEs inactive. Hence, some UEs have no throughput, which means the minimum throughput as well as the delay-sensitivity of the UEs is not satisfied. Second, we rigorously prove that our proposed policy achieves good performance with low (polynomial-time) complexity , while @cite_28 @cite_22 do not. Third, the schemes in @cite_28 @cite_22 are proposed for a specific network performance criterion and may not be flexible enough for other network performance criteria (such as the sum throughput). Finally, @cite_28 @cite_22 do not consider delay sensitivity of the UEs.
@cite_28 @cite_22
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The capacity of a wireless network could be considerably improved by employing directional antennas that are capable of illuminating multiple beams toward different directions. However, more beams from the same BS may lead to stronger inter-cell interference. In this paper, we consider coordinated beam scheduling schemes to mitigate the inter-cell interference. We first formulate this problem as a combinatorial optimization problem. We then reveal that the complexity of this problem hinges upon a single scalar termed as degree of constraint (DoC), which is related to the degree of conflict a beam is subject to. If the DoC is at least three, the general beam scheduling problem is NP-hard. If DoC is smaller than three, which corresponds to a relevant subclass of the beam scheduling problem arising in practice, this problem can be solved in polynomial time. We propose an optimal beam scheduling algorithm based on the auction method to this particular subclass of problem. This algorithm is of low complexity and is well suited for distributed implementations. We then extend the auction algorithm to solve the general multi-cell beam scheduling problem. The performance of the proposed algorithms is finally assessed through extensive simulation studies. In this paper, we consider CSMA policies for scheduling packet transmissions in multihop wireless networks with one-hop traffic. The main contribution of the paper is to propose a novel CSMA policy, called Unlocking CSMA (U-CSMA), that enables to obtain both high throughput and low packet delays in large wireless networks. More precisely, we show that for torus interference graph topologies with one-hop traffic, U-CSMA is throughput optimal and achieves order-optimal delay. For one-hop traffic, the delay performance is defined to be order-optimal if the delay stays bounded as the network-size increases. Simulations that we conducted suggest that (a) U-CSMA is throughput-optimal and achieves order-optimal delay for general geometric interference graphs and (b) that U-CSMA can be combined with congestion control algorithms to maximize the network-wide utility and obtain order-optimal delay. To the best of our knowledge, this is the first time that a simple distributed scheduling policy has been proposed that is both throughput utility optimal and achieves order-optimal delay. In this paper, we consider CSMA policies for scheduling of multihop wireless networks with one-hop traffic. The main contribution of this paper is to propose Unlocking CSMA (U-CSMA) policy that enables to obtain high throughput with low (average) packet delay for large wireless networks. In particular, the delay under U-CSMA policy becomes order-optimal. For one-hop traffic, delay is defined to be order-optimal if it is O(1), i.e., it stays bounded, as the network-size increases to infinity. Using mean field theory techniques, we analytically show that for torus (grid-like) interference topologies with one-hop traffic, to achieve a network load of @math , the delay under U-CSMA policy becomes @math as the network-size increases, and hence, delay becomes order optimal. We conduct simulations for general random geometric interference topologies under U-CSMA policy combined with congestion control to maximize a network-wide utility. These simulations confirm that order optimality holds, and that we can use U-CSMA policy jointly with congestion control to operate close to the optimal utility with a low packet delay in arbitrarily large random geometric topologies. To the best of our knowledge, it is for the first time that a simple distributed scheduling policy is proposed that in addition to throughput utility-optimality exhibits delay order-optimality. We consider the interference management problem in a multicell MIMO heterogeneous network. Within each cell there is a large number of distributed micro pico base stations (BSs) that can be potentially coordinated for joint transmission. To reduce coordination overhead, we consider user-centric BS clustering so that each user is served by only a small number of (potentially overlapping) BSs. Thus, given the channel state information, our objective is to jointly design the BS clustering and the linear beamformers for all BSs in the network. In this paper, we formulate this problem from a sparse optimization perspective, and propose an efficient algorithm that is based on iteratively solving a sequence of group LASSO problems. A novel feature of the proposed algorithm is that it performs BS clustering and beamformer design jointly rather than separately as is done in the existing approaches for partial coordinated transmission. Moreover, the cluster size can be controlled by adjusting a single penalty parameter in the nonsmooth regularized utility function. The convergence of the proposed algorithm (to a stationary solution) is guaranteed, and its effectiveness is demonstrated via extensive simulation. We consider the joint optimization of beamformers and linear receivers in a MIMO interference network. Each transmitter transmits a single beam corresponding to a rank-one precoder. When the number of users K is greater than the number of antennas at each terminal N, the maximum degrees of freedom is achieved via spatial interference alignment. Interference alignment is feasible for up to K = 2N−1 users, in which case there is a finite number of solutions to the alignment conditions. This number of solutions increases rapidly with N, and the solutions depend only on the cross-channel coefficients (i. e., they are independent of the direct channels). To maximize the achievable sum rate at high SNRs we therefore wish to select an aligned solution which is best matched to the direct channels. We evaluate the performance of this scheme for large K and N, assuming that the solution is the best out of a random subset of aligned solutions. We then compare numerically this performance with the performance of previously proposed numerical (e. g., forward-backward) techniques for optimizing beams, and a new technique which tracks the local optimum as the SNR is incrementally increased, similar to a homotopy method for improving convergence properties. We observe that the incremental technique typically achieves better performance than the previously proposed methods. In the interference scheduling problem, one is given a set of n communication requests described by source-destination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color class can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We introduce an instance-based measure of interference, denoted by I, that enables us to improve on previous results for the interference scheduling problem. We prove the upper and lower bounds in terms of I on the number of steps needed for scheduling a set of requests. For general power assignments, we prove a lower bound of @W(I ([email protected])) steps, where @D denotes the aspect ratio of the metric. When restricting to the two-dimensional Euclidean space (as in the previous work) the bound improves to @W(I [email protected]). Alternatively, when restricting to linear power assignments, the lower bound improves even to @W(I). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only O(Ilogn) steps. A more sophisticated algorithm computes a schedule using even only O(I+log^2n) steps. For dense instances in the two-dimensional Euclidean space, this gives a constant factor approximation for scheduling under linear power assignments, which shows that the price for using linear (and, hence, energy-efficient) power assignments is bounded by a factor of O([email protected]). In addition, we extend these results for single-hop scheduling to multi-hop scheduling and combined scheduling and routing problems, where our analysis generalizes the previous results towards general metrics and improves on the previous approximation factors. This paper characterizes the performance in terms of queueing stability of a network composed of multiple MIMO transmitter-receiver pairs taking into account the dynamic traffic pattern and the probing feedback cost. We adopt a centralized scheduling scheme that selects a number of active pairs in each time-slot. We consider that the transmitters apply interference alignment (IA) technique if two or more pairs are active, whereas in the special case where one pair is active point-to-point MIMO singular value decomposition (SVD) is used. We consider a time-division duplex (TDD) system where transmitters acquire their channel state information (CSI) by decoding the pilot sequences sent by the receivers. Since global CSI knowledge is required for IA, the transmitters have also to exchange their estimated CSIs over a backhaul of limited capacity (i.e. imperfect case). Under this setting, we characterize in this paper the stability region of the system under both the imperfect and perfect (i.e. unlimited backhaul) cases, then we examine the gap between these two resulting regions. Further, under each case we provide a centralized probing policy that achieves the max stability region. These stability regions and scheduling policies are given for the symmetric system, where all the path loss coefficients are equal to each other, as well as for the general system. For the symmetric system, we provide the conditions under which IA yields a queueing stability gain compared to SVD. Under the general system, the adopted scheduling policy is of a high computational complexity for moderate numbers of pairs, consequently we propose an approximate policy that has a reduced complexity but that achieves only a fraction of the system stability region. A characterization of this fraction is provided. Interference is a major performance bottleneck in Heterogeneous Network (HetNet) due to its multi-tier structure. We propose almost blank resource block (ABRB) for interference control in HetNet. When an ABRB is scheduled in a macro BS, a resource block (RB) with blank payload is transmitted and this eliminates the interference from this macro BS to the pico BSs. We study a two timescale hierarchical radio resource management (RRM) scheme for HetNet with dynamic ABRB control. The long term controls, such as dynamic ABRB, are adaptive to the large scale fading at a RRM server for co-Tier and cross-Tier interference control. The short term control (user scheduling) is adaptive to the local channel state information at each BS to exploit the multi-user diversity. The two timescale optimization problem is challenging due to the exponentially large solution space. We exploit the sparsity in the interference graph of the HetNet topology and derive structural properties for the optimal ABRB control. Based on that, we propose a two timescale alternative optimization solution for user scheduling and ABRB control. The solution has low complexity and is asymptotically optimal at high SNR. Simulations show that the proposed solution has significant gain over various baselines. We investigate spatial interference statistics for multigigabit outdoor mesh networks operating in the unlicensed 60-GHz "millimeter (mm) wave" band. The links in such networks are highly directional: Because of the small carrier wavelength (an order of magnitude smaller than those for existing cellular and wireless local area networks), narrow beams are essential for overcoming higher path loss and can be implemented using compact electronically steerable antenna arrays. Directionality drastically reduces interference, but it also leads to "deafness," making implicit coordination using carrier sense infeasible. In this paper, we make a quantitative case for rethinking medium access control (MAC) design in such settings. Unlike existing MAC protocols for omnidirectional networks, where the focus is on interference management, we contend that MAC design for 60-GHz mesh networks can essentially ignore interference and must focus instead on the challenge of scheduling half-duplex transmissions with deaf neighbors. Our main contribution is an analytical framework for estimating the collision probability in such networks as a function of the antenna patterns and the density of simultaneously transmitting nodes. The numerical results from our interference analysis show that highly directional links can indeed be modeled as pseudowired, in that the collision probability is small even with a significant density of transmitters. Furthermore, simulation of a rudimentary directional slotted Aloha protocol shows that packet losses due to failed coordination are an order of magnitude higher than those due to collisions, confirming our analytical results and highlighting the need for more sophisticated coordination mechanisms. The objective of this paper is to study the performance of a multicell vector perturbation (MVP) precoding technique under practical situations in a network multiple-input multiple-output (MIMO) scheme employing joint transmission. The conventional perturbation strategy that minimizes the total power is considered, and the power at each base station (BS) is properly scaled to enforce per-BS power constraints. In our scenario, we consider multiple-antenna users and use block diagonalization (BD) as the linear front-end precoder for VP. The sum rate for the MVP in the case of uniformly distributed input and an asymptotic upper bound on the sum rate at high signal-to-noise ratios (SNRs) are derived. In addition, using the asymptotic upper bound on the individual user rates, we propose a proportionally fair (PF) user scheduling algorithm of lower complexity and better performance compared with the benchmark fair semiorthogonal user selection (SUS) algorithm. As opposed to the PF-SUS, the proposed PF scheduling algorithm requires no predefined correlation threshold. Furthermore, we study the impact of backhaul delay on the performance of both VP and BD by deriving bounds on the sum rate. The numerical results show that MVP in the case of perfect channel state information (CSI) outperforms multicell BD. In the presence of a backhaul delay, the performance of MVP significantly degrades, but the upper bound on the sum rate for MVP is still higher than for multicell BD. In this paper, we revisit the problem of determining the minimum-length schedule that satisfies certain traffic demands in a wireless network. Traditional approaches for the determination of minimum-length schedules are based on a collision channel model, in which neighboring transmissions cause destructive interference if and only if they are within the "interference region" of the receiving nodes. By contrast, we adopt here a more realistic model for the physical layer by requiring that a threshold be exceeded by the signal-to-interference-plus-noise ratio (SINR) for a transmission to be successful. We present a novel formulation of the problem that incorporates various power and rate adaptation schemes while seamlessly integrating the generation of "matchings" (i.e., sets of links that can be activated simultaneously) by taking into consideration the SINR constraints at the receivers. For the formulated problem, we propose a column-generation-based solution method and show that it theoretically converges to a globally optimal solution, with a potential advantage of not having to enumerate all the feasible matchings a priori. We also discuss the influence of power control, spatial reuse, and variable transmission rates on network performance. Furthermore, we include aspects of the routing problem and provide computational results for our proposed column-generation-based solution procedure. Consider the multiple-input multiple-output (MIMO) interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to each other. The basic problem is to design linear beamformers that can maximize the system throughput. In this paper, we propose a linear transceiver design algorithm for weighted sum-rate maximization that is based on iterative minimization of weighted mean-square error (MSE). The proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum-rate maximization problem. Furthermore, the algorithm and its convergence can be extended to a general class of sum-utility maximization problem. The effectiveness of the proposed algorithm is validated by numerical experiments. In a cognitive radio scenario, we consider a single secondary user (SU) accessing a multichannel system. The SU senses the channels sequentially to detect if a primary user (PU) is occupying the channels and stops its search to access a channel if it offers a significantly high throughput. The optimal stopping rule and power control problem is considered. The problem is formulated as an SU's throughput-maximization problem under power, interference, and packet delay constraints. We first show the effect of the optimal stopping rule on packet delay and then solve this optimization problem for both the overlay system, where the SU transmits only at the spectrum holes, and the underlay system, where tolerable interference (or tolerable collision probability) is allowed. We provide closed-form expressions for the optimal stopping rule and show that the optimal power control strategy for this multichannel problem is a modified waterfilling approach. We extend the work to a multi-SU scenario and show that when the number of SUs is large, the complexity of the solution becomes smaller than that of the single-SU case. We discuss the application of this problem in typical networks where packets simultaneously arrive and have the same departure deadline. We further propose an online adaptation policy to the optimal stopping rule that meets the packets' hard-deadline constraint and, at the same time, gives higher throughput than the offline policy. We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of K -hop interference models. We define a K-hop interference model as one for which no two links within K hops can successfully transmit at the same time (Note that IEEE 802.11 DCF corresponds to a 2-hop interference model.) .For a given K, a throughput-optimal scheduler needs to solve a maximum weighted matching problem subject to the K-hop interference constraints. For K=1, the resulting problem is the classical Maximum Weighted Matching problem, that can be solved in polynomial time. However, we show that for K>1,the resulting problems are NP-Hard and cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, we show that for specific kinds of graphs, that can be used to model the underlying connectivity graph of a wide range of wireless networks, the resulting problems admit polynomial time approximation schemes. We also show that a simple greedy matching algorithm provides a constant factor approximation to the scheduling problem for all K in this case. We then show that under a setting with single-hop traffic and no rate control, the maximal scheduling policy considered in recent related works can achieve a constant fraction of the capacity region for networks whose connectivity graph can be represented using one of the above classes of graphs. These results are encouraging as they suggest that one can develop distributed algorithms to achieve near optimal throughput in case of a wide range of wireless networks. We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users. We consider the problem of designing an online scheduling scheme for a multi-hop wireless packet network with arbitrary topology and operating under arbitrary scheduling constraints. The objective is to design a scheme that achieves high throughput and low delay simultaneously. We propose a scheduling scheme that - for networks operating under primary interference constraints - guarantees a per-flow end-to-end packet delay bound of 5dj (1-ρj), at a factor 5 loss of throughput, where dj is the path length (number of hops) of flow j and ρj is the effective loading along the route of flow j. Clearly, dj is a universal lower bound on end-to-end packet delay for flow j. Thus, our result is essentially optimal. To the best of our knowledge, our result is the first one to show that it is possible to achieve a per-flow end-to-end delay bound of O(# of hops) in a constrained network. Designing such a scheme comprises two related subproblems: Global Scheduling and Local Scheduling. Global Scheduling involves determining the set of links that will be simultaneously active, without violating the scheduling constraints. While local scheduling involves determining the packets that will be transferred across active edges. We design a local scheduling scheme by adapting the Preemptive Last-In-First-Out (PL) scheme, applied for quasi-reversible continuous time networks, to an unconstrained discrete-time network. A global scheduling scheme will be obtained by using stable marriage algorithms to emulate the unconstrained network with the constrained wireless network. Our scheme can be easily extended to a network operating under general scheduling constraints, such as secondary interference constraints, with the same delay bound and a loss of throughput that depends on scheduling constraints through an intriguing "sub-graph covering" property. Consider a MIMO interference channel whereby each transmitter and receiver are equipped with multiple antennas. The basic problem is to design optimal linear transceivers (or beamformers) that can maximize system throughput. The recent work [13] suggests that optimal beamformers should maximize the total degrees of freedom and achieve interference alignment in high SNR. In this paper we first consider the interference alignment problem in spatial domain and prove that the problem of maximizing the total degrees of freedom for a given MIMO interference channel is NP-hard. Furthermore, we show that even checking the achievability of a given tuple of degrees of freedom for all receivers is NP-hard when each receiver is equipped with at least three antennas. Moreover, in case where each transmitter and receiver use at most two antennas, the same problem is polynomial time solvable. Finally, we propose a distributed algorithm for transmit covariance matrix design, while assuming each receiver uses a linear MMSE beamformer. The simulation results show that the proposed algorithm outperforms the existing interference alignment algorithms in terms of system throughput. We investigate the downlink throughput of cellular systems where groups of M antennas - either co-located or spatially distributed - transmit to a subset of a total population of K > M users in a coherent, coordinated fashion in order to mitigate intercell interference. We consider two types of coordination: the capacity-achieving technique based on dirty paper coding (DPC), and a simpler technique based on zero-forcing (ZF) beamforming with per-antenna power constraints. During a given frame, a scheduler chooses the subset of the K users in order to maximize the weighted sum rate, where the weights are based on the proportional-fair scheduling algorithm. We consider the weighted average sum throughput among K users per cell in a multi-cell network where coordination is limited to a neighborhood of M antennas. Consequently, the performance of both systems is limited by interference from antennas that are outside of the M coordinated antennas. Compared to a 12-sector baseline which uses the same number of antennas per cell site, the throughput of ZF and DPC achieve respective gains of 1.5 and 1.75. Consider media streaming in MIMO interference networks whereby multiple base stations (BS) simultaneously deliver media to their associated users using fixed data rates. The performance is fundamentally limited by the cross-link interference. We propose a cache-induced opportunistic cooperative MIMO (CoMP) for interference mitigation. By caching a portion of the media files, the BSs opportunistically employ CoMP to transform the cross-link interference into spatial multiplexing gain. We study a mixed-timescale optimization of MIMO precoding and cache control to minimize the transmit power under the rate constraint. The cache control is to create more CoMP opportunities and is adaptive to the long-term popularity of the media files. The precoding is to guarantee the rate requirement and is adaptive to the channel state information and cache state at the BSs. The joint stochastic optimization problem is decomposed into a short-term precoding and a long-term cache control problem. We propose a precoding algorithm which converges to a stationary point of the short-term problem. Based on this, we exploit the hidden convexity of the long-term problem and propose a low complexity and robust solution using stochastic subgradient. The solution has significant gains over various baselines and does not require explicit knowledge of the media popularity. Developing scheduling mechanisms that can simultaneously achieve throughput optimality and good delay performance often require solving the Maximum Independent Weighted Set (MWIS) problem. However, under most realistic network settings, the MWIS problem can be shown to be NP-hard. In non-fading environments, low-complexity scheduling algorithms have been provided that converge either to the MWIS solution in time or to a solution that achieves at least a provable fraction of the achievable throughput. However, in more practical systems the channel conditions can vary at faster time-scales than convergence occurs in these lower-complexity algorithms. Hence, these algorithms cannot take advantage of the opportunistic gain, and may no longer guarantee good performance. In this paper, we propose a low-complexity scheduling scheme that performs provably well under fading channels and is amenable to implement in a distributed manner. To the best of our knowledge, this is the first scheduling scheme under fading environments that requires only local information, has a low complexity that grows logarithmically with the network size, and achieves provable performance guarantees (which is arbitrarily close to that of the well-known centralized Greedy Maximal Scheduler). Through simulations we verify that both the throughput and the delay under our proposed distributed scheduling scheme are close to that of the optimal solution to MWIS. Further, we implement a preliminary version of our algorithm in a testbed by modifying the existing IEEE 802.11 DCF. The preliminary experiment results show that our implementation successfully accounts for wireless fading, and attains the opportunistic gains in practice, and hence substantially outperforms IEEE 802.11 DCF.