Topological Interference Management Research Articles

Topological interference management via low-rank tensor completion for time-varying topology networks

In this paper, we introduce a tensor-based topological interference management framework, in which a novel low-rank tensor completion (LRTC) model is proposed to manage interferences in time-varying topology networks. We use particular channel decomposition to design the precoding tensor and interference suppression tensor for TIM with multi-antenna users. Furthermore, we formulate the low-rank tensor completion model as a tensor rank minimization problem, which is then solved by resorting to the tensor nuclear norm (TNN) and the tensor sum of nuclear norm (SNN). Extensive simulation results show that the proposed two low-rank tensor completion TIM algorithms have superior degree of freedom (DoF) and sum rate performance in general time-varying networks.

Topological Interference Management With Adversarial Topology Perturbation: An Algorithmic Perspective

In this paper, we consider the topological interference management (TIM) problem in a dynamic setting, where an adversary perturbs network topology to prevent the exploitation of sophisticated coding opportunities (e.g., interference alignment). Focusing on a special class of network topology – chordal networks – we investigate algorithmic aspects of the TIM problem under adversarial topology perturbation. In particular, given the adversarial perturbation with respect to edge insertion/deletion, we propose a dynamic graph coloring algorithm that allows for a constant number of re-coloring updates against each inserted/deleted edge to achieve the information-theoretic optimality. This is a sharp reduction of the general graph re-coloring, whose optimal number of updates scales as the size of the network, thanks to the delicate exploitation of the structural properties of chordal graph classes.

Low-rank tensor recovery for topological interference management in time-varying networks

This paper investigates the topological interference management (TIM) problem in the face of measurement error in the time-varying network topology. On the one side, we consider multi-antenna users as a general application. On the other side, we consider that the observed network topology information may be incorrect due to some unknown factors. To handle the TIM problem in this scenario, a new optimization formulation for low-rank tensor recovery (LRTR) has been proposed as well as a new algorithm. Simulation results show that the novel low-rank tensor recovery TIM algorithm has superior performance in general networks.

Topological Interference Management With Confidential Messages

The topological interference management (TIM) problem refers to the study of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -user partially connected interference networks with no channel state information at the transmitters (CSIT), except for the knowledge of network topology. In this paper, we study the TIM problem with confidential messages (TIM-CM), where message confidentiality must be satisfied in addition to reliability constraints. In particular, each transmitted message must be decodable at its intended receiver and remain confidential at the remaining <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(K-1)$ </tex-math></inline-formula> receivers. Our main contribution is to present a comprehensive set of results for the TIM-CM problem by studying the symmetric secure degrees of freedom (SDoF). To this end, we first characterize necessary and sufficient conditions for feasibility of positive symmetric SDoF for any arbitrary topology. We next present two achievable schemes for the TIM-CM problem: For the first scheme, we use the concept of secure partition and, for the second one, we use the concept of secure independent sets. We also present outer bounds on symmetric SDoF for any arbitrary network topology. Using these bounds, we characterize the optimal symmetric SDoF of all <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K=2$ </tex-math></inline-formula> -user and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K=3$ </tex-math></inline-formula> -user network topologies.

Clustering for Topological Interference Management

To reduce the overhead and complexity of channel state information acquisition in interference alignment, the topological interference management (TIM) was proposed to manage interference, which only relied on the network topology information. The previous research on topological interference management via the low-rank matrix completion approach is known to be NP-hard. This paper considers the clustering method for the topological interference management problem, namely, the low-rank matrix completion for TIM is applied within each cluster. Based on the clustering result, we solve the low-rank matrix completion problem via nuclear norm minimization and Frobenius norm minimization function. Simulation results demonstrate that the proposed clustering method combined with TIM leads to significant gain on the achievable degrees of freedom.

Topological Pilot Assignment in Large-Scale Distributed MIMO Networks

We consider the pilot assignment problem in large-scale distributed multi-input multi-output (MIMO) networks, where a large number of remote radio head (RRH) antennas are randomly distributed in a wide area, and jointly serve a relatively smaller number of users (UE) coherently. By artificially imposing structures on the UE-RRH connectivity, we model the network by a partially-connected interference network, so that the pilot assignment problem can be cast as a topological interference management problem with multiple groupcast messages. Building upon such connection, we formulate the topological pilot assignment (TPA) problem in two different ways with respect to whether or not the to-be-estimated channel connectivity pattern is known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> . When it is known, we formulate the TPA problem as a low-rank matrix completion problem that can be solved by a simple alternating projection algorithm. Otherwise, we formulate it as a sequential maximum weight induced matching problem that can be solved by either a mixed integer linear program or a simple yet efficient greedy algorithm. With respect to two different formulations of the TPA problem, we evaluate the efficiency of the proposed algorithms under the cell-free massive MIMO setting.

Information dissemination in wireless ad-hoc networks under the weighted-TIM framework

We study communication from layer to layer of a network modeling it as a bipartite graph of transmitters and receivers. We seek to minimize the time needed for all receivers to get a message held by all transmitters. We study this Layer Dissemination problem under the Weighted Topological Interference Management (W-TIM) framework, which subsumes previous models of interference.We present randomized and deterministic protocols for Layer Dissemination, based on Selective-with-Interference Families, a combinatorial object related to group testing non-adaptive algorithms and superimposed codes.Our approach combines an engineering solution with theoretical guarantees. We characterize the network with a global measure of interference based on measurements in the specific deployment area. Then, our protocols distributedly produce an ad-hoc transmissions schedule for dissemination.We complement our theoretical study with simulations of a real network-deployment area to compare our protocols with previous work for models that ignore some physical constraints. The striking improvement in performance shown by our simulations with respect to using previous simplified models of interference shows the importance of using W-TIM to develop algorithms.

Multilevel Topological Interference Management: A TIM-TIN Perspective

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background of this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, we formulate a TIM-TIN problem for multilevel topological interference management, wherein only a coarse knowledge of channel strengths and no knowledge of channel phases is available to transmitters. To address the TIM-TIN problem, we first propose an analytical baseline approach, which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network. Next, a distributed numerical algorithm called ZEST is developed. The convergence of the algorithm is demonstrated, leading to the duality of the TIM-TIN problem in terms of generalized degrees-of-freedom (GDoF). Numerical results are also provided to demonstrate the superior sum-rate performance and fast convergence of ZEST.

Topological Interference Management With Inaccurate Topology of Network

In this letter, we investigate the topological interference management (TIM) problem in the presence of measurement error of the network topology. We formulate the TIM problem as a low-rank matrix recovery problem and then solve it through an alternating algorithm to recover the true network topology. Our numerical results demonstrate that the proposed low-rank matrix recovery model can significantly improve the achievable degrees of freedom of the network.

Analysis of Maximal Topologies and Their DoFs in Topological Interference Management

Topological interference management (TIM) can obtain degrees of freedom (DoF) gains with no channel state information at the transmitters (CSIT) except topological information of network in the interference channel. It was shown that TIM achieves symmetric DoF 1/2 when internal conflict does not exist among messages [7]. However, it is difficult to assure whether a specific topology can achieve symmetric DoF 1/2 without scrutinizing internal conflict. It is also hard to derive a specific topology directly from the conventional condition for symmetric DoF 1/2. Even except for the topology achieving symmetric DoF 1/2, topology achieving specific DoF less than 1/2 is not well known. With these problems in mind, we propose a method to derive all maximal topologies directly in TIM, named as alliance construction in K-user interference channel. That is, it is proved that a topology is maximal if and only if it is derived from alliance construction. Further we translate a topology design by alliance construction in the alignment-conflict graph into topology matrix and propose conditions for maximal topology matrix (MTM). Moreover, we propose a generalized alliance construction that derives topologies achieving DoF 1/n for n ≥ 3 by generalizing sub-alliances. A topology matrix can also be used to analyze topologies with DoF 1/n .

A Framework of Topological Interference Management and Clustering for D2D Networks

In this paper, we develop a joint clustering and topological interference management (TIM) framework for a device-to-device (D2D) network. This scheme divides the whole network into multiple groups, each served on a different frequency, and the interference within each group is managed by TIM, based only on the connectivity pattern and not on the instantaneous channel state information (CSI). To this end, we model TIM as a low-rank-matrix-completion problem (LRMC) problem and solve it using a novel and low-complex scheme based on semidefinite programming (SDP). As for the clustering part, we develop a clustering algorithm that is suited for the LRMC approach to solve TIM while building on the SDP relaxation of the maximum- $k$ -cut algorithm, and extending it to account for each cluster’s capacity. This clustering problem turns out to be a capacitated maximum- $k$ -cut problem, for which we derive a relatively tight upper bound, that helps in determining the performance guarantee of many clustering algorithms. Simulation results show that the joint clustering-TIM can help, in some cases, improve the system degrees-of-freedom (DoF), especially in large D2D networks. Our proposed scheme also reduces the computation time of the LRMC-based TIM approach.

Opportunistic Topological Interference Management

The topological interference management (TIM) problem studies the degrees of freedom (DoF) of partially-connected interference networks with no channel state information (CSI) at the transmitters except the network topology (i.e., partial connectivity). In this paper, we consider a variant of the TIM problem with uncertainty in network topology, where the channel state with partial connectivity is only known to belong to one of $M$ states at the transmitters. In particular, the transmitter has access to all network topological information over $M$ states, but is unaware of which state it falls in exactly for communication. The receiver at any state is aware of the exact state it falls in besides the network topologies of all states, and wish to recover as much highly-prioritized information at current state as possible. We formulate it as the opportunistic TIM problem with network uncertainty modeled by $M$ state-varying network topologies. To adapt to network topology uncertainty and different message decoding priority, joint encoding and opportunistic decoding are enabled at the transmitters and receivers respectively. Specifically, being aware of all possible network topologies, each transmitter sends a signal jointly encoded from all messages desired over $M$ states, say $M$ distinct messages, and at a certain State $m$ , Receiver $k$ wishes to opportunistically decode the first $\pi _{k}(m) \in \{1,2,\cdots,M\}$ higher-priority messages. Under this opportunistic TIM setting, we construct a multi-state conflict graph to capture the mutual conflict of messages over $M$ states, and characterize the optimal DoF region of two classes of network topologies via polyhedral combinatorics. A remarkable fact is that, under an additional mild monotonous condition, the optimality conditions of orthogonal access and one-to-one interference alignment still apply to TIM with uncertainty in network topology.

Topological Interference Management for MIMO Interference Broadcast Channels

In this paper, we investigate the topological interference management (TIM) for MIMO interference broadcast channels (IBC) under the fixed topology, where only topology information is needed to cancel the inter-cell interference (ICI). For the single user case, where the MIMO IBC network is reduced to the MIMO interference channel (IC) networks, we propose one novel TIM scheme by exploiting the solution to the corresponding SISO IC TIM based on topology information. And also, we present one theorem to characterize the achievable degrees of freedom (DoFs). For the multiple user case, assuming that each BS not only knows topology information but also knows the channel state information at transmitters (CSIT) within its own cell, we propose two novel TIM schemes, i.e., the virtual user compression-based scheme and the virtual base station extension-based scheme. For each scheme, we design transceivers to cancel both the ICI only based on the topology information by exploiting the solution to the corresponding SISO IC TIM and the multiple user interference (MUI) within its own cell based on the CSIT. Furthermore, we present one theorem to characterize the achievable DoF, respectively. Moreover, we prove that the DoF achieved by the virtual base station extension-based scheme is higher than or equal to that achieved by the virtual user compression-based scheme. Hence, the achievable DoF of MIMO IBC TIM is lower bounded by the optimal DoF attainable for the base station extension scheme. Furthermore, the numerical results show that our schemes can achieve significant performance gain against the traditional interference avoidance scheme.

Topological Interference Management With Transmitter Cooperation for MIMO Interference Channels

In this paper, we investigate the transmitter cooperation based topological interference management (TIM) scheme for MIMO Interference Channels (IC), where there is no channel state information beyond only the topology information at transmitters and receivers to cancel the interference. Specifically, for two different scenarios, i.e., there exists a Hamiltonian cycle or a perfect matching in the alignment-feasible graph, we propose different transmitter cooperation based TIM schemes by jointly designing the precoding and decoding matrices and present one theorem to characterize the achievable degrees of freedom (DoF) of the proposed TIM schemes. Moreover, the numeric results show that the DoF of the proposed scheme can be significantly higher than that by the TIM scheme without transmitter cooperation.

Topological Interference Management Framework for Device-to-Device Communication

This letter considers the topological interference management (TIM) problem in a partially connected network where Device-to-Device (D2D) enabled devices are not aware of the surrounding devices’ channel state information but only of the network connectivity to cancel the interference occurred. We model TIM as a low-rank-matrix-completion problem and solve it using a novel scheme based on semidefinite programming while overcoming TIM matrix special structure with hard constraints. Our simulations show a matrix rank reduction ability that outperforms other existing methods, and thus corresponds to a lessening in signal interference: a key need in D2D networks.

Topological Interference Management With Decoded Message Passing

The topological interference management (TIM) problem studies partially-connected interference networks with no channel state information except for the network topology (i.e., connectivity graph) at the transmitters. In this paper, we consider a similar problem in the uplink cellular networks, while message passing is enabled at the receivers (e.g., base stations), so that the decoded messages can be routed to other receivers via backhaul links to help further improve network performance. For this TIM problem with decoded message passing (TIM-MP), we model the interference pattern by conflict digraphs, connect orthogonal access to the acyclic set coloring on conflict digraphs, and show that one-to-one interference alignment boils down to orthogonal access because of message passing. With the aid of polyhedral combinatorics, we identify the structural properties of certain classes of network topologies where orthogonal access achieves the optimal degrees-of-freedom (DoF) region in the information-theoretic sense. The relation to the conventional index coding with simultaneous decoding is also investigated by formulating a generalized index coding problem with successive decoding as a result of decoded message passing. The properties of reducibility and criticality are also studied, by which we are able to prove the linear optimality of orthogonal access in terms of symmetric DoF for the networks up to four users with all possible network topologies (218 instances). Practical issues of the tradeoff between the overhead of message passing and the achievable symmetric DoF are also discussed, in the hope of facilitating efficient backhaul utilization.

TDMA is Optimal for All-Unicast DoF Region of TIM if and only if Topology is Chordal Bipartite

The main result of this paper is that an orthogonal access scheme, such as time division multiple access achieves the all-unicast degrees of freedom (DoF) region of the topological interference management problem if and only if the network topology graph is chordal bipartite, i.e., every cycle that can contain a chord, does contain a chord. The all-unicast DoF region includes the DoF region for any arbitrary choice of a unicast message set, so e.g., the results of Maleki and Jafar on the optimality of orthogonal access for the sum-DoF of one-dimensional convex networks are recovered as a special case. The result is also established for the corresponding topological representation of the index coding problem.

Topological Interference Management for Wireless Networks

Topological interference management (TIM) is considered under the condition that only topology-related information is available at the transmitters, but no accurate channel state information is fed back to them, which is capable of significantly reducing the overhead imposed on the network. TIM schemes can be classified into two broad categories, relying either on a fixed topology or on alternating connectivity. In this paper, we review the family of TIM schemes. Specifically, for the fixed topology, we discuss the attainable degrees of freedom (DoFs) under the condition that the channel coefficient values are either constant or time varying. For constant channel coefficients, we discuss the multiple groupcast networks/multiple unicast networks, interference channel networks, and interference broadcast channel networks; while for time-varying channel coefficients, we discuss interference channel networks and interference broadcast channel networks. Furthermore, in the context of alternating connectivity, we discuss the attainable DoF for interference channel networks, as well as X networks, vector broadcast channel networks, and interference broadcast channel networks. Finally, promising research directions are identified for TIM schemes.

Topological Interference Management With User Admission Control via Riemannian Optimization

Topological interference management (TIM) provides a promising way to manage interference only based on the network connectivity information. Previous works on the TIM problem mainly focus on using the index coding approach and graph theory to establish conditions of network topologies to achieve the feasibility of topological interference management. In this paper, we propose a novel user admission control approach via sparse and low-rank optimization to maximize the number of admitted users for achieving the feasibility of topological interference management. To assist efficient algorithms design for the formulated rank-constrained (i.e., degrees-of-freedom (DoF) allocation) l0-norm maximization (i.e., user capacity maximization) problem, we propose a regularized smoothed l1- norm minimization approach to induce sparsity pattern, thereby guiding the user selection. We further develop a Riemannian trust-region algorithm to solve the resulting rank-constrained smooth optimization problem via exploiting the quotient manifold of fixed-rank matrices. Simulation results demonstrate the effectiveness and near-optimal performance of the proposed Riemannian algorithm to maximize the number of admitted users for topological interference management.

Fundamental Limits of Non-Coherent Interference Alignment via Matroid Theory

We consider the problem of non-coherent interference alignment, in which the goal is to align the signals of multiple interfering transmitters at a single receiver where the transmitters are not aware of the channel state information. We cast this problem as a problem of determining rank loss conditions for a column concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. We determine necessary and sufficient conditions for the design of each matrix, such that the random ensemble will almost surely lose rank by a certain amount. The result is proved by converting the problem to determining rank loss conditions for the union of some specific matroids, and then using tools from matroid and graph theories to derive the necessary and sufficient conditions. As an application, we discuss how this result can be applied to the problem of topological interference management, and characterize the linear symmetric degrees of freedom for a class of network topologies.