Nikolaos D. Sidiropoulos

On uniqueness in CANDECOMP/PARAFAC

One of the basic issues in the analysis of three-way arrays by CANDECOMP/PARAFAC (CP) has been the question of uniqueness of the decomposition. Kruskal (1977) has proved that uniqueness is guaranteed when the sum of thek-ranks of the three component matrices involved is at least twice the rank of the solution plus 2. Since then, little has been achieved that might further qualify Kruskals sufficient condition. Attempts to prove that it is also necessary for uniqueness (except for rank 1 or 2) have failed, but counterexamples to necessity have not been detected. The present paper gives a method for generating the class of all solutions (or at least a subset of that class), given a CP solution that satisfies certain conditions. This offers the possibility to examine uniqueness for a great variety of specific CP solutions. It will be shown that Kruskals condition is necessary and sufficient when the rank of the solution is three, but that uniqueness may hold even if the condition is not satisfied, when the rank is four or higher.

Modelling and Optimization of Stochastic Routing for Wireless Multi-Hop Networks

We introduce a novel approach to multi-hop routing in wireless networks. Instead of the usual graph description we characterize the network by the packet delivery ratio matrix whose entries represent the probability that a given node decodes the packet transmitted by any other node. The model lends itself naturally to the formulation of stochastic routing protocols in which packets are randomly routed to neighboring nodes; and routing algorithms search for a matrix of routing probabilities according to properly defined optimality criteria. The goal of the paper is to show that this novel framework offers a useful model to aid in the design of optimal routing algorithms. In particular, it is established that: (i) performance is improved with respect to graph descriptions; and (ii) optimal routes can be obtained as the solution of optimization problems, many of which turn out to be convex and can thus be solved in polynomial time using interior point methods.

Achieving Wireline Random Access Throughput in Wireless Networking Via User Cooperation

Well appreciated at the physical layer, user cooperation is introduced here as a diversity enabler for wireless random access (RA) at the medium access control sublayer. This is accomplished through a two-phase protocol in which active users start with a low power transmission attempting to reach nearby users and follow up with a high power transmission in cooperation with the users recruited in the first phase. We show that such a cooperative protocol yields a significant increase in throughput. Specifically, we prove that for networks with a large number of users, the throughput of a cooperative wireless RA network operating over Rayleigh-fading links approaches the throughput of an RA network operating over additive white Gaussian noise links-thus justifying the title of the paper. The message borne out of this result is that user cooperation offers a viable choice for migrating diversity benefits to the wireless RA regime, thus bridging the gap to wireline RA networks, without incurring a bandwidth or energy penalty

Cooperative random access with long PN spreading codes

Cooperative wireless communication systems have attracted much attention in recent years, due to the diversity advantage they can afford. Existing cooperative transmission modalities have been developed in conjunction with fixed-rate multiplexing based on TDMA, CDMA or FDMA. We advocate user cooperation as the method of choice for enabling diversity in wireless random access networks. The specific protocol developed herein exploits the fact that user cooperation can be viewed as a form of multipath, and capitalizes on the suitability of long pseudo-noise (PN) spreading codes for dealing with multipath channels. Analysis and numerical results confirm that throughput increases considerably when random access via spread-spectrum slotted Aloha protocols is aided by user collaboration.

Egonet tensor decomposition for community identification

Real-world networks are known to exhibit community structure, characterized by presence of dense node clusters with loose edge connections among them. Although identification of communities is a well-studied subject, most approaches only focus on edge-based criteria which may not incorporate important grouping information captured by higher-order structures e.g., cliques and cycles, to name a few. In order to overcome this limitation, the present paper advocates a novel three-way tensor network representation that captures spatial dependencies among node neighborhoods. Each tensor slice captures a connectivity matrix pertaining to a unique egonet, defined as the subgraph induced by a node and its single-hop neighbors. Constrained tensor factorization is pursued to reveal the hidden and possibly overlapping community structure. Numerical tests on synthetic and real world networks corroborate the efficacy of the novel approach.

Distributed Routing Algorithms for Wireless Multihop Networks

We introduce distributed algorithms to find rate-optimal routes based on local knowledge of the pairwise error probability (reliability) matrix. The distributed algorithms are built by (re)-formulating optimization problems amenable to application of dual decomposition techniques. Convergence of our algorithms to the optimal routing matrix is guaranteed under mild conditions. Many rate-optimality criteria of practical interest can be casted in our framework including maximization of: i)worst users rate; ii) weighted sum of rates; iii) product of rates; and iv) relay network rate. We test robustness of our algorithms to node mobility.

Distributed back-pressure power control for wireless multi-hop networks

A key problem in wireless networking is how to choose a link activation schedule and associated powers in concert with routing decisions to optimize throughput. Back-pressure control policies are optimal in this context, but the underlying power control problem is non-convex. Back-pressure power control (BPPC) was recently shown to be NP-hard, yet amenable to successive convex approximation strategies that deliver manifold improvements in end-to-end throughput relative to the prior art in wireless networking. A drawback is that existing implementations are centralized, whereas practical power control has to be distributed across the network. This paper fills this gap by developing a distributed version of the core step of successive convex approximation of the BPPC problem, building upon the Alternating Direction Method of Multipliers (ADMoM). The resulting protocol enjoys favorable properties relative to dual decomposition - based implementations, and allows tight approximation of the BPPC objective in all interference regimes. Judicious simulations reveal that the proposed algorithm matches the performance of its centralized counterpart, as well as pertinent trade-offs in terms of the design parameters.

Quasi-ML hop period estimation from incomplete data

Given a noisy sequence of (possibly shifted) integer multiples of a certain period, it is often of interest to estimate the period (and offset). With known integer regressors, the problem is classical linear regression. In many applications, however, the actual regressors are unknown; only categorical information (i.e., the regressors are integers) and, perhaps, loose bounds are available. Examples include hop timing estimation, pulse repetition interval (PRI) analysis, and passive rotating-beam radio scanning. With unknown regressors, this seemingly simple problem exhibits many surprising twists. Even for small sample sizes, a proposed quasi-maximum likelihood approach essentially meets the clairvoyant CRB at moderately high SNR - the latter assumes knowledge of the unknown regressors. This is quite unusual, and it holds despite the fact that our algorithm ignores noise color. We outline analogies and differences between our problem and classical linear regression and harmonic retrieval, and corroborate our findings with careful simulations.