Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP)networks and layered networks.KPP networks, can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4.For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks.For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable.Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. We also give alternative and often simpler proofs of several existing results and show that codes achieving full diversity on a MIMO Rayleigh fading channel achieve full diversity on arbitrary fading channels. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT

On the Limits of Spatial Reuse and Cooperative Communication for Dense Wireless Networks

We consider a dense ad hoc wireless network comprising n nodes confined to a given two dimensional region of fixed area. For the Gupta-Kumar random traffic model and a realistic interference and path loss model (i.e., the channel power gains are bounded above, and are bounded below by a strictly positive number), we study the scaling of the aggregate end-to-end throughput with respect to the network average power constraint, P macr, and the number of nodes, n. The network power constraint P macr is related to the per node power constraint, P macr, as P macr = np. For large P, we show that the throughput saturates as Theta(log(P macr)), irrespective of the number of nodes in the network. For moderate P, which can accommodate spatial reuse to improve end-to-end throughput, we observe that the amount of spatial reuse feasible in the network is limited by the diameter of the network. In fact, we observe that the end-to-end path loss in the network and the amount of spatial reuse feasible in the network are inversely proportional. This puts a restriction on the gains achievable using the cooperative communication techniques studied in and, as these rely on direct long distance communication over the network.

An EDC-based turbulent premixed combustion model

In the present study, a new turbulent premixed combustion model is proposed by integrating the Coherent Flame Model with the modified eddy dissipation concept, and relating the fine structure mass fraction to the flame surface density. First, experimental results of turbulent flame speed available from literature are compared with the predicted results at different turbulence intensities to validate the flame surface density model. It is observed that the model is able to predict the turbulent burning speeds accurately. Then, a comprehensive validation is carried out utilizing data on a turbulent lifted methane flame issuing into a vitiated co-flow. Detailed comparison of temperature and species concentrations between experiment and simulation is performed at different heights of the flame. Overall, the model is found to predict both the spatial variation and peak values of the scalars at various heights satisfactorily.

SOLVING VOLUME INTEGRAL EQUATION USING ScaLAPACK

In this article, we investigate the performance of a volume integral equation code on BlueGene/L system. Volume integral equation (VIE) is solved for homogeneous and inhomogeneous dielectric objects for radar cross section (RCS) calculation in a highly parallel environment. Pulse basis functions and point matching technique is used to convert the volume integral equation into a set of simultaneous linear equations and is solved using parallel numerical library ScaLAPACK on IBM's distributed-memory supercomputer BlueGene/L by different number of processors to compare the speed-up and test the scalability of the code.

RCS ENHANCEMENT DUE TO BRAGG SCATTERING

With the advances of techniques for RCS reduction, it has become practical to develop aircraft which are invisible to modern day radars. In order to detect such low visible targets it is necessary to explore other phenomenon that contributes to the scattering of incident electromagnetic wave. It is well known from the developments from the clear air scattering using RASS induced acoustic wave could be used to create dielectric constant fluctuation. The scattering from these fluctuations rather than from the aircraft have been observed to enhance the RCS of clear air, under the condition when the incident EM wave is half of the acoustic wave, the condition of Bragg scattering would be met and RCS would be enhanced. For detecting low visibility targets which are at significant distance away from the main radar, inducement of EM fluctuation from acoustic source collocated with the acoustic source is infeasible. However the flow past aircraft produces acoustic disturbances around the aircraft can be exploited to detect low visibility targets. In this paper numerical simulation for RCS enhancement due to acoustic disturbances is presented. In effect, this requires the solution of scattering from 3D inhomogeneous complex shaped bodies. In this volume surface integral equation (VSIE) is used to compute the RCS from fluctuation introduced through the acoustic disturbances. Though the technique developed can be used to study the scattering from radars of any shape and acoustic disturbances of any shape. For illustrative condition, enhancement due to the Bragg scattering are shown to improve the RCS by nearly 30dB, for air synthetic sinusoidal acoustic variation profile for a spherical scattering volume

Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure

Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.

Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure

Consider a J-component series system which is put on Accelerated Life Test (ALT) involving K stress variables. First, a general formulation of ALT is provided for log-location-scale family of distributions. A general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, log-linear model, etc., as special cases. Later, the component lives are assumed to be independent Weibull random variables with a common shape parameter. A full Bayesian methodology is then developed by letting only the scale parameters of the Weibull component lives depend on the stress variables through the general stress translation function. Priors on all the parameters, namely the stress coefficients and the Weibull shape parameter, are assumed to be log-concave and independent of each other. This assumption is to facilitate Gibbs sampling from the joint posterior. The samples thus generated from the joint posterior is then used to obtain the Bayesian point and interval estimates of the system reliability at usage condition.

Subexponential Algorithm for d-Cluster Edge Deletion: Exception or Rule?

The correlation clustering problem is a fundamental problem in both theory and practice, and it involves identifying clusters of objects in a data set based on their similarity. A traditional modeling of this question as a graph theoretic problem involves associating vertices with data points and indicating similarity by adjacency. Clusters then correspond to cliques in the graph. The resulting optimization problem, Cluster Editing (and several variants) are very well-studied algorithmically. In many situations, however, translating clusters to cliques can be somewhat restrictive. A more flexible notion would be that of a structure where the vertices are mutually ``not too far apart'', without necessarily being adjacent. One such generalization is realized by structures called s-clubs, which are graphs of diameter at most s. In this work, we study the question of finding a set of at most k edges whose removal leaves us with a graph whose components are s-clubs. Recently, it has been shown that unless Exponential Time Hypothesis fail (ETH) fails Cluster Editing (whose components are 1-clubs) does not admit sub-exponential time algorithm STACS, 2013]. That is, there is no algorithm solving the problem in time 2 degrees((k))n(O(1)). However, surprisingly they show that when the number of cliques in the output graph is restricted to d, then the problem can be solved in time O(2(O(root dk)) + m + n). We show that this sub-exponential time algorithm for the fixed number of cliques is rather an exception than a rule. Our first result shows that assuming the ETH, there is no algorithm solving the s-Club Cluster Edge Deletion problem in time 2 degrees((k))n(O(1)). We show, further, that even the problem of deleting edges to obtain a graph with d s-clubs cannot be solved in time 2 degrees((k))n(O)(1) for any fixed s, d >= 2. This is a radical contrast from the situation established for cliques, where sub-exponential algorithms are known.

The X-C center dot center dot center dot pi (X = F, Cl, Br, CN) Carbon Bond

High-level ab initio calculations have been used to study the interactions between the CH3 group of CH3X (X = F, Cl, Br, CN) molecules and pi-electrons. These interactions are important because of the abundance of both the CH3 groups and pi-electrons in biological systems. Complexes between C2H4/C2H2 and CH3X molecules have been used as model systems. Various theoretical methods such as atoms in molecules theory, reduced density gradient analysis, and natural bond orbital analysis have been used to discern these interactions. These analyses show that the interaction of the p-electrons with the CH3X molecules leads to the formation of X-C...p carbon bonds. Similar complexes with other tetrel molecules, SiH3X and GeH3X, have also been considered.

On linear series and a conjecture of D. C. Butler

Let C be a smooth irreducible projective curve of genus g and L a line bundle of degree d generated by a linear subspace V of H-0 (L) of dimension n+1. We prove a conjecture of D. C. Butler on the semistability of the kernel of the evaluation map V circle times O-C -> L and obtain new results on the stability of this kernel. The natural context for this problem is the theory of coherent systems on curves and our techniques involve wall crossing formulae in this theory.

Large-Scale Multiuser SM-MIMO Versus Massive MIMO

Spatial modulation (SM) is attractive for multiantenna wireless communications. SM uses multiple transmit antenna elements but only one transmit radio frequency (RF) chain. In SM, in addition to the information bits conveyed through conventional modulation symbols (e.g., QAM), the index of the active transmit antenna also conveys information bits. In this paper, we establish that SM has significant signal-to-noise (SNR) advantage over conventional modulation in large-scale multiuser (multiple-input multiple-output) MIMO systems. Our new contribution in this paper addresses the key issue of large-dimension signal processing at the base station (BS) receiver (e.g., signal detection) in large-scale multiuser SM-MIMO systems, where each user is equipped with multiple transmit antennas (e.g., 2 or 4 antennas) but only one transmit RF chain, and the BS is equipped with tens to hundreds of (e.g., 128) receive antennas. Specifically, we propose two novel algorithms for detection of large-scale SM-MIMO signals at the BS; one is based on message passing and the other is based on local search. The proposed algorithms achieve very good performance and scale well. For the same spectral efficiency, multiuser SM-MIMO outperforms conventional multiuser MIMO (recently being referred to as massive MIMO) by several dBs. The SNR advantage of SM-MIMO over massive MIMO can be attributed to: (i) because of the spatial index bits, SM-MIMO can use a lower-order QAM alphabet compared to that in massive MIMO to achieve the same spectral efficiency, and (ii) for the same spectral efficiency and QAM size, massive MIMO will need more spatial streams per user which leads to increased spatial interference.

LDPC Code Designs Based on root I Matrices

LDPC codes can be constructed by tiling permutation matrices that belong to the square root of identity type and similar algebraic structures. We investigate into the properties of such codes. We also present code structures that are amenable for efficient encoding.

Low Complexity Power and Scheduling Policies for Wireless Networks to Provide Quality of Service

We consider optimal power allocation policies for a single server, multiuser system. The power is consumed in transmission of data only. The transmission channel may experience multipath fading. We obtain very efficient, low computational complexity algorithms which minimize power and ensure stability of the data queues. We also obtain policies when the users may have mean delay constraints. If the power required is a linear function of rate then we exploit linearity and obtain linear programs with low complexity.