Date 2326 Sept. 2008
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Network coding for computing
Publication Year: 2008 , Page(s): 1  6
Cited by: Papers (5)The following network computation problem is considered. A set of source nodes in an acyclic network generates independent messages and a single receiver node computes a function f of the messages. The objective is to characterize the maximum number of times f can be computed per network usage. The network coding problem for a single receiver network is a special case of the network computation problem (taking f to be the identity map) in which all of the source messages must be reproduced at the receiver. For network coding with a single receiver, routing is known to be rateoptimal and achieves the network mincut upper bound. We give a generalized mincut upper bound for the network computation problem. We show that the bound reduces to the usual network mincut when f is the identity and the bound is tight for the computation of ldquodivisible functionsrdquo over ldquotree networksrdquo. We also show that the bound is not tight in general. View full abstract»

Landmarkbased position and movement detection of wireless sensor network devices
Publication Year: 2008 , Page(s): 7  14
Cited by: Patents (4)The demand for reliable indoor positioning of mobile devices is wide and the computing and communication hardware are evolving rapidly. Thus, it is meaningful to consider a spectrum of techniques that reflect different constraints and tradeoffs of hardware investment, computational complexity, setup cost, and positioning accuracy. The present paper strives to achieve high accuracy with low hardware investment and moderate setup cost, but with somewhat sophisticated computations. We not only describe a successful positioning system, but also suggest a set of formal techniques that proved to work well in the real setting, and can be implemented using standard wireless sensor network hardware. The overall philosophy of utilizing the full distribution information of signal measurements at each location (proved implementable after careful algorithm design) distinguishes sharply from most existing works. Compared with the earlier work within our group, the present paper introduces new elements such as profiling the signal measurement distributions over the coverage area using a special interpolation technique; a twotier tracking scheme that improves the efficiency of localization (in the commonly used sense) by adding movement detection (lower energy cost); and the joint clusterhead placement optimization for both localization and movement detection. Experimentally, our system achieved an accuracy equivalent to 95% < 5 meters and 87% < 3 meters, which should be considered a highquality result compared to wellknown contemporary systems that use similar lowcost hardware. View full abstract»

Rangebased geolocation in fading environments
Publication Year: 2008 , Page(s): 15  20
Cited by: Papers (2)We consider source geolocation based on range estimates from sensors with known coordinates. In a fading propagation environment, where a lineofsight (LOS) path may be weak or essentially nonexistent, range estimates may have positive biases. We study this problem by considering a weighted least squares (WLS) location estimator, based on noisy range estimates, each of which is contaminated by additive Gaussian noise and possibly a positive bias. We derive the mean and meansquare error (MSE) of the WLS estimator, showing that in general the estimator produces biased estimates. The error expressions are developed via firstorder perturbation analysis. They provide a means to study achievable localization performance, as a function of the measurement bias and variance, as well as the sensor network geometry. View full abstract»

Union support recovery in highdimensional multivariate regression
Publication Year: 2008 , Page(s): 21  26
Cited by: Papers (3)In the problem of multivariate regression, a Kdimensional response vector is regressed upon a common set of p covariates, with a matrix B* isin Ropf^{ptimesK} of regression coefficients. We study the behavior of the group Lasso using lscr_{1}/lscr_{2} regularization for the union support problem, meaning that the set of s rows for which B* is nonzero is recovered exactly. Studying this problem under highdimensional scaling, we show that group Lasso recovers the exact row pattern with high probability over the random design and noise for scalings of (n, p, s) such that the sample complexity parameter given by thetas(n, p, s) := n/[2psi(B*) log(p  s)] exceeds a critical threshold. Here n is the sample size, p is the ambient dimension of the regression model, s is the number of nonzero rows, and psi(B*) is a sparsityoverlap function that measures a combination of the sparsities and overlaps of the Kregression coefficient vectors that constitute the model. This sparsityoverlap function reveals that, if the design is uncorrelated on the active rows, block lscr_{1}/lscr_{2} regularization for multivariate regression never harms performance relative to an ordinary Lasso approach, and can yield substantial improvements in sample complexity (up to a factor of K) when the regression vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the group Lasso. View full abstract»

Diversitymultiplexing tradeoff of the halfduplex relay channel
Publication Year: 2008 , Page(s): 27  33
Cited by: Papers (22)We show that the diversitymultiplexing tradeoff of a halfduplex singlerelay channel with identically distributed Rayleigh fading channel gains meets the 2 by 1 MISO bound. We generalize the result to the case when there are N noninterfering relays and show that the diversitymultiplexing tradeoff is equal to the N + 1 by 1 MISO bound. View full abstract»

Reducedcomplexity transmit power optimization techniques for multiuser MIMO with perantenna power constraint
Publication Year: 2008 , Page(s): 34  38
Cited by: Patents (2)For a multiuser (MU)MIMO precoded transmission with individual constraints on the maximum power of each transmit antenna, the transmit power optimization problem is a nonlinear convex optimization problem with a high level of computational complexity. In this paper, we propose three methods in order to reduce the computational complexity associated with this problem. The reductions in computational complexity achieved with the proposed methods are evaluated under the sumrate maximization criterion assuming i.i.d Rayleigh fading MIMO channels and block diagonalization zeroforcing as a precoder. View full abstract»

Optimal resource allocation for MIMO ad hoc cognitive radio networks
Publication Year: 2008 , Page(s): 39  45
Cited by: Papers (2)  Patents (1)Maximization of the weighted sumrate of secondary users (SUs) possibly equipped with multiantenna transmitters and receivers is considered in the context of cognitive radio (CR) networks with coexisting primary user(s) (PU). Total interference power received at the primary receiver is constrained to maintain reliable communication for the PU. An interference channel configuration is considered for ad hoc networking, where the receivers treat the interference from undesired transmitters as noise. Without the CR constraint, a distributed algorithm is developed to obtain (at least) a locally optimal solution. With the CR constraint, a semidistributed algorithm is also introduced along with an alternative centralized algorithm based on geometric programming and network duality. View full abstract»

Maximizing the sum rate in symmetric networks of interfering links under flat power constraints
Publication Year: 2008 , Page(s): 46  53
Cited by: Papers (2)We consider the power control problem of maximizing the sum rate of a symmetric network of interfering links in Gaussian noise. We consider a static network: there is no timevarying fading and the power allocation is also mandated to be time and frequency flat. All transmitters have a maximum allowable average transmit power, the same for all transmitters. We solve this nonconvex problem by identifying some underlying convex structure, and show that the solution is either one link blasting at full power, or all links blasting at full power. We provide a characterization of the solution in terms of the level of crossgain between the interfering links. There is a phase transition between these two states, as the crossgain traverses a threshold. View full abstract»

Minimum energyperbit multihop wireless networks
Publication Year: 2008 , Page(s): 54  61
Cited by: Papers (1)In this paper, the tradeoff between the total energy consumption and the endtoend rate in wireless multihop networks is considered. An energy consumption model that incorporates both the energy radiated by the transmitter and the energy consumed by the circuits that process the received signals is proposed. The endtoend rate of communication is considered for the number of information bits transmitted (endtoend) per coded symbol transmitted by any node in the network that is forwarding the data. The tradeoff between the minimum total energy consumption and the endtoend rate of communication is analyzed. It is shown that the performance (either energy or rate) depends on the transmission strategy of each node, the location of the relay nodes and the data rate used by each node. Two communication schemes that capture the inherent constraints of networks, bandwidth and energy respectively are then investigated. For a given distribution of relays it is shown that the total energy consumption can be minimized with an optimal selection of endtoend rate for both schemes. View full abstract»

Minimization of transceiver energy consumption in wireless sensor networks with AWGN channels
Publication Year: 2008 , Page(s): 62  66
Cited by: Papers (7)In this paper, we determine how to minimize energy consumption per information bit in a single link, with the consideration of packet retransmission and overhead. This is achieved by deriving expressions for the optimum target bit error probability and packet length at different transmission distances. Furthermore, the energy consumptions of different modulation schemes are compared over an additive white Gaussian noise (AWGN) channel. Finally, it is shown that the optimum target bit error probability and packet length converge to a constant value for long distances. Numerical results show that at short distances, it is optimum to use bandwidth efficient modulation with large packets and low target BER, and at long distances, it is optimum to use energy efficient modulation with short packets and high target BER. View full abstract»

Modeling and analysis of energy harvesting nodes in wireless sensor networks
Publication Year: 2008 , Page(s): 67  71
Cited by: Papers (8)A Markov based unified model for energy harvesting nodes in wireless sensor networks is proposed. Using the presented model, the probability of event loss due to energy run out as well as an analytical vulnerability metric, namely average time to energy runout, are derived. The results provide insight into the performance of energy harvesting nodes in wireless sensor networks as well as design requirements for such nodes. The proposed vulnerability metric can be used in the various harvesting aware techniques at different protocol layers. View full abstract»

Powerbandwidth tradeoff in multiuser relay channels with opportunistic scheduling
Publication Year: 2008 , Page(s): 72  78
Cited by: Papers (1)The goal of this paper is to understand the key merits of multihop relaying techniques jointly in terms of their energy efficiency and spectral efficiency advantages in the presence of multiuser diversity gains from opportunistic (i.e., channelaware) scheduling and identify the regimes and conditions in which relayassisted multiuser communication provides a clear advantage over direct multiuser communication. For this purpose, we use Shannontheoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the powerbandwidth tradeoff) over a fading multiuser relay channel with K users in the asymptotic regime of large (but finite) number of users (i.e., dense network). Benefiting from the extremevalue theoretic results of [1], we characterize the powerbandwidth tradeoff and the associated energy and spectral efficiency measures of the bandwidthlimited high signaltonoise ratio (SNR) and powerlimited low SNR regimes, and utilize them in investigating the large system behavior of the multiuser relay channel as a function of the number of users and physical channel SNRs. Our analysis results in very accurate closedform formulas in the large (but finite) K regime that quantify energy and spectral efficiency performance, and provides insights on the impact of multihop relaying and multiuser diversity techniques on the powerbandwidth tradeoff. View full abstract»

Opportunistic multiantenna downlink transmission with finiterate feedback
Publication Year: 2008 , Page(s): 79  86
Cited by: Papers (1)Multipleantenna downlink transmission offers significant capacity improvement when the transmitside channel state information (CSI) is available. The sumrate capacity with infiniterate feedback (full or partial CSI) scales linearly with the number of transmit antennas (multiplexing gain) and double logarithmically with the number of users (multiuser diversity gain). In this paper we present a new scheduling scheme which requires only finiterate feedback and yet retains the optimal multiplexing and multiuser diversity gains achievable by dirtypaper coding and show that its sumrate throughput scales like N_{t} log log KN_{r} where N_{t} and N_{r} are the number of transmit and receive antennas and K is the number of users. While our scheduling schemes is asymptotically optimal, it also exhibits a good performance for practical network sizes. We also show that by appropriate design of the feedback mechanism, we can refrain the aggregate amount of feedback from increasing with the number of users and for asymptotically large networks the total number of feedback bits is bounded by N_{t} log N_{t}. We also demonstrate that despite having an opportunistic user selection, fairness among the users is maintained and all are equality likely to be scheduled. View full abstract»

Diversitymultiplexing tradeoff in multiplerelay networkpart I: Proposed scheme and singleantenna networks
Publication Year: 2008 , Page(s): 87  94
Cited by: Papers (2)This paper studies the setup of a multiplerelay network in which K halfduplex multipleantenna relays assist in the transmission between a/several multipleantenna source(s) and a multipleantenna destination. Each two nodes are assumed to be either connected through a quasistatic Rayleigh fading channel, or disconnected. This paper is comprised of two parts. In this part of the paper, we propose a new scheme, which we call random sequential (RS), based on the amplifyandforward relaying. We derive diversitymultiplexing tradeoff (DMT) of the proposed RS scheme for general singleantenna multiplerelay networks. As a result, we show that for singleantenna twohop multipleaccess multiplerelay (K > 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple access single relay setup, we show that the RS scheme reduces to the naive amplifyandforward relaying and is not optimum in terms of DMT, while the dynamic decodeandforward scheme is shown to be optimum for this scenario. View full abstract»

Diversitymultiplexing tradeoff in multiplerelay networkpart II: Multipleantenna networks
Publication Year: 2008 , Page(s): 95  102
Cited by: Papers (5)This paper studies the setup of a multiplerelay network in which K halfduplex multipleantenna relays assist in the transmission between a/several multipleantenna source(s) and a multipleantenna destination. Each two nodes are assumed to be either connected through a quasistatic Rayleigh fading channel, or disconnected. This paper is comprised of two parts. In this part of the paper, we study multipleantenna multiplerelay network. We prove that the Random Sequential (RS) scheme proposed in achieves the maximum diversity gain in a general multipleantenna multiplerelay network. Moreover, we show that utilizing independent random unitary matrix multiplication at the relay nodes enables the RS scheme to achieve better diversitymultiplexing tradeoff (DMT) results comparing with the traditional amplifyandforward relaying. Indeed, using the RS scheme, we derive a new achievable DMT for the MIMO parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the MIMO halfduplex parallel 2relay (K = 2) setup. Finally, we show that utilizing random unitary matrix multiplication also improves the DMT of the NonOrthogonal amplifyandforward relaying scheme of in the MIMO single relay channel. View full abstract»

Diversity multiplexing tradeoff of asynchronous cooperative relay networks
Publication Year: 2008 , Page(s): 103  110
Cited by: Papers (1)The assumption of nodes in a cooperative communication relay network operating in synchronous fashion is often unrealistic. In the present paper we consider two different models of asynchronous operation in cooperativediversity networks experiencing slow fading and examine the corresponding diversitymultiplexing tradeoffs (DMT). For both models, we propose protocols and distributed spacetime codes that asymptotically achieve the transmit diversity bound for all multiplexing gains and for number of relays N ges 2. View full abstract»

Some geometric methods for construction of spacetime codes in Grassmann manifolds
Publication Year: 2008 , Page(s): 111  118Geometric methods for construction of codes in the Grassmann manifolds are presented. The methods follow the geometric approach to spacetime coding for the noncoherent MIMO channel where the code design is interpreted as a packing problem on Grassmann manifolds. The differential structure of the Grassmann manifold provides parametrization with the tangent space at the identity element. Grassmann codes for the noncoherent channel are constructed by mapping suitable subsets of lattices from the tangent space to the Grassmann manifold via the exponential map. As examples, constructions from the rotated Gosset, BarnesWall and Leech lattice are presented. Due to the specifics of the mapping, some of the structure is preserved after the mapping to the manifold. The method is further improved by modifying the mapping from the tangent space to the manifold. Ideas for other constructions of Grassmann codes are also presented and discussed. View full abstract»

Broadcast channel: Degrees of freedom with no CSIR
Publication Year: 2008 , Page(s): 119  125
Cited by: Papers (5)We analyze a broadcast channel with no initial assumption of channel state information neither at the base station (BS) nor at the users' side. For the case when there is no possibility of feedback to the BS and it remains oblivious of the channel state information throughout the transmission, it is shown that the capacity region is bounded by the capacity of a pointtopoint MISO link and hence the prelog of the sum rate is (1  1/T ) for a block fading channel of coherence length T. When the BS is allowed to acquire channel knowledge, operating under timedivision duplex (TDD) mode, we give a very simple scheme through which BS and all users get necessary channel state information and the high SNR sum rate shows significant multiplexing gain or degrees of freedom (DOF). View full abstract»

On replica symmetry breaking in vector precoding for the Gaussian MIMO broadcast channel
Publication Year: 2008 , Page(s): 126  132
Cited by: Papers (4)The socalled ldquoreplica methodrdquo of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multipleinput multipleoutput (MIMO) broadcast channel. Focusing on discrete complex input alphabets, the transmitter is assumed to comprise a linear frontend combined with nonlinear precoding, that minimizes the frontend imposed transmit energy penalty. The energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, are derived while harnessing what is referred to as the first order replica symmetry breaking (1RSB) ansatz. Particularizing to a ldquozeroforcingrdquo (ZF) linear frontend, and noncooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain uxy, where u is the channel input, x is the equivalent precoder output, and y is the channel output. An illustrative example is considered, based on discretelattice alphabet relaxation, for which the impact of replica symmetry breaking is demonstrated. A comparative spectral efficiency analysis reveals significant performance gains compared to linear ZF precoding in the medium to high E_{b}/N_{0} region. The performance vs. complexity tradeoff of the nonlinear precoding scheme is also shortly discussed. View full abstract»

Complementary codes based channel estimation for MIMOOFDM systems
Publication Year: 2008 , Page(s): 133  138We present a pilotassisted method for estimating the frequency selective channel in a MIMOOFDM (multiple input multiple output orthogonal frequency division multiplexing) system. The pilot sequence is designed using the DFT (discrete Fourier transform) of the Golay complementary sequences. Novel exploitation of the perfect autocorrelation property of the Golay codes, in conjunction with OSTBC (orthogonal spacetime block code) based pilot waveform scheduling across multiple OFDM frames, facilitates simple separation of the channel mixtures at the receive antennas. The DFT length used to transform the complementary sequence into the frequency domain is shown to be a key critical parameter for correctly estimating the channel. NMSE (normalized mean squared error) between the actual and the estimated channel is used to characterize the estimation performance. View full abstract»

An adaptive limited feedback scheme for MIMOOFDMA based on optimal stopping
Publication Year: 2008 , Page(s): 139  145We propose and analyze a limited feedback scheme for downlink MIMOOFDMA. Our analysis explicitly accounts for the feedback overhead by assuming a time division duplex system in which all feedback and data transmission must occur with a coherence time. As the fraction of coherence time devoted to feedback increases, the base station can allocate resources more efficiently, but has less time available for data transmission. In the proposed scheme, the basestation sequentially receives feedback from the users and decides when to stop receiving additional feedback and begin data transmission. Each user feeds back their best codeword (beam) selected from a beamforming codebook on each group of OFDM subchannels, provided that the channel gain exceeds a given threshold. For a given feedback threshold, the optimal stopping rule used by the base station is derived. With this rule we show that the total throughput of this scheme scales linearly with the number of users, provided that the number of OFDM subchannels also scales with fixed ratio. The effect of varying the coherence time and feedback rate is also characterized. View full abstract»

A codedfeedback construction of locally minimumcost multicast network codes
Publication Year: 2008 , Page(s): 146  153There are two common network models for network coded traffic: one is the fractional rate model (the primary model for noncoded communication) and the other is the integer rate model used for detailed coding analysis on packetbypacket behaviors. The existing approach of finding minimumcost multicast network codes is based on the fractional rate model and solves the corresponding linearprogramming (LP) problem. The LPbased network optimization generally converges slowly due to the small step size and does not take care of the packetbypacket coding behavior of network coding. This paper develops a minimumcost multicast scheme based on the integer rate model. The new scheme exploits a new concept of coded feedback, takes full advantages of the forward networkcoded traffic, and possesses many practical advantages for efficient implementation. The complexity and performance of the codedfeedback scheme are studied both analytically and through simulations. View full abstract»

Network coding with periodic recomputation for minimum energy multicasting in mobile adhoc networks
Publication Year: 2008 , Page(s): 154  161We consider the problem of minimumenergy multicast using network coding in mobile ad hoc networks (MANETs). The optimal solution can be obtained by solving a linear program every time slot, but it leads to high computational complexity. In this paper, we consider a lowcomplexity approach, network coding with periodic recomputation, which recomputes an approximate solution at fixed time intervals, and uses this solution during each time interval. As the network topology changes slowly, we derive a theoretical bound on the performance gap between our suboptimal solution and the optimal solution. For complexity analysis, we assume that interiorpoint method is used to solve a linear program at the first time slot of each interval. Moreover, we can use the suboptimal solution in the preceding interval as a good initial solution of the linear program at each fixed interval. Based on this interiorpoint method with a warm start strategy, we obtain a bound on complexity. Finally, we consider an example network scenario and minimize the complexity subject to the condition that our solution achieves a given optimality gap. View full abstract»

Toward an optimal 1+N protection strategy
Publication Year: 2008 , Page(s): 162  169
Cited by: Papers (1)This paper introduces an implementation of the network codingbased generalized 1+N protection technique presented earlier by the author in [1] to protect against single link failures. Instead of using two protection circuits for a group of connections which are to be protected together as in [1], only one protection circuit is used, which takes the form of a tree. The protection circuit carries linear combinations of the data units originally transmitted on the working circuits, and these linear combinations can be used to recover lost data due to link failures. This recovery is carried out with the assistance of one node on the protection tree, which is chosen to reduce the recovery time. Moreover, unlike the scheme in [1] which protects unidirectional connections, this scheme is used to protect bidirectional connections. This protection technique requires exactly the same amount of protection resources used by 1:N protection, and can therefore be considered as a step towards achieving optimal 1+N protection. The paper also makes a number of other contributions. It introduces an integer linear program (ILP) formulation to evaluate the cost of protection using this technique, and compares it to the cost of 1+1 protection. The comparison shows that a significant saving in cost can be achieved, while still recovering from failures within a short time. View full abstract»

MPerf: An available bandwidth estimation tool for multicast applications
Publication Year: 2008 , Page(s): 170  176
Cited by: Papers (2)In this paper, we present MPerf, a tool to estimate the total available bandwidth to each receiver in a multicast session where total available bandwidth is defined as the maximum flow rate from the source to the receiver in a given directed acyclic graph. MPerf achieves this objective using a technique called network coding. Therefore, unlike endtoend bandwidth estimation tools, MPerf requires support from forwarding nodes. Such support is easily available for application layer multicasts in overlay networks. It may also become available in the future for network layer multicast through lower layer support for network coding. We show that MPerf accurately estimates the available bandwidth using two overlay networks: localarea overlay at University of Wisconsin and widearea overlay on Planetlab [1]. We also integrate MPerf into a multimedia streaming application to demonstrate a usage case scenario and further evaluate its effectiveness. View full abstract»