This paper focuses on the problem of broadcasting information in the most efficient manner in a large 2-D ad hoc wireless network at low SNR and under line-of-sight propagation. A new communication scheme is proposed, where source nodes first broadcast their data to the entire network, despite the lack of sufficient available power. The signal's power is then reinforced via successive back-and-forth beamforming transmissions between different groups of nodes in the network, so that all nodes are able to decode the transmitted information at the end. This scheme is shown to achieve asymptotically the broadcast capacity of the network, which is expressed in terms of the largest singular value of the matrix of fading coefficients between the nodes in the network. A detailed mathematical analysis is then presented to evaluate the asymptotic behavior of this largest singular value.

We characterize the maximum achievable broadcast rate in a wireless network at low SNR and under line-of-sight fading assumption. Our result shows that this rate depends negatively on the sparsity of the network. This is to be put in contrast with the number of degrees of freedom available in the network, which have been shown previously to increase with the sparsity of the network.

The present paper focuses on the problem of broadcasting information in the most efficient manner in a large two-dimensional ad hoc wireless network at low SNR and under line-of-sight propagation. A new communication scheme is proposed, where source nodes first broadcast their data to the entire network, despite the lack of sufficient available power. The signal's power is then reinforced via successive back-and-forth beamforming transmissions between different groups of nodes in the network, so that all nodes are able to decode the transmitted information at the end. This scheme is shown to achieve asymptotically the broadcast capacity of the network, which is expressed in terms of the largest singular value of the matrix of fading coefficients between the nodes in the network. A detailed mathematical analysis is then presented to evaluate the asymptotic behavior of this largest singular value.

We consider a slow fading two-hop relay channel where a source terminal communicates with a destination through a layer of relays without a direct link. First, we introduce the notion of time-varying distributed rotation and propose a linear relaying scheme called rotate-and-forward (RF). The main idea is to create a time-varying channel and to convert the spatial diversity to time diversity. It is shown that this scheme achieves the optimal diversity-multiplexing tradeoff (DMT) of the channel with full-duplex relays. While more involved non-linear relaying schemes previously proposed in the literature are optimal in the same setting, we show here that simple linear relaying can also be DMT optimal. Then, we extend the RF scheme to the relay channel with multiple hops where the DMT optimality of the two-antenna case is shown. Finally, we apply the idea of distributed rotation to the decode-and-forward relays. The same diversity order as previous schemes can be achieved with low signaling complexity.

Diversity analysis of multihop free-space optical (FSO) transmission shows the efficiency of this scheme to mitigate atmospheric turbulence. The significant performance of serial relaying is fundamentally a consequence of the distance-dependent channel variance. This prompts us to further investigate the requirements of different FSO networks to achieve a given diversity order. In other words, we aim at converting a network with multiple source and destination pairs to serially relayed transmissions. This indeed requires assisting nodes and reasonably efficient routing protocols. Besides presenting diversity analysis of multihop FSO transmission, this paper investigates how the number of relay nodes scales in terms of the number of source-destination pairs with respect to the geometry of the network and the required diversity order. Moreover, it proposes an optimal routing strategy for specific FSO networks with predefined placement of relay nodes.

While the efficiency of MIMO transmissions in a rich scattering environment has been demonstrated, less is known about the situation where the fading matrix coefficients come from a line-of-sight model. In this paper, we study in detail how this line-of-sight assumption affects the performance of distributed MIMO transmissions between far away clusters of nodes in a wireless network. Our analysis pertains to the study of a new class of random matrices.

We consider a wireless network with n users distributed over a square area A = n. Under line-of-sight propagation, this network has Θ(√n) degrees of freedom. At high SNR, these degrees of freedom can be readily achieved by multi-hop relaying between nodes. At low SNR however, the performance is determined by the power transfer in the network. We show that none of the existing architectures can achieve optimal capacity scaling. We develop a beamforming architecture where signals are relayed by coherent combining over multiple clusters. The key ingredient is an analysis of the beamforming gain achievable between two clusters of nodes under the line-of-sight propagation model. This result reveals a new regime for large two-dimensional wireless networks, where beamforming techniques are needed to achieve capacity.

We consider a large distributed MIMO system where wireless users with single transmit and receive antenna cooperate in clusters to form distributed transmit and receive antenna arrays. We characterize how the capacity of the distributed MIMO transmission scales with the number of cooperating users, the area of the clusters and the separation between them, in a line-of-sight propagation environment. We use this result to answer the following question: can distributed MIMO provide significant capacity gain over traditional multi-hop in large ad hoc networks with n source-destination pairs randomly distributed over an area A? Two diametrically opposite answers [24] and [26] have emerged in the current literature. We show that neither of these two results are universal and their validity depends on V the relation between the number of users n and √A/λ, which we identify as the spatial degrees of freedom in the network. λ is the carrier wavelength. When √A/λ ≥ n, there are n degrees of freedom in the network and distributed MIMO with hierarchical cooperation can achieve a capacity scaling linearly in n as in [24], while capacity of multihop scales only as √n. On the other hand, when √A/λ ≤ √n as in [26], there are only √n degrees of freedom in the network and they can be readily achieved by multihop. Our results also reveal a third regime where √n ≤ √A/λ ≤ n. Here, the number of degrees of freedom are smaller than n but larger than what can be achieved by multi-hop. We construct scaling optimal architectures for this intermediate regime.

We consider a wireless network with a large number of source-destination pairs distributed over a line. Under line-of-sight propagation, this network has only one degree of freedom for communication. At high SNR, this one degree of freedom can be readily achieved by multi-hop relaying between nodes. At low SNR, however, the performance is determined by the power transfer in the network. We show that none of the existing architectures can achieve optimal capacity scaling. We develop a digital hierarchical beamforming architecture and show that it is scaling optimal. This result reveals a new regime for large wireless networks, where beamforming techniques are needed to achieve capacity.

Multi-hop is the traditional architecture for wireless adhoc networks. In this paper, we investigate the potential gains from more sophisticated cooperation in large wireless adhoc networks. While the capacity of multi-hop is limited to ⊖(√(n)) due to interference, we show that a hierarchical cooperation architecture can achieve linear capacity scaling in the number of users n. We also characterize how the cooperation gain is affected when the network is limited in either power or space.

In this paper, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. The DMT expression is given as the solution of a minimization problem in general, and an explicit expression is found when the relay channel is symmetric in terms of number of antennas, i.e., the source and the destination have n antennas each, and the relay has m antennas. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas. Besides, the derivation of the upper bound involves a new asymptotic study of spherical integrals (that is, integrals with respect to the Haar measure on the unitary groupU(n)), which is a topic of mathematical interest in itself.

In analyzing the point-to-point wireless channel, insights about two qualitatively different operating regimes-bandwidth and power-limited-have proven indispensable in the design of good communication schemes. In this paper, we propose a new scaling law formulation for wireless networks that allows us to develop a theory that is analogous to the point-to-point case. We identify fundamental operating regimes of wireless networks and derive architectural guidelines for the design of optimal schemes. Our analysis shows that in a given wireless network with arbitrary size, area, power, bandwidth, etc., there are three parameters of importance: the short-distance signal-to-noise ratio (SNR), the long-distance SNR, and the power path loss exponent of the environment. Depending on these parameters, we identify four qualitatively different regimes. One of these regimes is especially interesting since it is fundamentally a consequence of the heterogeneous nature of links in a network and does not occur in the point-to-point case; the network capacity is both power and bandwidth limited. This regime has thus far remained hidden due to the limitations of the existing formulation. Existing schemes, either multihop transmission or hierarchical cooperation, fail to achieve capacity in this regime; we propose a new hybrid scheme that achieves capacity.

Hierarchical cooperation has recently been shown to achieve better throughput scaling than classical multihop schemes under certain assumptions on the channel model in static wireless networks. However, the end-to-end delay of this scheme turns out to be significantly larger than those of multihop schemes. A modification of the scheme is proposed here that achieves a throughput-delay tradeoffD(n) = (logn)2T(n) forT(n) between¿(¿(n)/logn) and¿(n/logn), whereD(n) andT(n) are respectively the average delay per bit and the aggregate throughput in a network ofnnodes. This tradeoff complements the previous results of El Gamal et al. , which show that the throughput-delay tradeoff for multihop schemes is given byD(n) =T(n) whereT(n) lies between¿(1)and¿(¿(n).

In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. The relay channel is assumed to be symmetric in terms of number of antennas, i.e. the source and the destination have n antennas each, and the relay has m antennas. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas.

The rate region achievable by two transmitter-receiver pairs who wish to communicate over a Gaussian interference channel has been the subject of intense study over the last decades. Recently, the high SNR capacity region of this channel has been completely characterized in a work by Etkin, Tse and Wang (2007). In this paper, we study the effect of adding random fading into the picture, as well as multiple antennas at the transmitters and the receivers. Under the fast fading assumption, we recover a result of the same type as that obtained in the above mentioned paper. Under the slow fading assumption, we obtain an upper bound on the maximally achievable diversity order for a given target rate pair, which we conjecture to be tight.

In analyzing the point-to-point wireless channel, insights about two qualitatively different operating regimes-bandwidth- and power-limited-have proven indispensable in the design of good communication schemes. In this paper, we propose a new scaling law formulation for wireless networks that allows us to develop a theory that is analogous to the point-to-point case. We identify fundamental operating regimes of wireless networks and derive architectural guidelines for the design of optimal schemes. Our analysis shows that in a given wireless network with arbitrary size, area, power, etc., there are three parameters of importance: the short-distance SNR, the long-distance SNR, and the power path loss exponent. Depending on these parameters we identify four qualitatively different regimes. One of these regimes is especially interesting since it is fundamentally a consequence of the heterogeneous nature of links in a network and does not occur in the point-to-point case; the network capacity is both power- and bandwidth-limited. This regime has thus far remained hidden due to the limitations of the existing formulation. Existing schemes, either multihop transmission or hierarchical cooperation, fail to achieve capacity in this regime; we propose a new hybrid scheme that achieves capacity.

This paper presents the multiple-input multiple-output (MIMO) channel capacity over the Nakagami-m fading channel. The joint eigenvalue density function of W = HH' where H is the channel matrix, is derived in closed form for H (2 times 2) and any integer values of m, as well as for H (2 times 3) with to = 2 and to = 3. The marginal eigenvalue distribution of W is also derived in a closed-form expression. All the results are validated by numerical Monte Carlo simulations and are in excellent agreement.

We provide a tight approximate characterization of then-dimensional product multicommodity flow (PMF) region for a wireless network ofnnodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in both an information-theoretic sense and for a combinatorial interference model (e.g., protocol model). These provide an inner approximation to then2-dimensional capacity region. Our results hold for general node distributions, traffic models, and channel fading models. We first establish that the random source-destination model assumed in many previous results on capacity scaling laws, is essentially a one-dimensional approximation to the capacity region and a special case of PMF. We then build on the results for a wireline network (graph) that relate PMF to its spectral (or cut) properties. Specifically, for a combinatorial interference model given by a network graph and a conflict graph, we relate the PMF to the spectral properties of the underlying graphs resulting in simple computational upper and lower bounds. These results show that the 1/radicnscaling law obtained by Gupta and Kumar for a geometric random network can be explained in terms of the scaling law of the conductance of a geometric random graph. For the more interesting random fading model with additive white Gaussian noise (AWGN), we show that the scaling laws for PMF can again be tightly characterized by the spectral properties of appropriately defined graphs-such a characterization for general wireless networks has not been available before. As an implication, we obtain computationally efficient upper and lower bounds on the PMF for any wireless network with a guaranteed approximation factor.

This paper presents the MIMO channel capacity over the Nakagami-m fading channel. The joint eigenvalue density function of W = HHdagger, where H is the channel matrix, is derived in a closed form in the 2 times 2 case and for integer values of m, as well as for m rarr infin. The marginal eigenvalue distribution of W is also derived in closed form solution. For the more general r times t case, an asymptotic formulation is presented and is shown to be close to simulations, even for a small number of antennas. All the results are validated by numerical Monte Carlo simulations and are in excellent agreement.

n source and destination pairs randomly located in a fixed area want to communicate with each other. It is well known that classical multihop architectures that decode and forward packets can deliver at most a radicn-scaling of the aggregate throughput. The performance is limited by the mutual interference between communicating nodes. We show however that a linear scaling of the capacity with n can in fact be achieved by more intelligent node cooperation and distributed MIMO communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation.

n source and destination pairs randomly located in an area extending linearly with n want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power attenuation of r-αand random phase changes. Classical multihop architectures that decode and forward packets can deliver a √n-scaling of the aggregate throughput, while recently proposed hierarchical cooperation achieves n2-α/2-scaling, which is superior to multi-hop for α4, while the moderate-attenuation regime (2 ≤ α ≤ 4) remains uncharacterized. We close this gap by deriving a tight upper bound on the scaling of the aggregate throughput, valid for all α ≥ 2. Our result shows that the mentioned schemes are scaling-optimal, namely that no other scheme can beat hierarchical cooperation when α < 3, nor can it beat classical multi-hop when α ≥ 3. The key ingredient is a careful evaluation of the scaling of the cut-set bound.

This paper analyzes the capacity of a wireless relay network composed of a large number of nodes that operate in an amplify-and-forward mode and that divide into a fixed number of levels. The capacity computation relies on the study of products of large random matrices, whose limiting eigenvalue distribution is computed via a set of recursive equations.

The capacity scaling of extended two-dimensional wireless networks is known in the high-attenuation regime, i.e., when the power path loss exponent alpha is greater than 4. This has been accomplished by deriving information-theoretic upper bounds for this regime that match the corresponding lower bounds. On the contrary, not much is known in the so-called low-attenuation regime when 2lesalphales4. (For one-dimensional networks, the uncharacterized regime is 1lesalphales2.5.) The dichotomy is due to the fact that while communication is highly power-limited in the first case and power-based arguments suffice to get tight upper bounds, the study of the low-attenuation regime requires a more precise analysis of the degrees of freedom involved. In this paper, we study the capacity scaling of extended wireless networks with an emphasis on the low-attenuation regime and show that in the absence of small scale fading, the low attenuation regime does not behave significantly different from the high attenuation regime.

n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power loss of r-alphaas well as a random phase. We identify the scaling laws of the information-theoretic capacity of the network when nodes can relay information for each other. In the case of dense networks, where the area is fixed and the density of nodes increasing, we show that the total capacity of the network scales linearly with n. This improves on the best known achievability result of n2/3of Aeron and Saligrama. In the case of extended networks, where the density of nodes is fixed and the area increasing linearly with n, we show that this capacity scales as n2-alpha/2for 2lesalpha4. Thus, much better scaling than multihop can be achieved in dense networks, as well as in extended networks with low attenuation. The performance gain is achieved by intelligent node cooperation and distributed multiple-input multiple-output (MIMO) communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation.

Starting with the seminal work of Gupta and Kumar (2000), there have been many interesting results that give information theoretic outer and inner approximations to the rate region for wireless networks. While these bounds are almost tight for geometric random networks, not much is known about their tightness for arbitrary wireless networks. In contrast, Leighton and Rao (1988) established a powerful result that uniform multi-commodity flow (UMCF) is within a factor of log n of the natural min-cut capacity for any graph (equivalent to a wireline network) of n nodes. Our motivation is to obtain a similar simple and general characterization for UMCF (shown to be equivalent to the characterization for a much wider class of traffic models) for any wireless network. In this paper, we apply and extend known results to obtain such characterization for networks with Gaussian fading channels. For channel state information (CSI) only at the receivers, we establish that UMCF is within a Delta2log n factor of the information theoretic min-cut capacity of a wireless network, where Delta is the max-degree of a sub-graph induced by the underlying wireless network. For deterministic AWGN channels, we show that UMCF is within square root of the min-cut bound for any network

We obtain a precise information theoretic upper bound on the rate per communication pair in a one-dimensional ad hoc wireless network. The key ingredient of our result is a uniform upper bound on the determinant of the Cauchy matrix

We obtain a precise information-theoretic upper bound on the rate per communication pair in a one-dimensional ad hoc wireless network. The key ingredient of our result is a uniform upper bound on the determinant of the Cauchy matrix.

We derive an information-theoretic upper bound on the rate per communication pair in a large ad hoc wireless network. We show that under minimal conditions on the attenuation due to the environment and for networks with a constant density of users, this rate tends to zero as the number of users gets large.

We derive an information theoretic upper bound on the maximum achievable rate per communication pair in a large extended ad-hoc wireless network. We show that under a reasonably weak assumption on the attenuation due to environment, this rate tends to zero as the number of users gets large

In this paper, initial localization problems are solved by using set-membership estimation. The method can be used with any robot and any kind of sensor(s), provided that a computable model of the environment/sensor interaction is available. With a pedagogical aim in mind, it is detailed in the case of the localization of a vehicle from range measurements in a polygonal environment. Salient properties of the method are as follows. First, it does not need any explicit management of matching hypotheses. Second, it is able to deal with ambiguous situations where several radically different vehicle configurations are consistent with the measurements. Third, it can be made robust to outliers. Fourth, it can deal with nonlinear observation models without any approximation. Fifth, the result is guaranteed in the sense that no configuration consistent with the data and the hypotheses can be missed.