Ayfer Özgür

Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks

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-alpha as 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 n2/3 of 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/2 for 2lesalpha<3 and radicn for a alphages3. The best known earlier result of Xie and Kumar identified the scaling law for alpha > 4. 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.

Hierarchical Cooperation Achieves Linear Capacity Scaling in Ad Hoc Networks

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.

Approximately achieving Gaussian relay network capacity with lattice codes

Recently, it has been shown that a quantize-map-and-forward scheme approximately achieves (within a constant number of bits) the Gaussian relay network capacity for arbitrary topologies [1]. This was established using Gaussian codebooks for transmission and random mappings at the relays. In this paper, we show that the same approximation result can be established by using lattices for transmission and quantization along with structured mappings at the relays.

Spatial Degrees of Freedom of Large Distributed MIMO Systems and Wireless Ad Hoc Networks

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.

Near Optimal Energy Control and Approximate Capacity of Energy Harvesting Communication

We consider an energy-harvesting communication system where a transmitter powered by an exogenous energy arrival process and equipped with a finite battery of size Bmax communicates over a discrete-time AWGN channel. We first concentrate on a simple Bernoulli energy arrival process where at each time step, either an energy packet of size E is harvested with probability p, or no energy is harvested at all, independent of the other time steps. We provide a near optimal energy control policy and a simple approximation to the information-theoretic capacity of this channel. Our approximations for both problems are universal in all the system parameters involved (p, E and Bmax), i.e., we bound the approximation gaps by a constant independent of the parameter values. Our results suggest that a battery size Bmax ≥ E is (approximately) sufficient to extract the infinite battery capacity of this channel. We then extend our results to general i.i.d. energy arrival processes. Our approximate capacity characterizations provide important insights for the optimal design of energy harvesting communication systems in the regime where both the battery size and the average energy arrival rate are large.

Scaling Laws for One- and Two-Dimensional Random Wireless Networks in the Low-Attenuation Regime

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.

Throughput-Delay Tradeoff for Hierarchical Cooperation in Ad Hoc Wireless Networks

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 tradeoff <i>D</i>(<i>n</i>) = (log<i>n</i>)² <i>T</i>(<i>n</i>) for <i>T</i>(<i>n</i>) between <i>¿(¿(n)</i>/log<i>n</i>) and <i>¿(n</i>/log<i>n</i>), where <i>D</i>(<i>n</i>) and <i>T</i>(<i>n</i>) are respectively the average delay per bit and the aggregate throughput in a network of <i>n</i> nodes. This tradeoff complements the previous results of El Gamal et al. , which show that the throughput-delay tradeoff for multihop schemes is given by <i>D</i>(<i>n</i>) = <i>T</i>(<i>n</i>) where <i>T</i>(<i>n</i>) lies between <i>¿(1)</i> and <i>¿(¿(n</i>).

Approximately Achieving Gaussian Relay Network Capacity With Lattice-Based QMF Codes

Recently, a new relaying strategy, quantize-map-and-forward (QMF) scheme, has been demonstrated to approximately achieve (within an additive constant number of bits) the Gaussian relay network capacity, universally, i.e., for arbitrary topologies, channel gains, and SNRs. This was established using Gaussian codebooks for transmission and random mappings at the relays. In this paper, we develop structured lattice codes that implement the QMF strategy. The main result of this paper is that such structured lattice codes can approximately achieve the Gaussian relay network capacity universally, again within an additive constant. In addition, we establish a similar result for half-duplex networks, where we demonstrate that one can approximately achieve the capacity using fixed transmit-receive (TX-RX) schedules for the relays with no transmit power optimization across the different TX-RX states of the network.

Achieving the capacity of the N-relay Gaussian diamond network within logn bits

We consider the N-relay Gaussian diamond network where a source node communicates to a destination node via N parallel relays through a cascade of a Gaussian broadcast (BC) and a multiple access (MAC) channel. Introduced in 2000 by Schein and Gallager, the capacity of this relay network is unknown in general. The best currently available capacity approximation, independent of the coefficients and the SNRs of the constituent channels, is within an additive gap of 1.3 N bits, which follows from the recent capacity approximations for general Gaussian relay networks with arbitrary topology. In this paper, we approximate the capacity of this network within 2 log N bits. We show that two strategies can be used to achieve the information-theoretic cutset upper bound on the capacity of the network up to an additive gap of O(log N) bits, independent of the channel configurations and the SNRs. The first of these strategies is simple partial decode-and-forward. Here, the source node uses a superposition codebook to broadcast independent messages to the relays at appropriately chosen rates; each relay decodes its intended message and then forwards it to the destination over the MAC channel. A similar performance can be also achieved with compress-and-forward type strategies (such as quantize-map-and-forward and noisy network coding) that provide the 1.3 N-bit approximation for general Gaussian networks, but only if the relays quantize their observed signals at a resolution inversely proportional to the number of relay nodes N. This suggest that the rule-of-thumb to quantize the received signals at the noise level in the current literature can be highly suboptimal.

Wireless network simplification: The Gaussian N-relay diamond network

We consider the Gaussian