Capacity of Cellular Wireless Network

Earlier definitions of capacity for wireless networks, e.g., transport or transmission capacity, for which exact theoretical results are known, are well suited for ad hoc networks but are not directly applicable for cellular wireless networks, where large-scale basestation (BS) coordination is not possible, and retransmissions/ARQ under the SINR model is a universal feature. In this paper, cellular wireless networks, where both BS locations and mobile user (MU) locations are distributed as independent Poisson point processes are considered, and each MU connects to its nearest BS. With ARQ, under the SINR model, the effective downlink rate of packet transmission is the reciprocal of the expected delay (number of retransmissions needed till success), which we use as our network capacity definition after scaling it with the BS density. Exact characterization of this natural capacity metric for cellular wireless networks is derived. The capacity is shown to first increase polynomially with the BS density in the low BS density regime and then scale inverse exponentially with the increasing BS density. Two distinct upper bounds are derived that are relevant for the low and the high BS density regimes. A single power control strategy is shown to achieve the upper bounds in both the regimes. This result is fundamentally different from the well known capacity results for ad hoc networks, such as transport and transmission capacity that scale as the square root of the (high) BS density. Our results show that the strong temporal correlations of SINRs with PPP distributed BS locations is limiting, and the realizable capacity in cellular wireless networks in high-BS density regime is much smaller than previously thought. A byproduct of our analysis shows that the capacity of the ALOHA strategy with retransmissions is zero.Comment: A shorter version to appear in WiOpt 201

Upper Bounds to the Capacity of Wireless Networks

In this thesis, I mainly focus on the evaluation of the upper bounds to the capacity of wireless networks. With the consideration of the two measures, the maximal transmission rate for any source-destination pair and the transport capacity of wireless networks, I summarize the most recent results to the upper bounds of these two measures first in this thesis. At the same time, I also improve and modify the previous results given in these papers. Moreover, I present a proof to the upper bound of maximal transmission rate with high probability by taking the fading of the channel into account when the full CSI is only known to the receivers. With a simple extension of the result, I derive an upper bound to the transport capacity of wireless networks without full CSI at the receiver side. A linear scaling of the upper bound to transport capacity is also derived when the path loss exponent is greater than three. Compared with the previous results, it is shown that the upper bound given in this thesis is much better for relatively large alpha and a minimum distance constraint

Network Coding: Exploiting Broadcast and Superposition in Wireless Networks

In this thesis we investigate improvements in efficiency of wireless communication networks, based on methods that are fundamentally different from the principles that form the basis of state-of-the-art technology. The first difference is that broadcast and superposition are exploited instead of reducing the wireless medium to a network of point-to-point links. The second difference is that the problem of transporting information through the network is not treated as a flow problem. Instead we allow for network coding to be used.\ud \ud First, we consider multicast network coding in settings where the multicast configuration changes over time. We show that for certain problem classes a universal network code can be constructed. One application is to efficiently tradeoff throughput against cost.\ud \ud Next, we deal with increasing energy efficiency by means of network coding in the presence of broadcast. It is demonstrated that for multiple unicast traffic in networks with nodes arranged on two and three dimensional rectangular lattices, network coding can reduce energy consumption by factors of four and six, respectively, compared to routing.\ud \ud Finally, we consider the use of superposition by allowing nodes to decode sums of messages. We introduce different deterministic models of wireless networks, representing various ways of handling broadcast and superposition. We provide lower and upper bounds on the transport capacity under these models. For networks with nodes arranged on a hexagonal lattice it is found that the capacity under a model exploiting both broadcast and superposition is at least 2.5 times, and no more than six times, the transport capacity under a model of point-to-point links

Spatial Interference Cancelation for Mobile Ad Hoc Networks: Perfect CSI

Interference between nodes directly limits the capacity of mobile ad hoc networks. This paper focuses on spatial interference cancelation with perfect channel state information (CSI), and analyzes the corresponding network capacity. Specifically, by using multiple antennas, zero-forcing beamforming is applied at each receiver for canceling the strongest interferers. Given spatial interference cancelation, the network transmission capacity is analyzed in this paper, which is defined as the maximum transmitting node density under constraints on outage and the signal-to-interference-noise ratio. Assuming the Poisson distribution for the locations of network nodes and spatially i.i.d. Rayleigh fading channels, mathematical tools from stochastic geometry are applied for deriving scaling laws for transmission capacity. Specifically, for small target outage probability, transmission capacity is proved to increase following a power law, where the exponent is the inverse of the size of antenna array or larger depending on the pass loss exponent. As shown by simulations, spatial interference cancelation increases transmission capacity by an order of magnitude or more even if only one extra antenna is added to each node.Comment: 6 pages; submitted to IEEE Globecom 200

Product Multicommodity Flow in Wireless Networks

We provide a tight approximate characterization of the $n$-dimensional product multicommodity flow (PMF) region for a wireless network of $n$ nodes. 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 the $n^2$ dimensional capacity region. These results answer the following questions which arise naturally from previous work: (a) What is the significance of $1/\sqrt{n}$ in the scaling laws for the Protocol interference model obtained by Gupta and Kumar (2000)? (b) Can we obtain a tight approximation to the "maximum supportable flow" for node distributions more general than the geometric random distribution, traffic models other than randomly chosen source-destination pairs, and under very general assumptions on the channel fading model? We first establish that the random source-destination model is essentially a one-dimensional approximation to the capacity region, and a special case of product multi-commodity flow. Building on previous results, for a combinatorial interference model given by a network and a conflict graph, we relate the product multicommodity flow to the spectral properties of the underlying graphs resulting in computational upper and lower bounds. 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. As an implication, we obtain computationally efficient upper and lower bounds on the PMF for any wireless network with a guaranteed approximation factor.Comment: Revised version of "Capacity-Delay Scaling in Arbitrary Wireless Networks" submitted to the IEEE Transactions on Information Theory. Part of this work appeared in the Allerton Conference on Communication, Control, and Computing, Monticello, IL, 2005, and the Internation Symposium on Information Theory (ISIT), 200

Information-theoretic Capacity of Clustered Random Networks

We analyze the capacity scaling laws of clustered ad hoc networks in which nodes are distributed according to a doubly stochastic shot-noise Cox process. We identify five different operational regimes, and for each regime we devise a communication strategy that allows to achieve a throughput to within a poly-logarithmic factor (in the number of nodes) of the maximum theoretical capacity.Comment: 6 pages, in Proceedings of ISIT 201