The transport capacity of wireless networks over fading channels

We consider networks consisting of nodes with radios, and without any wired infrastructure, thus necessitating all communication to take place only over the shared wireless medium. The main focus of this paper is on the effect of fading in such wireless networks. We examine the attenuation regime where either the medium is absorptive, a situation which generally prevails, or the path loss exponent is greater than 3. We study the transport capacity, defined as the supremum over the set of feasible rate vectors of the distance weighted sum of rates. We consider two assumption sets. Under the first assumption set, which essentially requires only a mild time average type of bound on the fading process, we show that the transport capacity can grow no faster than O(n), where n denotes the number of nodes, even when the channel state information (CSI) is available noncausally at both the transmitters and the receivers. This assumption includes common models of stationary ergodic channels; constant, frequency-selective channels; flat, rapidly varying channels; and flat slowly varying channels. In the second assumption set, which essentially features an independence, time average of expectation, and nonzeroness condition on the fading process, we constructively show how to achieve transport capacity of /spl Omega/(n) even when the CSI is unknown to both the transmitters and the receivers, provided that every node has an appropriately nearby node. This assumption set includes common models of independent and identically distributed (i.i.d.) channels; constant, flat channels; and constant, frequency-selective channels. The transport capacity is achieved by nodes communicating only with neighbors, and using only point-to-point coding. The thrust of these results is that the multihop strategy, toward which much protocol development activity is currently targeted, is appropriate for fading environments. The low attenuation regime is open.     

Information-theoretic upper bounds on the capacity of large extended ad hoc wireless networks

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.     

Broadcast capacity of wireless networks

We present an upper bound on the broadcast capacity of arbitrary ad hoc wireless networks. The throughput obtainable by each node for broadcasting to-all-of the other nodes in a network consisting of n nodes with- fixed transmission ranges and C bits per second channel capacity is bounded by O(C/n), which is equivalent to the upper bound for per node capacity of a fully connected single-hop network.     

The capacity of wireless networks

When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput λ(n) obtainable by each node for a randomly chosen destination is Θ(W/√(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is Θ(W√An) bit-meters per second. Thus even under optimal circumstances, the throughput is only Θ(W/√n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance     

The nominal capacity of wireless mesh networks

Wireless mesh networks are an alternative technology for last-mile broadband Internet access. In WMNs, similar to ad hoc networks, each user node operates not only as a host but also as a router; user packets are forwarded to and from an Internet-connected gateway in multihop fashion. The meshed topology provides good reliability, market coverage, and scalability, as well as low upfront investments. Despite the recent startup surge in WMNs, much research remains to be done before WMNs realize their full potential. This article tackles the problem of determining the exact capacity of a WMN. The key concept we introduce to enable this calculation is the bottleneck collision domain, defined as the geographical area of the network that bounds from above the amount of data that can be transmitted in the network. We show that for WMNs the throughput of each node decreases as O(1/n), where n is the total number of nodes in the network. In contrast with most existing work on ad hoc network capacity, we do not limit our study to the asymptotic case. In particular, for a given topology and the set of active nodes, we provide exact upper bounds on the throughput of any node. The calculation can be used to provision the network, to ensure quality of service and fairness. The theoretical results are validated by detailed simulations.     

Stability and capacity of regular wireless networks

We study the stability and capacity problems in regular wireless networks. In the first part of the paper, we provide a general approach to characterizing the capacity region of arbitrary networks, find an outer bound to the capacity region in terms of the transport capacity, and discuss connections between the capacity formulation and the stability of node buffers. In the second part of the paper, we obtain closed-form expressions for the capacity of Manhattan (two-dimensional grid) and ring networks (circular array of nodes). We also find the optimal (i.e., capacity-achieving) medium access and routing policies. Our objective in analyzing regular networks is to provide insights and design guidelines for general networks. The knowledge of the exact capacity enables us to quantify the loss incurred by suboptimal protocols such as slotted ALOHA medium access and random-walk-based routing. Optimal connectivity and the effects of link fading on network capacity are also investigated.     

Upper bounds on capacity for a constrained Gaussian channel

A low-pass and a bandpass additive white Gaussian noise channel with a peak-power constraint imposed on otherwise arbitrary input signals are considered. Upper bounds on the capacity of such channels are derived. They are strictly less than the capacity of the channel when the peak-power constrain is removed and replaced by the average-power constraint, for which the Gaussian inputs are optimum. This provides the answer to an often-posed question: peak-power limiting in the case of bandlimited channels does reduce capacity, whereas in infinite bandwidth channels it does not, as is well known. For an ideal low-pass filter of bandwidth B, the upper bound is Blog 0.934P/(N₀B) for P/( N₀B)≫1, where P is the peak power of the input signal and N₀/2 is the double-sided power spectral density of the additive white Gaussian noise     

Upper bounds on the capacity of Gaussian channels with feedback

The capacity of the discrete-time additive Gaussian channel without feedback is known. A class of upper bounds on the capacity with noiseless feedback that are quite good for some exemplary channels is obtained     

Sum capacity and TSC bounds in collaborative multibase wireless systems

We consider a wireless system with base stations which collaborate, and derive bounds on sum capacity and total squared correlation for uniform channels between users and bases. The correspondence also investigates structural properties which must be satisfied by user transmit covariance matrices at the optimal sum capacity/total squared correlation (TSC) point, and shows that for multibase systems, maximizing sum capacity and minimizing TSC are, in general, not equivalent problems.     

Analyzing the capacity of wireless ad hoc networks

In this paper we develop analytical closed form expression for the capacity of a wireless ad hoc network. First, for the general case when nodes can adapt their communication rates to the link quality, a proper formulation for the total network capacity is presented based on the cumulative distribution function (CDF) of the signal to interference power ratio (SIR). Then, a closed form expression for this CDF is analytically derived. This closed form is further studied by fitting it to a normal distribution. Afterwards, the capacity of the network is investigated. By examining the effect of the outage threshold, it is shown that in order to obtain a higher capacity, one may use simple non-adaptive transceivers with higher threshold on the received SIR. These results are obtained by conducting analytical and simulation studies.     

Assigning codes in wireless networks: bounds and scaling properties

In the Code Division Multiple Access (CDMA) framework, collisions that can occur in wireless networks are eliminated by assigning orthogonal codes to stations, a problem equivalent to that of coloring graphs associated to the physical network. In this paper we present new upper and lower bounds for two versions of the problem (hidden and primary collision avoidance – HPCA – or hidden collision avoidance only – HCA). In particular, optimal assignments for special topologies and heuristics for general topologies are proposed. The schemes show better average results with respect to existing alternatives. Furthermore, the gaps between the upper bound given by the heuristic solution, the lower bound obtained from the maximumclique problem, and the optimal solution obtained by branch and bound are investigated in the different settings. A scaling law is then proposed to explain the relations between the number of codes needed in Euclidean networks with different station densities and connection distances. The substantial difference between the two versions HPCA and HCA of the problem is investigated by studying the probabilistic distribution of connections as a function of the distance, and the asymptotic size of the maximum cliques.     

An overview of local capacity in wireless networks

This article introduces a metric for performance evaluation of medium access schemes in wireless ad hoc networks known as local capacity. Although deriving the end-to-end capacity of wireless ad hoc networks is a difficult problem, the local capacity framework allows us to quantify the average information rate received by a receiver node randomly located in the network. In this article, the basic network model and analytical tools are first discussed and applied to a simple network to derive the local capacity of various medium access schemes. Our goal is to identify the most optimal scheme and also to see how does it compare with more practical medium access schemes. We analyzed grid pattern schemes where simultaneous transmitters are positioned in a regular grid pattern, ALOHA schemes where simultaneous transmitters are dispatched according to a uniform Poisson distribution and exclusion schemes where simultaneous transmitters are dispatched according to an exclusion rule such as node coloring and carrier sense schemes. Our analysis shows that local capacity is optimal when simultaneous transmitters are positioned in a grid pattern based on equilateral triangles and our results show that this optimal local capacity is at most double the local capacity of ALOHA based scheme. Our results also show that node coloring and carrier sense schemes approach the optimal local capacity by an almost negligible difference. At the end, we also discuss the shortcomings in our model as well as future research directions.     

Event-to-sink reliable transport in wireless sensor networks

Wireless sensor networks (WSNs) are event-based systems that rely on the collective effort of several microsensor nodes. Reliable event detection at the sink is based on collective information provided by source nodes and not on any individual report. However, conventional end-to-end reliability definitions and solutions are inapplicable in the WSN regime and would only lead to a waste of scarce sensor resources. Hence, the WSN paradigm necessitates a collective event-to-sink reliability notion rather than the traditional end-to-end notion. To the best of our knowledge, reliable transport in WSN has not been studied from this perspective before. In order to address this need, a new reliable transport scheme for WSN, the event-to-sink reliable transport (ESRT) protocol, is presented in this paper. ESRT is a novel transport solution developed to achieve reliable event detection in WSN with minimum energy expenditure. It includes a congestion control component that serves the dual purpose of achieving reliability and conserving energy. Importantly, the algorithms of ESRT mainly run on the sink, with minimal functionality required at resource constrained sensor nodes. ESRT protocol operation is determined by the current network state based on the reliability achieved and congestion condition in the network. This self-configuring nature of ESRT makes it robust to random, dynamic topology in WSN. Furthermore, ESRT can also accommodate multiple concurrent event occurrences in a wireless sensor field. Analytical performance evaluation and simulation results show that ESRT converges to the desired reliability with minimum energy expenditure, starting from any initial network state.     

Lower bounds on lifetime of ultra wide band wireless sensor networks

The asymptotic lower bounds on the lifetime of time hopping impulse radio ultra wide band (TH-IR UWB) wireless sensor networks are derived using percolation theory arguments. It is shown that for static dense TH-IR UWB wireless sensor network, which sensor nodes are distributed in a square of unit area according to a Poisson point process of intensity n, the lower bound on the lifetime is \( \Upomega \left( {\left( {{{\sqrt n } \mathord{\left/ {\vphantom {{\sqrt n } {\log \sqrt n }}} \right. \kern-\nulldelimiterspace} {\log \sqrt n }}} \right)^{\alpha - 2} } \right) \), where α > 2 is the path loss exponent, thus dense TH-IR UWB wireless sensor network is fit to be employed in large-scale network. For static extended TH-IR UWB wireless sensor network which sensor nodes are distributed in a square \( \left[ {0,\sqrt n } \right] \times \left[ {0,\sqrt n } \right] \) according to a Poisson point process of unit intensity, the lower bound on the lifetime is \( \Upomega \left( {{{\left( {\log \sqrt n } \right)^{2 - \alpha } } \mathord{\left/ {\vphantom {{\left( {\log \sqrt n } \right)^{2 - \alpha } } n}} \right. \kern-\nulldelimiterspace} n}} \right) \), therefore large-scale extended network will lead to shorten network lifetime. The results also indicate that the lower bound on the lifetime in the ideal case is longer than that of a static network by a factor of \( n^{1/2} \left( {\log \sqrt n } \right)^{\alpha - 4} \). Hence mobility of sensor nodes can improve network lifetime.     

Transmission capacity for inhomogeneous overlaid wireless Ad-hoc networks

In the analysis of overlaid wireless Ad-hoc networks, the underlying node distributions are commonly assumed to be two independent homogeneous Poisson point processes. In this paper, by using stochastic geometry tools, a new inhomogeneous overlaid wireless Ad-hoc network model is studied and the outage probability are analyzed. By assuming that primary （PR） network nodes are distributed as a Poisson point process （PPP） and secondary （SR） network nodes are distributed as a Matern cluster processes, an upper and a lower bounds for the transmission capacity of the primary network and that of the secondary network are presented. Simulation results show that the transmission capacity of the PR and SR network will both have a small increment due to the inhomogeneity of the SR network.     

High system capacity pre-scheduler for multi-cell wireless networks

Wireless Networks - With the constant increase of throughput demands, maximizing the wireless network capacity has always been a crucial issue. Network densification becomes one of the adopted...     

Upper and lower bounds for the power consumption of passive networks

Bounds are derived for the power consumption of a passive network driven by sinusoidal generators. Two Constraints on the excitation are considered. They require that the sum of the voltage magnitudes and the sum of the available powers of the generators are equal to unity.     

Quantized lower bounds on grid-based localization algorithm for wireless sensor networks

In this paper, we introduce a Quantized Cramer Rao Bound (Q-CRB) method, which adapts the use of the CRB to handle grid-based localization algorithms with certain constraints, such as localization boundaries. In addition, we derive a threshold granularity level which identifies where the CRB can be appropriately applied to this type of algorithm. Moreover, the derived threshold value allows the users of grid-based LSE techniques to probably avoid some unnecessary complexities associated with using high grid resolutions. To examine the feasibility of the new proposed bound, the grid-based least square estimation (LSE) technique was implemented. The Q-CRB was used to evaluate the performance of the LSE method under extensive simulation scenarios. The results show that the Q-CRB provided a tight bound in the sense that the Q-CRB can characterize the behaviour of location errors of the LSE technique at various system parameters, e.g. granularity levels, measurement accuracies, and in the presence or absence of localization boundaries.     

Mobility increases the capacity of ad hoc wireless networks

The capacity of ad hoc wireless networks is constrained by the mutual interference of concurrent transmissions between nodes. We study a model of an ad hoc network where n nodes communicate in random source-destination pairs. These nodes are assumed to be mobile. We examine the per-session throughput for applications with loose delay constraints, such that the topology changes over the time-scale of packet delivery. Under this assumption, the per-user throughput can increase dramatically when nodes are mobile rather than fixed. This improvement can be achieved by exploiting a form of multiuser diversity via packet relaying.     

Asymptotic analysis for transmission capacity of wireless Ad-hoc networks

This article puts forward a new solution to the bound of the outage probability and transmission capacity of Ad-hoc networks. For the proofs of the upper and lower bounds are too complex, a much easier way is introduced to get the same results, and by using Taylor series, the asymptotic bound is derived. By comparing with the simulation results, we found that the asymptotic bound is sufficient accurate when the network parameters are selected properly, and is tighter than the upper and lower bounds.