A deterministic approach to throughput scaling in wireless networks

We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider n identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second. We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain /spl Omega/(/spl radic/n) throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the /spl radic/n//spl radic/(logn) throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided.     

Capacity of ad hoc wireless networks with infrastructure support

We determine the asymptotic scaling for the per user throughput in a large hybrid ad hoc network, i.e., a network with both ad hoc nodes, which communicate with each other via shared wireless links of capacity W bits/s, and infrastructure nodes which in addition are interconnected with each other via high capacity links. Specifically, we consider a network model where ad hoc nodes are randomly spatially distributed and choose to communicate with a random destination. We identify three scaling regimes, depending on the growth of the number of infrastructure nodes, m relative to the number of ad hoc nodes n, and show the asymptotic scaling for the per user throughput as n becomes large. We show that when m /spl lsim/ /spl radic/n/logn the per user throughput is of order W//spl radic/n log n and could be realized by allowing only ad hoc communications, i.e., not deploying the infrastructure nodes at all. Whenever /spl radic/n/log n /spl lsim/ m /spl lsim/ n/log n, the order for the per user throughput is Wm/n and, thus, the total additional bandwidth provided by m infrastructure nodes is effectively shared among ad hoc nodes. Finally, whenever m /spl gsim/ n/log n, the order of the per user throughput is only W/log n, suggesting that further investments in infrastructure nodes will not lead to improvement in throughput. The results are shown through an upper bound which is independent of the routing strategy, and by constructing scenarios showing that the upper bound is asymptotically tight.     

Towards an information theory of large networks: an achievable rate region

We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel (DMC). We propose an information-theoretic constructive scheme for obtaining an achievable rate region in such networks. Many well-known capacity-defining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reversely degraded relay channels, the Gaussian multiple-access channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities. Applying the proposed scheme to a specific wireless network of n nodes located in a region of unit area, we show that a transport capacity of /spl Theta/(n) bit-meters per second (bit-meters/s) is feasible in a certain family of networks, as compared to the best possible transport capacity of /spl Theta/(/spl radic/n) bit-meters/s in Gupta et al. (2000), where the receiver capabilities were limited. Even though the improvement is shown for a specific class of networks, a clear implication is that designing and employing more sophisticated multiuser coding schemes can provide sizable gains in at least some large wireless networks.     

A minimum cost heterogeneous sensor network with a lifetime constraint

We consider a heterogeneous sensor network in which nodes are to be deployed over a unit area for the purpose of surveillance. An aircraft visits the area periodically and gathers data about the activity in the area from the sensor nodes. There are two types of nodes that are distributed over the area using two-dimensional homogeneous Poisson point processes; type 0 nodes with intensity (average number per unit area) /spl lambda//sub 0/ and battery energy E/sub 0/; and type 1 nodes with intensity /spl lambda//sub 1/ and battery energy E/sub 1/. Type 0 nodes do the sensing while type 1 nodes act as the cluster heads besides doing the sensing. Nodes use multihopping to communicate with their closest cluster heads. We determine them optimum node intensities (/spl lambda//sub 0/, /spl lambda//sub 1/) and node energies (E/sub 0/, E/sub 1/) that guarantee a lifetime of at least T units, while ensuring connectivity and coverage of the surveillance area with a high probability. We minimize the overall cost of the network under these constraints. Lifetime is defined as the number of successful data gathering trips (or cycles) that are possible until connectivity and/or coverage are lost. Conditions for a sharp cutoff are also taken into account, i.e., we ensure that almost all the nodes run out of energy at about the same time so that there is very little energy waste due to residual energy. We compare the results for random deployment with those of a grid deployment in which nodes are placed deterministically along grid points. We observe that in both cases /spl lambda//sub 1/ scales approximately as /spl radic/(/spl lambda//sub 0/). Our results can be directly extended to take into account unreliable nodes.     

Optimal throughput-delay scaling in wireless networks - part I: the fluid model

Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per source-destination pair is /spl Theta/(1//spl radic/(nlogn)). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per source-destination pair. In most applications, delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughput-delay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughput-delay tradeoff is given by D(n)=/spl Theta/(nT(n)), where T(n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of /spl Theta/(1) for the Grossglauser-Tse scheme is given and the associated delay scaling is shown to be /spl Theta/(nlogn). The optimal throughput-delay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random-walk (RW) model for node mobility is assumed. It is shown that for throughput of /spl Oscr/(1//spl radic/(nlogn)), which can also be achieved in static networks, the throughput-delay tradeoff is the same as in static networks, i.e., D(n)=/spl Theta/(nT(n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be /spl Theta/(nlogn), which is the delay for throughput of /spl Theta/(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in real-world networks would necessitate an abrupt and very large increase in delay.     

Communication over a wireless network with random connections

A network of nodes in which pairs communicate over a shared wireless medium is analyzed. We consider the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. The model in this paper differs substantially from the many existing approaches in that the channel connections in this network are entirely random: rather than being governed by geometry and a decay-versus-distance law, the strengths of the connections between nodes are drawn independently from a common distribution. Such a model is appropriate for environments where the first-order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. It is shown that the aggregate traffic flow as a function of the number of nodes n is a strong function of the channel distribution. In particular, for certain distributions the aggregate traffic flow is at least n/(logn)/sup d/ for some d>0, which is significantly larger than the O(/spl radic/n) results obtained for many geometric models. The results provide guidelines for the connectivity that is needed for large aggregate traffic. The relation between the proposed model and existing distance-based models is shown in some cases.     

Asymptotic distribution of the number of isolated nodes in wireless ad hoc networks with Bernoulli nodes

Nodes in wireless ad hoc networks may become inactive or unavailable due to, for example, internal breakdown or being in the sleeping state. The inactive nodes cannot take part in routing/relaying, and thus may affect the connectivity. A wireless ad hoc network containing inactive nodes is then said to be connected, if each inactive node is adjacent to at least one active node and all active nodes form a connected network. This paper is the first installment of our probabilistic study of the connectivity of wireless ad hoc networks containing inactive nodes. We assume that the wireless ad hoc network consists of n nodes which are distributed independently and uniformly in a unit-area disk, and are active (or available) independently with probability p for some constant 0

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Dynamic power allocation and routing for time-varying wireless networks

We consider dynamic routing and power allocation for a wireless network with time-varying channels. The network consists of power constrained nodes that transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be transmitted through the network to their destinations. We establish the capacity region of all rate matrices (/spl lambda//sub ij/) that the system can stably support-where /spl lambda//sub ij/ represents the rate of traffic originating at node i and destined for node j. A joint routing and power allocation policy is developed that stabilizes the system and provides bounded average delay guarantees whenever the input rates are within this capacity region. Such performance holds for general arrival and channel state processes, even if these processes are unknown to the network controller. We then apply this control algorithm to an ad hoc wireless network, where channel variations are due to user mobility. Centralized and decentralized implementations are compared, and the stability region of the decentralized algorithm is shown to contain that of the mobile relay strategy developed by Grossglauser and Tse (2002).     

Random properties of the highest level sequences of primitive sequences over Z(2/sup e/)

Using the estimates of the exponential sums over Galois rings, we discuss the random properties of the highest level sequences /spl alpha//sub e-1/ of primitive sequences generated by a primitive polynomial of degree n over Z(2/sup e/). First we obtain an estimate of 0, 1 distribution in one period of /spl alpha//sub e-1/. On the other hand, we give an estimate of the absolute value of the autocorrelation function |C/sub N/(h)| of /spl alpha//sub e-1/, which is less than 2/sup e-1/(2/sup e-1/-1)/spl radic/3(2/sup 2e/-1)2/sup n/2/+2/sup e-1/ for h/spl ne/0. Both results show that the larger n is, the more random /spl alpha//sub e-1/ will be.     

On the /spl theta/-coverage and connectivity of large random networks

Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for /spl theta/-coverage is found for wireless networks modeled as n points uniformly distributed in a unit square, with every node connecting to its /spl phi//sub n/ nearest neighbors. A network is called /spl theta/-covered if every node, except those near the boundary, can find one of its /spl phi//sub n/ nearest neighbors in any sector of angle /spl theta/. For all /spl theta//spl isin/(0,2/spl pi/), if /spl phi//sub n/=(1+/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, it is shown that the probability of /spl theta/-coverage goes to one as n goes to infinity, for any /spl delta/>0; on the other hand, if /spl phi//sub n/=(1-/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, the probability of /spl theta/-coverage goes to zero. This sharp characterization of /spl theta/-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if /spl phi//sub n/=(1+/spl delta/)log/sub 2/n. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed.     

Algebraic gossip: a network coding approach to optimal multiple rumor mongering

The problem of simultaneously disseminating k messages in a large network of n nodes, in a decentralized and distributed manner, where nodes only have knowledge about their own contents, is studied. In every discrete time-step, each node selects a communication partner randomly, uniformly among all nodes and only one message can be transmitted. The goal is to disseminate rapidly, with high probability, all messages to all nodes. It is shown that a random linear coding (RLC) based protocol disseminates all messages to all nodes in time ck+/spl Oscr/(/spl radic/kln(k)ln(n)), where c<3.46 using pull-based dissemination and c<5.96 using push-based dissemination. Simulations suggest that c<2 might be a tighter bound. Thus, if k/spl Gt/(ln(n))/sup 3/, the time for simultaneous dissemination RLC is asymptotically at most ck, versus the /spl Omega/(klog/sub 2/(n)) time of sequential dissemination. Furthermore, when k/spl Gt/(ln(n))/sup 3/, the dissemination time is order optimal. When k/spl Lt/(ln(n))/sup 2/, RLC reduces dissemination time by a factor of /spl Omega/(/spl radic/k/lnk) over sequential dissemination. The overhead of the RLC protocol is negligible for messages of reasonable size. A store-and-forward mechanism without coding is also considered. It is shown that this approach performs no better than a sequential approach when k=/spl prop/n. Owing to the distributed nature of the system, the proof requires analysis of an appropriate time-varying Bernoulli process.     

Channel capacity and state estimation for state-dependent Gaussian channels

We formulate a problem of state information transmission over a state-dependent channel with states known at the transmitter. In particular, we solve a problem of minimizing the mean-squared channel state estimation error E/spl par/S/sup n/ - S/spl circ//sup n//spl par/ for a state-dependent additive Gaussian channel Y/sup n/ = X/sup n/ + S/sup n/ + Z/sup n/ with an independent and identically distributed (i.i.d.) Gaussian state sequence S/sup n/ = (S/sub 1/, ..., S/sub n/) known at the transmitter and an unknown i.i.d. additive Gaussian noise Z/sup n/. We show that a simple technique of direct state amplification (i.e., X/sup n/ = /spl alpha/S/sup n/), where the transmitter uses its entire power budget to amplify the channel state, yields the minimum mean-squared state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. We characterize the optimal tradeoff between the rate R of the independent information that can be reliably transmitted and the mean-squared state estimation error D. We show that any optimal (R, D) tradeoff pair can be achieved via a simple power-sharing technique, whereby the transmitter power is appropriately allocated between pure information transmission and state amplification.     

A cone-based distributed topology-control algorithm for wireless multi-hop networks

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology-control (CBTC) algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p/sub u,/spl alpha// required to ensure that in every cone of degree /spl alpha/ around u, there is some node that u can reach with power p/sub u,/spl alpha//. We show that taking /spl alpha/=5/spl pi//6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if /spl alpha//spl les/5/spl pi//6, there is still a path in the smallest symmetric graph G/sub /spl alpha// containing all edges (u,v) such that u can communicate with v using power p/sub u,/spl alpha//. On the other hand, if /spl alpha/>5/spl pi//6, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations.     

Real-time imaging using a 4.3-THz quantum cascade laser and a 320 /spl times/ 240 microbolometer focal-plane array

We report the use of a /spl sim/50-mW peak power 4.3-THz quantum cascade laser (QCL) as an illumination source for real-time imaging with a 320 /spl times/ 240 element room-temperature microbolometer focal-plane array detector. The QCL is modulated synchronously with the focal-plane array for differential imaging. Signal-to-noise ratios of /spl sim/340 are achieved at a 20-frame/s acquisition rate, and the optical noise equivalent power of the detector array at 4.3 THz is estimated to be /spl sim/320 pW//spl radic/Hz. Both reflection and transmission mode imaging are demonstrated.     

Bounds on the throughput gain of network coding in unicast and multicast wireless networks

Gupta and Kumar established that the per node throughput of ad hoc networks with multi-pair unicast traffic scales with an increasing number of nodes n as lambda(n) = ominus(1/radic(n log n)), thus indicating that performance does not scale well. However, Gupta and Kumar did not consider network coding and wireless broadcasting, which recent works suggest have the potential to significantly improve throughput. Here, we establish bounds on the improvement provided by such techniques. For random networks of any dimension under either the protocol or physical model that were introduced by Gupta and Kumar, we show that network coding and broadcasting lead to at most a constant factor improvement in per node throughput. For the protocol model, we provide bounds on this factor. We also establish bounds on the throughput benefit of network coding and broadcasting for multiple source multicast in random networks. Finally, for an arbitrary network deployment, we show that the coding benefit ratio is at most O(log n) for both the protocol and physical communication models. These results give guidance on the application space of network coding, and, more generally, indicate the difficulty in improving the scaling behavior of wireless networks without modification of the physical layer.     

Power allocation and routing in multibeam satellites with time-varying channels

We consider power and server allocation in a multibeam satellite downlink which transmits data to N different ground locations over N time-varying channels. Packets destined for each ground location are stored in separate queues and the server rate for each queue, i, depends on the power, p/sub i/(t), allocated to that server and the channel state, c/sub i/(t), according to a concave rate-power curve /spl mu//sub i/(p/sub i/,c/sub i/). We establish the capacity region of all arrival rate vectors (/spl lambda//sub 1/,...,/spl lambda//sub N/) which admit a stabilizable system. We then develop a power-allocation policy which stabilizes the system whenever the rate vector lies within the capacity region. Such stability is guaranteed even if the channel model and the specific arrival rates are unknown. Furthermore, the algorithm is shown to be robust to arbitrary variations in the input rates and a bound on average delay is established. As a special case, this analysis verifies stability and provides a performance bound for the choose-the-K-largest-connected-queues policy when channels can be in one of two states (ON or OFF ) and K servers are allocated at every timestep (K相似文献   

Double circulant quadratic residue codes

We give a lower bound for the minimum distance of double circulant binary quadratic residue codes for primes p/spl equiv//spl plusmn/3(mod8). This bound improves on the square root bound obtained by Calderbank and Beenker, using a completely different technique. The key to our estimates is to apply a result by Helleseth, to which we give a new and shorter proof. Combining this result with the Weil bound leads to the improvement of the Calderbank and Beenker bound. For large primes p, their bound is of order /spl radic/(2p) while our new improved bound is of order 2/spl radic/p. The results can be extended to any prime power q and the modifications of the proofs are briefly indicated.     

A 1-V 3.5-mW CMOS switched-opamp quadrature IF circuitry for Bluetooth receivers

A 1-V switched-capacitor (SC) quadrature IF circuitry for Bluetooth receivers is demonstrated using switched-opamp technique. To achieve double power efficiency while maintaining low sensitivity to finite opamp gain effects for the SC IF circuitry, half-delay integrator-based filters and /spl Sigma//spl Delta/ modulator have been proposed. The proposed quadrature IF circuitry employs a seventh-order IF filter for channel selection and a third-order /spl Sigma//spl Delta/ modulator for analog-to-digital conversion. A noise-shaping extension technique is employed to enhance the resolution of the low-pass /spl Sigma//spl Delta/ modulator by 16 dB while operating at the same oversampling ratio and power consumption. At a 1-V supply, the quadrature IF circuitry achieves a measured IIP3 of -3 dBm at a nominal gain of 24 dB with a 48-dB variable gain control while consuming a total power dissipation of 3.5 mW.     

A 6.5-GHz energy-efficient BFSK modulator for wireless sensor applications

A 6.5-GHz FSK modulator suitable for low power wireless sensor network is presented. The energy efficient modulator employs closed-loop direct VCO modulation to achieve high data rate, multistage variable loop bandwidth technique for fast startup time and /spl Sigma/-/spl Delta/ for reduced power consumption in the synthesizer with fine resolution in frequency channel selection. The modulator, implemented using 0.25-/spl mu/m CMOS, achieves 20-/spl mu/s startup time with an effective data rate of 2.5 Mb/s while consuming 22 mW.     

Design of a low-power 3.5-GHz broad-band CMOS transimpedance amplifier for optical transceivers

This paper describes a novel low-power low-noise CMOS voltage-current feedback transimpedance amplifier design using a low-cost Agilent 0.5-/spl mu/m 3M1P CMOS process technology. Theoretical foundations for this transimpedance amplifier by way of gain, bandwidth and noise analysis are developed. The bandwidth of the amplifier was extended using the inductive peaking technique, and, simulation results indicated a -3-dB bandwidth of 3.5 GHz with a transimpedance gain of /spl ap/60 dBohms. The dynamic range of the amplifier was wide enough to enable an output peak-to-peak voltage swing of around 400 mV for a test input current swing of 100 /spl mu/A. The output noise voltage spectral density was 12 nV//spl radic/Hz (with a peak of /spl ap/25 nV//spl radic/Hz), while the input-referred noise current spectral density was below 20 pA//spl radic/Hz within the amplifier frequency band. The amplifier consumes only around 5 mA from a 3.3-V power supply. A test chip implementing the transimpedance amplifier was also fabricated using the low-cost CMOS process.