We are motivated by the need, in some applications, for impromptu or as-you-go deployment of wireless sensor networks. A person walks along a line, making link quality measurements with the previous relay at equally spaced locations, and deploys relays at some of these locations, so as to connect a sensor placed on the line with a sink at the start of the line. In this paper, we extend our earlier work on the problem (see [1]) to incorporate two new aspects: (i) inclusion of path outage in the deployment objective, and (ii) permitting the deployment agent to make measurements over several consecutive steps before selecting a placement location among them (which we call backtracking). We consider a light traffic regime, and formulate the problem as a Markov decision process. Placement algorithms are obtained for two cases: (i) the distance to the source is geometrically distributed with known mean, and (ii) the average cost per step case. We motivate the per-step cost function in terms of several known forwarding protocols for sleep-wake cycling wireless sensor networks. We obtain the structures of the optimal policies for the various formulations, and provide some sensitivity results about the policies and the optimal values. We then provide a numerical study of the algorithms, thus providing insights into the advantage of backtracking, and a comparison with simple heuristic placement policies.
In the framework of @cite_1 , the deployment agent can only move forward. In the present paper we introduce backtracking," which permits the deployment agent to compare the link qualities over several potential placement locations before deploying the relay at any one of them.
@cite_1
2952542244 2122027153 2336775896 1984466682 2097480027 2110916358 2153829573 1969099455 2154718413 135016661 2167353407 2070085078 2076773434 2086672759 2119948204 2152137554 2130343868 2791237814 1592266906 1498202041
We study the problem of optimal sequential ("as-you-go") deployment of wireless relay nodes as a person walks along a line of random length (with a known distribution). The objective is to create an impromptu multihop wireless network for connecting a packet source to be placed at the end of the line with a sink node located at the starting point, to operate in the light traffic regime. As the deployment person walks along the line from the sink towards the source, at every step, he measures the channel quality to one (or more) previously placed relays, and places the relay nodes based on these measurements, so as to minimize either the sum power or the maximum power from the source to the sink node in the resultant network, subject to a constraint on the expected number of relays placed. For each of these two objectives, two different relay selection strategies are considered: (i) each relay communicates with the sink via its immediate previous relay, (ii) the communication path can skip some of the deployed relays. With appropriate modeling assumptions, we formulate each of these problems as a Markov decision process (MDP). We provide the optimal policy structures for all these cases, and provide illustrations, via numerical results, for some typical parameters. Our work is motivated by impromptu (or ''as-you-go'') deployment of wireless relay nodes along a path, a need that arises in many situations. In this paper, the path is modeled as starting at the origin (where there is the data sink, e.g., the control center), and evolving randomly over a lattice in the positive quadrant. A person walks along the path deploying relay nodes as he goes. At each step, the path can, randomly, either continue in the same direction or take a turn, or come to an end, at which point a data source (e.g., a sensor) has to be placed, that will send packets to the data sink. A decision has to be made at each step whether or not to place a wireless relay node. Assuming that the packet generation rate by the source is very low, and simple link-by-link scheduling, we consider the problem of sequential relay placement so as to minimize the expectation of an end-to-end cost metric (a linear combination of the sum of convex hop costs and the number of relays placed). This impromptu relay placement problem is formulated as a total cost Markov decision process. First, we derive the optimal policy in terms of an optimal placement set and show that this set is characterized by a boundary (with respect to the position of the last placed relay) beyond which it is optimal to place the next relay. Next, based on a simpler one-step-look-ahead characterization of the optimal policy, we propose an algorithm which is proved to converge to the optimal placement set in a finite number of steps and which is faster than value iteration. We show by simulations that the distance threshold based heuristic, usually assumed in the literature, is close to the optimal, provided that the threshold distance is carefully chosen. In this paper, we investigate the potential benefits of deploying relays in outdoor millimeter-wave (mmWave) networks. We study the coverage probability from sources to a destination for such systems aided by relays. The sources and the relays are modeled as independent homogeneous Poisson point processes (PPPs). We present a relay modeling technique for mmWave networks considering blockages and compute the density of active relays that aid the transmission. Two relay selection techniques are discussed, namely best path selection and best relay selection. For the first technique, we provide a closed form expression for end-to-end signal-to-noise ratio (SNR) and compute the best random relay path in a mmWave network using order statistics. Moreover, the maximum end-to-end SNR of random relay paths is investigated asymptotically by using extreme value theory. For the second technique, we provide a closed form expression for the best relay node having the maximum path gain. Finally, we analyze the coverage probability and transmission capacity of the network and validate them with simulation results. Our results show that deploying relays in mmWave networks can increase the coverage probability and transmission capacity of such systems. The paper studies broadcasting in radio networks whose stations are represented by points in the Euclidean plane. In any given time step, a station can either receive or transmit. A message transmitted from station (v) is delivered to every station (u) at distance at most (1) from (v), but (u) successfully hears the message if and only if (v) is the only station at distance at most (1) from (u) that transmitted in this time step. A designated source station has a message that should be disseminated throughout the network. All stations other than the source are initially idle and wake up upon the first time they hear the source message. It is shown in [11] that the time complexity of broadcasting depends on two parameters of the network, namely, its diameter (in hops) (D) and a lower bound (d) on the Euclidean distance between any two stations. The inverse of (d) is called the granularity of the network, denoted by (g). Specifically, the authors of [11] present a broadcasting algorithm that works in time (O (D g)) and prove that every broadcasting algorithm requires Ω (D √g) time. In this paper, we distinguish between the arbitrary deployment setting, originally studied in [11], in which stations can be placed everywhere in the plane, and the new grid deployment setting, in which stations are only allowed to be placed on a (d)-spaced grid. Does the latter (more restricted) setting provides any speedup in broadcasting time complexity? Although the (O (D g)) broadcasting algorithm of [11] works under the (original) arbitrary deployment setting, it turns out that the Ω (D √g) lower bound remains valid under the grid deployment setting. Still, the above question is left unanswered. The current paper answers this question affirmatively by presenting a provable separation between the two deployment settings. We establish a tight lower bound on the time complexity of broadcasting under the arbitrary deployment setting proving that broadcasting cannot be completed in less than Ω ( D √g) time. For the grid deployment setting, we develop a broadcasting algorithm that runs in time O ( D g5 6 log g), thus breaking the linear dependency on (g). We consider the communication scenario where a source-destination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. For this scenario, an interesting question is whether the relay node should be deployed at all. That is, whether cooperation with an untrusted relay node can ever be beneficial. We first provide an achievable secrecy rate for the general untrusted relay channel, and proceed to investigate this question for two types of relay networks with orthogonal components. For the first model, there is an orthogonal link from the source to the relay. For the second model, there is an orthogonal link from the relay to the destination. For the first model, we find the equivocation capacity region and show that answer is negative. In contrast, for the second model, we find that the answer is positive. Specifically, we show, by means of the achievable secrecy rate based on compress-and-forward, that by asking the untrusted relay node to relay information, we can achieve a higher secrecy rate than just treating the relay as an eavesdropper. For a special class of the second model, where the relay is not interfering itself, we derive an upper bound for the secrecy rate using an argument whose net effect is to separate the eavesdropper from the relay. The merit of the new upper bound is demonstrated on two channels that belong to this special class. The Gaussian case of the second model mentioned above benefits from this approach in that the new upper bound improves the previously known bounds. For the Cover-Kim deterministic relay channel, the new upper bound finds the secrecy capacity when the source-destination link is not worse than the source-relay link, by matching with achievable rate we present. Dealing with network failures effectively is a major operational challenge for Internet service providers. Commonly deployed link state routing protocols such as OSPF react to link failures through global (i.e., network-wide) link state advertisements and routing table recomputations, causing significant forwarding discontinuity after a failure. The drawback with these protocols is that they need to trade off routing stability and forwarding continuity. To improve failure resiliency without jeopardizing routing stability, we propose a proactive local rerouting based approach called failure insensitive routing (FIR). The proposed approach prepares for failures using interface-specific forwarding, and upon a failure, suppresses the link state advertisement and instead triggers local rerouting using a backwarding table. In this paper, we prove that when no more than one link failure notification is suppressed, FIR always finds a loop-free path to a destination if one such path exists. We also formally analyze routing stability and network availability under both proactive and reactive approaches, and show that FIR provides better stability and availability than OSPF. The paper investigates the effect of link delays on the capacity of relay networks. The relay-with-delay is defined as a relay channel with relay encoding delay d isin Z of units, or equivalently, a delay of units on the link from the sender to the relay, zero delay on the links from the transmitter to the receiver and from the relay to the receiver, and zero relay encoding delay. Two special cases are studied. The first is the relay-with-unlimited look-ahead, where each relay transmission can depend on its entire received sequence, and the second is the relay-without-delay, where the relay transmission can depend only on current and past received symbols, i.e., d=0. Upper and lower bounds on capacity for these two channels that are tight in some cases are presented. It is shown that the cut-set bound for the classical relay channel, corresponding to the case where d=1, does not hold for the relay-without-delay. Further, it is shown that instantaneous relaying can be optimal and can achieve higher rates than the classical cut-set bound. Capacity for the classes of degraded and semi-deterministic relay-with-unlimited-look-ahead and relay-without-delay are established. These results are then extended to the additive white Gaussian noise (AWGN) relay-with-delay case, where it is shown that for any dles0, capacity is achieved using amplify-and-forward when the channel from the sender to the relay is sufficiently weaker than the other two channels. In addition, it is shown that a superposition of amplify-and-forward and decode-and-forward can achieve higher rates than the classical cut-set bound. The relay-with-delay model is then extended to feedforward relay networks. It is shown that capacity is determined only by the relative delays of paths from the sender to the receiver and not by their absolute delays. A new cut-set upper bound that generalizes both the classical cut-set bound for the classical relay and the upper bound for the relay-without-delay on capacity is established. We consider two variants of the task of spreading a swarm of agents uniformly on a ring graph. Ant-like oblivious agents having limited capabilities are considered. The agents are assumed to have little memory, they all execute the same algorithm and no direct communication is allowed between them. Furthermore, the agents do not possess any global information. In particular, the size of the ring (n) and the number of agents in the swarm (k) are unknown to them. The agents are assumed to operate on an unweighted ring graph. Every agent can measure the distance to his two neighbors on the ring, up to a limited range of V edges. The first task considered, is dynamical (i.e. in motion) uniform deployment on the ring. We show that if either the ring is unoriented, or the visibility range is less than @?n [email protected]?, this is an impossible mission for the agents. Then, for an oriented ring and V>[email protected]?n [email protected]?, we propose an algorithm which achieves the deployment task in optimal time. The second task discussed, called quiescent spread, requires the agents to spread uniformly over the ring and stop moving. We prove that under our model, in which every agent can measure the distance only to his two neighbors, this task is impossible. Subsequently, we propose an algorithm which achieves quiescent but only almost uniform spread. The algorithms we present are scalable and robust. In case the environment (the size of the ring) or the number of agents changes during the run, the swarm adapts and re-deploys without requiring any outside interference. This paper studies a deployment problem for a group of robots where individual agents operate with outdated information about each other's locations. Our objective is to understand to what extent outdated information is still useful and at which point it becomes essential to obtain new, up-to-date information. We propose a self-triggered coordination algorithm based on spatial partitioning techniques with uncertain information. We analyze its correctness in synchronous and asynchronous scenarios, and establish the same convergence guarantees that a synchronous algorithm with perfect information at all times would achieve. The technical approach combines computational geometry, set-valued stability analysis, and event-based systems. We study the problem of exploration by a mobile entity (agent) of a class of dynamic networks, namely the periodically-varying graphs (the PV-graphs, modeling public transportation systems, among others). These are defined by a set of carriers following infinitely their prescribed route along the stations of the network. Flocchini, Mans, and Santoro [FMS09] (ISAAC 2009) studied this problem in the case when the agent must always travel on the carriers and thus cannot wait on a station. They described the necessary and sufficient conditions for the problem to be solvable and proved that the optimal number of steps (and thus of moves) to explore a n-node PV-graph of k carriers and maximal period p is in Θ(k·p2) in the general case. In this paper, we study the impact of the ability to wait at the stations. We exhibit the necessary and sufficient conditions for the problem to be solvable in this context, and we prove that waiting at the stations allows the agent to reduce the worst-case optimal number of moves by a multiplicative factor of at least Θ(p), while the time complexity is reduced to Θ(n·p). (In any connected PV-graph, we have n≤k·p.) We also show some complementary optimal results in specific cases (same period for all carriers, highly connected PV-graphs). Finally this new ability allows the agent to completely map the PV-graph, in addition to just explore it. The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set. We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be beneficial in our setup that the informed source uses a part of its power to partially cancel the effect of the interference so that the uninformed relay benefits from this cancellation, and so the source benefits in turn. We consider spatial stochastic models of downlink heterogeneous cellular networks (HCNs) with multiple tiers, where the base stations (BSs) of each tier have a particular spatial density, transmission power and path-loss exponent. Prior works on such spatial models of HCNs assume, due to its tractability, that the BSs are deployed according to homogeneous Poisson point processes. This means that the BSs are located independently of each other and their spatial correlation is ignored. In the current paper, we propose two spatial models for the analysis of downlink HCNs, in which the BSs are deployed according to @a-Ginibre point processes. The @a-Ginibre point processes constitute a class of determinantal point processes and account for the repulsion between the BSs. Besides, the degree of repulsion is adjustable according to the value of @[email protected]?(0,1]. In one proposed model, the BSs of different tiers are deployed according to mutually independent @a-Ginibre processes, where the @a can take different values for the different tiers. In the other model, all the BSs are deployed according to an @a-Ginibre point process and they are classified into multiple tiers by mutually independent marks. For these proposed models, we derive computable representations for the coverage probability of a typical user-the probability that the downlink signal-to-interference-plus-noise ratio for the typical user achieves a target threshold. We exhibit the results of some numerical experiments and compare the proposed models and the Poisson based model. In this paper, we focus on the Markov model of IEEE 802.11 distributed coordination function with power saving mode. The throughput evaluation is based on the model, with the comparison with the simulation result for validation. Furthermore, we notice that after each beacon transmission, there're more stations in contention than usual. Excessive contention results in high collision probability and low throughput. To solve this problem, we propose a downlink access scheme which can be used in both the basic access scheme and the access scheme with RTS CTS. This novel scheme enables AP to constrain the number of stations in contention to be an optimal value. Simulation results prove the performance improvement declared. The proposed scheme can be extended for multi-rate or multi-service WLANs. In this paper we propose a novel relay selection method for cooperation communication networks using fuzzy logic. Many efforts have been made in the literature to select the superior relay based on relay's SNR SER and or relay's reputation (in cooperation stimulation methods). We jointly consider four criteria for the process of relay selection, relay's SNR SER, relay's reputation, relaying strategy and relay location. We consider the condition in which network users employ different relaying strategies, i.e., some relay nodes employ decode-and-forward strategy, some nodes employ amplify-and-forward strategy, and the other ones employ compress-and-forward strategy. Also, we categorize the network users into LM clusters and take into account the relative distance of potential relay nodes from the source and destination nodes in the process of relay selection. This relative distance has significant impact on the average achievable rate in destination node. Finally, by using a fuzzy logic decision making method, we select the “best relay” based on these four criteria. In this paper, we consider a discrete memoryless state-dependent relay channel with non-causal Channel State Information (CSI). We investigate three different cases in which perfect channel states can be known non-causally: i) only to the source, ii) only to the relay or iii) both to the source and to the relay node. For these three cases we establish lower bounds on the channel capacity (achievable rates) based on using Gel'fand-Pinsker coding at the nodes where the CSI is available and using Compress-and-Forward (CF) strategy at the relay. Furthermore, for the general Gaussian relay channel with additive independent and identically distributed (i.i.d) states and noise, we obtain lower bounds on the capacity for the cases in which CSI is available at the source or at the relay. We also compare our derived bounds with the previously obtained results which were based on Decode-and-Forward (DF) strategy, and we show the cases in which our derived lower bounds outperform DF based bounds, and can achieve the rates close to the upper bound. In this paper a novel approach to the problem of decentralized agreement toward a common point in space in a multi-agent system is proposed. Our method allows the agents to agree on the relative location of the network centroid respect to themselves, on a common reference frame and therefore on a common heading. Using this information a global positioning system for the agents using only local measurements can be achieved. In the proposed scenario, an agent is able to sense the distance between itself and its neighbors and the direction in which it sees its neighbors with respect to its local reference frame. Furthermore only point-to-point asynchronous communications between neighboring agents are allowed thus achieving robustness against random communication failures. The proposed algorithms can be thought as general tools to locally retrieve global information usually not available to the agents. The integration of wireless power transfer (WPT) with the low-power backscatter communications provides a promising way to sustain battery-less wireless networks. In this paper, we consider a backscatter communication network wirelessly powered by a power beacon station (PBS). Each backscatter radio uses the harvested energy to power its data transmissions, in which some other radios can help as the wireless relays with an aim to improve throughput performance by cooperative transmission. Under this setting, we formulate a throughput maximization problem to jointly optimize WPT and the relay strategy of the backscatter radios. An iterative algorithm with reduced complexity and communication overhead is proposed to decompose the original problem into two sub-problems distributed at the PBS and the backscatter receiver. Moreover, we take uncertain channel information into consideration and formulate robust counter-parts of the throughput maximization problem when either the backscatter or relay channel is subject to estimation errors. The difficulty of the robust counter-part lies in the coupling of the PBS’ power allocation and relay strategy in matrix inequalities, which is addressed by alternating optimization with guaranteed convergence. Numerical results reveal that the cooperative relay strategy of the backscatter radios significantly improves the throughput performance. In this paper we study efficient rendezvous of two mobile agents moving asynchronously in the Euclidean 2d-space. Each agent has limited visibility, permitting it to see its neighborhood at unit range from its current location. Moreover, it is assumed that each agent knows its own initial position in the plane given by its coordinates. The agents, however, are not aware of each others position. The agents possess coherent compasses and the same unit of length, which permit them to consider their current positions within the same system of coordinates. The cost of the rendezvous algorithm is the sum of lengths of the trajectories of both agents. This cost is taken as the maximum over all possible asynchronous movements of the agents, controlled by the adversary. We propose an algorithm that allows the agents to meet in a local neighborhood of diameter O(d), where d is the original distance between the agents. This seems rather surprising since each agent is unaware of the possible location of the other agent. In fact, the cost of our algorithm is O(d2+e), for any constant e > 0. This is almost optimal, since a lower bound of Ω(d2) is straightforward. The only up to date paper [12] on asynchronous rendezvous of bounded-visibility agents in the plane provides the feasibility proof for rendezvous, proposing a solution exponential in the distance d and in the labels of the agents. In contrast, we show here that, when the identity of the agent is based solely on its original location, an almost optimal solution is possible. An integral component of our solution is the construction of a novel type of non-simple space-filling curves that preserve locality. An infinite curve of this type visits specific grid points in the plane and provides a route that can be adopted by the mobile agents in search for one another. This new concept may also appear counter-intuitive in view of the result from [22] stating that for any simple space-filling curve, there always exists a pair of close points in the plane, such that their distance along the space-filling curve is arbitrarily large. We study rendezvous of two anonymous agents, where each agent knows its own initial position in the environment. Their task is to meet each other as quickly as possible. The time of the rendezvous is measured by the number of synchronous rounds that agents need to use in the worst case in order to meet. In each round, an agent may make a simple move or it may stay motionless. We consider two types of environments, finite or infinite graphs and Euclidean spaces. A simple move traverses a single edge (in a graph) or at most a unit distance (in Euclidean space). The rendezvous consists in visiting by both agents the same point of the environment simultaneously (in the same round). In this paper, we propose several asymptotically optimal rendezvous algorithms. In particular, we show that in the line and trees as well as in multidimensional Euclidean spaces and grids the agents can rendezvous in time O(d), where d is the distance between the initial positions of the agents. The problem of location-aware rendezvous was studied before in the asynchronous model for Euclidean spaces and multi-dimensional grids, where the emphasis was on the length of the adopted rendezvous trajectory. We point out that, contrary to the asynchronous case, where the cost of rendezvous is dominated by the size of potentially large neighborhoods, the agents are able to meet in all graphs of at most n nodes in time almost linear in d, namely, O(d log2 n). We also determine an infinite family of graphs in which synchronized rendezvous takes time Ω(d).