Communication over an interference channel, which is fundamental and pervasive in the wireless and wireline environment, is often intended to carry information among different transmitter-receiver pairs. For applications that require time critical updates, it is desirable to maintain the freshness of the received information, which is quantified by the age metric (unlike the familiar delay metric). In this paper, we consider the case of two transmitter-receiver pairs, and address the impact of interference on information freshness by formulating a two-player “interference” game, in which each player is a transmitter desiring to maintain the freshness of the information updates it sends to its receiver. The strategy of a player is the choice of power level at which it will transmit. We then derive both Nash and Stackelberg strategies for the game. Our analysis shows that the Stackelberg strategy uses less power than the Nash strategy, and that it dominates the Nash strategy (i.e., the Stackelberg total cost function is lower than the Nash total cost function). Our obtained Nash and Stackelberg strategies are desirable user operating points in competitive situations.

We study the age of information, which is a measure of the freshness of a continually updated piece of information as observed at a remote monitor. The age of information metric has been studied for a variety of different queueing systems, and in this paper, we introduce a packet deadline as a control mechanism to study its impact on the average age of information for an M/M/1/2 queueing system. We analyze the system for the cases of a fixed deadline and a random exponential deadline and derive closed-form expressions for the average age. We also derive a closed-form expression for the optimal average deadline for the random exponential case. Our numerical results show the relationship of the age performance to that of the M/M/1/1 and M/M/1/2 systems, and we demonstrate that using a deadline can outperform both the M/M/1/1 and M/M/1/2 without deadline.

We propose a model for mobile caching in which the rate of requests for content is dependent on the popularity and the freshness of the information. We model popularity based on the history of requests and freshness based on the age of the content. We consider a discrete time (slotted) system in which new packets arrive at a limited capacity cache at discrete times. We prove that the optimal policy for choosing the set of packets to reside in a full cache when a packet arrives is to reject the one with the lowest request rate in that particular slot. Thus, there is no advantage to separately knowing the history of requests or the age of the content. Since the optimal policy depends on the profile of the request process, we also study the expected behavior of the request model. We provide a sufficient condition under which the change in the request rate goes to zero and provide some numerical examples that illustrate this behavior. We also consider a slight alteration to the model, in which only the recent history of requests is used for determining the request rate. In this case, we provide a sufficient condition for when the rate is equal to zero, which approximates the duration of requests for content.

For time critical updates, it is desirable to maintain the freshness of the received information. We address the impact of hostile interference on information freshness by formulating a non-zero-sum two-player game, in which one player is the transmitter aiming to maintain the freshness of the information updates it sends to its receiver, and the other player is the interferer aiming to prevent this. The strategy of a player is the power level transmitted by that player. We then derive the equilibria for both Nash and Stackelberg strategies. We show that both players have the same power cost at Nash equilibrium. In addition, the Stackelberg strategy dominates the Nash strategy, i.e., the Stackelberg utility function exceeds the Nash utility function.

We study the age of information, which is a recently introduced metric for measuring the freshness of a continually updated piece of information as observed at a remote monitor. The age of information metric has been studied for a variety of different queuing systems. In this work, we introduce a packet deadline as a control mechanism and study its impact on the average age of information for an M/M/1/2 queuing system. We analyze the system for a fixed deadline and derive a mathematical expression for the average age. We numerically evaluate the expression and show the relationship of the age performance to that of the M/M/1/1 and M/M/1/2 systems. We show that the system with a deadline constraint can outperform both the M/M/1/1 and M/M/1/2 without such a deadline.

We formulate the interaction between communication and hostile interference in wireless systems as a non-zero-sum two-player game. One player is the transmitter aiming to establish or maintain the communication to its receivers, and the other player is the interferer aiming to prevent or disrupt the communication. The strategy of the transmitter is a transmission power level, while the strategy of the interferer is an interfering power level. We provide closed-form equilibria for both Nash and Stackelberg models. We show that, while a Stackelberg equilibrium always exists, a Nash equilibrium exists only when the wireless channel is affected by fading. In addition, for the case of Rayleigh channel fading, we show that both players have the same power cost at Nash equilibrium.

This paper focuses on status age, which is a metric for measuring the freshness of a continually updated piece of information (i.e., status) as observed at a remote monitor. In paper, we study a system in which a sensor sends random status updates over a dynamic network to a monitor. For this system, we consider the impact of having messages take different routes through the network on the status age. First, we consider a network with plentiful resources (i.e., many nodes that can provide numerous alternate paths), so that packets need not wait in queues at each node in a multihop path. This system is modeled as a single queue with an infinite number of servers, specifically as an M/M/∞ queue. Packets routed over a dynamic network may arrive at the monitor out of order, which we account for in our analysis for the M/M/∞ model. We then consider a network with somewhat limited resources, so that packets can arrive out of order but also must wait in a queue. This is modeled as a single queue with two servers, specifically an M/M/2 queue. We present the exact approach to computing the analytical status age, and we provide an approximation that is shown to be close to the simulated age. We also compare both models with M/M/1, which corresponds to severely limited network resources, and we demonstrate the tradeoff between the status age and the unnecessary network resource consumption.

We consider a wireless network consisting of source-destination pairs, in which each source is required to transmit a given bit volume to its destination. The goal is for all the sources to transmit the given bit volumes, under a time constraint, so that the total transmission energy is minimized. Our approach is the joint optimization of link scheduling and power control for minimum energy. We show that TDMA scheduling is appropriate for this goal, in the sense that TDMA is asymptotically optimal when the time constraint approaches infinity. When the time constraint is strictly bounded, we show that TDMA is also optimal for the case of equal channel gains.

We study the energy-efficient transmission problem for a time-varying interference channel. Assume that each source transmits in each time slot according to a transmission probability, which is a continuous value between 0 and 1. Our goal is to determine the values of the transmission probabilities and the transmission power levels so that the network energy efficiency is maximized. We show that the energy efficiency is maximized when the transmission probabilities are either 0 or 1. We also show that simultaneous transmissions reduce energy efficiency. We then address the impact of the accuracy and timeliness of channel state information (CSI) on energy efficiency. The following cases are considered: perfect CSI, erroneous CSI, delayed CSI, and unknown CSI.

This paper addresses fundamental issues in a shared channel where the users have different priority levels. In particular, we study a two-user cognitive shared channel consisting of a primary (higher-priority) and a secondary user, operating in the cognitive underlay fashion, but in a novel way where interference suffered by the primary user is compensated by requiring the secondary user to cooperatively relay some of the primary's packets. We start by analyzing the case of no node cooperation, where nodes transmit their own packets to their respective destinations. We then extend the analysis to a system in which the secondary node acts as a relay for the primary user, in addition to serving its own packets. Specifically, in the cognitive cooperation case, the secondary node forwards those packets to the primary destination that it receives successfully from the primary source. In such cognitive shared channels, a tradeoff arises in terms of activating the secondary along with the primary so that both transmissions may be successful, but with a lower probability, compared to the case of the secondary node staying idle when the primary user transmits. Results show the benefits of relaying for both the primary as well as the secondary nodes in terms of the stable-throughput region.

We evaluate the throughput that can be achieved under BER constraints by combined use of transmission scheduling and multiuser detection. A schedule is a rule that specifies which subset of users is allowed to simultaneously transmit in a time slot. These subsets of overlapping transmissions, which can vary in different time slots of the transmission frame, are decoded by receivers equipped with multiuser detection. The goal is to find the largest such subsets under the requirement that each transmission satisfies a BER constraint. The joint problem of scheduling and multiuser-detection is highly complex in general. However, for certain class of multiuser detectors, the problem has efficient and optimal solution. By constructing transmission schedules that directly reflect the performance and exploit the capability of the multiuser detection receivers, as expected, multiuser detection-based scheduling significantly outperforms other methods such as TDMA and the conventional single-user detection-based scheduling.

In this work, we investigate the queue stability of a two-user cognitive radio system with multicast traffic. We study the impact of network-level cooperation, in which one of the nodes can relay the packets of the other user that are not received at the destinations. Under this approach, if a packet transmitted by the primary user is not successfully received by the destination set but is captured by the secondary source, then the secondary user assumes responsibility for completing the transmission of the packet; therefore, the primary releases it from its queue, enabling it to process the next packet. We demonstrate that the stability region of this cooperative approach is larger than that of the noncooperative approach, which translates into a benefit for both users of this multicast system. Our system model allows for the possibility of multipacket reception, and the optimal transmission strategies for different levels of multipacket reception capability are observed in our numerical results.

The underwater acoustic channel is characterized by a path loss that is dependent on both the distance and the frequency of communication. Given this dependence, it has been previously demonstrated that for a given communication distance, there is an optimal operating frequency, where conditions for signal propagation and noise are most favorable. In this work, we consider extending this optimal frequency concept to scenarios in which the frequencies that can be employed by the system are constrained. Such constraints are important considerations for practical system design. The first problem we study is to find a single frequency that minimizes the energy over a number of links of varying lengths. An approximate model for this frequency is proposed that is very close to the true optimal. We then generalize this problem to finding the best frequency band, within which the frequency can be tuned for different link lengths. We demonstrate how our model is applied to a 2-D network scenario. We simulate random node placement for such a network, and we observe that the optimal frequencies are very close to the proposed model.

In this paper, we consider the problem of calculating the stability region of a two-user cognitive shared channel where the secondary (lower priority) user, whose channel is modeled as a two-state Gilbert-Elliott channel, utilizes the channel state information to adapt its transmission probabilities accordingly. The analysis also takes into account the compound effects of multipacket reception at the receiver as well as the cooperative relaying capability of the secondary node, on the stability region of the cognitive network. Results clearly illustrate that the knowledge of the secondary channel state benefits not only the secondary user, but also the primary user as well.

This paper addresses fundamental issues in a shared channel where the users have different priority levels. In particular, we characterize the stable-throughput region in a two user cognitive shared channel where the primary (higher priority) user transmits whenever it has packets to transmit while the secondary (cognitive) node transmits its packets with probability p. Therefore, in this system, the secondary link is allowed to share the channel along with the primary link, in contrast to the traditional notion of cognitive radio, in which the secondary user is required to relinquish the channel as soon as the primary is detected. The analysis also takes into account the compound effects of multi-packet reception as well as of the relaying capability on the stability region of the network. We start by analyzing the non-cooperation case where nodes transmit their own packets to their respective destinations. We then extend the analysis to a system where the secondary node cooperatively relays some of the primary's packets. Specifically, in the cooperation case, the secondary node relays those packets that it receives successfully from the primary, but are not decoded properly by the primary destination. In such cognitive shared channels, a tradeoff arises in terms of activating the secondary along with the primary so that both transmissions may be successful, but with a lower probability, compared to the case of the secondary node staying idle when the primary user transmits. Results show the benefits of relaying for both the primary as well as the secondary nodes in terms of the stable-throughput region.

We study transmission strategies in a multiple-source, multiple-destination wireless network. Each source transmits packets that are intended for a particular destination. However, a transmitted packet can cause interference at other destinations. Our primary performance measure is throughput, which we define to be the average number of packets that are successfully received per intended destination per time slot. The sources are first divided into groups, based on the intended destination of their packets. In our parallel method, each group operates according to its own local protocol (e.g., TDMA), concurrently with and independently of the other groups. Our results show the impact of transmission schedules, channel fading, receiver noise, and other-user interference on network performance. We then show that, for given channel statistics and topology configurations, the network performance can be significantly improved when the groups in the network coordinate their transmissions according to an optimal schedule. Further, in many cases, even the use of randomly generated parallel schedules can provide considerably higher performance than traditional TDMA.

We study cellular-like wireless networks in which the cells may overlap substantially, and a common channel is used for all cells. Thus, transmissions intended for one destination (or base station) can cause interference at neighboring destinations. We assume the use of a ¿collision-channel¿ model, in which arbitrary communication and interference regions are associated with each destination. The interaction between such cells is best exemplified if the protocol of access in each cell is pure random access, i.e., Slotted Aloha. We derive a mathematical formula for the maximum achievable throughput for multiple-cell networks that satisfy a ¿balance¿ condition, which is related to (but not as stringent as) symmetry. This formula implies that the throughput achieved in a cell is affected only by the degree of overlap with adjacent cells, i.e., a cell's throughput is not affected by transmissions that are outside of its interference region. Moreover, we show that, at the point of maximum throughput, the expected channel traffic is one packet per slot in each cell, an extension of the result obtained many years ago for single-destination networks.

In this paper, we revisit the problem of determining the minimum-length schedule that satisfies certain traffic demands in a wireless network. Traditional approaches for the determination of minimum-length schedules are based on a collision channel model, in which neighboring transmissions cause destructive interference if and only if they are within the “interference region” of the receiving nodes. By contrast, we adopt here a more realistic model for the physical layer by requiring that a threshold be exceeded by the signal-to-interference-plus-noise ratio (SINR) for a transmission to be successful. We present a novel formulation of the problem that incorporates various power and rate adaptation schemes while seamlessly integrating the generation of “matchings” (i.e., sets of links that can be activated simultaneously) by taking into consideration the SINR constraints at the receivers. For the formulated problem, we propose a column-generation-based solution method and show that it theoretically converges to a globally optimal solution, with a potential advantage of not having to enumerate all the feasible matchings a priori. We also discuss the influence of power control, spatial reuse, and variable transmission rates on network performance. Furthermore, we include aspects of the routing problem and provide computational results for our proposed column-generation-based solution procedure.

CRCs have desirable properties for effective error detection. But their software implementation, which relies on many steps of the polynomial division, is typically slower than other codes such as weaker checksums. A relevant question is whether there are some particular CRCs that have fast implementation. In this paper, we introduce such fast CRCs as well as an effective technique to implement them. For these fast CRCs, even without using table lookup, it is possible either to eliminate or to greatly reduce many steps of the polynomial division during their computation.

We study power-based capture, under which a transmission is correctly decoded at the destination, even in the presence of other transmissions, if the received signal-to-interference-plus-noise ratio (SINR) exceeds a threshold bges0. Most previous studies have expressed throughput in terms of packets per slot as a function of b. However, since the value of b is a function of parameters such as data rate and the specified value of bit-error rate (BER), it is actually more appropriate to consider throughput in terms of bits per second per Hz at a specified value of BER. In this paper, we address the relationships between the throughput that can be achieved (using a specific modulation scheme and BER criterion) and the threshold value b.

Under power-based capture, a transmission is correctly decoded at the destination, even in the presence of other transmissions, if the received signal-to-interference-plus-noise ratio (SINR) exceeds a threshold b ges 0. Studies on capture are often limited to the case b ges 1. In this paper, we study capture for systems with arbitrary b ges 0, i.e., our formulation includes both wide-band (0 les 1) and narrow-band (b > 1) systems. We also point out some ambiguity from the existing literature on capture analysis

For original paper by Zorzi and Rao, see IEEE J. Sel. Areas Commun., vol.12, no.8, p.1289-98 (1994 October)

Most studies of wireless random-access systems have addressed single-destination networks (e.g., an isolated base station in a cellular network). Here, we consider networks with many users and multiple destinations, where omnidirectional antennas are used for communication over a common channel, and transmissions intended for one destination can interfere with those intended for others. Our previous work on such networks assumed a simplified model for the physical layer, under which communication and interference ranges were characterized by fixed values and capture was not possible. In this paper, we use a more-realistic threshold model for the physical layer, under which a packet is successfully received if its received signal strength is sufficiently greater than the combined power of all other packets transmitted in the same slot. We use simulation to evaluate the maximum throughput that can be achieved by Slotted Aloha for multiple-destination networks. Throughput performance results demonstrate the impact of the degree of overlap of these clusters, as well as the impact of capture

Binary CRCs are very effective for error detection, but their software implementation is not very efficient. Thus, many binary nonCRC codes (which are not as strong as CRCs, but can be more efficiently implemented in software) are proposed as alternatives to CRCs. The nonCRC codes include WSC, CXOR, one's-complement checksum, Fletcher checksum, and block-parity code. We present a general algorithm for constructing a family of binary error-detection codes. This family is large because it contains all these nonCRC codes, CRCs, perfect codes, as well as other linear and nonlinear codes. In addition to unifying these apparently disparate codes, our algorithm also generates some nonCRC codes that have minimum distance 4 (like CRCs) and efficient software implementation.

We consider ad hoc wireless networks that use directional antennas and have limited energy resources. The performance objectives of such networks depend largely on the application. However, a robust performance measure is the total traffic volume that the network can deliver when all nodes are equipped with a finite and non-renewable amount of energy. We show that the network's lifetime can be extended significantly by incorporating a simple measure of a node's residual energy into the node's cost function. To explore quantitatively the advantage offered by the use of directional antennas over the case of omnidirectional antennas, we consider the case of connection-oriented multicast traffic. Building upon our prior work on multicasting algorithms, we introduce two protocols that exploit the use of directional antennas and evaluate their performance. We observe significant improvement with respect to the omnidirectional case.

We take initial steps toward developing energy-efficient broadcast algorithms for ad hoc wireless networks that operate under changing connectivity conditions. Such algorithms need to be distributed. To be distributed these algorithms need to probe neighboring nodes to determine possible connectivities at different power levels. We proceed toward this goal by revisiting and modifying previously obtained broadcast algorithms that were centralized and in which the exact levels of minimally necessary RF power to reach neighboring nodes could be determined. Instead, we now constrain RF power to take values from a finite discrete set, and evaluate the impact on algorithm performance. We then discuss further modifications for distributed operation.

We consider ad hoc wireless networks that use directional antennas and have limited energy resources. To explore quantitatively the advantage offered by the use of directional antennas over the case of omnidirectional antennas, we consider the case of connection-oriented multicast traffic. Building upon our prior work on multicasting algorithms, we introduce two protocols that exploit the use of directional antennas and evaluate their performance, We observe significant improvement with respect to the omnidirectional case, in terms of both energy efficiency and network lifetime. Additionally, we show that further substantial increase in the network's lifetime can be achieved by incorporating a simple measure of a node's residual energy into the node's cost function.

The wireless networking environment presents formidable challenges to the study of broadcasting and multicasting problems. After addressing the characteristics of wireless networks that distinguish them from wired networks, we introduce and evaluate algorithms for tree construction in infrastructureless, all-wireless applications. The performance metric used to evaluate broadcast and multicast trees is energy-efficiency. We develop the broadcast incremental power algorithm, and adapt it to multicast operation as well. This algorithm exploits the broadcast nature of the wireless communication environment, and addresses the need for energy-efficient operation. We demonstrate that our algorithm provides better performance than algorithms that have been developed for the link-based, wired environment.

A queueing model with two finite-size buffers, a single constant rate server using a serving strategy based on buffer thresholds is studied. Exact relationships for buffer size, overflow probabilities, and queueing delay are obtained. The queueing model is very general, and an application in ATM switching is described. The results are presented in-graphs that are useful in selecting a threshold pair that satisfies certain constraints on delay and cell loss.>

Closed-form reliability functions for the dual homing configuration for the fiber distributed data interface (FDDI) are derived by the combinatorial method. The new reliability functions are then compared to that of the dual ring configuration via numerical examples, which show that in most cases the dual homing network is more reliable than the dual ring network. The model analysis also shows that dual homing is recommended only if certain network parameter constraints are met.