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.

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.

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.

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.

We consider a random-access-based ad hoc network, where different links use mini-slots to contend for the channel, and then successful links transmit data packets, as in CSMA. The focus of our study is to develop optimal strategies for physicallayer- aware (PHY-aware) distributed scheduling, which involves a joint process of channel probing and distributed scheduling. Because of channel fading and cochannel interference, the signalto- interference-plus-noise-ratio (SINR) across links is highly dynamic and can exhibit significant variation. In the low SINR case, further channel probing is likely to lead to better SINR conditions and hence yield higher throughput. The desired tradeoff boils down to judiciously choosing the optimal stopping strategy for channel probing before data transmissions. In this paper, we investigate PHY-aware distributed scheduling, aiming to maximize the overall network throughput. The problem under consideration is inherently challenging: 1) multiple links can transmit successfully simultaneously and the number of simultaneously transmitting links is random; and 2) the network throughput is the sum rate of all transmitting links, but each link involved in the transmission has no knowledge of the instantaneous rates of other links, and the stopping decision is made in a distributed manner based on local information only. We use optimal stopping theory to tackle this challenge, and show that the optimal policy for distributed scheduling has a threshold structure. Accordingly, after a channel probing, a link would proceed with data transmissions only if a function of its instantaneous rate is greater than the optimal rate threshold. Observing that the network throughput depends heavily on the contention probability of each link, we generalize the study to jointly optimize the rate threshold and the contention probability, and propose a two-stage algorithm for computing the pair of optimal rate threshold and contention probability by using fractional optimization and geometric programming.

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)

We consider a wireless ad hoc network where each node employs a single-beam directional antenna and is provisioned with limited energy. We are interested in an online multicast routing algorithm for successive multicast communication requests with the aim of maximizing network lifetime. The beamforming property associated with single-beam directional antenna introduces some unique problems that do not exist for omnidirectional antennas and therefore significantly increases the design space for routing algorithms. The contributions of this paper are twofold. First, we provide some important theoretical understanding on various multicast problems and deduce that even an offline version of this problem is NP-hard. Second, we develop a highly competitive online heuristic algorithm that takes network lifetime consideration directly into iterative calculations and show that an algorithm designed under this methodology provides consistently better performance than the current state-of-the-art algorithm that takes remaining energy into iterative calculations. The theoretical results and heuristic algorithm in this paper offer some important insights on algorithmic design for energy-constrained wireless ad hoc networks with directional antennas.

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

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.

We develop an approach to the analysis of average queueing delay in a tree network of discrete-time queues with constant service time. The analysis of such systems is pertinent to packet-switched data networks with fixed-length packets. Our solution is based on considering an equivalent network, in which at each node packets in transit are given priority over exogenous arrivals. The solution to the equivalent model is easily computed, and, hence, the solution to the original model can be obtained.

We address the problem of "link activation" or "scheduling" in multihop packet radio networks. The objective is to determine a conflict-free schedule of minimum length that satisfies the specified end-to-end communication requirements. It is well known that this problem, in almost all of its forms, is a combinatorial-optimization problem of high complexity. We approach this problem by the use of a Hopfield neural network model in which the method of Lagrange multipliers is used to vary dynamically the values of the coefficients used in the connection weights.>

Addresses the major issues associated with channel access in integrated wireless networks, and proposes and analyzes the "wireless integrated multiple access" (WIMA) protocol. This scheme is based on a mixture of boundary ideas for integration and of previously introduced protocols for wireless access, and is well suited to either satellite or to terrestrial networks. A two-dimensional first-order Markov chain model for this scheme is presented, and techniques that exploit the structural properties of this chain to simplify the evaluation of the equilibrium state, without sacrificing accuracy, are described. Analytical models for the evaluation of data-packet delay for both fixed- and movable-boundary versions of this protocol and for voice-call blocking probability are presented. Performance results illustrate the dependence of performance on system parameters, and demonstrate the improved performance that can be achieved through the use of the movable-boundary version.>

The authors study the voice-call admission control problem in integrated voice/data multihop radio networks. They develop an efficient simulation model based on the use of the standard clock (SC) approach, which permits the simultaneous simulation of a large number of admission-control policies, thereby reducing computation time significantly. They then demonstrate the effectiveness of ordinal-optimization techniques, which provide a remarkably good ranking of admission-control policies after relatively short simulation runs, thereby facilitating the rapid determination of good policies. Moreover, they demonstrate that the use of crude and inaccurate analytical and simulation models can provide highly accurate policy rankings that can be used in conjunction with ordinal-optimization methods, provided that they incorporate the key aspects of system operation.>

The issues of routing and scheduling the activation of links in packet radio networks are highly interdependent. The authors consider a form of the problem of routing for the minimization of congestion as a step toward the study of the joint routing-scheduling problem. They formulate this as a combinatorial-optimization problem, and they use Hopfield neural networks (NN) for its solution. The determination of the coefficients in the connection weights is the most critical issue in the design and simulation of Hopfield NN models. They use the method of Lagrange multipliers, which permits these coefficients to vary dynamically along with the evolution of the system state. Extensive software simulation results demonstrate the capability of their approach to determine good sets of routes in large heavily congested networks.>

Admission-control schemes for voice traffic in circuit-switched multihop radio networks are studied. The problem formulation is based on the methodology of multiple-service, multiple-resource (MSMR) modeling, and only those admission-control policies that yield a coordinate convex state space are considered. This restriction, in conjunction with reasonable modeling assumptions, results in a product-form stationary distribution for the system state. A recursive procedure to accelerate the evaluation of a large number of different admission-control policies and a descent-search method to minimize the number of policies that must be evaluated in searching for the optimal one are developed. Numerical examples indicate that performance can be improved by administering admission control, but the improvement is typically small unless different revenues or costs are associated with the various call types.>

The authors present a performance analysis of the wireless integrated multiple access (WIMA) protocol, which is well suited to either satellite or terrestrial networks. A two-dimensional first-order Markov chain model for this scheme is presented, and techniques that exploit the structural properties of this chain to simplify the evaluation of the equilibrium state, without sacrificing accuracy, are described. Analytical models for the evaluation of data-packet delay for both fixed- and movable-boundary versions of this protocol and for voiceband blocking probability are presented. Performance results illustrate the dependence of performance on system parameters, and demonstrate the improved performance that can be achieved through the use of the movable-boundary version.>

The problem of routing is addressed for the minimization of congestion as a first step toward the solution of the joint routing-scheduling problem in packet radio networks. This is formulated as a combinatorial-optimization problem, and a Hopfield neural network model is developed for its solution. The method of Lagrange multipliers is used, which permits these coefficients to vary dynamically along with the evolution of the system state. Extensive software simulation results demonstrate the ability of this approach to determine good sets of routes in large, heavily-congested networks.>

The authors introduce a class of protocols for integrated voice/data radio networks called the voice/data interleaved-frame fixed-length (VD-IFFL) protocols. The IFFL protocols, which are similar to the interleaved-frame flush-out (IFFO) protocols (a class of schemes developed for data-only applications), except that they have a fixed frame length, a desirable feature in voice communication, are discussed. The VD-IFFL protocols use a movable-boundary mechanism to share the channel between voice and data traffic. Voice traffic is handled on a reservation basis, while data traffic is handled using a hybrid IFFL scheme that combines reservation and contention. These protocols are characterized by infinite Markov chains, whose transition probabilities have been evaluated exactly.>

In frequency-hopped (FH) code-division multiple-access (CDMA) systems, a number of users can transmit their packets simultaneously by using quasi-orthogonal FH patterns (codes). In applications where time is unslotted, the symbol-error probability is not the same for each symbol because the number of interfering users varies throughout the packet duration. Packet-error probability for such systems is evaluated by first enumerating all possible interference states and then averaging the packet-error probability associated with each of these states. The use of Reed-Solomon error-control coding is assumed. The computational task for this evaluation is enormous. Therefore, upper bounds and an alternate less-detailed approximate model are developed for easier computation. This approximate model generates results that are very close to those obtained using the authors' first model (1988) for the cases in which those results are computable. The conclusions of this study confirm the observation, originally made elsewhere, that the widely used threshold-based model for other-user interference is not an accurate one.>

The authors present an exact analysis of framed ALOHA for the case of a finite number of users. This analysis, which is based on the use of a novel combinatorial technique, does not require any restrictive assumptions on channel traffic. This model can accommodate a general model for capture, in which the probability that one packet is received successfully depends on the number of packets involved in the collision. Performance results are presented for both uncontrolled and dynamically controlled systems.>

In some multiuser radio systems the receiver is not allowed to transmit feedback information to the senders. In other applications, the transmitters cannot receive feedback information sent by the receiver. For these cases, a multiple-access protocol is needed that maintains satisfactory performance in the absence of feedback. Such a protocol is introduced and an exact analysis and performance evaluation of it is provided. The protocol, which uses an unconventional reservation mechanism, exploits the capability of interference rejection that code-division multiple access (CDMA) provides.>

The design of a packet radio network must reflect the operational requirements and environmental constraints to which it is subject. In this paper, we outline those features that distinguish the High Frequency (HF) Intra Task Force (ITF) Network from other packet radio networks, and we present a design concept for this network that encompasses organizational structure, waveform design, and channel access. Network survivability is achieved through the use of distributed network control and frequency hopping spread-spectrum signaling. We demonstrate how the execution of the fully distributed Linked Cluster Algorithm can enable a network to reconfigure itself when it is affected by connectivity changes such as those resulting from jamming. Additional resistance against jamming is provided by frequency hopping, which leads naturally to the use of code division mutiple access (CDMA) techniques that permit the simultaneous successful transmission by several users. Distributed algorithms that exploit CDMA properties have been developed to schedule contention-free transmissions for much of the channel access in this network. Contention-based channel access protocols can also be implemented in conjunction with the Linked Cluster network structure. The design concept presented in this paper provides a high degree of survivability and flexibility, to accommodate changing environmental conditions and user demands.

In this paper we derive the probability of correct packet reception and the resulting channel throughput achievable in an asynchronous slow-frequency-hopped multiple user channel. Reed-Solomon coding is used to correct errors caused by other-user interference in an otherwise noiseless channel. We analyze and evaluate anM-ary FSK signaling scheme, which permits the discrimination against interfering signals that are present for a sufficiently small fraction of the hop duration, and results in substantial increases in channel throughput over previous models.