In status update systems, multiple features carried by the status updating process require pursuit of objectives beyond timeliness measured by the age of information of updates. We consider such a problem where the transmitter sends status update messages through a noiseless binary energy harvesting channel that is equivalent to a timing channel. The transmitter aims to amplify or mask the energy state information that is carried in the updating process. The receiver extracts encoded information, infers the energy state sequence while maintaining timeliness of status updates. Consequently, the timings of the updates must be designed to control the message rate, the energy state uncertainty, and the age of information. We investigate this three-way trade-off between the achievable rate, the reduction in energy arrival state uncertainty, and the age of information, for zero and infinite battery cases.

We consider an intermittent status updating problem where updates arrive randomly. An energy harvesting node performs non-preemptive sensing/computing (S/C) to generate a status update when an arrival occurs. The node subsequently chooses to either transmit (Tx) or wait for another update to generate a new one. The S/C time for each update is independent with a general distribution. S/C and Tx operations each cost a single energy unit. The transmitter has a data buffer to save the latest update and a single transmitter where Tx time is independent general distributed. Any update arriving in Tx stage is discarded. We focus on one unit battery and infinite battery; and we show that average peak age of information (AoI) at the receiver is minimized by a threshold-based policy that allows only young packets to be transmitted. Our numerical results provide average peak AoI performance comparisons.

A combination of mobile edge computing (MEC) and cloud computing paradigms has the potential to greatly alleviate the challenges facing Internet of Things (IoT). We consider a tiered IoT infrastructure in which data generated by an IoT sensor/device is delivered to a data center for processing through an intermediate MEC server. The MEC server can either directly transmit the data to the data center or pre-process the data and then transmit it to the data center over a shared channel. The goal is to maintain the freshness of the data delivered to the data center. In this paper, we assume a probabilistic model for pre-processing by the MEC server. Sensor data is assumed to be generated as a Poisson process and the transmission times over the two paths are assumed to have general distributions.We use Age of Information (AoI) as a measure of data freshness at the data center. We perform stationary distribution analysis in this system and obtain closed form expressions for average AoI and average peak AoI. We focus on selecting the offloading probabilities in conjunction with the mean service times for each server for optimal operation determined by average AoI and peak AoI. Our numerical results show the effect of path diversity in the selection of best offloading probability and service times.

Edge computing applications typically require generated data to be preprocessed at the source and then transmitted to an edge server. In such cases, transmission time and preprocessing time are coupled, yielding a tradeoff between them to achieve the targeted objective. This paper presents analysis of such a system with the objective of optimizing freshness of received data at the edge server. We model this system as two queues in tandem whose service times are independent but the transmission service time is monotonically dependent on the computation service time in mean value. This dependence captures the natural decrease in transmission time due to lower offloaded computation. We analyze various queue management schemes in this tandem queue where the compute queue has a single server, Poisson packet arrivals, general independent service and no extra buffer to save incoming packets. The transmit queue has a single server receiving packets from the compute queue with memoryless service time. We consider the transmit queue in two forms: (i) No data buffer and (ii) One unit data buffer and last come first serve with discarding. We analyze various non-preemptive as well as preemptive cases. We perform stationary distribution analysis and obtain closed form expressions for average age of information (AoI) and average peak AoI. Our numerical results illustrate analytical findings on how computation and transmission times could be traded off to optimize AoI and reveal a consequent tradeoff between average AoI and average peak AoI.

We consider a novel intermittent status updating model motivated by intermittent operations in energy harvesting nodes. In particular, we consider status updating through non-preemptive sensing and transmission operations, each costing a single energy recharge of the node. The sensing time for each update is independent with a general distribution. The transmission queue has a single server receiving packets generated after sensing operation, general service time distribution and a single data buffer to save the latest arriving update packet. Once energy is harvested, the node has to decide whether to activate sensing to generate a new update or transmission to send the existing update (if any) to the receiver. We prove that average peak age of information (AoI) at the receiver is minimized by a threshold-based stopping rule that accepts only young packets to the transmission server. We then use this result to address average AoI optimization over the considered stopping rules through novel hybrid waiting and thresholding schemes. Our numerical results show the improvements in average AoI maintained by hybrid schemes.

Motivated by the inherent value of packets arising in many cyber-physical applications (e.g., due to precision of the information content or an alarm message), we consider status update systems with update packets carrying values as well as their generation time stamps. Once generated, a status update packet has a random initial value and a deterministic deadline after which it is not useful (ultimate staleness). In our model, value of a packet decreases in time (even after reception) starting from its generation to ultimate staleness when it vanishes. The value of information (VoI) at the receiver is additive in that the VoI is the sum of the current values of all packets held by the receiver. We investigate various queuing disciplines under potential dependence between value and service time and provide closed form expressions for average VoI at the receiver. Numerical results illustrate the average VoI for different scenarios and the contrast between average age of information (AoI) and average VoI.

In this paper, we explore the potential of server waiting before packet transmission in improving the Age of Information (AoI) in status update systems. We consider a non-preemptive queue with Poisson arrivals and independent general service distribution and we incorporate waiting before serving in two packet management schemes: M/GI/1/1 and M/GI/1/2*. In M/GI/1/1 there is no data buffer and a packet is taken to server only when it is idle whereas in M/GI/1/2* there is a single unit buffer that captures the latest arriving status update packet. In both schemes, we introduce “server waiting”: In M/GI/1/1 scheme, the server waits for a deterministic time immediately after a packet enters the server. In M/GI/1/2* scheme, depending on queue state, the server waits for a deterministic time before starting service. In both cases, if a newer arrival is captured, existing packet is discarded with no reset of the waiting period. Different from most existing works, we analyze AoI evolution by indexing the incoming packets, which is enabled by an alternative method of partitioning the area under the evolution of instantaneous AoI to calculate its time average. We obtain expressions for average AoI and average peak AoI for both queueing disciplines with waiting. Our numerical results demonstrate that waiting before service can bring significant improvement in average age, particularly, for heavy-tailed service distributions. This improvement comes at the expense of an increase in average peak AoI. We highlight the trade-off between average and average peak AoI generated by waiting before serving.

In this paper, we introduce a new data freshness metric, relative Age of Information (rAoI), and examine it in a single server system with various packet management schemes. The (classical) AoI metric was introduced to measure the end to end freshness of status updates at the receiver with respect to their generation at the source. In order to understand the efficiency of the update delivery system in isolation, we introduce rAoI metric to measure how fresh the data is at the receiver with respect to the data at the transmitter. This metric introduces an explicit dependence on the arrival process in the evaluation of age. We investigate several queuing disciplines and provide closed form expressions for rAoI and numerical comparisons.

This paper is motivated by emerging edge computing applications in which generated data are preprocessed at the source and then transmitted to an edge server. In such a scenario, there is typically a tradeoff between the amount of pre-processing and the amount of data to be transmitted. We model such a system by considering two non-preemptive queues in tandem whose service times are independent over time but the transmission service time is dependent on the computation service time in mean value. The first queue is in M/GI/1/1 form with a single server, memoryless exponential arrivals, general independent service and no extra buffer to save incoming status update packets. The second queue is in GI/M/1/2*form with a single server receiving packets from the first queue, memoryless service and a single data buffer to save incoming packets. Additionally, mean service times of the first and second queues are dependent through a deterministic monotonic function. We perform stationary distribution analysis in this system and obtain closed form expressions for average age of information (AoI) and average peak AoI. Our numerical results illustrate the analytical findings and highlight the tradeoff between average AoI and average peak AoI generated by the tandem nature of the queueing system with dependent service times.

We consider an energy harvesting transmitter sending status updates regarding a physical phenomenon it observes to a receiver. Different from the existing literature, we consider a scenario where the status updates carry information about an independent message. The transmitter encodes this message into the timings of the status updates. The receiver needs to extract this encoded information, as well as update the status of the observed phenomenon. The timings of the status updates, therefore, determine both the age of information (AoI) and the message rate (rate). We study the tradeoff between the achievable message rate and the achievable average AoI. We propose several achievable schemes and compare their rate-AoI performances.

We consider a two-user energy harvesting multiple access channel where the temperatures of the nodes are affected by the electromagnetic waves caused by the data transmission. To protect the nodes from excess heat, power allocation policies should take into consideration the temperature of all the nodes. In this paper, we study the optimal power allocations when the temperatures of the nodes are subject to peak temperature constraints. We first study the general case where each node has a different peak temperature requirement and the nodes have different temperature parameters. For this case, we show that the capacity region of the single energy arrival case is a single pentagon. We also show that the optimal policy for the multiple energy arrivals can be obtained by using generalized water-filling. We then study the temperature limited case where the transmitters have abundant energy and the only binding constraints are the temperature constraints. We study the optimal power allocation in this case and we derive sufficient conditions under which the rate region collapses to a single pentagon.

With a motivation to understand the effects of temperature sensitivity on wireless data transmission performance, we consider an energy harvesting communication system, where the temperature dynamics are governed by the transmission power policy. Different from the previous work, we consider a discrete time system where transmission power is kept constant in each slot. We consider two models that capture different effects of temperature. In the first model, the temperature is constrained to be below a critical temperature at all time instants; we coin this the explicit temperature constrained model. We investigate throughput optimal power allocation for multiple energy arrivals under general, as well as temperature and energy limited regimes. We show that the optimal power allocation for the temperature limited case is monotone decreasing. In the second model, we consider the effect of the temperature on the channel quality via its influence on additive noise power; we coin this the implicit temperature constrained model. In this model, the change in the variance of the additive noise due to previous transmissions is non-negligible. In particular, transmitted signals contribute as interference for all subsequent slots and thus affect the signal to interference plus noise ratio (SINR). In this case, we investigate throughput optimal power allocation under general, as well as low and high SINR regimes. We show in the low SINR regime that the optimal allocation dictates the transmitter to save its harvested energy till the last slot. In the high SINR regime, we show that the optimal power sequence is monotone increasing. Finally, we consider the case in which implicit and explicit temperature constraints are simultaneously active and we show under certain conditions that the optimal power sequence is monotone decreasing.

We consider an energy harvesting communication system where the temperature dynamics is governed by the transmission power policy. Different from the previous work, we consider a discrete time system where transmission power is kept constant in each slot. We consider two models that capture different effects of temperature. In the first model, the temperature is constrained to be below a critical temperature at all time instants; we coin this model as explicit temperature constraint model. We investigate throughput optimal power allocation for multiple energy arrivals under general, as well as temperature and energy limited regimes. In the second model, we consider the effect of the temperature on the channel quality; we coin this model as implicit temperature constraint model. As the dynamic range of the temperature changes significantly, the change in the thermal noise becomes non-negligible, affecting the signal to interference plus noise ratio (SINR). In effect, transmitted signals contribute as interference for all subsequent slots. In this case, we investigate throughput optimal power allocation under general, as well as low and high SINR regimes.

Temperature constraints arise naturally in communication scenarios where the act of data transmission causes heat dissipation. We address this problem in point to point communications over an additive white Gaussian noise channel in an information theoretic setting. In the specific scenario, transmitted code symbols cause heat dissipation as an input to a first order discrete time heat circuit and the output of this dynamical system, being the temperature, has to remain below a critical level Tc. Additionally, we allow the transmitter to use an energy harvesting device to power its transmission. We investigate channel capacity for various combinations of peak and average temperature, average power, and energy harvesting constraints on the transmitted code symbols.

We consider a binary energy harvesting communication channel with a finite-sized battery at the transmitter. In this model, the channel input is constrained by the available energy at each channel use, which is driven by an external energy harvesting process, the size of the battery, and the previous channel inputs. We consider an abstraction where energy is harvested in binary units and stored in a battery with the capacity of a single unit, and the channel inputs are binary. Viewing the available energy in the battery as a state, this is a state-dependent channel with input-dependent states, memory in the states, and causal state information available at the transmitter only. We find an equivalent representation for this channel based on the timings of the symbols, and determine the capacity of the resulting equivalent timing channel via an auxiliary random variable. We present achievable rates based on certain selections of this auxiliary random variable, which resemble lattice coding for the timing channel. We develop upper bounds for the capacity by using a genie-aided method, and also by quantifying the leakage of the state information to the receiver. We show that the proposed achievable rates are asymptotically capacity achieving for small energy harvesting rates. We extend the results to the case of ternary channel inputs. We numerically observe that our achievable rates are notably close to the upper bounds, and outperform basic Shannon strategies that only consider instantaneous battery states, for all parameter values.

We consider the delay minimization problem in an energy harvesting communication network with energy cooperation. In this network, nodes harvest energy from nature to sustain the power needed for data transmission, and may transfer a portion of their harvested energies to neighboring nodes through energy cooperation. For fixed data and energy routing topologies, we determine the optimum data rates, transmit powers, and energy transfers, subject to flow and energy conservation constraints, to minimize the network delay. We start with a simplified problem where data flows are fixed and optimize energy management at each node for the case of a single energy harvest per node. This is tantamount to distributing each node's available energy over its outgoing data links and energy transfers to neighboring nodes. For this case, with no energy cooperation, we show that each node should allocate more power to links with more noise and/or more data flow. In addition, when there is energy cooperation, our numerical results indicate that the energy is routed from nodes with lower data loads to nodes with higher data loads. We then extend this setting to the case of multiple energy harvests per node over time. In this case, we optimize each node's energy management over its outgoing data links and its energy transfers to neighboring nodes, over multiple time slots. For this case, with no energy cooperation, we show that, for any given node, the sum of powers on the outgoing links over time is equal to the single-link optimal power over time. Finally, we consider the problem of joint flow control and energy management for the entire network. We determine the necessary conditions for joint optimality of a power control, energy transfer, and routing policy. We provide an iterative algorithm that updates the data flows, energy flows, and power distribution over outgoing data links sequentially. We show that this algorithm converges to a Pareto-optimal operating point.

Motivated by the damage due to heating in sensor operation, we consider the throughput optimal offline data scheduling problem in an energy harvesting transmitter, such that the resulting temperature remains below a critical level. We model the temperature dynamics of the transmitter as a linear system and determine the optimal transmit power policy under such temperature constraints as well as energy harvesting constraints over an additive white Gaussian noise channel. We first derive the structural properties of the solution for the general case with multiple energy arrivals. We show that the optimal power policy is piecewise monotone decreasing with possible jumps at the energy harvesting instants. We derive analytical expressions for the optimal solution in the single energy arrival case. We show that, in the single energy arrival case, the optimal power is monotone decreasing, the resulting temperature is monotone increasing, and both remain constant after the temperature hits the critical level. We then generalize the solution for the multiple energy arrival case.

A noiseless binary energy harvesting channel with on-off fading is considered. When causal fading state information is available at the transmitter only, an equivalent timing channel with additive geometric noise and noise information known at the transmitter is obtained. In this channel, the transmitter's strategy is a stopping rule with respect to the channel fade levels given the message and the additive noise. Next, capacity when energy arrival information is available at the receiver and capacity when both energy arrival and fading information are available at the receiver are obtained. Additionally, several achievable schemes are proposed and evaluated.

Motivated by damage due to heating in sensor operation, we consider the throughput optimal offline data scheduling problem in an energy harvesting transmitter such that resulting temperature increase remains below a critical level. We model the temperature dynamics of the transmitter as a linear system and determine the optimal transmit power policy under such temperature constraints as well as energy harvesting constraints over an AWGN channel. We first derive the structural properties of the solution for the general case with multiple energy arrivals. We, then, obtain closed form solutions for the case of a single energy arrival. We observe that the optimal power policy is piecewise monotone decreasing with possible jumps at the energy harvesting instants, and remains constant after the temperature reaches the critical level.

We consider the Gaussian wiretap channel with amplitude and variance constraints on the channel input. We first show that the entire rate-equivocation region of the Gaussian wiretap channel with an amplitude constraint is obtained by discrete input distributions with finite support. We prove this result by considering the existing single-letter description of the rate-equivocation region, and showing that discrete distributions with finite support exhaust this region. Our result highlights an important difference between the peak power (amplitude) constrained and the average power (variance) constrained cases. Although, in the average power constrained case, both the secrecy capacity and the capacity can be achieved simultaneously, our results show that in the peak power constrained case, in general, there is a tradeoff between the secrecy capacity and the capacity, in the sense that, both may not be achieved simultaneously. We also show that under sufficiently small amplitude constraints the possible tradeoff between the secrecy capacity and the capacity does not exist and they are both achieved by the symmetric binary distribution. Finally, we prove the optimality of discrete input distributions in the presence of an additional variance constraint.

We determine the capacity of a discrete memoryless communication channel with an energy harvesting transmitter and its battery state information available at the transmitter and the receiver. This capacity is an upper bound for the problem where side information is available only at the transmitter. Since channel output feedback does not increase the capacity in this case, we equivalently study the resulting finite-state Markov channel with feedback. We express the capacity in terms of directed information. Additionally, we provide sufficient conditions under which the capacity expression is further simplified to include the stationary distribution of the battery state. We also obtain a single-letter expression for the capacity with battery state information at both sides and an infinite-sized battery. Lastly, we consider achievable schemes when side information is available only at the transmitter for the case of an arbitrary finite-sized battery. We numerically evaluate the capacity and achievable rates with and without receiver side information.

We consider a binary energy harvesting channel (BEHC) where the encoder has unit energy storage capacity. We first show that an encoding scheme based on block indexing is asymptotically optimal for small energy harvesting rates. We then present a novel upper bounding technique, which upper bounds the rate by lower-bounding the rate of information leakage to the receiver regarding the energy harvesting process. Finally, we propose a timing based hybrid encoding scheme that achieves rates within 0.03 bits/channel use of the upper bound; hence determining the capacity to within 0.03 bits/channel use.

We determine the capacity of a discrete memoryless communication channel with an energy harvesting transmitter and the energy arrival information available at the receiver as well as the transmitter. We obtain an n-letter capacity expression and prove that the capacity is achieved by an encoding scheme that depends only on the current battery state. Moreover, the capacity is invariant to the non-causal knowledge of energy arrivals. Finally, we show that the capacity expression is equivalently the maximum directed mutual information and that the channel output feedback does not increase the capacity in this case. We obtain upper and lower bounds on the capacity and numerically evaluate them for comparison.

In this paper, we consider a binary energy harvesting transmitter that wishes to control the amount of side information the receiver can obtain about its energy harvests. Specifically, we study state amplification and state masking, which define the maximum and minimum amount of state information conveyed to the receiver for a given message rate, respectively. For an independent and identically distributed energy harvesting process, we first find the amplification and masking regions for a transmitter without a battery and a transmitter with an infinite battery. Next, we find inner bounds for these regions for a unit-sized battery at the transmitter using two different encoding schemes, using instantaneous Shannon strategies and using a scheme based on the equivalent timing channel introduced in our previous work. We observe that the former provides better state amplification, while the latter provides better state masking.

In this paper, we investigate a two-way communication channel where users can harvest energy from nature and energy can be transferred in one-way from one of the users to the other. Energy required for data transmission is randomly harvested by the users throughout the communication duration and users have unlimited batteries to store energy for future use. In addition, there is a separate wireless energy transfer unit that facilitates energy transfer only in one-way and with efficiency α. We study the energy cooperation made possible by wireless energy transfer in the two-way channel. Assuming that both users know the energy arrivals in advance, we find jointly optimal offline energy management policies that maximize the sum throughput of the users. We show that this problem is a convex optimization problem, and find the solution by a generalized two-dimensional directional water-filling algorithm which transfers energy from one user to another while maintaining that the energy is allocated in the time dimension optimally. Optimal solution equalizes the energy levels as much as possible both among users and among slots, permitted by causality constraints of the energy arrivals and one-way energy transfer.

We consider data transmission with an energy harvesting transmitter which has a hybrid energy storage unit composed of a perfectly efficient super-capacitor (SC) and an inefficient battery. The SC has finite space for energy storage while the battery has unlimited space. The transmitter can choose to store the harvested energy in the SC or in the battery. The energy is drained from the SC and the battery simultaneously. In this setting, we consider the offline throughput maximization problem by a deadline over a point-to-point channel. In contrast to previous works, the hybrid energy storage model with finite and unlimited storage capacities imposes a generalized set of constraints on the transmission policy. As such, we show that the solution generalizes that for a single battery and is obtained by applying directional water-filling algorithm multiple times.

We consider the capacity of an energy harvesting communication channel with a finite-sized battery. As an abstraction of this problem, we consider a system where energy arrives at the encoder in multiples of a fixed quantity, and the physical layer is modeled accordingly as a finite discrete alphabet channel based on this fixed quantity. Further, for tractability, we consider the case of binary energy arrivals into a unit-capacity battery over a noiseless binary channel. Viewing the available energy as state, this is a state-dependent channel with causal state information available only at the transmitter. Further, the state is correlated over time and the channel inputs modify the future states. We show that this channel is equivalent to an additive geometric-noise timing channel with causal information of the noise available at the transmitter. We provide a single-letter capacity expression involving an auxiliary random variable, and evaluate this expression with certain auxiliary random variable selection, which resembles noise concentration and lattice-type coding in the timing channel. We evaluate the achievable rates by the proposed auxiliary selection and extend our results to noiseless ternary channels.

In energy harvesting communications, users transmit messages using energy harvested from nature during the course of communication. With an optimum transmit policy, the performance of the system depends only on the energy arrival profiles. In this paper, we introduce the concept of energy cooperation, where a user wirelessly transmits a portion of its energy to another energy harvesting user. This enables shaping and optimization of the energy arrivals at the energy-receiving node, and improves the overall system performance, despite the loss incurred in energy transfer. We consider several basic multi-user network structures with energy harvesting and wireless energy transfer capabilities: relay channel, two-way channel and multiple access channel. We determine energy management policies that maximize the system throughput within a given duration using a Lagrangian formulation and the resulting KKT optimality conditions. We develop a two-dimensional directional water-filling algorithm which optimally controls the flow of harvested energy in two dimensions: in time (from past to future) and among users (from energy-transferring to energy-receiving) and show that a generalized version of this algorithm achieves the boundary of the capacity region of the two-way channel.

Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables:U, for rate splitting andV, for channel prefixing. In this paper, we explore specific classes of wiretap channels for which the evaluation of the rate-equivocation region is simpler. We show that if the wiretap channel is more capable,V=Xis optimal and the boundary of the rate-equivocation region is achieved by varying rate splittingUalone. Conversely, we show under a mild condition that if the wiretap channel is not more capable, thenV=Xis strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We show that optimal rate splittingUthat achieves the boundary of the rate-equivocation region is uniform with cardinality |X| and the prefix channel between optimalUandVis expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable. We provide a special class of cyclic shift symmetric wiretap channels for whichU=φ is optimal. We apply our results to the binary-input cyclic shift symmetric wiretap channels and thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels.

We consider the two-user additive Gaussian multiple access channel (MAC) where the transmitters communicate by using energy harvested from nature. Energy arrivals of the users are i.i.d. in time, and for any given time, they are distributed according to a joint distribution. Energy arrivals cause time-variations for the amplitude constraints of the users. We first consider the static amplitude constrained Gaussian MAC and prove that the boundary of the capacity region is achieved by discrete input distributions of finite support. When both of the transmitters are equipped with no battery, Shannon strategies applied by users provide an inner bound for the capacity region. We prove that the boundary of this inner bound is achieved by input distributions with support set of zero Lebesgue measure.

We consider a simple multi-hop communication scenario composed of a source node, a relay node and a destination node where the source and the relay can harvest energy from the nature. Energy required for communication arrives (is harvested) at the transmitter and an unlimited battery stores it before being consumed for transmission. In addition, the source can assist the relay by transferring a portion of its energy to the relay through a separate energy transfer unit. We address this energy cooperation between the source and the relay in a deterministic setting. Assuming that the source and the relay nodes are informed of the energy arrivals in advance, we find jointly optimal offline energy management policies for the source and the relay that maximize the end-to-end throughput. We show that this problem is a convex problem. In order to gain insight about the structure of the solution, we consider specific scenarios. In particular, we show that if the relay energy profile is higher at the beginning and lower at the end with only one intersection, then matching the power sequences of the source and the relay slot-by-slot is optimal. We also consider the case when the energy of the source is available at the beginning and show that transferring energy in the first slot is optimal.

In energy harvesting communication systems, the energy required for message transmission is maintained by an exogenous energy arrival process independent of the message. This links the problem of communication with an energy harvesting transmitter to the problem of communication over state-dependent channels. In particular, if the transmitter has no battery, the available energy can be viewed as a state and the resulting channel is a state-dependent channel with causal state information at the transmitter only. In general, information transmission blurs the state information that the receiver can get from the received signal. In this paper, we explore the trade-off between the information rate R and the entropy reduction of the energy arrival process Δ at the receiver side over an AWGN channel with an energy harvesting transmitter. If the transmitter has no battery, the trade-off points are achieved by Shannon strategies and we show that the optimal input distributions are discrete. Next, we consider the state amplification problem for an energy harvesting transmitter with an unlimited battery. We show that the optimal trade-off region in this extreme case is expressed explicitly in a simple form and its boundary is achieved by a combination of best-effort-transmit and random binning schemes with an i.i.d. Gaussian codebook of average power equal to the average recharge rate. Finally, we propose an uncoded state amplification scheme that splits the energy between message transmission and entropy reduction and study its performance in a numerical example.

We study the Gaussian wiretap channel with an energy harvesting transmitter which does not have a battery to save energy. In the absence of a battery, the necessary transmission energy is maintained by an i.i.d. energy arrival process. We observe that this channel is an instance of the state-dependent wiretap channel with state available only to the transmitter causally, where the state is the available energy at the transmitter. We prove that the entire capacity-equivocation region can be obtained by single-letter Shannon strategies and its boundary is achieved by input distributions with support set of Lebesgue measure zero.

We consider the Gaussian wiretap channel with an amplitude constraint, i.e., a peak power constraint, on the channel input. We show that the entire rate-equivocation region of the Gaussian wiretap channel with an amplitude constraint is obtained by discrete input distributions with finite support. We prove this result by considering the existing single-letter description of the rate-equivocation region, and showing that discrete distributions with finite support exhaust this region. Our result highlights an important difference between the peak power constraint and the average power constraint cases: Although, in the average power constraint case, both the secrecy capacity and the capacity can be achieved simultaneously, our results show that in the peak power constraint case, in general, there is a tradeoff between the secrecy capacity and the capacity, in the sense that, both may not be achieved simultaneously.

In energy harvesting communication systems, an exogenous recharge process supplies energy necessary for data transmission and the arriving energy can be buffered in a battery before consumption. We determine the information-theoretic capacity of the classical additive white Gaussian noise (AWGN) channel with an energy harvesting transmitter with an unlimited sized battery. As the energy arrives randomly and can be saved in the battery, codewords must obey cumulative stochastic energy constraints. We show that the capacity of the AWGN channel with such stochastic channel input constraints is equal to the capacity with an average power constraint equal to the average recharge rate. We provide two capacity achieving schemes: save-and-transmit and best-effort-transmit. In the save-and-transmit scheme, the transmitter collects energy in a saving phase of proper duration that guarantees that there will be no energy shortages during the transmission of code symbols. In the best-effort-transmit scheme, the transmission starts right away without an initial saving period, and the transmitter sends a code symbol if there is sufficient energy in the battery, and a zero symbol otherwise. Finally, we consider a system in which the average recharge rate is time varying in a larger time scale and derive the optimal offline power policy that maximizes the average throughput, by using majorization theory.

We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in an M-user AWGN broadcast channel where the transmitter is able to harvest energy from the nature, using a finite storage capacity rechargeable battery. The harvested energy is modeled to arrive (be harvested) at the transmitter during the course of transmissions at arbitrary time instants. The transmitter has fixed number of packets for each receiver. Due to the finite battery capacity, energy may overflow without being utilized for data transmission. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We analyze the structural properties of the optimal transmission policy using a dual problem. We find the optimal total transmit power sequence by a directional water-filling algorithm. We prove that there exist M-1 cut-off power levels such that user i is allocated the power between the i-1st and the ith cut-off power levels subject to the availability of the allocated total power level. Based on these properties, we propose an algorithm that gives the globally optimal offline policy. The proposed algorithm uses directional water-filling repetitively. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings.

In this paper, we investigate the transmission completion time minimization problem in an additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the transmitter during the course of transmissions. The transmitter has a fixed number of packets to be delivered to each receiver. The objective is to minimize the time by which all of the packets are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates in a deterministic setting. We first analyze the structural properties of the optimal transmission policy in a two-user broadcast channel via the dual problem of maximizing the departure region by a fixed time T. We prove that the optimal total transmit power sequence has the same structure as the optimal single-user transmit power sequence in . In addition, the total power is split optimally based on a cut-off power level; if the total transmit power is lower than this cut-off level, all transmit power is allocated to the stronger user; otherwise, all transmit power above this level is allocated to the weaker user. We then extend our analysis to an M-user broadcast channel. We show that the optimal total power sequence has the same structure as the two-user case and optimally splitting the total power among M users involves M-1 cut-off power levels. Using this structure, we propose an algorithm that finds the globally optimal policy. Our algorithm is based on reducing the broadcast channel problem to a single-user problem as much as possible. Finally, we illustrate the optimal policy and compare its performance with several suboptimal policies under different settings.

In this paper, we investigate the transmission completion time minimization problem in a two-user additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature. The harvested energy is modeled to arrive at the transmitters randomly. In this paper, under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. The transmitter has a fixed number of packets to be delivered to each receiver. Our goal is to minimize the time by which all of the packets for both users are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates intended for both users. We first analyze the structural properties of the optimal transmission policy. We prove that the optimal total transmit power has the same structure as the optimal single-user transmit power. We also prove that there exists a cut-off power level for the stronger user. If the optimal total transmit power is lower than this level, all transmit power is allocated to the stronger user, and when the optimal total transmit power is larger than this level, all transmit power above this level is allocated to the weaker user. Based on these structural properties of the optimal policy, we propose an algorithm that yields the globally optimal off-line scheduling policy.

Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nodes need to adapt to these harvested energy arrivals. In this paper, we consider optimization of the transmission policy of an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel. In particular, we identify the optimal offline transmission policies that maximize the number of bits delivered by a deadline, and minimize the transmission completion time of the communication session. We introduce a directional water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions as well as energy storage capacity and causality. We solve the throughput maximization problem for the fading channel using the directional water-filling algorithm, which simultaneously adapts to the energy harvested as well as the channel variations in time. We then solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart.

Csiszár and Körner's characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables: U, which represents rate splitting and V, which represents channel prefixing. For some channels, one or both of these auxiliary random variables are unnecessary, simplifying the expression and evaluation of the rate-equivocation region. In this paper, we provide new conditions under which channel prefixing or rate splitting does not improve the rate-equivocation region. In particular, we show that when the main channel is more capable than the eavesdropping channel, channel prefixing is unnecessary; the entire rate-equivocation region can be achieved by rate splitting alone. Conversely, we show under a mild assumption that if the main receiver is not more capable, then channel prefixing is strictly necessary. Moreover, we show that if the main channel is more capable but not less noisy, then rate splitting is strictly necessary. Next, we focus on the set of cyclic shift symmetric channels. We prove that for these channels, if in addition I(X; Y) - I(X;Z) is maximized at the uniform distribution, then rate splitting is unnecessary. Our results apply to BSC-BEC and BEC-BSC wiretap channels. We identify the conditions on the parameters of the BSC and BEC under which channel prefixing and/or rate splitting are unnecessary.

We consider the minimization of the transmission completion time with a battery limited energy harvesting transmitter in a two-user AWGN broadcast channel. The transmitter has fixed number of packets for each receiver and energy is modeled to arrive (be harvested) at the transmitter at random instants. The battery at the transmitter has a finite storage capacity, hence energy may overflow without being utilized for data transmission. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We analyze the structural properties of the optimal transmission policy using a dual problem. We find the optimal total transmit power sequence by a directional water-filling algorithm. We prove that there exists a cut-off power level such that if the allocated power is lower than this level, then only the stronger user is served in that epoch; otherwise, the power above this level is allocated to the weaker user. Based on these properties, we propose an algorithm that gives the globally optimal offline policy. The proposed algorithm uses directional water-filling repetitively.

Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nodes need to adapt to these harvested energy arrivals. In this paper, we consider optimization of point-to-point data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel. We consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session. We optimize these objectives by controlling the time sequence of transmit powers subject to energy storage capacity and causality constraints. We, first, study optimal offline policies. We introduce a directional water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of an adaptive directional water-filling algorithm for the throughput maximization problem. We solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart. Next, we consider online policies. We use stochastic dynamic programming to solve for the optimal online policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes with causal channel state feedback. We also propose near-optimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies under various different configurations.

In this work we consider the allocation of buffer space to data streams sharing a common high-speed wireless transmitter. As an example, we focus on an OFDMA-based downlink system scenario. Scheduling for maximum throughput has been extensively studied in the literature. However, the practically interesting case of a finite buffer has not been sufficiently addressed before. Especially in the case of overloaded packet queues, the choice of buffer management policy substantially affects the throughput performance. We consider a physicallayer scheduling scheme that allocates users to subcarriers based on channel state, in order to make the most use of multiuser diversity. We then consider optimal buffer partitioning to accommodate the resulting rates. We study the system throughput by simulations. As a benchmark, we also simulate MaxWeight, a well-known cross-layer channel and queue-aware scheduling policy that is throughput-optimal in the absence of a finite buffer constraint. We observe that a suitable buffer management policy with a simple channel-aware queuing policy achieves cross-layer scheduling performance, and can exceed it.