Optimal Stochastic Power Control for Energy Harvesting Systems with Statistical Delay Constraint

We study the stochastic user scheduling and power control problem for an uplink multi-user network over time-varying channels, where the users randomly harvest renewable energies from the environment. For each user, the renewable energies and arriving data packets with a constant rate are stored in energy (battery) and data buffers, respectively. Users have statistical packet delay constraints in terms of maximum acceptable delay-outage probabilities. We classify the users as prioritized and non-prioritized users. Our goal is to maximize the arrival rate of the non-prioritized user while supporting the minimum data rate requirements for the prioritized users. We reformulate the problem as an infinite-horizon Markov decision process (MDP) using asymptotic delay analysis and study the optimal scheduling and power control policy. Since the optimal policy requires centralized processing with high computational complexity, we develop a reduced-complexity distributed algorithm, which can be implemented at each individual user. Online algorithm is devised, which does not require the statistical knowledge of the channel fading and energy harvesting (EH) processes. Numerical results demonstrate the effectiveness of the centralized and distributed schemes for different delay constraints and EH settings.

In this paper, secure communication over a buffer-aided two-hop communication link, in which a source sends data to a destination with the aid of a trusted half-duplex relay node in the presence of a passive eavesdropper, is studied. It is assumed that there is no direct link between the source and the destination, and the buffer-aided relay forwards the information to the destination by employing the decode-and-forward (DF) scheme. Both the source and the relay transmissions are assumed to be vulnerable to the eavesdropper. The perfect channel side information (CSI) of the network is assumed to be available at the source and the relay. Initially, conventional relaying protocols where equal partition of the time for the reception and transmission of the relay is considered. Then, the optimal time fraction with the optimal power control policy that maximizes the secrecy throughput is identified. Subsequently, the optimal joint link selection and power control policy that maximizes the secrecy throughput is derived. Numerical results demonstrate that the joint link selection and power control scheme can significantly improve the achievable secrecy throughput of the buffer-aided two-hop communication system.

This paper studies optimal power control policies that maximize the achievable rates of underlay cognitive radio systems with arbitrary input distributions under both peak/average transmit power and peak/average interference power constraints for general fading distributions. In particular, optimal power adaptation schemes are formulated and low-complexity optimal power control algorithms are proposed. Additionally, simpler approximations of optimal power control policies in the low-power regime are determined. By considering gamma distributed channel power gains of the interference link between the secondary transmitter and the primary receiver and of the transmission link between the secondary transmitter and the secondary receiver, closed-form expressions for the maximum achievable rate attained with optimal power control in the low-power regime are provided. Through numerical results, the impact of the fading severity of both interference and transmission links and transmit power and interference power constraints on the maximum achievable rate of the cognitive user for different practical constellations and Gaussian signals are investigated.

Energy harvesting from the surroundings is a promising solution to perpetually power-up wireless sensor communications. This paper presents a data-driven approach of finding optimal transmission policies for a solar-powered sensor node that attempts to maximize net bit rates by adapting its transmission parameters, power levels and modulation types, to the changes of channel fading and battery recharge. We formulate this problem as a discounted Markov decision process (MDP) framework, whereby the energy harvesting process is stochastically quantized into several representative solar states with distinct energy arrivals and is totally driven by historical data records at a sensor node. With the observed solar irradiance at each time epoch, a mixed strategy is developed to compute the belief information of the underlying solar states for the choice of transmission parameters. In addition, a theoretical analysis is conducted for a simple on-off policy, in which a predetermined transmission parameter is utilized whenever a sensor node is active. We prove that such an optimal policy has a threshold structure with respect to battery states and evaluate the performance of an energy harvesting node by analyzing the expected net bit rate. The design framework is exemplified with real solar data records, and the results are useful in characterizing the interplay that occurs between energy harvesting and expenditure under various system configurations. Computer simulations show that the proposed policies significantly outperform other schemes with or without the knowledge of short-term energy harvesting and channel fading patterns.

This paper considers the jointly optimal pilot and data power allocation in single cell uplink massive MIMO systems. A closed form solution for the optimal length of the training interval is derived. Using the spectral efficiency (SE) as performance metric and setting a total energy budget per co- herence interval the power control is formulated as optimization problems for two different objective functions: the minimum SE among the users and the sum SE. The optimal power control policy is found for the case of maximizing the minimum SE by converting it to a geometric program (GP). Since maximizing the sum SE is an NP-hard problem, an efficient algorithm is developed for finding KKT (local maximum) points. Simulation results show the advantage of optimizing the power control over both pilot and data power, as compared to heuristic power control policies.

In this work, the achievable rate of three-node relay systems with selection relaying under statistical delay constraints, imposed on the limitations of the maximum end-to-end delay violation probabilities, is investigated. It is assumed that there are queues of infinite size at both the source and relay node, and the source can select the relay or destination for data reception. Given selection relaying policy, the effective bandwidth of the arrival processes of the queue at the relay is derived. Then, the maximum constant arrival rate can be identified as the maximum effective capacity as a function of the statistical end-to-end queueing delay constraints, signal-to-noise ratios (SNR) at the source and relay, the fading distributions of the links, and the relay policy. Subsequently, a relay policy that incorporates the statistical delay constraints is proposed. It is shown that the proposed relay policy can achieve better performance than existing protocols. Moreover, it is demonstrated that buffering relay model can still help improve the throughput of relay systems in the presence of statistical delay constraints and source-destination link.

We study power control for an energy harvesting communication system with independent and identically distributed Bernoulli energy arrivals. It is assumed that the transmitter is equipped with a finite-sized rechargeable battery and is able to look ahead to observe a fixed number of future arrivals. A complete characterization is provided for the optimal power control policy that achieves the maximum long-term average throughput over an additive white Gaussian noise channel.

Power control typically constitutes the adaptation of transmit power to fading. It is argued that in packet data systems, there is another important aspect of power control, and that is the adaptation of the transmit power to the traffic load. The traffic load is defined as the number of users who wish to transmit data to the base station, and this traffic load changes with time. Adaptation of the reverse link transmit power to the traffic load is shown to improve the power-delay tradeoff. The optimal power control policy is computed using dynamic programming, and is compared with some simple suboptimal power control schemes.

In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Using the Markov chain approximation method and recent advances in sampling-based algorithms for deterministic path planning, we propose a novel algorithm called the incremental Markov Decision Process to incrementally compute control policies that approximate arbitrarily well an optimal policy in terms of the expected cost. The main idea behind the algorithm is to generate a sequence of finite discretizations of the original problem through random sampling of the state space. At each iteration, the discretized problem is a Markov Decision Process that serves as an incrementally refined model of the original problem. We show that with probability one, (i) the sequence of the optimal value functions for each of the discretized problems converges uniformly to the optimal value function of the original stochastic optimal control problem, and (ii) the original optimal value function can be computed efficiently in an incremental manner using asynchronous value iterations. Thus, the proposed algorithm provides an anytime approach to the computation of optimal control policies of the continuous problem. The effectiveness of the proposed approach is demonstrated on motion planning and control problems in cluttered environments in the presence of process noise.

In this paper, we propose online discrete-rate discrete-power adaptation policies based on 1-bit channel feedback for energy harvesting (EH) wireless communications. The receiver periodically sends 1-bit feedback by comparing the channel power gain with a predetermined threshold. The EH transmitter correspondingly adjusts M-ary modulation level and transmission power based on 1-bit feedback and battery energy. To determine the optimal channel threshold, adaptive modulation levels and corresponding power allocations, we formulate a constrained optimization problem to maximize the throughput within a finite horizon. We show that this problem follows a Markov decision process and can be solved via backward induction method. To alleviate the computational complexity of the backward induction method, we further propose a suboptimal policy that uses the best effort modulation level and the channel threshold that is optimized by maximizing the ergodic spectral efficiency over channel fading and EH processes. Simulation results show that the proposed policies have considerable throughput performance gain compared to other heuristic policies, and the suboptimal policy has negligible performance loss compared to the optimal policy.

The optimal transmitter power control policy in an interleave division multiple access (IDMA) spread spectrum uplink channel is derived. The policy is applied to an IDMA channel with repetition code and a chip-by-chip maximum-likelihood decoder whose sum-rate is compared to the capacity of a linear minimum mean square error multiuser detector and to the Cover-Wyner capacity

A general theory of online power control for discrete-time battery limited energy harvesting communications is developed, which leads to, among other things, an explicit characterization of a maximin optimal policy. This policy only requires the knowledge of the (effective) mean of the energy arrival process and maximizes the minimum asymptotic expected average reward (with the minimization taken over all energy arrival distributions of a given (effective) mean). Moreover, it is universally near optimal and has a strictly better worst-case performance as well as a strictly improved lower multiplicative factor in comparison with the fixed fraction policy proposed by Shaviv and \"{O}zg\"{u}r when the objective is to maximize the throughput over an additive white Gaussian noise channel. The competitiveness of this maximin optimal policy is also demonstrated via numerical examples.

This work considers the relay selection and resource allocation problem (i.e., link scheduling, and rate allocation) for multi-source, multi-relay dual-hop wireless networks. The relays employ buffers to store the received data from the sources for future transmissions. End-to-end (E2E) delay of each traffic flow originated from a source or a relay is constrained in terms of maximum allowable delay-outage probability. To solve this problem, we first study the resource allocation problem to maximize the constant supportable arrival rate of a non-prioritized source under minimum rate requirements of the prioritized sources and relays for a given relay selection solution. Then, the optimal relay selection can be determined to support the largest rate of the non-prioritized source among all possible relay selection solutions. We derive the resource allocation solutions using asymptotic delay analysis and convex optimization techniques. We also develop an online allocation algorithm which does not require the knowledge of the fading statistics by using stochastic approximation theory. Numerical results are presented to demonstrate the usefulness of the proposed resource allocation design for relay selection under different delay and rate constraint regimes.

In this paper, we first study the Decode-and-Forward strategy for secrecy in a single-relay network. We propose a suboptimal Decode-and-Forward with Zero Forcing (DF/ZF) strategy for which we obtain the optimal power control policy. Next, we consider the multiple relay problem. We propose three different strategies based on DF/ZF. The first strategy is a single-hop strategy in which all the relays decode the source message at the same time, then perform beamforming such that all the relays' signals are eliminated from the eavesdropper's observation (full zero-forcing). We give the achievable rate by this strategy and derive the optimal power control policy. We show that, in this strategy, the relays which are far from the source create a bottleneck and limit the achievable rate. The second strategy is a multiple hop strategy that overcomes the drawback of the first strategy, however, with the disadvantage of enabling partial zero-forcing only, assuming that all the relays are required to transmit fresh information in every transmission block. The third strategy is also a multiple hop strategy in which full zero-forcing is possible and the rate achieved does not suffer from the drawback of the first strategy.

This paper studies energy-efficiency (EE) and throughput optimization in the presence of randomly arriving data and quality of service (QoS) constraints. For this purpose, maximum average arrival rates supported by transmitting signals with arbitrary input distributions are initially characterized in closed form by employing the effective bandwidth of time-varying sources (e.g., discrete-time Markov and Markov fluid sources, and discrete-time and continuous-time Markov modulated Poisson sources) and effective capacity of the time-varying wireless channel. Subsequently, EE is formulated as the ratio of the maximum average arrival rate to the total power consumption, in which circuit power is also taken into account. Following these characterizations, the optimal power control policies maximizing the EE or maximizing the throughput under a minimum EE constraint are obtained. Through numerical results, the performance of the optimal power control policies is evaluated for different signal constellations and is also compared with that of constant power transmission. The impact of QoS constraints, source characteristics, circuit power, input distributions on the EE, and the throughput is analyzed.