An energy harvesting (EH) transmitter communicating over a time-correlated wireless channel is considered. The transmitter is capable of sensing the current channel state, albeit at the cost of both energy and transmission time. The EH transmitter aims to maximize its long-term throughput by choosing one of the following actions: 1) defer its transmission to save energy for future use; 2) transmit reliably at a low rate; 3) transmit at a high rate; and 4) sense the channel to reveal the channel state at a cost of energy and transmission time, and then decide to defer or to transmit. The problem is formulated as a partially observable Markov decision process with a belief on the channel state. The optimal policy is shown to exhibit a threshold behavior on the belief state, with battery-dependent threshold values. The optimal threshold values and performance are characterized numerically via the value iteration algorithm as well as a policy search algorithm that exploits the threshold structure of the optimal policy. Our results demonstrate that, despite the associated time and energy cost, sensing the channel intelligently to track the channel state improves the achievable long-term throughput significantly as compared to the performance of those protocols lacking this ability as well as the one that always senses the channel.
Gilbert-Elliott channel model has been previously investigated in the context of scheduling an EH transmitter in @cite_25 , where the transmitter always has perfect CSI, obtained by sensing at every time slot. The transmitter makes a decision to defer or to transmit based on the current CSI and the battery state. Similarly, without considering the channel sensing capability, @cite_11 addresses the problem of optimal power management for an EH sensor over a multi-state wireless channel with memory. Unlike previous work, we take into account the energy cost of channel sensing which can be significant for a low-power EH transmitter. Therefore, in order to minimize the energy consumed for channel sensing, an EH transmitter does not necessarily sense the channel at every time slot, and instead, it keeps an updated belief of the channel state according to its past observations, and only occasionally senses the current channel state.
@cite_25 @cite_11
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This paper considers the problem of power management and throughput maximization for energy neutral operation when using an energy harvesting sensor (EHS) to send data over a wireless link. The EHS is assumed to be able to harvest energy at a constant rate, and use a fixed part of the energy harvested in a slot for measuring the channel state. The rest of the energy harvested is available for transmission, however, it can be stored in an inefficient battery if it is not fully utilized. The key constraint that the EHS needs to satisfy is energy neutrality, i.e., the expected energy drawn from the battery should equal the expected energy deposited into the battery. In this scenario, two popular models for data transmission are contrasted: the constant bit rate (CBR) model and the variable bit rate (VBR) model. In the CBR model, it is assumed that the EHS are designed to transmit data at a constant rate (using a fixed modulation and coding scheme) but are power-controlled. In the VBR model, the EHS selects both the transmit power and the data rate of transmission in each slot based on the channel instantiation. A framework under which the system designer can optimize several parameters of the EHS that determine the average data rate performance when the channel is Rayleigh fading is developed. Using this framework, the two transmission schemes are contrasted. It is shown that, with the right choice of parameter settings, the CBR scheme can perform nearly as well as the VBR scheme at significantly lower complextiy. The usefulness and validity of the framework developed is illustrated through simulations for specific examples. This paper addresses the problem of finding outage- optimal power control policies for wireless energy harvesting sensor (EHS) nodes with automatic repeat request (ARQ)-based packet transmissions. The power control policy of the EHS specifies the transmission power for each packet transmission attempt, based on all the information available at the EHS. In particular, the acknowledgement (ACK) or negative acknowledgement (NACK) messages received provide the EHS with partial information about the channel state. We solve the problem of finding an optimal power control policy by casting it as a partially observable Markov decision process (POMDP). We study the structure of the optimal power policy in two ways. First, for the special case of binary power levels at the EHS, we show that the optimal policy for the underlying Markov decision process (MDP) when the channel state is observable is a threshold policy in the battery state. Second, we benchmark the performance of the EHS by rigorously analyzing the outage probability of a general fixed-power transmission scheme, where the EHS uses a predetermined power level at each slot within the frame. Monte Carlo simulation results illustrate the performance of the POMDP approach and verify the accuracy of the analysis. They also show that the POMDP solutions can significantly outperform conventional ad hoc approaches. We study RF-enabled wireless energy transfer (WET) via energy beamforming, from a multi-antenna energy transmitter (ET) to multiple energy receivers (ERs) in a backscatter communication system such as RFID. The acquisition of the forward-channel (i.e., ET-to-ER) state information (F-CSI) at the ET (or RFID reader) is challenging, since the ERs (or RFID tags) are typically too energy-and-hardware-constrained to estimate or feedback the F-CSI. The ET leverages its observed backscatter signals to estimate the backscatter-channel (i.e., ET-to-ER-to-ET) state information (BS-CSI) directly. We first analyze the harvested energy obtained using the estimated BS-CSI. Furthermore, we optimize the resource allocation to maximize the total utility of harvested energy. For WET to single ER, we obtain the optimal channel-training energy in a semiclosed form. For WET to multiple ERs, we optimize the channel-training energy and the energy allocation weights for different energy beams. For the straightforward weighted-sum-energy (WSE) maximization, the optimal WET scheme is shown to use only one energy beam, which leads to unfairness among ERs and motivates us to consider the complicated proportional-fair-energy (PFE) maximization. For PFE maximization, we show that it is a biconvex problem, and propose a block-coordinate-descent-based algorithm to find the close-to-optimal solution. Numerical results show that with the optimized solutions, the harvested energy suffers slight reduction of less than 10 , compared to that obtained using the perfect F-CSI. In this paper, we study resource allocation in a downlink OFDMA system assuming imperfect channel state information (CSI) at the transmitter. To achieve the individual QoS of the users in OFDMA system, adaptive resource allocation is very important, and has therefore been an active area of research. However, in most of the the previous work perfect CSI at the transmitter is assumed which is rarely possible due to channel estimation error and feedback delay. In this paper, we study the effect of channel estimation error on resource allocation in a downlink OFDMA system. We assume that each user terminal estimates its channel by using an MMSE estimator and sends its CSI back to the base station through a feedback channel. We approach the problem by using convex optimization framework, provide an explicit closed form expression for the users' transmit power and then develop an optimal margin adaptive resource allocation algorithm. Our proposed algorithm minimizes the total transmit power of the system subject to constraints on users' average data rate. The algorithm has polynomial complexity and solves the problem with zero optimality gaps. Simulation results show that our algorithm highly improves the system performance in the presence of imperfect channel estimation.