Optimum Energy Efficient Communications for Hybrid ARQ Systems Gang Wang ∗ , Jingxian Wu ∗ , and Yahong Rosa Zheng † ∗ Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701, USA † Dept. of Electrical & Computer Eng., Missouri University of Science & Technology, Rolla, MO 65409, USA Abstract—The optimum energy efficient communication of a hybrid automatic repeat request (HARQ) system with Chase combining is studied in this paper. The proposed scheme minimizes the energy required to successfully deliver a bit from a source to its destination by identifying the optimum energy distribution, i.e., the sequence of transmission energy that should be employed during the retransmissions of a packet. The optimum energy distribution is calculated with a new backward sequential method, where the energy of the retransmission round k is expressed as a closed- form expression of the energy of the retransmission rounds i>k. The optimum design is performed by considering a wide range of practical system parameters, such as circuit power and coding in the physical layer, and frame length and protocol overhead in the media access control layer. Both analytical and simulation results demonstrate that the proposed scheme can achieve significant energy savings compared to conventional HARQ systems that employ equal energy in all retransmissions. I. I NTRODUCTION Energy efficient communication can reduce energy con- sumption, extends the battery life of wireless terminals, and reduces heat dissipation and the electromagnetic pollution to the surrounding environment. Energy efficiency in a commu- nication system is usually measured as the energy required to transmit a bit [1] and [2]. With the growing gap between battery technology and the demands for high rate broadband communications, it is imperative to develop communication technologies that can reduce energy consumptions. There are a large number of works in the literature devoted to the development of energy efficient communication systems. Many energy efficient communication systems are designed across multiple protocol layers [3] - [7]. In [3], cross-layer en- ergy efficiency design is studied with an energy-rate-distortion framework that covers the physical layer and the application layer by considering the trade-offs among source distortion, data rate, and hardware complexity, yet with an assumption of error-free channel. In [4], the average transmission energy consumption is minimized for automatic repeat request (ARQ) system by assigning increased energy in the retransmission of one packet in single-hop and multi-hop cases with a delay constraint. In [5], the optimum energy assignment for the hybrid ARQ (HARQ) system in quasi-static fading channels is studied to minimize the average transmission energy consumption. To simplify analysis, it is assumed in [5] that a retransmission occurs if the signal-to-noise ratio (SNR) is below a threshold, yet in practical systems a packet is retransmitted if there are unrecoverable errors in the packets received from the previous rounds. Neither [4] nor [5] considers the circuit energy consumption, which is shown to be non-negligible especially for short range communications [6]. In [7] and [8], the energy per bit in an ARQ system is minimized by considering many practical system parameters including packet length, circuit energy, overhead, modulation and coding schemes, and frame error rate (FER). In this paper, we study the optimum transmission of coded HARQ systems with Chase combining, where the signals from all transmission attempts of the same packet are combined coherently at the receiver during the detection process. The optimum design is performed by identifying the optimum energy distribution, i.e., the sequence of transmission energy that should be used at different transmission attempts, such that the overall energy required to successfully deliver a bit from a source to its destination is minimized. A large number of practical system parameters, such as the efficiency of the energy amplifier, the energy consumption of digital hardware, data rate, modulation and coding schemes, frame length, FER, and the protocol overhead, etc., are considered during the design. With the help of a new backward sequential method, the optimum transmission energy is expressed as closed-form expressions of all the practical system parameters. Both simulation and analytical results demonstrate that the proposed energy efficient system design can achieve significant energy savings over conventional systems. II. SYSTEM MODEL Consider a transmitter and a receiver separated by a distance d. The information bits are divided into frames. There are L b uncoded information bits and L 0 overhead bits in each frame. The information bits and overhead bits are encoded with a channel encoder with a code rate r. For a system with modulation level M , the number of symbols in each frame is L s = L b +L0 r log 2 M , where L b is chosen in a way such that L s is an integer. The signal is transmitted through a flat Rayleigh fading channel. Due to the effects of channel fading and noise, the receiver might not be able to successfully recover the transmitted signal. In case of a detection failure in a system with HARQ, the receiver will send back to the transmitter Globecom 2013 - Wireless Networking Symposium 978-1-4799-1353-4/13/$31.00 ©2013 IEEE 4656