# Reliable and Energy-Efficient LEO Satellite Communication with IR-HARQ via Power Allocation
## 1 Introduction
### Related Work  
Recently, there have been many studies on HARQ protocols in satellite communication systems. In [8], the throughput of the incremental redundancy HARQ (IR-HARQ) in free space optical (FSO) based satellite systems is analyzed. In [9], the author analyzes the impact of the number of parallel HARQ processes on the system memory size and throughput of a LEO satellite communication system. It also provides corresponding solutions to control the system throughput and memory size at an acceptable level. A virtual HARQ protocol is proposed in a geostationary earth orbit (GEO) satellite communication system in [10]. The virtual HARQ protocol can greatly improve the spectrum efficiency while ensuring the transmission reliability of the satellite communication system. In [11], considering fast multipath fading, type-I HARQ is adopted to achieve good bit error ratio (BER) performance in Ka-band LEO satellite mobile communication systems. In [12], the throughput performance of different HARQ protocols is analyzed in a hybrid satellite-terrestrial relay network. Moreover, the impact of HARQ transmission rounds and the information transmission rate on throughput performance is also analyzed. In [13], the author deduces the outage probability performance and diversity gain of three different HARQ protocols in the satellite-terrestrial transmission system. All the above HARQ schemes can improve the reliability of satellite communication systems. However, they do not consider the energy efficiency of HARQ in satellite communication systems which has an influence on satellite launch cost and lifetime [14]. Several energy-efficient HARQ protocols in terrestrial communication systems are proposed. An equal power transmission scheme for the HARQ protocol is designed in [15; 16; 17; 18]. In [15], the optimal energy efficiency of the chase combining HARQ (CC-HARQ) protocol is achieved by optimizing the information length and the fixed transmission power level. In [16], the energy consumption of the CC-HARQ protocol is reduced by optimizing the maximum number of transmission rounds. In [17], under the block-fading channel, the total power used by all users in the system is minimized by optimizing the fixed transmission power of the IR-HARQ protocol. A simplified energy efficiency expression is obtained by using Gaussian approximation for the outage probability in the IR-HARQ protocol [18]. The transmission power and the IR-HARQ transmission rounds are optimized to reduce the energy consumption. Variable-power allocation methods for IR-HARQ protocols are studied in [19; 20; 21; 22; 23; 24]. In these schemes, the transmission power in each HARQ round can be adjusted. The Lagrange multiplier method is used to optimize the power sequence of the CC-HARQ protocol under quasi-static channel conditions in [19; 20]. The experimental results show that the power allocation algorithm can reduce the average total power required compared to the equal power transmission scheme. In [21], the outage probability of CC-HARQ in the block-fading channel is approximated. The energy optimization is transformed into a geometric programming problem to solve. However, the approximation of outage probability is only suitable for the high signal to noise ratio (SNR) region, which causes a large error in low SNR conditions. Reference [22] proposes a suboptimal optimization algorithm to obtain the transmission power of the IR-HARQ protocol in each round. This reference only studies the special condition of two transmission rounds, which cannot be extended to the case of multiple transmission rounds. In [23; 24], the author studies the energy efficiency of different HARQ protocols in time-correlated channels. By approximating the outage probability, the closed expression of each transmission power can be obtained using the Karush-Kuhn-Tucker (KKT) conditions. The simulation results show that the IR-HARQ protocol can obtain the best energy efficiency compared with other HARQ protocols.