Optimum Energy- and Spectral-Efficient Transmissions for Delay-Constrained Hybrid ARQ Systems

This paper discusses the energy- and spectral-efficient transmissions for delay-constrained wireless communication systems utilizing hybrid automatic repeat request (HARQ). Three design metrics are considered: 1) the energy efficiency (EE) measured by the average energy required to successfully deliver one information bit from a source to its destination; 2) the spectral efficiency (SE) defined as the average data rate per unit bandwidth; and 3) the average energy per bit normalized by the SE. Optimum system designs with respect to different metrics are developed by analytically identifying the sequence of transmission energy that should be employed at different retransmissions. The optimum energy distributions are calculated with a new backward sequential calculation method, where the energy at each retransmission round is expressed as a closed-form expression of a wide range of practical system parameters, such as circuit power and channel coding in the physical layer and frame length and protocol overhead in the media access control layer. Reducing the SE-normalized energy per bit yields a balanced tradeoff between EE and SE. Numerical results demonstrate that reducing the SE-normalized energy per bit achieves a 26.7% SE gain over the system that minimizes the average energy per bit; yet, the EE of the two systems is almost identical.