Maximizing the spectral and energy efficiency of ARQ with a fixed outage probability

This paper studies the spectral and energy efficiency of automatic repeat request (ARQ) in Nakagami-m block-fading channels. The source encodes each packet into L similar sequences and transmits them to the destination in the L subsequent time slots. The destination combines the L sequences using maximal ratio combining and tries to decode the information. In case of decoding failure, the destination feeds back a negative acknowledgment and then the source sends the same L sequences to the destination. This process continues until successful decoding occurs at the destination with no limit on the number of retransmissions. We consider two optimization problems. In the first problem, we maximize the spectral efficiency of the system with respect to the rate for a fixed power. In the second problem, we maximize the energy efficiency with respect to the transmitted power for a fixed rate.