Diversity Fairness in Tomlinson–Harashima Precoded Multiuser MIMO Through Retransmission

We study the diversity unfairness associated with the conventional Tomlinson–Harashima precoding (THP) in multiuser multiple-input multiple-output downlink transmission. A single-retransmission scheme that combines two THP signals at each user with a complementary multi-user suppression order is investigated. For a system with
$M$
antennas at the transmitter and a single antenna at each user, the proposed scheme provides a diversity order
$M+1$
for all users and ensures diversity fairness. We study two retransmission policies, where the users either consider only the current received codeword or combine both codewords for decoding. An asymptotic analysis of the outage probability for both THP retransmission schemes is provided. In addition, a power allocation policy that minimizes the outage probability and accommodates the same coding gain at each user is discussed by formulating a geometric optimization problem.