Union Bound on the Bit Error Rate for MIMO-GFDM Systems

In this paper, a union bound on the bit error rate (BER) for multiple input multiple output generalized frequency division multiplexing (MIMO-GFDM) systems is derived based on exact pairwise error probabilities. The moment-generating function is used to calculate the exact pairwise error probability under the assumption that a maximum likelihood detector is used at the receiver. A realistic multipath MIMO channel environment is investigated in which the spatial correlation between antennas and the channel estimation errors are included. The Kronecker model and an additive model are used to describe the spatial correlation and channel estimation errors, respectively. The impacts of the spatial correlation and the channel estimation errors on the derived bound are investigated. The performances of MIMO-GFDM systems using different modulation techniques are also examined. Numerical calculations of the union bound and computer-based Monte-Carlo simulations of BER are carried out to verify the derived bound. Numerical results show that the derived union bound is a tight upper bound on the BER for MIMO-GFDM systems in a reasonable \(E_s/N_0\) region.