  We first conceive a novel transmission protocol for a multi-relay
multiple-input--multiple-output orthogonal frequency-division multiple-access
(MIMO-OFDMA) cellular network based on joint transmit and receive beamforming.
We then address the associated network-wide spectral efficiency (SE) and energy
spectral efficiency (ESE) optimization problems. More specifically, the
network's MIMO channels are mathematically decomposed into several effective
multiple-input--single-output (MISO) channels, which are essentially spatially
multiplexed for transmission. Hence, these effective MISO channels are referred
to as spatial multiplexing components (SMCs). For the sake of improving the
SE/ESE performance attained, the SMCs are grouped using a pair of proposed
grouping algorithms. The first is optimal in the sense that it exhaustively
evaluates all the possible combinations of SMCs satisfying both the
semi-orthogonality criterion and other relevant system constraints, whereas the
second is a lower-complexity alternative. Corresponding to each of the two
grouping algorithms, the pair of SE and ESE maximization problems are
formulated, thus the optimal SMC groups and optimal power control variables can
be obtained for each subcarrier block. These optimization problems are proven
to be concave, and the dual decomposition approach is employed for obtaining
their solutions. Relying on these optimization solutions, the impact of various
system parameters on both the attainable SE and ESE is characterized. In
particular, we demonstrate that under certain conditions the lower-complexity
SMC grouping algorithm achieves 90% of the SE/ESE attained by the
exhaustive-search based optimal grouping algorithm, while imposing as little as
3.5% of the latter scheme's computational complexity.
