A downlink (DL) system comprises a centralized base station (BS) communicating to a number of users physically scattered around. The purpose of resource allocation at the BS is to intelligently allocate the limited radio resources, e.g. transmit power, time slots and frequency bandwidth, among users to meet their data rate requirements. Adaptive resource allocation has been shown to achieve significantly higher performance than fixed resource allocation by adapting resource allocation with respect to varying channel fading, interference scenario and traffic load. This thesis deals with the problem of DL adaptive resource allocation in a multi-user MIMO OFDM system. In a multi-user MIMO OFDM system, multiple users can simultaneously transmit data and be separated in frequency domain or in spatial domain, i.e. via different sub-carriers or via orthogonal beams, respectively. Thus, adaptive resource allocation in such a system is highly challenging because of the high degree of freedom for resources. Firstly, an approach of jointly optimizing the resource allocation in frequency and spatial domains is proposed in this thesis. Two types of optimization problems, namely power minimization and rate maximization, are addressed. For the power minimization case, the joint approach is shown to achieve a near-optimal solution with low complexity. For the rate maximization case, several variants of the joint approach are proposed in order to take into account different user fairness strategies and different power constraints. Compared to fixed resource allocation, adaptive resource allocation needs signaling for acquisition of channel and traffic knowledge as well as for delivery of allocation results, which causes additional overhead, thus mitigating the adaptation gain. Hence, the reduction of the signaling overhead is as important as the increase of the adaptation gain in order to maximize the system performance. The following investigations targeting at reduction of signaling overhead are considered in this thesis: - By defining a chunk as a block of adjacent sub-carriers and OFDM symbols and letting it be the basic resource unit, the signaling for delivery of allocation results from a base station to all users it served can be reduced by a factor of the chunk dimension, but the adaptation gain also decreases with increasing chunk dimension. In order to find the optimal chunk dimension, the adaptation gain as a function of the chunk dimension is analytically derived. - To cope with the time-variant property of the channel fading, users' channel knowledge needs to be periodically updated. To find the optimal update interval, both the overhead reduction and the performance loss due to outdated channel knowledge should be evaluated. Therefore, the performance is firstly derived as a function of the update interval by means of a semi-analytical method and then the optimal update interval as a function of the velocity can be analytically derived accordingly. - Zero-forcing beamforming enables multiple users to transmit simultaneously over orthogonal beams, but requires the complete channel matrices, which leads to high signaling overhead especially at very high velocities. Generalized eigenbeamforming and fixed grid-of-beam beamforming are two alternative techniques to enable spatial division multiple access (SDMA) but require only partial channel knowledge and less signaling compared to zero-forming beamforming. Under the assumption that instantaneous channel quality indication is additionally available, adaptive resource allocation based on these two beamforming techniques is investigated and their performance is assessed. - Random access is commonly used by users to transmit bandwidth requests which inform the BS about the traffic load of the uplink transmission. Typically, slotted ALOHA protocol is used in conjunction with truncated binary exponential back-off algorithm for random access. Its performance in the considered system is firstly analytically analyzed, and then a novel grouping mechanism, yielding a more efficient usage of the resources for random access, is proposed. Finally, since fixed relay nodes (RNs) has been shown to extend the coverage of the BS or enhance the cell-edge capacity by forwarding data between BS and users, DL adaptive resource allocation in a relay-enhanced cell (REC) is addressed in this thesis. Different from the BS, the RN has no wired connection to the core network, but it also provides radio access to the users, and so both BS and RN are called access points (APs). It is expected that the system performance in such a REC can be enhanced by letting the BS adapt the resource allocation with respect to the interference among the multiple APs in the REC. Since a complete centralized resource allocation approach performed at the BS is not applicable in practical systems due to the extremely high computational complexity and huge signaling for the exchange of channel and interference information among APs, a two-level approach which requires much less signaling is proposed in this thesis. On a long-term basis, e.g. for each super-frame, each AP dynamically groups users with high spatial correlation into so-called logical beams, and then the BS allocates resources to logical beams in such a way that end-to-end throughput is maximized and mutual interference diversity is exploited by allowing logical beams with sufficiently low mutual interference to share the same time-frequency resource. On a short-term basis, e.g. for each frame, each AP exploits multi-user diversity by adaptively selecting one user from each logical beam for each time-frequency resource assigned to that logical beam.