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This book presents reduced complexity and proportional data rate fairness resource allocation schemes for next generation broadband mobile wireless communication systems. At first we present proportional data rate fairness resource allocation scheme for Multi-Input Multi-Output Orthogonal Frequency Division Multiple Access (MIMO- OFDMA) broadband mobile wireless communication system. In this scheme, users are separated in frequency domain and they cannot transmit their data in same frequency with other users at the same time. Therefore, second resource allocation considers to use the radio frequency spectrum more efficiently by using same frequency to transmit for different user s data at the same time in the system. Therefore, we can use scarce spectral resources more efficiently in the MIMO-OFDM wireless communication system environments under the consideration of proportional data rate fairness constraint and QoS requirements among users in the system. Reduced complexity antenna selection method for practical MIMO communication system is also presented based on Singular value decomposition (SVD) and polarization effect in the wireless communication system.