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In spite of their potential to improve the performance of wireless communication systems, relay-based communication systems face significant challenges, resource wastage. In this article we discuss resource efficiency in relay systems, particularly in two-way and full-duplex relay systems that utilize multiple antennas and improved duplexing to enhance system efficiency. We compare in detail the features, frame structures, performances, advantages and disadvantages, and technical challenges associated with TWRs and FDRs. Using illustrations of quantitative performance, we demonstrate that both of these approaches can efficiently reduce resource wastage in relay-based communication systems.