In order to increase performance of a system while saving power consumption, multiple hop MIMO relay systems\n(MHMRSs) have been considered. There are many researches on the physical (PHY) layer, medium access control\n(MAC) layer, and MAC-PHY cross-layer to avoid a co-channel interference, such as the matched/orthogonal weight\nalgorithm, TDMA-based smart antenna and so on. The matched/orthogonal algorithm is available for bi-directional\ncommunications; however, it requests at least three antenna elements at every relay. Consequently, it is unavailable\nfor small wireless devices that are being demanded. In this paper, we propose an algorithm to cancel the co-channel\ninterference of bi-directional communication MHMRSs by signal processing at receivers using precoding at\ntransmitters. The proposal algorithm can perform with only two antenna elements while maintaining character of\nMIMO. The proposal algorithm is compared to the TDMA-based smart antenna algorithm which also can perform\nwith two antenna elements, in both perfect and imperfect channel state information (CSI) schemes. Numerical\ncalculation results indicate that a channel capacity of proposal algorithm is much higher than that of TDMA-based\nsmart antenna algorithm in the perfect CSI scheme due to complete cancellation of co-channel interference and\nviability of bi-directional communications of proposal algorithm. In the imperfect CSI scheme, the channel capacity of\nthe TDMA-based smart antenna algorithm is more robust when channel estimation errors increase; however, the\nchannel capacity of proposal algorithm is still higher when the channel estimation error is large.
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