Physical-layer MIMO relaying

Abstract

Abstract-The physical-layer network coding (PNC) approach provides improved performance in many scenarios over "traditional" relaying techniques or network coding. This work addresses the generalization of PNC to wireless scenarios where network nodes have multiple antennas. We use a recent matrix decomposition, which allows, by linear pre-and postprocessing, to simultaneously transform both channel matrices to triangular forms, where the diagonal entries, corresponding to both channels, are equal. This decomposition, in conjunction with precoding, allows to convert any two-input multiple-access channel (MAC) into parallel MACs, over which single-antenna PNC may be used. The technique is demonstrated using the two-way relay channel with multiple antennas. For this case it is shown that, in the high signal-to-noise regime, the scheme approaches the cut-set bound, thus establishing the asymptotic network capacity.

Multiple-Input Multiple-Output Two-Way Relaying: A Space-Division Approach

“…Two time-slots are employed for each round of information exchange. Following the convention in [16]- [18], we assume that the two time-slots have the same duration. The extension of our results to the case of unequal durations is straightforward.…”

“…Then, each user recovers the message of the other user with the help of perfect knowledge of the self-message. From [16]- [18], the downlink rate-regions for the two strategies are the same given by (12) with (13a) (13b) Finally, an achievable rate-region of the overall scheme is the intersection of and .…”

“…Note that since both represent the common space of and . In , the signal directions of the two users can be efficiently aligned to a common set of directions, providing a platform to carry out PNC, as in [16]- [18]. On the other hand, in and , the two users do not interfere with each other; hence, the CD strategy can be employed.…”

“…In this case, efficient channel alignment techniques have been proposed in [16]- [18] for the implementation of PNC. In what follows, we are mainly interested in the case of , i.e., there exist valued between, but not including, 1 and 2.…”

“…Recall that is a square matrix, and the efficient design of PNC for this case has been studied in [16]- [18]. Here, we follow the GSVD-based approach in [16], as briefly described below.…”