TY - GEN
T1 - Optimal partial decode-and-forward rates for the Gaussian MIMO relay channel using the GSVD
AU - Gerdes, Lennart
AU - Weiland, Lorenz
AU - Utschick, Wolfgang
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014/10/31
Y1 - 2014/10/31
N2 - In this paper, we consider the partial decode-and-forward (PDF) strategy for the Gaussian multiple-input multiple-output (MIMO) relay channel. The input distribution that maximizes the achievable PDF rate for this channel is still unknown in general. Therefore, it has so far only been possible to determine the maximum PDF rate if the best PDF strategy is equivalent to the decode-and-forward (DF) strategy, point-to-point (P2P) transmission from source to destination, or if PDF achieves the cut-set bound (CSB), i.e., for special cases where Gaussian channel inputs are known to be optimal. In this work, we exploit the properties of the generalized singular value decomposition (GSVD) to show that the maximum PDF rate for the Gaussian MIMO relay channel is also achieved by Gaussian inputs if the row spaces of the source-relay and the source-destination channel gain matrices are disjoint. Furthermore, we show that the optimal PDF rate can be determined as the solution of a convex optimization problem in that case.
AB - In this paper, we consider the partial decode-and-forward (PDF) strategy for the Gaussian multiple-input multiple-output (MIMO) relay channel. The input distribution that maximizes the achievable PDF rate for this channel is still unknown in general. Therefore, it has so far only been possible to determine the maximum PDF rate if the best PDF strategy is equivalent to the decode-and-forward (DF) strategy, point-to-point (P2P) transmission from source to destination, or if PDF achieves the cut-set bound (CSB), i.e., for special cases where Gaussian channel inputs are known to be optimal. In this work, we exploit the properties of the generalized singular value decomposition (GSVD) to show that the maximum PDF rate for the Gaussian MIMO relay channel is also achieved by Gaussian inputs if the row spaces of the source-relay and the source-destination channel gain matrices are disjoint. Furthermore, we show that the optimal PDF rate can be determined as the solution of a convex optimization problem in that case.
KW - Gaussian relay channel
KW - MIMO
KW - generalized singular value decomposition
KW - partial decode-and-forward
UR - https://www.scopus.com/pages/publications/84932622076
U2 - 10.1109/SPAWC.2014.6941597
DO - 10.1109/SPAWC.2014.6941597
M3 - Conference contribution
AN - SCOPUS:84932622076
T3 - IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC
SP - 259
EP - 263
BT - 2014 IEEE 15th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 15th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2014
Y2 - 22 June 2014 through 25 June 2014
ER -