The spatially correlated MIMO broadcast channel has grown in importance due to emerging interest in massive MIMO and mm-wave communication, but much about this channel remains unknown. In this paper, we study a two-user MIMO broadcast channel where the spatial correlation matrices corresponding to the two receivers have eigenspaces that are neither identical nor disjoint, but are partially overlapped. Spatially correlated channels occur in e.g. massive MIMO and furthermore different links may credibly have correlation eigenspaces that are neither disjoint nor equal, therefore this problem is practically motivated. This paper develops a new approach for this scenario and calculates the corresponding degrees of freedom. Our technique involves a careful decomposition of the signaling space to allow a combination of pre-beamforming along directions that depend on the relative positioning of the non-overlapping and overlapping components of the eigenspaces, along with the product superposition technique. The ideas are demonstrated with a toy example, are developed in two conditions of varying complexity, and are illuminated by numerical results.
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Transmit Correlation Diversity: Generalization, New Techniques, and Improved Bounds
When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. This idea was conceived for channels in which transmit correlation matrices have mutually exclusive eigenspaces, allowing non-interfering training and transmission. This paper broadens the scope of transmit correlation diversity to the case of partially and fully overlapping eigenspaces and introduces techniques to harvest these generalized gains. For the two-user MIMO broadcast channel, we derive achievable degrees of freedom (DoF) and achievable rate regions with/without channel state information at the receiver (CSIR). When CSIR is available, the proposed achievable DoF region is tight in some configurations of the number of receive antennas and the channel correlation ranks. We then extend the DoF results to the K-user case by analyzing the interference graph that characterizes the overlapping structure of the eigenspaces. Our achievability results employ a combination of product superposition in the common part of the eigenspaces, and pre-beamforming (rate splitting) to create multiple data streams in non-overlapping parts of the eigenspaces. Massive MIMO is a natural example in which spatially correlated link gains are likely to occur. We study the achievable downlink sum rate for a frequency-division duplex massive MIMO system under transmit correlation diversity.
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- NSF-PAR ID:
- 10317201
- Date Published:
- Journal Name:
- IEEE Transactions on Information Theory
- ISSN:
- 0018-9448
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TIT.2022.3146523
