Abstract
Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser multiple-input multiple-output (MIMO) and interference alignment. Such CSIT is usually obtained by feedback from the receivers, but the feedback is subject to delays. The usual approach is to use the fed back information to predict the current channel state and then apply a scheme designed assuming perfect CSIT. When the feedback delay is large compared to the channel coherence time, such a prediction approach completely fails to achieve any multiplexing gain. In this paper, we show that even in this case, the completely stale CSI is still very useful. More concretely, we show that in an MIMO broadcast channel with K transmit antennas and K receivers each with 1 receive antenna, K/1+1/2+⋯+1/K(>1) degrees of freedom is achievable even when the fed back channel state is completely independent of the current channel state. Moreover, we establish that if all receivers have independent and identically distributed channels, then this is the optimal number of degrees of freedom achievable. In the optimal scheme, the transmitter uses the fed back CSI to learn the side information that the receivers receive from previous transmissions rather than to predict the current channel state. Our result can be viewed as the first example of feedback providing a degree-of-freedom gain in memoryless channels.
| Original language | English (US) |
|---|---|
| Article number | 6177666 |
| Pages (from-to) | 4418-4431 |
| Number of pages | 14 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 58 |
| Issue number | 7 |
| DOIs | |
| State | Published - 2012 |
| Externally published | Yes |
Bibliographical note
Funding Information:Manuscript received September 26, 2011; revised February 23, 2012; accepted March 27, 2012. Date of publication April 03, 2012; date of current version June 12, 2012. This work was supported in part by a gift from Qualcomm, Inc. and by the Air Force Office of Scientific Research under Grant FA9550-09-1-0317. An initial version of this paper has been reported as Technical Report No. UCB/EECS-2010-122 at the University of California–Berkeley, September 6, 2010. The material in this paper was presented in part at the 48th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, September 2010.
Keywords
- Feedback delay
- interference alignment
- multiple-antenna channels
- network coding, output feedback
- side information
- vector Gaussian broadcast channels