Completely Stale Transmitter Channel State Information is Still Very Useful

• Published in: IEEE transactions on information theory Vol. 58; no. 7; pp. 4418 - 4431
• Main Authors: Maddah-Ali, Mohammad Ali, Tse, David
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antennas; Applied sciences; Communication channels; Delay; Detection, estimation, filtering, equalization, prediction; Equations; Exact sciences and technology; Feedback; Feedback delay; Information theory; Information, signal and communications theory; Input output; interference alignment; multiple-antenna channels; network coding; output feedback; Radiocommunications; Receivers & amplifiers; Receiving antennas; side information; Signal and communications theory; Signal to noise ratio; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters. Receivers; Transmitting antennas; vector Gaussian broadcast channels; Multiplexing; Parameter estimation; side information; Transmitter; Feedback regulation; interference alignment; multiple-antenna channels; Channel estimation; Broadcast channels; Intermediate frequency; Delay time; Optimal planning; Receiving antenna; Antenna array; MIMO system; Multiple access; Feedback delay; Packet switching; vector Gaussian broadcast channels; Gaussian channel; Memoryless channel; Transmitting antenna; Coherence; Network coding; Multiple channel; Output feedback
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2012.2193116

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 transmit antennas and 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.