In many practical wireless systems, the Signal-to-Interference-and-Noise Ratio (SINR) that is applicable to a certain transmission, referred to as Channel State Information (CSI), can only be learned after the transmission has taken place and is thereby outdated (delayed). For example, this occurs under intermittent interference. We devise the backward retransmission (BRQ) scheme, which uses the delayed CSIT to send the optimal amount of incremental redundancy (IR). BRQ uses fixed-length packets, fixed-rate R transmission codebook, and operates as Markov block coding, where the correlation between the adjacent packets depends on the amount of IR parity bits. When the delayed CSIT is full and R grows asymptotically, the average throughput of BRQ becomes equal to the value achieved with prior CSIT and a fixed-power transmitter; however, at the expense of increased delay. The second contribution is a method for employing BRQ when a limited number of feedback bits is available to report the delayed CSIT. The main novelty is the idea to assemble multiple feedback opportunities and report multiple SINRs through vector quantization. This challenges the conventional wisdom in ARQ protocols where feedback bits are used to only quantize the CSIT of the immediate previous transmission.
@cite_1: The degrees of freedom (DoF) region of the two-user MIMO interference channel (IC) is completely characterized in the presence of noiseless channel output feedback from each receiver to its respective transmitter and with the assumption of delayed channel state information (CSI) at the transmitters. It is shown that having output feedback and delayed CSI at the transmitters can strictly enlarge the DoF region when compared to the case in which only delayed CSI is available at the transmitters. Furthermore, cases are identified in which output feedback and delayed CSI alone are sufficient to achieve the DoF region achievable with perfect, instantaneous CSI.
@cite_4: 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.
We remark here that the issue of delayed CSIT has recently sparkled a significant interest in terms of improvements that can be achieved in terms of Degrees of Freedom at high SNRs @cite_4 @cite_1 . However, that line of work does not deal with HARQ protocols and is directed towards multi-user scenarios, while in our case we consider relatively low SNR and a single link.