Optimal Use of Current and Outdated Channel State Information - Degrees of Freedom of the MISO BC with Mixed CSIT

We consider a multiple-input-single-output (MISO) broadcast channel with mixed channel state information at the transmitter (CSIT) that consists of imperfect current CSIT and perfect outdated CSIT. Recent work by Kobayashi et al. presented a scheme which exploits both imperfect current CSIT and perfect outdated CSIT and achieves higher degrees of freedom (DoF) than possible with only imperfect current CSIT or only outdated CSIT individually. In this work, we further improve the achievable DoF in this setting by incorporating additional private messages, and provide a tight information theoretic DoF outer bound, thereby identifying the DoF optimal use of mixed CSIT. The new result is stronger even in the original setting of only delayed CSIT, because it allows us to remove the restricting assumption of statistically equivalent fading for all users

Degrees of Freedom of Time Correlated MISO Broadcast Channel with Delayed CSIT

We consider the time correlated multiple-input single-output (MISO) broadcast channel where the transmitter has imperfect knowledge on the current channel state, in addition to delayed channel state information. By representing the quality of the current channel state information as P^-{\alpha} for the signal-to-noise ratio P and some constant {\alpha} \geq 0, we characterize the optimal degree of freedom region for this more general two-user MISO broadcast correlated channel. The essential ingredients of the proposed scheme lie in the quantization and multicasting of the overheard interferences, while broadcasting new private messages. Our proposed scheme smoothly bridges between the scheme recently proposed by Maddah-Ali and Tse with no current state information and a simple zero-forcing beamforming with perfect current state information.Comment: revised and final version, to appear in IEEE transactions on Information Theor

On the Degrees of Freedom of time correlated MISO broadcast channel with delayed CSIT

We consider the time correlated MISO broadcast channel where the transmitter has partial knowledge on the current channel state, in addition to delayed channel state information (CSI). Rather than exploiting only the current CSI, as the zero-forcing precoding, or only the delayed CSI, as the Maddah-Ali-Tse (MAT) scheme, we propose a seamless strategy that takes advantage of both. The achievable degrees of freedom of the proposed scheme is characterized in terms of the quality of the current channel knowledge.Comment: 7 pages, 1 figure, submitted to ISIT 2012, extended version with detailed proof

Interference and X Networks with Noisy Cooperation and Feedback

The Gaussian $K$-user interference and $M\times K$ X channels are investigated with no instantaneous channel state information (CSI) at transmitters. First, it is assumed that the CSI is fed back to all nodes after a finite delay (delayed CSIT), and furthermore, the transmitters operate in full-duplex mode, i.e., they can transmit and receive simultaneously. Achievable results are obtained on the degrees of freedom (DoF) of these channels under the above assumption. It is observed that, in contrast with no CSIT and full CSIT models, when CSIT is delayed, the achievable DoFs for both channels with full-duplex transmitter cooperation are greater than the best available achievable results on their DoF without transmitter cooperation. Our results are the first to show that the full-duplex transmitter cooperation can potentially improve the channel DoF with delayed CSIT. Then, $K$-user interference and $K\times K$ X channels are considered with output feedback, wherein the channel output of each receiver is causally fed back to its corresponding transmitter. Our achievable results with output feedback demonstrate strict DoF improvements over those with the full-duplex delayed CSIT when $K>5$ in the $K$-user interference channel and $K>2$ in the $K\times K$ X channel. Next, the combination of delayed CSIT and output feedback, known as Shannon feedback, is studied and strictly higher DoFs compared to the output feedback model are achieved in the $K$-user interference channel when K=5 or $K>6$, and in the $K\times K$ X channel when $K>2$. Although being strictly greater than 1 and increasing with size of the networks, the achievable DoFs in all the models studied in this paper approach limiting values not greater than 2.Comment: 53 pages, 15 figures; Submitted to IEEE Transactions on Information Theory, May 2012. To be presented in part in ISIT 2012, Cambridge, MA, US