GDoF of the MISO BC: Bridging the gap between finite precision CSIT and perfect CSIT

This work bridges the gap between sharply contrasting results on the degrees of freedom of the K user broadcast channel where the transmitter is equipped with K transmit antennas and each of the K receivers is equipped with a single antenna. This channel has K DoF when channel state information at the transmitter (CSIT) is perfect, but as shown recently, it has only 1 DoF when the CSIT is limited to finite precision. By considering the full range of partial CSIT assumptions parameterized by β ⋯ [0,1], such that the strength of the channel estimation error terms scales as ∼ SNR-β relative to the channel strengths which scale as ∼ SNR, it is shown that this channel has 1 - β + Kβ DoF. For K = 2 users with arbitrary βij parameters, the DoF are shown to be 1 + mini,j βij. To explore diversity of channel strengths, the results are further extended to the symmetric Generalized Degrees of Freedom setting where the direct channel strengths scale as ∼ SNR and the cross channel strengths scale as ∼ SNRα, α ⋯ [0,1], β ⋯ [0,α]. Here, the roles of α and β are shown to counter each other on equal terms, so that the sum GDoF value in the K user setting is (α - β) + K(1 - (α-β )) and for the 2 user setting with arbitrary βij, is 2 - α + mini,j βij

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

The Degrees of Freedom Region of Temporally Correlated MIMO Networks With Delayed CSIT

We consider the temporally-correlated Multiple-Input Multiple-Output (MIMO) broadcast channels (BC) and interference channels (IC) where the transmitter(s) has/have (i) delayed channel state information (CSI) obtained from a latency-prone feedback channel as well as (ii) imperfect current CSIT, obtained, e.g., from prediction on the basis of these past channel samples based on the temporal correlation. The degrees of freedom (DoF) regions for the two-user broadcast and interference MIMO networks with general antenna configuration under such conditions are fully characterized, as a function of the prediction quality indicator. Specifically, a simple unified framework is proposed, allowing to attain optimal DoF region for the general antenna configurations and current CSIT qualities. Such a framework builds upon block-Markov encoding with interference quantization, optimally combining the use of both outdated and instantaneous CSIT. A striking feature of our work is that, by varying the power allocation, every point in the DoF region can be achieved with one single scheme. As a result, instead of checking the achievability of every corner point of the outer bound region, as typically done in the literature, we propose a new systematic way to prove the achievability.Comment: Revised to IEEE Trans. Inf. Theory. A new simple and unified framework is proposed, allowing to attain optimal DoF region for general antenna configurations and current CSIT qualities. A striking feature is that, every corner point in the DoF region can be achieved with one single scheme, and hence a new systematic way is proposed to prove the achievability instead of checking every corner poin