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

Elements of Cellular Blind Interference Alignment --- Aligned Frequency Reuse, Wireless Index Coding and Interference Diversity

We explore degrees of freedom (DoF) characterizations of partially connected wireless networks, especially cellular networks, with no channel state information at the transmitters. Specifically, we introduce three fundamental elements --- aligned frequency reuse, wireless index coding and interference diversity --- through a series of examples, focusing first on infinite regular arrays, then on finite clusters with arbitrary connectivity and message sets, and finally on heterogeneous settings with asymmetric multiple antenna configurations. Aligned frequency reuse refers to the optimality of orthogonal resource allocations in many cases, but according to unconventional reuse patterns that are guided by interference alignment principles. Wireless index coding highlights both the intimate connection between the index coding problem and cellular blind interference alignment, as well as the added complexity inherent to wireless settings. Interference diversity refers to the observation that in a wireless network each receiver experiences a different set of interferers, and depending on the actions of its own set of interferers, the interference-free signal space at each receiver fluctuates differently from other receivers, creating opportunities for robust applications of blind interference alignment principles

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

Degrees of freedom of wireless interference network

Wireless communication systems are different from the wired systems mainly in three aspects: fading, broadcast, and superposition. Wireless communication networks, and multi-user communication networks in general, have not been well understood from the information-theoretic perspective: the capacity limits of many multi-user networks are not known. For example, the capacity region of a two-user single-antenna interference channel is still not known, though recent result can bound the region up to a constant value. Characterizing the capacity limits of multi-user multiple-input multiple-output (MIMO) interference network is usually even more difficult than the single antenna setup. To alleviate the difficulty in studying such networks, the concept of degrees of freedom (DoF) has been adopted, which captures the first order behavior of the capacities or capacity regions. One important technique developed recently for quantifying the DoF of multi-user networks is the so-called interference alignment. The purpose of interference alignment is to design the transmit signals structurally so that the interference signals from multiple interferers are aligned to reduce the signal dimensions occupied by interference. In this thesis, we mainly study two problems related to DoF and interference alignment: 1) DoF region of MIMO full interference channel (FIC) and Z interference channel (ZIC) with reconfigurable antennas, and 2) the DoF region of an interference network with general message demands. For the first problem, we derive the outer bound on the DoF region and show that it is achievable via time-sharing or beamforming except for one special case. As to this particular special case, we develop a systematic way of constructing the DoF-achieving nulling and beamforming matrices. Our results reveal the potential benefit of using the reconfigurable antenna in MIMO FIC and ZIC. In addition, the achievability scheme has an interesting space-frequency interpretation. For the second problem, we derive the DoF region of a single antenna interference network with general message demands, which includes the multiple unicasts and multiple multicasts as special cases. We perform interference alignment using multiple base vectors and align the interference at each receiver to its largest interferer. Furthermore, we show that the DoF region is determined by a subset of receivers, and the DoF region can be achieved by considering a smaller number of interference alignment constraints so as to reduce the number of time expansion. Finally, as a related research topic, we also include a result on the average throughput of a MIMO interference channel with single-user detector at receivers and without channel state information at transmitters. We present a piecewise linear approximation of the channel throughput under weak, moderate and strong interference regimes. Based on that we determine the optimal number of streams that a transmitter should use for different interference levels