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 X Networks

We explore the degrees of freedom of $M\times N$ user wireless $X$ networks, i.e. networks of $M$ transmitters and $N$ receivers where every transmitter has an independent message for every receiver. We derive a general outerbound on the degrees of freedom \emph{region} of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the \emph{total} number of degrees of freedom of the $X$ network is equal to $\frac{MN}{M+N-1}$ per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for $X$ networks that can come arbitrarily close to the outerbound on degrees of freedom. For the case where either M=2 or N=2 we find that the outerbound is exactly achievable. While $X$ networks have significant degrees of freedom benefits over interference networks when the number of users is small, our results show that as the number of users increases, this advantage disappears. Thus, for large $K$, the $K\times K$ user wireless $X$ network loses half the degrees of freedom relative to the $K\times K$ MIMO outerbound achievable through full cooperation. Interestingly, when there are few transmitters sending to many receivers ($N\gg M$) or many transmitters sending to few receivers ($M\gg N$), $X$ networks are able to approach the $\min(M,N)$ degrees of freedom possible with full cooperation on the $M\times N$ MIMO channel. Similar to the interference channel, we also construct an example of a 2 user $X$ channel with propagation delays where the outerbound on degrees of freedom is achieved through interference alignment based on a simple TDMA strategy.Comment: 26 page

Feedback and Cooperation in Wireless Networks

The demand for wireless data services has been dramatically growing over the last decade. This growth has been accompanied by a significant increase in the number of users sharing the same wireless medium, and as a result, interference management has become a hot topic of research in recent years. In this dissertation, we investigate feedback and transmitter cooperation as two closely related tools to manage the interference and achieve high data rates in several wireless networks, focusing on additive white Gaussian noise (AWGN) interference, X, and broadcast channels. We start by a one-to-many network, namely, the three-user multiple-input multiple-output (MIMO) Gaussian broadcast channel, where we assume that the transmitter obtains the channel state information (CSI) through feedback links after a finite delay. We also assume that the feedback delay is greater than the channel coherence time, and thus, the CSI expires prior to being exploited by the transmitter for its current transmission. Nevertheless, we show that this delayed CSI at the transmitter (delayed CSIT) can help the transmitter to achieve significantly higher data rates compared to having no CSI. We indeed show that delayed CSIT increases the channel degrees of freedom (DoF), which is translated to an unbounded increase in capacity with increasing signal-to-noise-ratio (SNR). For the symmetric case, i.e. with the same number of antennas at each receiver, we propose different transmission schemes whose achievable DoFs meet the upper bound for a wide range of transmit-receive antenna ratios. Also, for the general non-symmetric case, we propose transmission schemes that characterize the DoF region for certain classes of antenna configurations. Subsequently, we investigate channels with distributed transmitters, namely, Gaussian single-input single-output (SISO) K-user interference channel and 2×K X channel under the delayed CSIT assumption. In these channels, in major contrast to the broadcast channel, each transmitter has access only to its own messages. We propose novel multiphase transmission schemes wherein the transmitters collaboratively align the past interference at appropriate receivers using the knowledge of past CSI. Our achievable DoFs are greater than one (which is the channel DoF without CSIT), and strictly increasing in K. Our results are yet the best available reported DoFs for these channels with delayed CSIT. Furthermore, we consider the K-user r-cyclic interference channel, where each transmitter causes interference on only r receivers in a cyclic manner. By developing a new upper bound, we show that this channel has K/r DoF with no CSIT. Moreover, by generalizing our multiphase transmission ideas, we show that, for r=3, this channel can achieve strictly greater than K/3 DoF with delayed CSIT. Next, we add the capability of simultaneous transmission and reception, i.e. full-duplex operation, to the transmitters, and investigate its impact on the DoF of the SISO Gaussian K-user interference and M×K X channel under the delayed CSIT assumption. By proposing new cooperation/alignment techniques, we show that the full-duplex transmitter cooperation can potentially yield DoF gains in both channels with delayed CSIT. This is in sharp contrast to the previous results on these channels indicating the inability of full-duplex transmitter cooperation to increase the channel DoF with either perfect instantaneous CSIT or no CSIT. With the recent technological advances in implementation of full-duplex communication, it is expected to play a crucial role in the future wireless systems. Finally, we consider the Gaussian K-user interference and K×K X channel with output feedback, wherein each transmitter causally accesses the output of its paired receiver. First, using the output feedback and under no CSIT assumption, we show that both channels can achieve DoF values greater than one, strictly increasing in K, and approaching the limiting value of 2 as K→∞. Then, we develop transmission schemes for the same channels with both output feedback and delayed CSIT, known as Shannon feedback. Our achievable DoFs with Shannon feedback are greater than those with the output feedback for almost all values of K

The DoF of the Asymmetric MIMO Interference Channel with Square Direct Link Channel Matrices

This paper studies the sum Degrees of Freedom (DoF) of $K$-user {\em asymmetric} MIMO Interference Channel (IC) with square direct link channel matrices, that is, the $u$-th transmitter and its intended receiver have $M_u\in\mathbb{N}$ antennas each, where $M_u$ need not be the same for all $u\in[1:K]$. Starting from a $3$-user example, it is shown that existing cooperation-based outer bounds are insufficient to characterize the DoF. Moreover, it is shown that two distinct operating regimes exist. With a {\it dominant} user, i.e., a user that has more antennas than the other two users combined, %(say $M_1\geq M_2+M_3$), it is DoF optimal to let that user transmit alone on the IC. Otherwise, it is DoF optimal to {\em decompose} and operate the 3-user MIMO IC as an $(M_1+ M_2+M_3)$-user SISO IC. This indicates that MIMO operations are useless from a DoF perspective in systems without a dominant user. The main contribution of the paper is the derivation of a novel outer bound for the general $K$-user case that is tight in the regime where a dominant user is not present; this is done by generalizing the insights from the 3-user example to an arbitrary number of users.Comment: Presented at 52nd Allerton Conference, 201

Signal-Aligned Network Coding in K-User MIMO Interference Channels with Limited Receiver Cooperation

In this paper, we propose a signal-aligned network coding (SNC) scheme for K-user time-varying multiple-input multiple-output (MIMO) interference channels with limited receiver cooperation. We assume that the receivers are connected to a central processor via wired cooperation links with individual limited capacities. Our SNC scheme determines the precoding matrices of the transmitters so that the transmitted signals are aligned at each receiver. The aligned signals are then decoded into noiseless integer combinations of messages, also known as network-coded messages, by physical-layer network coding. The key idea of our scheme is to ensure that independent integer combinations of messages can be decoded at the receivers. Hence the central processor can recover the original messages of the transmitters by solving the linearly independent equations. We prove that our SNC scheme achieves full degrees of freedom (DoF) by utilizing signal alignment and physical-layer network coding. Simulation results show that our SNC scheme outperforms the compute-and-forward scheme in the finite SNR regime of the two-user and the three-user cases. The performance improvement of our SNC scheme mainly comes from efficient utilization of the signal subspaces for conveying independent linear equations of messages to the central processor.Comment: 12 pages, 4 figures, submitted to the IEEE Transactions on Vehicular Technolog