When Does Spatial Correlation Add Value to Delayed Channel State Information?

Fast fading wireless networks with delayed knowledge of the channel state information have received significant attention in recent years. An exception is networks where channels are spatially correlated. This paper characterizes the capacity region of two-user erasure interference channels with delayed knowledge of the channel state information and spatially correlated channels. There are instances where spatial correlation eliminates any potential gain from delayed channel state information and instances where it enables the same performance that is possible with instantaneous knowledge of channel state. The key is an extremal entropy inequality for spatially correlated channels that separates the two types of instances. It is also shown that to achieve the capacity region, each transmitter only needs to rely on the delayed knowledge of the channels to which it is connected.Comment: To appear in ISIT 2016. arXiv admin note: text overlap with arXiv:1503.0344

On the Degrees of Freedom of MIMO X Networks with Non-Cooperation Transmitters

Due to limited backhaul/feedback link capacity and channel state information (CSI) feedback delay, obtaining global and instantaneous channel state information at the transmitter (CSIT) is a main obstacle in practice. In this paper, novel transmission schemes are proposed for a class of interference networks that can achieve new trade-off regions between the sum of degrees of freedom (sum-DoF) and CSI feedback delay with distributed and temperately-delayed CSIT. More specifically, a distributed space-time interference alignment (STIA) scheme is proposed for the two-user multiple-input multiple-output (MIMO) X channel via a novel precoding method called Cyclic Zero-padding. The achieved sum-DoFs herein for certain antenna configurations are greater than the best known sum-DoFs in literature with delayed CSIT. Furthermore, we propose a distributed retrospective interference alignment (RIA) scheme that achieves more than 1 sum-DoF for the K-user single-input single-output (SISO) X network. Finally, we extend the distributed STIA to the MxN user multiple-input single-output (MISO) X network where each transmitter has N-1 antennas and each receiver has a single antenna, yielding the same sum-DoF as that in the global and instantaneous CSIT case. The discussion and the result of the MISO X network can be extended to the MIMO case due to spatial scale invariance property.Comment: version 2, 31 pages, 7 figures, submitte

Approximate Capacity Region of the Two-User MISO Broadcast Channels with Delayed CSIT

We consider the problem of multiple-input single-output Broadcast Channels with Rayleigh fading where the transmitter has access to delayed knowledge of the channel state information. We first characterize the capacity region of this channel with two users to within constant number of bits for all values of the transmit power. The proposed signaling strategy utilizes the delayed knowledge of the channel state information and the previously transmitted signals, in order to create a signal of common interest for both receivers. This signal would be the quantized version of the summation of the previously transmitted signals. A challenge that arises in deriving the result for finite signal-to-noise ratio regimes is the correlation that exists between the quantization noise and the signal. To guarantee the independence of quantization noise and signal, we extend the framework of lattice quantizers with dither together with an interleaving step. For converse, we use the fact that the capacity region of this problem is upper-bounded by the capacity region of a physically degraded broadcast channel with no channel state information where one receiver has two antennas. Then, we derive an outer-bound on the capacity region of this degraded broadcast channel. Finally, we show how to extend our results to obtain the approximate capacity of the $K$-user multiple-input single-output Broadcast Channel with delayed knowledge of the channel state information at the transmitter to within $2 \log_2 \left( K + 2 \right)$ bits/s/Hz.Comment: Accepted for publication in IEEE Transactions on Communications. Preliminary results presented at the Fifty-First Annual Allerton Conference on Communication, Control, and Computin

Informational Bottlenecks in Two-Unicast Wireless Networks with Delayed CSIT

We study the impact of delayed channel state information at the transmitters (CSIT) in two-unicast wireless networks with a layered topology and arbitrary connectivity. We introduce a technique to obtain outer bounds to the degrees-of-freedom (DoF) region through the new graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed CSIT, and imply asymmetric DoF bounds of the form $mD_1 + D_2 \leq m$. Combining this outer-bound technique with new achievability schemes, we characterize the sum DoF of a class of two-unicast wireless networks, which shows that, unlike in the case of instantaneous CSIT, the DoF of two-unicast networks with delayed CSIT can take an infinite set of values.Comment: In proceedings of the 53rd Annual Allerton Conference on Communication, Control, and Computin

Throughput Region of Spatially Correlated Interference Packet Networks

In multi-user wireless packet networks interference, typically modeled as packet collision, is the throughput bottleneck. Users become aware of the interference pattern via feedback and use this information for contention resolution and for packet retransmission. Conventional random access protocols interrupt communication to resolve contention which reduces network throughput and increases latency and power consumption. In this work we take a different approach and we develop opportunistic random access protocols rather than pursuing conventional methods. We allow wireless nodes to communicate without interruption and to observe the interference pattern. We then use this interference pattern knowledge and channel statistics to counter the negative impact of interference. We prove the optimality of our protocols using an extremal rank-ratio inequality. An important part of our contributions is the integration of spatial correlation in our assumptions and results. We identify spatial correlation regimes in which inherently outdated feedback becomes as good as idealized instantaneous feedback, and correlation regimes in which feedback does not provide any throughput gain. To better illustrate the results, and as an intermediate step, we characterize the capacity region of finite-field spatially correlated interference channels with delayed channel state information at the transmitters.Comment: Accepted for publication in IEEE Transactions on Information Theor

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

Achieving Full DoF in Heterogeneous Parallel Broadcast Channels with Outdated CSIT

We consider communication over heterogeneous parallel channels, where a transmitter is connected to two users via two parallel channels: a MIMO broadcast channel (BC) and a noiseless rate-limited multicast channel. We characterize the optimal degrees of freedom (DoF) region of this setting when the transmitter has delayed channel state information (CSIT) regarding the MIMO BC. Our results show that jointly coding over the two channels strictly outperforms simple channel aggregation and can even achieve the instantaneous CSIT performance with completely outdated CSIT on the MIMO BC in the sum DoF sense; this happens when the multicast rate of the second channel is larger than a certain threshold. The main idea is to send information over the MIMO BC at a rate above its capacity and then use the second channel to send additional side information to allow for reliable decoding at both receivers. We call this scheme a two-phase overload-multicast strategy. We show that such a strategy is also sum DoF optimal for the K-user MIMO BC with a parallel multicast channel when the rate of the multicast channel is high enough and can again achieve the instantaneous CSIT performance (optimal sum DoF) with completely outdated CSIT. For the regime where the capacity of the multicast channel is small, we propose another joint coding strategy which is sum DoF optimal.Comment: Submitted to IEEE Transactions on Information Theory, September 2014. This work was presented in part at ISIT201

Retrospective Interference Alignment for Two-Cell Uplink MIMO Cellular Networks with Delayed CSIT

In this paper, we propose a new retrospective interference alignment for two-cell multiple-input multiple-output (MIMO) interfering multiple access channels (IMAC) with the delayed channel state information at the transmitters (CSIT). It is shown that having delayed CSIT can strictly increase the sum-DoF compared to the case of no CSIT. The key idea is to align multiple interfering signals from adjacent cells onto a small dimensional subspace over time by fully exploiting the previously received signals as side information with outdated CSIT in a distributed manner. Remarkably, we show that the retrospective interference alignment can achieve the optimal sum-DoF in the context of two-cell two-user scenario by providing a new outer bound.Comment: 7 pages, 2 figures, to appear in IEEE ICC 201

Layered Interference Networks with Delayed CSI: DoF Scaling with Distributed Transmitters

The layered interference network is investigated with delayed channel state information (CSI) at all nodes. It is demonstrated how multi-hopping can be utilized to increase the achievable degrees of freedom (DoF). In particular, a multi-phase transmission scheme is proposed for the $K$-user $2K$-hop interference network in order to systematically exploit the layered structure of the network and delayed CSI to achieve DoF values that scale with $K$. This result provides the first example of a network with distributed transmitters and delayed CSI whose DoF scales with the number of users.Comment: 32 pages, 6 figures, 4 tables; Accepted for publication in IEEE Transactions on Information Theor

The Synergistic Gains of Coded Caching and Delayed Feedback

In this paper, we consider the $K$-user cache-aided wireless MISO broadcast channel (BC) with random fading and delayed CSIT, and identify the optimal cache-aided degrees-of-freedom (DoF) performance within a factor of 4. The achieved performance is due to a scheme that combines basic coded-caching with MAT-type schemes, and which efficiently exploits the prospective-hindsight similarities between these two methods. This delivers a powerful synergy between coded caching and delayed feedback, in the sense that the total synergistic DoF-gain can be much larger than the sum of the individual gains from delayed CSIT and from coded caching. The derived performance interestingly reveals --- for the first time --- substantial DoF gains from coded caching, even when the (normalized) cache size $\gamma$ (fraction of the library stored at each receiving device) is very small. Specifically, a microscopic $\gamma \approx e^{-G}$ can come within a factor of $G$ from the interference-free optimal. For example, storing at each device only a \emph{thousandth} of what is deemed as `popular' content ($\gamma\approx 10^{-3}$), we approach the interference-free optimal within a factor of $ln(10^3) \approx 7$ (per user DoF of $1/7$), for any number of users. This result carries an additional practical ramification as it reveals how to use coded caching to essentially buffer CSI, thus partially ameliorating the burden of having to acquire real-time CSIT.Comment: 7 pages. Smaller part from a bigger journal submission arXiv:1511.0396