The Generalized Degrees of Freedom (GDoF) of the two user interference channel are characterized for all parameter regimes under the assumption of finite precision channel state information at the transmitters (CSIT), when a limited amount of (half-duplex or full-duplex) cooperation is allowed between the transmitters in the form of $π$ DoF of shared messages. In all cases, the number of over-the-air bits that each cooperation bit buys is shown to be equal to either $0, 1, 1/2$ or $1/3$. The most interesting aspect of the result is the $1/3$ slope, which appears only under finite precision CSIT and strong interference, and as such has not been encountered in previous studies that invariably assumed perfect CSIT. Indeed, the achievability and converse for the parameter regimes with $1/3$ slope are the most challenging aspects of this work. In particular, the converse relies on non-trivial applications of Aligned Images bounds.
Aligned-Images Sumset Inequalities are used in this work to study the Generalized Degrees of Freedom (GDoF) of the symmetric layered multi-hop interference channel under the robust assumption that the channel state information at the transmitters (CSIT) is limited to finite precision. First, the sum-GDoF value is characterized for the $2\times 2\times 2$ setting that is comprised of $2$ sources, $2$ relays, and $2$ destinations. It is shown that the sum-GDoF do not improve even if perfect CSIT is allowed in the first hop, as long as the CSIT in the second hop is limited to finite precision. Th…
For the $K=2$ user MISO BC, i.e., the wireless broadcast channel where a transmitter equipped with $K=2$ antennas sends independent messages to $K=2$ receivers each of which is equipped with a single antenna, the sum generalized degrees of freedom (GDoF) are characterized for arbitrary channel strength and channel uncertainty levels for each of the channel coefficients. The result is extended to $K>2$ users under additional restrictions which include the assumption of symmetry.
The generalized degrees of freedom (GDoF) region of the multiple-input multiple-output (MIMO) Gaussian Z-interference channel with an arbitrary number of antennas at each node is established under the assumption of delayed channel state information at transmitters (CSIT). The GDoF region is parameterized by $α$, which links the interference-to-noise ratio (INR) to the signal-to-noise ratio (SNR) via $INR=SNR^α$. A new outer bound for the GDoF region is established by maximizing a bound on the weighted sum-rate of the two users, which in turn is obtained by using a combination of genie-aided si…
Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limi…
Generalized Degrees of Freedom (GDoF) are characterized for the symmetric $K$-user Multiple Input Multiple Output (MIMO) Interference Channel (IC) under the assumption that the channel state information at the transmitters (CSIT) is limited to finite precision. In this symmetric setting, each transmitter is equipped with $M$ antennas, each receiver is equipped with $N$ antennas, each desired channel (i.e., a channel between a transmit antenna and a receive antenna belonging to the same user) has strength $\sim P$, while each undesired channel has strength $\sim P^α$, where $P$ is a nominal SNR…
In this paper, we investigate the generalized degrees-of-freedom (GDoF) of the asymmetric interference channel with delayed channel state information at the transmitter (CSIT), where each transmitter has two antennas, each receiver has one antenna, and the strength for each interfering link can vary. The optimal sum-GDoF is characterized by matched converse and achievability proof. Through our results, we also reveal that in our antenna setting, the symmetric GDoF lower bound in [Mohanty et. al, TIT 2019] can be elevated, and the symmetric GDoF upper bound in [Mohanty et. al, TIT 2019] is tigh…
The generalized degrees of freedom (GDoF) characterization of the symmetric K-user interference channel is obtained under finite precision channel state information at the transmitters (CSIT). The symmetric setting is where each cross channel is capable of carrying degrees of freedom (DoF) while each direct channel is capable of carrying 1 DoF. Remarkably, under finite precision CSIT the symmetric K-user interference channel loses all the GDoF benefits of interference alignment. The GDoF per user diminish with the number of users everywhere except in the very strong (optimal for every receiver…
In this work, we study the generalized degrees-of-freedom (GDoF) of downlink and uplink cellular networks, modeled as Gaussian interfering broadcast channels (IBC) and Gaussian interfering multiple access channels (IMAC), respectively. We focus on regimes of low inter-cell interference, where single-cell transmission with power control and treating inter-cell interference as noise (mc-TIN) is GDoF optimal. Recent works have identified two relevant regimes in this context: one in which the GDoF region achieved through mc-TIN for both the IBC and IMAC is a convex polyhedron without the need for …
We study the generalized degrees-of-freedom (GDoF) of cellular networks under finite precision channel state information at the transmitters (CSIT). We consider downlink settings modeled by the interfering broadcast channel (IBC) under no multi-cell cooperation, and the overloaded multiple-input-single-output broadcast channel (MISO-BC) under full multi-cell cooperation. We focus on three regimes of interest: the mc-TIN regime, where a scheme based on treating inter-cell interference as noise (mc-TIN) was shown to be GDoF optimal for the IBC; the mc-CTIN regime, where the GDoF region achievabl…
We study the $K=3$ user multiple input single output (MISO) broadcast channel (BC) with $M=3$ antennas at the transmitter and $1$ antenna at each receiver, from the generalized degrees of freedom (GDoF) perspective, under the assumption that the channel state information at the transmitter (CSIT) is limited to finite precision. In particular, our goal is to identify a parameter regime where a simple layered superposition (SLS) coding scheme achieves the entire GDoF region. With $α_{ij}$ representing the channel strength parameter for the link from the $j^{th}$ antenna of the transmitter to the…
We consider the cache-aided MISO broadcast channel (BC) in which a multi-antenna transmitter serves $K$ single-antenna receivers, each equipped with a cache memory. The transmitter has access to partial knowledge of the channel state information. For a symmetric setting, in terms of channel strength levels, partial channel knowledge levels and cache sizes, we characterize the generalized degrees of freedom (GDoF) up to a constant multiplicative factor. The achievability scheme exploits the interplay between spatial multiplexing gains and coded-multicasting gain. On the other hand, a cut-set-ba…
This work analyses the Generalized Degrees-of-Freedom (GDoF) of the 2-User Multiple-Input Single-Output (MISO) Broadcast Channel (BC) in the so-called Distributed CSIT regime, with application to decentralized wireless networks. This regime differs from the classical limited CSIT one in that the CSIT is not just noisy but also imperfectly shared across the transmitters (TXs). Hence, each TX precodes data on the basis of local CSIT and statistical quality information at other TXs. We derive the GDoF result and obtain the surprising outcome that by specific accounting of the pathloss information…
Significant progress has been made recently in Generalized Degrees of Freedom (GDoF) characterizations of wireless interference channels (IC) and broadcast channels (BC) under the assumption of finite precision channel state information at the transmitters (CSIT), especially for smaller or highly symmetric network settings. A critical barrier in extending these results to larger and asymmetric networks is the inherent combinatorial complexity of such networks. Motivated by other fields such as extremal combinatorics and extremal graph theory, we explore the possibility of an extremal network t…
The impact of cooperation on interference management is investigated by studying an elemental wireless network, the so called symmetric interference relay channel (IRC), from a generalized degrees of freedom (GDoF) perspective. This is motivated by the fact that the deployment of relays is considered as a remedy to overcome the bottleneck of current systems in terms of achievable rates. The focus of this work is on the regime in which the interference link is weaker than the source-relay link in the IRC. Our approach towards studying the GDoF goes through the capacity analysis of the linear de…
The generalized degrees of freedom (GDoF) of the two user symmetric multiple input multiple output (MIMO) interference channel (IC) are characterized as a function of the channel strength levels and the level of channel state information at the transmitters (CSIT). In this symmetric setting, each transmitter is equipped with M antennas, each receiver is equipped with N antennas, and both cross links have the same strength parameter $α$ and the same channel uncertainty parameter $β$. The main challenge resides in the proof of the outer bound which is accomplished by a generalization of the alig…
Handling interference is one of the main challenges in the design of wireless networks. In this paper we study the application of cooperation for interference management in the weak interference (WI) regime, focusing on the Z-interference channel with a causal relay (Z-ICR), when the channel coefficients are subject to ergodic phase fading, all transmission powers are finite, and the relay is full-duplex. In order to provide a comprehensive understanding of the benefits of cooperation in the WI regime, we characterize, for the first time, two major performance measures for the ergodic phase fa…
The question of whether the degrees of freedom (DoF) of multi-user networks can be enhanced even under isotropic fading and no channel state information (or output feedback) at the transmitters (CSIT) is investigated. Toward this end, the two-user MIMO (multiple-input, multiple-output) broadcast and interference channels are studied with no side-information whatsoever at the transmitters and with receivers equipped with full-duplex radios. The full-duplex feature allows for receiver cooperation because each receiver, in addition to receiving the signals sent by the transmitters, can also simul…
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 w…
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…
In this work, we study the problem of the optimal dissemination of channel state information (CSI) among K spatially distributed transmitters (TXs) jointly cooperating to serve K receivers (RXs). One of the particularities of this work lies in the fact that the CSI is distributed in the sense that each TX obtains its own estimate of the global multi-user MIMO channel with no further exchange of information being allowed between the TXs. Although this is well suited to model the cooperation between non-colocated TXs, e.g., in cellular Coordinated Multipoint (CoMP) schemes, this type of setting …
Obtaining accurate Channel State Information (CSI) at the transmitters (TX) is critical to many cooperation schemes such as Network MIMO, Interference Alignment etc. Practical CSI feedback and limited backhaul-based sharing inevitably creates degradations of CSI which are specific to each TX, giving rise to a distributed form of CSI. In the Distributed CSI (D-CSI) broadcast channel setting, the various TXs design elements of the precoder based on their individual estimates of the global multiuser channel matrix, which intuitively degrades performance when compared with the commonly used centra…
Recently, it has been shown that in a cache-enabled interference channel, the storage at the transmit and receive sides are of equal value in terms of Degrees of Freedom (DoF). This is derived by assuming full Channel State Information at the Transmitter (CSIT). In this paper, we consider a more practical scenario, where a training/feedback phase should exist for obtaining CSIT, during which instantaneous channel state is not known to the transmitters. This results in a combination of delayed and current CSIT availability, called mixed CSIT. In this setup, we derive DoF of a cache-enabled inte…
In this work, the role of unidirectional limited rate transmitter cooperation is studied in the case of the 2-user Z interference channel (Z-IC) with secrecy constraints at the receivers, on achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings usi…
The K-user symmetric multiple input multiple output (MIMO) Gaussian interference channel (IC) where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log (INR) / log (SNR) level. Three outer bounds are derived, under different assumpti…
This work investigates the degrees of freedom (DoF) of the K-user multiple-input single-output (MISO) interference channel (IC) with imperfect delayed channel state information at the transmitters (dCSIT). For this setting, new DoF inner bonds are provided, and benchmarked with cooperation-based outer bounds. The achievability result is based on a precoding scheme that aligns the interfering received signals through time, exploiting the concept of Retrospective Interference Alignment (RIA). The proposed approach outperforms all previous known schemes. Furthermore, we study the proposed scheme …
In this paper, we analyze the ergodic sum-rate of a multi-cell downlink system with base station (BS) cooperation using regularized zero-forcing (RZF) precoding. Our model assumes that the channels between BSs and users have independent spatial correlations and imperfect channel state information at the transmitter (CSIT) is available. Our derivations are based on large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the BS and users approach to infinity with some fixed ratios. In particular, a deterministic equivalent expression of the ergodic sum-r…
This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e. where each transmitter has its individual channel knowledge, while the message can be assumed to be partially or entirely shared a priori betwee…
In this work, we study the value of cooperative transmission in wireless networks if no channel state information is available at the transmitters (no CSIT). Our focus is on large locally connected networks, where each transmitter is connected to the receiver that has the same index as well as L succeeding receivers. The cases of L=1 and L=2 represent Wyner's asymmetric and symmetric network models, respectively. The considered rate criterion is the per user Degrees of Freedom (puDoF) as the number of transmitter-receiver pairs goes to infinity. For the case when L=1, it was shown in previous …
Interference networks with no channel state information at the transmitter (CSIT) except for the knowledge of the connectivity graph have been recently studied under the topological interference management (TIM) framework. In this paper, we consider a similar problem with topological knowledge but in a distributed broadcast channel setting, i.e. a network where transmitter cooperation is enabled. We show that the topological information can also be exploited in this case to strictly improve the degrees of freedom (DoF) as long as the network is not fully connected, which is a reasonable assump…
The interference channel with common information (IC-CI) consists of two transmit-receive pairs that communicate over a common noisy medium. Each transmitter has an individual message for its paired receiver, and additionally, both transmitters have a common message to deliver to both receivers. In this paper, through explicit inner and outer bounds on the capacity region, we establish the capacity region of the Gaussian IC-CI to within a bounded gap of one bit, independently of the values of all channel parameters. Using this constant-gap characterization, the generalized degrees of freedom (…
The two-user multiple-input multiple-output (MIMO) fast-fading interference channel (IC) with an arbitrary number of antennas at each of the four terminals is studied under the settings of Shannon feedback, limited Shannon feedback, and output feedback, wherein all or certain channel matrices and outputs, or just the channel outputs, respectively, are available to the transmitters with a finite delay. While for most numbers of antennas at the four terminals, it is shown that the DoF regions with Shannon feedback and for the limited Shannon feedback settings considered here are identical, and e…
We consider the downlink of a multi-cell system with multi-antenna base stations and single-antenna user terminals, arbitrary base station cooperation clusters, distance-dependent propagation pathloss, and general "fairness" requirements. Base stations in the same cooperation cluster employ joint transmission with linear zero-forcing beamforming, subject to sum or per-base station power constraints. Inter-cluster interference is treated as noise at the user terminals. Analytic expressions for the system spectral efficiency are found in the large-system limit where both the numbers of users and…
A general time-varying feedback coding scheme is proposed for $M$-user fully connected symmetric Gaussian interference channels. Based on the analysis of the general coding scheme, we prove a theorem which gives a criterion for designing good time-varying feedback codes for Gaussian interference channels. The proposed scheme improves the Suh-Tse and Kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when $M=2$. This capacity improvement is more significant when the signal-to-noise ratio (SNR) is not very high. In addition, our coding scheme can b…
