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In order to gain new insights into multiple-input-multiple-output (MIMO) interference networks, the optimality ofσk=1 K Mk/2 (half the cake per user) degrees of freedom is explored for a K-user MIMO interference channel where the cross-channels have arbitrary rank constraints, and the k th transmitter and receiver are equipped with Mk antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have M antennas; and by Tang et al., of full rank interference channels where the k th user pair has Mk antennas. The broader outcome of this paper is a novel class of replication-based outer bounds for arbitrary rank-constrained MIMO interference networks where replicas of existing users are added as auxiliary users and the network connectivity is chosen to ensure that any achievable scheme for the original network also works in the new network. The replicated network creates a new perspective of the problem, so that even simple arguments such as user cooperation become quite powerful when applied in the replicated network, giving rise to stronger outer bounds, than when applied directly in the original network. Remarkably, the replication-based bounds are broadly applicable not only to MIMO interference channels with arbitrary rank-constraints, but much more broadly, even beyond Gaussian settings.

Aligned-Images Sum-set 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 does 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. The sum GDoF characterization is then generalized to the $2\times 2\times \cdots \times 2$ setting that is comprised of $L$ hops. Remarkably, for large $L$ , the sum-GDoF value approaches that of the one-hop broadcast channel that is obtained by full cooperation among the two transmitters of the last hop, with finite precision CSIT. Previous studies of multi-hop interference networks either identified sophisticated GDoF optimal schemes under perfect CSIT, such as aligned interference neutralization and network diagonalization, that are powerful in theory but too fragile to be practical, or studied robust achievable schemes like classical amplify/decode/compress-and-forward without claims of information-theoretic optimality. In contrast, under finite precision CSIT, we show that the benefits of fragile schemes are lost, while a combination of classical random coding schemes that are simpler and much more robust, namely a rate-splitting between decode-and-forward and amplify-and-forward, is shown to be GDoF optimal. As such, this work represents another step towards bridging the gap between theory (optimality) and practice (robustness) with the aid of Aligned-Images Sum-set Inequalities. [ABSTRACT FROM AUTHOR]

In order to discover larger networks and parameter regimes where sharp Generalized Degrees of Freedom (GDoF) characterizations may be found based on the optimality of robust schemes for interference and broadcast networks with channel state information at the transmitters (CSIT) limited to finite precision, we explore the impact of secrecy constraints. In the absence of secrecy constraints, the largest such parameter regime for $K$ user interference networks is the CTIN regime (so named for the Convexity of the GDoF region achieved by Treating Interference as Noise (TIN)) originally discovered by Yi and Caire, whose optimality was established by Chan et al. For the corresponding broadcast networks the largest regime is the SLS (Simple Layered Superposition) regime discovered by Davoodi and Jafar, but only for small networks with $K\leq 3$ users. By including secrecy constraints, we identify much larger regimes, the STIN regime and the SLS regime, where GDoF are fully characterized for arbitrary number of users under finite precision CSIT, for interference networks and broadcast networks, respectively. The optimal achievable scheme in both cases is based on TIN along with power control and jamming. Proofs of optimality rely on a combination of secrecy constraints and Aligned Images sum-set inequalities. [ABSTRACT FROM AUTHOR]

Blind Interference Alignment (BIA) schemes create and exploit channel coherence patterns without the knowledge of channel realizations at transmitters, while beamforming schemes rely primarily on channel knowledge available to the transmitters without regard to channel coherence patterns. In order to explore the compatibility of these disparate ideas and the possibility of synergistic gains, this work studies the Degrees of Freedom (DoF) of the 2-user ${(M_{1}\times N_{1})(M_{2}\times N_{2})}$ Multiple-Input Multiple-Output (MIMO) Interference Channel (IC) where Transmitter 1 is equipped with reconfigurable antennas and has no channel knowledge, while Transmitter 2 has partial channel knowledge but no reconfigurable antennas. Taking a fundamental dimensional analysis perspective, the main question is to identify which antenna configurations allow synergistic DoF gains. The main results of this work are two-fold. The first result identifies antenna configurations where both reconfigurable antennas and partial channel knowledge are individually beneficial, as those where $M_{1}< N_{1}< \min (M_{2},N_{2})$. The second result shows that synergistic gains exist in each of these settings, over the best known solutions that rely on either reconfigurable antennas or partial channel knowledge alone. Coding schemes that jointly exploit partial channel knowledge and reconfigurable antennas emerge as a byproduct of the analysis. [ABSTRACT FROM AUTHOR]

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background of this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, we formulate a TIM-TIN problem for multilevel topological interference management, wherein only a coarse knowledge of channel strengths and no knowledge of channel phases is available to transmitters. To address the TIM-TIN problem, we first propose an analytical baseline approach, which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network. Next, a distributed numerical algorithm called ZEST is developed. The convergence of the algorithm is demonstrated, leading to the duality of the TIM-TIN problem in terms of generalized degrees-of-freedom (GDoF). Numerical results are also provided to demonstrate the superior sum-rate performance and fast convergence of ZEST. [ABSTRACT FROM AUTHOR]

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 $\pi $ 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. [ABSTRACT FROM AUTHOR]

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 theory, i.e., a study of extremal networks within particular regimes of interest. As our test application, we study the GDoF benefits of transmitter cooperation in a K user IC over the simple scheme of power control and treating interference as Gaussian noise (TIN) for three regimes of interest – a TIN regime identified by Geng et al. where TIN was shown to be GDoF optimal for the K user interference channel, a CTIN regime identified by Yi and Caire where the GDoF region achievable by TIN is convex without time-sharing, and an SLS regime identified by Davoodi and Jafar where a simple layered superposition (SLS) scheme is shown to be optimal in the K user MISO BC, albeit only for $ {K}\leq 3$. The SLS regime includes the CTIN regime, and the CTIN regime includes the TIN regime. As our first result, we show that under finite precision CSIT, TIN is GDoF optimal for the K user IC throughout the CTIN regime. Furthermore, under finite precision CSIT, appealing to extremal network theory we obtain the following results. In the TIN regime as well as the CTIN regime, we show that the extremal GDoF gain from transmitter cooperation over TIN is bounded regardless of the number of users. In fact, the gain is exactly a factor of 3/2 in the TIN regime, and $2-1/{K}$ in the CTIN regime, for arbitrary number of users ${K}>1$. However, in the SLS regime, the gain is $\Theta (\log _{2}({K}))$ , i.e., it scales logarithmically with the number of users. [ABSTRACT FROM AUTHOR]

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 the 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 $\alpha _{ij}$ representing the channel strength parameter for the link from the $j^{th}$ antenna of the transmitter to the $i^{th}$ receiver, we prove that the SLS is GDoF optimal without the need for time-sharing if $\max (\alpha _{ki},\alpha _{im})\leq \alpha _{ii}$ and $\alpha _{ki}+\alpha _{im}\le \alpha _{ii}+\alpha _{km}$ for all $i,k\in [{3}],m\in [M]$. The GDoF region under this condition is a convex polyhedron. The result generalizes to arbitrary $M\geq 3$. [ABSTRACT FROM AUTHOR]

Generalized degrees of freedom (GDoF) are characterized for the symmetric $K$ -user multiple-input multiple-output interference channel under the assumption that the channel-state information at the transmitters (CSITs) 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^\alpha $ , where $P$ is a nominal SNR parameter. The result generalizes a previous GDoF characterization for the SISO setting $(M=N=1)$ and is enabled by a significant extension of the aligned image sets bound that is broadly useful. GDoF per user take the form of a $W$ -curve with respect to $\alpha $ for fixed values of $M$ and $N$. Under finite precision CSIT, in spite of the presence of multiple antennas, all the benefits of interference alignment are lost. [ABSTRACT FROM AUTHOR]

The generalized degrees of freedom of the two-user symmetric multiple input multiple output interference channel are characterized as a function of the channel strength levels and the level of channel state information at the transmitters. 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 $\alpha $ and the same channel uncertainty parameter $\beta $. The main challenge resides in the proof of the outer bound which is accomplished by a generalization of the aligned image sets approach. [ABSTRACT FROM AUTHOR]

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 generalized degrees of freedom (GDoFs) region 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. [ABSTRACT FROM AUTHOR]

In this letter, we revisit the duality of treating interference as noise from the generalized degrees-of-freedom (GDoF) perspective. Specifically, in a general $K$ -user interference channel, where interference is treated as Gaussian noise, we demonstrate, for any given GDoF tuple and its power allocation, how to derive a power allocation that yields a dominant GDoF tuple in its reciprocal channel. This finding naturally leads to a fast iterative GDoF-duality-based power control algorithm. Numerical results show that the proposed algorithm achieves competitive sum-rate performance with sophisticated signal-to-interference-plus-noise ratio-based power control scheme. [ABSTRACT FROM PUBLISHER]

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 $\alpha $ 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 to decode all messages) and very weak (optimal to treat all interference as noise) interference regimes. The result stands in sharp contrast to prior work on the symmetric setting under perfect CSIT, where the GDoF per user remain undiminished due to interference alignment. The result also stands in contrast to prior work on a subclass of asymmetric settings under finite precision CSIT, i.e., the topological interference management problem, where interference alignment plays a crucial role and provides substantial GDoF benefits. [ABSTRACT FROM PUBLISHER]

The benefits of partial and full transmitter cooperation are evaluated for a two user interference channel under finite precision channel state information at the transmitters (CSITs), using the generalized degrees of freedom (GDoFs) metric. Under finite precision CSIT, the benefits of interference alignment are completely lost, so that the $X$ channel obtained by partial transmitter cooperation does no better than the underlying interference channels. Full transmitter cooperation produces a vector broadcast channel, which has a strict GDoF advantage over partial cooperation ( $X$ channel) and whose GDoF is fully achieved by interference enhancement. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel “genie chains” approach to obtain information theoretic degrees of freedom (DoF) outer bounds for MIMO wireless interference networks. This new approach creates a chain of mappings from genie signals provided to a receiver to the exposed signal spaces at that receiver, and then the exposed signal spaces serve as the genie signals for the next receiver in the chain subject to certain linear independence requirements. Our approach essentially converts an information theoretic DoF outer bound problem into a linear algebra problem. Several applications of the genie chains approach are presented. [ABSTRACT FROM AUTHOR]

In a $K$ -user Gaussian interference channel, it has been shown by Geng et al. that if for each user, the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then power control and treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we generalize the optimality of TIN to compound networks. We show that for a $K$ -user compound Gaussian interference channel, if in every possible state for each receiver, the channel always satisfies the TIN-optimality condition identified by Geng et al., then the GDoF region of the compound channel is the intersection of the GDoF regions of all possible network realizations, which is achievable by power control and TIN. Furthermore, we demonstrate that for a general $K$ -user compound interference channel, regardless of the number of states of each receiver, we can always construct a counterpart $K$ -user regular interference channel that has the same TIN region as the original compound channel. The regular interference channel has only one state for each receiver, which may be different from all of the original states. Solving the GDoF-based power control problem for the compound channel is equivalent to solving the same problem in its regular counterpart. Exploring the power control problem further we develop a centralized power control scheme for $K$ -user compound interference channels, to achieve all the Pareto optimal GDoF tuples. Finally, based on this scheme, we devise an iterative power control algorithm which requires at most $K$ updates to obtain the globally optimal power allocation for any feasible GDoF tuple. [ABSTRACT FROM PUBLISHER]

We study the degrees of freedom (DoF) of the layered $2 \times 2 \times 2$ multiple-input-multiple-output (MIMO) interference channel where each node is equipped with arbitrary number of antennas, the channels between the nodes have arbitrary rank constraints, and subject to the rank-constraints the channel coefficients can take arbitrary values. The DoF outer bounds reveal a fundamental rank-matching phenomenon, reminiscent of impedance matching in circuit theory. It is well known that the maximum power transfer in a circuit is achieved not for the maximum or minimum load impedance but for the load impedance that matches the source impedance. Similarly, the maximum DoF in the rank-constrained $2 \times 2 \times 2$ MIMO interference network is achieved not for the maximum or minimum ranks of the destination hop, but when the ranks of the destination hop match the ranks of the source hop. In fact, for mismatched settings of interest, the outer bounds identify a DoF loss penalty that is precisely equal to the rank-mismatch between the two hops. For symmetric settings, we also provide achievability results to show that along with the min-cut max-flow bounds, the rank-mismatch bounds are the best possible, i.e., they hold for all channels that satisfy the rank-constraints and are tight for almost all channels that satisfy the rank-constraints. Limited extensions—from sum-DoF to DoF region, from 2 unicasts to $X$ message sets, from 2 hops to more than 2 hops and from 2 nodes per layer to more than 2 nodes per layer—are considered to illustrate how the insights generalize beyond the elemental $2 \times 2 \times 2$ channel model. [ABSTRACT FROM AUTHOR]

Recently, Geng et al. have shown that from the perspective of generalized degrees of freedom (GDoF), power control and treating interference as noise (TIN) is optimal for a broad class of Gaussian interference channels. In this work, we show that for TIN-optimal interference channels identified by Geng et al., secrecy constraints on unintended messages incur no GDoF penalty, which leads us to a secure capacity region characterization within a constant gap. [ABSTRACT FROM PUBLISHER]

In a $K$ -user Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we show that for such TIN-optimal interference channels, even if the message set is expanded to include an independent message from each transmitter to each receiver, operating the new channel as the original interference channel and treating interference as noise is still optimal for the sum capacity up to a constant gap. Furthermore, we extend the result to the sum-GDoF optimality of TIN in the general setting of $X$ channels with arbitrary numbers of transmitters and receivers. [ABSTRACT FROM PUBLISHER]

We characterize the degrees of freedom (DoF) of multiple-input and multiple-output (MIMO) interference channels with rank-deficient channel matrices. For the two-user rank-deficient MIMO interference channel, we provide a tight outer bound to show that the previously known achievable DoF in the symmetric case is optimal and generalize the result to fully asymmetric settings. For the $K$ -user rank-deficient interference channel, we improve the previously known achievable DoF and provide a tight outer bound to establish optimality in symmetric settings. In particular, we show that for the K$ -user rank-deficient interference channel, when all nodes have M$ antennas, all direct channels have rank , all cross channels are of rank D$ , and the channels are otherwise generic, the optimal DoF value per user is \min (D_{0},M-({\min (M,(K-1)D)}/{2})) . Notably for interference channels, the rank-deficiency of direct channels does not help and the rank deficiency of cross-channels does not hurt. The main technical challenge is to account for the spatial dependences introduced by rank deficiencies in the interference alignment schemes that typically rely on the independence of channel coefficients. [ABSTRACT FROM PUBLISHER]

Starting from the elemental $2\times 2\times 2$ interference channel, there has been much progress in the understanding of multihop multiflow wireless networks through degrees of freedom (DoF) studies that have produced important ideas such as (aligned) interference neutralization. However, much of this progress has been limited to layered connectivity models that are essentially motivated by the assumption that wireless networks can only operate in half-duplex mode. Motivated by recent breakthroughs in full-duplex radio technology, in this work, we expand the $2\times 2\times 2$ interference channel model beyond layered connectivity in order to study the impact of full-duplex operation. In particular, we study the impact of intra-layer connectivity between relays that are in the same layer, the impact of direct inter-layer connectivity between sources and destinations, and the impact of intermediate inter-layer connectivity that connects sources or destinations, not directly to each other, but to relay nodes in non-adjacent layers in a $2\times 2\times 2\times 2$ interference channel. We show that intra-layer links and intermediate inter-layer interference links do not cause a collapse of DoF, whereas direct interference links do cause a collapse of DoF. [ABSTRACT FROM PUBLISHER]

This paper explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over \(\mathbb {F}_{\!p^n}\) are analogous to \(n\times n\) vector (MIMO) channels in the wireless setting, but with an important distinction—there is additional structure due to finite field arithmetic, which enforces commutativity of matrix multiplication and limits the channel diversity to \(n\) , making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2-user X channel and linear capacity of the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over \(\mathbb {F}_{\!p^n}\) also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between \(p\) and SNR, and \(n\) and diversity. [ABSTRACT FROM AUTHOR]

We show that the three-user MT\times MR Multiple-Input Multiple-Output (MIMO) interference channel where each transmitter is equipped with MT antennas and each receiver is equipped with MR antennas has $d(M,N)\triangleq\min\left({{M}\over{2-1/\kappa}},{{N}\over{2+1/\kappa}}\right) degrees of freedom (DoF) normalized by time, frequency, and space dimensions, where M\triangleq\min(MT,MR) , N\triangleq\max(MT,MR) , $\kappa\triangleq\lceil{{M}\over{N-M}}\rceil . While the DoF outer bound of d(M,N) is established for every d(M,N) DoF is established in general subject to a normalization with respect to spatial extensions, i.e., the scaling of the number of antennas at all nodes. In particular, we show that q d(M,N) MIMO interference channel, for some positive integer q , which may be seen as a spatial extension factor. q is the scaling factor needed to make the value qd(M,N) an integer. Given spatial extensions, the achievability relies only on linear beamforming based interference alignment schemes and requires neither channel extensions nor channel variations in time or frequency. In the absence of spatial extensions, it is shown through examples how essentially the same interference alignment scheme may be applied over time-extensions over either constant or time-varying channels. The central new insight to emerge from this paper is the notion of subspace alignment chains as the DoF bottlenecks. The subspace alignment chains are instrumental both in identifying the extra dimensions to be provided by a genie to a receiver for the DoF outer bound, as well as in the construction of the optimal interference alignment schemes. The DoF value d(M,N) is a piecewise linear function of M , N , with either and \cal B\triangleq\1/3,3/5,5/7,\ldots\ . The set A contains all those values of M/N and only those values of M/N for which there is redundancy in both M and N contains all those values of M/N and only those values of M/N for which there is no redundancy in either M or N and \cal B represent settings with maximum and minimum redundancy, essentially they are the basis for the DoF outer bounds and inner bounds, respectively. Our results settle the question of feasibility of linear interference alignment, introduced previously by Cenk et al. , for the three-user MT\times MR MIMO interference channel, completely for all values of MT , MR . In particular, we show that the linear interference alignment problem (MT\times MR, d)^{3} (as defined in previous paper by Cenk et al. ) is feasible if and only if d\leq\lfloor d(M,N)\rfloor . With the exception of the values M/N\in{\cal B} , and only with that exception, we show that for every M/N value there are proper systems (as defined by Cenk et al. ) that are not feasible. Evidently the redundancy contained in all other values of M/N manifests itself as superfluous variables that are not discounted in the definition of proper systems, thus creating a discrepancy between proper and feasible systems. Our results show that M/N\in{\cal A} are the only values for which there is no DoF benefit of joint processing among co-located antennas at the transmitters or receivers. This may also be seen as a consequence of the maximum redundancy in the M/N\in{\cal A}$ settings. [ABSTRACT FROM AUTHOR]

This paper develops a new communication strategy, ergodic interference alignment, for the K-user interference channel with time-varying fading. At any particular time, each receiver will see a superposition of the transmitted signals plus noise. The standard approach to such a scenario results in each transmitter–receiver pair achieving a rate proportional to 1/K its interference-free ergodic capacity. However, given two well-chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two observations, each receiver can obtain its desired signal without any interference. If the channel gains have independent, uniform phases, this technique allows each user to achieve at least 1/2 its interference-free ergodic capacity at any signal-to-noise ratio. Prior interference alignment techniques were only able to attain this performance as the signal-to-noise ratio tended to infinity. Extensions are given for the case where each receiver wants a message from more than one transmitter as well as the “X channel” case (with two receivers) where each transmitter has an independent message for each receiver. Finally, it is shown how to generalize this strategy beyond Gaussian channel models. For a class of finite field interference channels, this approach yields the ergodic capacity region. [ABSTRACT FROM PUBLISHER]

We explore the capacity and generalized degrees of freedom (GDOF) of the two-user Gaussian X channel, i.e., a generalization of the two-user interference channel where there is an independent message from each transmitter to each receiver. There are three main results in this paper. First, we characterize the sum capacity of the deterministic X channel under a symmetric setting. Second, we characterize the GDOF of the Gaussian X channel under a similar symmetric model. Third. we extend the sum capacity characterization previously obtained for the Gaussian interference channel in the noisy interference regime to the Gaussian X channel. Specifically, we show that the Gaussian X channel has the same sum capacity as the underlying Gaussian interference channel in this regime. [ABSTRACT FROM PUBLISHER]

We show that the 2\,\times \,2\,\times \,2 interference network, i.e., the multihop interference network formed by concatenation of two two-user interference channels achieves the min-cut outer bound value of 2 DoF, for almost all values of channel coefficients, for both time-varying or fixed-channel coefficients. The key to this result is a new idea, called aligned interference neutralization, that provides a way to align interference terms over each hop in a manner that allows them to be canceled over the air at the last hop. [ABSTRACT FROM PUBLISHER]

Maddah-Ali and Tse recently introduced the idea of retrospective interference alignment, i.e., achieving interference alignment with only outdated (stale) channel state information at the transmitter (CSIT), in the context of the vector broadcast channel. Since the scheme relies on the centralized transmitter's ability to reconstruct all the interference seen in previous symbols, it is not clear if retrospective interference alignment can be applied in interference networks consisting of distributed transmitters and receivers, where interference is contributed by multiple transmitters, each of whom can reconstruct only the part of the interference caused by themselves. In this work, we prove that even in such settings, retrospective interference alignment is feasible. Specifically, we show that it is possible to achieve more than 1 degrees of freedom (DoF) based on only delayed CSIT in the 3-user interference channel and the 2-user X channel consisting of only single antenna nodes. Retrospective interference alignment is also shown to be possible in other settings, such as the 2-user multiple-input and multiple-output (MIMO) interference channel and with delayed channel output feedback. [ABSTRACT FROM PUBLISHER]

We study the effect of the absence of channel knowledge at the transmitters for multiple-input-multiple-output (MIMO) networks. Specifically, we assume perfect channel state information at the receivers, no channel state information at the transmitter(s), and independent identically distributed (i.i.d.) Rayleigh fading across antennas, users and time slots. We provide the characterization of the degrees of freedom (DoF) region for a 2-user MIMO broadcast channel. We then provide a DoF region outer bound for a 2-user MIMO interference channel. This bound is shown to be tight for all possible combinations of the number of antennas at each node except for one case. To analyze the unsolved case, we point out the potential of interference alignment in the 2-user MIMO interference channel with no channel state information at the transmitters. As a byproduct, we explore a special class of MIMO broadcast channels where the capacity region is established by using the outer bound developed in the DoF analysis. [ABSTRACT FROM AUTHOR]

Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work, we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory. [ABSTRACT FROM AUTHOR]

We provide inner bound and outer bound for the total number of degrees of freedom of the K user multiple-input multiple-output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver if the channel coefficients are time-varying and drawn from a continuous distribution. The bounds are tight when the ratio \max(M,N) \over \min(M,N)=R is equal to an integer. For this case, we show that the total number of degrees of freedom is equal to \min(M,N)K if K \leq R and \min(M,N)R \over R+1K if K > R. Achievability is based on interference alignment. We also provide examples where using interference alignment combined with zero forcing can achieve more degrees of freedom than merely zero forcing for some MIMO interference channels with constant channel coefficients. [ABSTRACT FROM PUBLISHER]

We explore the feasibility of interference alignment in signal vector space—based only on beamforming—for K-user MIMO interference channels. Our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry. It is well known, e.g., from Bezout's theorem, that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables. Following this intuition, we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables. Rigorous connections between feasible and proper systems are made through Bernshtein's theorem for the case where each transmitter uses only one beamforming vector. The multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems. In this case, we show that the connection between feasible and proper systems can be further strengthened (since the equivalency between feasible and proper systems does not always hold) by including standard information theoretic outer bounds in the feasibility analysis. [ABSTRACT FROM PUBLISHER]