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In this paper, we consider $K$ –user interference channels with $M$ antennas per node and with backhaul collaboration in one side (among the transmitters or among the receivers), for $M,K\in \mathbb {N}$ , and investigate the tradeoff between the rate in the channel versus the communication load in the backhaul. In this investigation, each node is equipped with $M$ antennas and we focus on a first order approximation result, where the rate of the wireless channel is measured by the degrees of freedom (DoF) per user, and the load of the backhaul is measured by the entropy of backhaul messages per user normalized by $\log $ of transmit power, at high power regimes. This tradeoff is fully characterized for the case of even values of $K$ and approximately characterized for the case of odd values of $K$ , with vanishing approximation gap as $K$ grows. To achieve DoF of $M$ per user, this result establishes the asymptotic optimality of the most straightforward scheme, called central processing, in which the messages are collected at one of the nodes, centrally processed, and forwarded back to each node. In addition, this result shows that the gain of the schemes, relying on distributed processing, through pairwise communication among the nodes (e.g., cooperative alignment) does not scale with the size of the network. For the converse, we develop a new outer-bound on the tradeoff based on splitting the set of collaborative nodes (transmitters or receivers) into two subsets and assuming full cooperation within each group. We further present a sufficient condition on the wireless channel connectivity, which although more relaxed, guarantees the validity of the above tradeoff. Finally, we show that verifying this condition takes a polynomial time in the network size. [ABSTRACT FROM AUTHOR]

We consider a system, comprising a library of N files (e.g., movies) and a wireless network with a K_{T} transmitters, each equipped with a local cache of size of M_{T} files and a KR receivers, each equipped with a local cache of size of MR files. Each receiver will ask for one of the $N$ files in the library, which needs to be delivered. The objective is to design the cache placement (without prior knowledge of receivers’ future requests) and the communication scheme to maximize the throughput of the delivery. In this setting, we show that the sum degrees-of-freedom (sum-DoF) of $\min \left \{{\frac {K_{T} M_{T}+K_{R} M_{R}}{N},K_{R}}\right \}$ is achievable, and this is within a factor of 2 of the optimum, under uncoded prefetching and one-shot linear delivery schemes. This result shows that (i) the one-shot sum-DoF scales linearly with the aggregate cache size in the network (i.e., the cumulative memory available at all nodes), (ii) the transmitters’ caches and receivers’ caches contribute equally in the one-shot sum-DoF, and (iii) caching can offer a throughput gain that scales linearly with the size of the network. To prove the result, we propose an achievable scheme that exploits the redundancy of the content at transmitter’s caches to cooperatively zero-force some outgoing interference, and availability of the unintended content at the receiver’s caches to cancel (subtract) some of the incoming interference. We develop a particular pattern for cache placement that maximizes the overall gains of cache-aided transmit and receive interference cancellations. For the converse, we present an integer optimization problem which minimizes the number of communication blocks needed to deliver any set of requested files to the receivers. We then provide a lower bound on the value of this optimization problem, hence leading to an upper bound on the linear one-shot sum-DoF of the network, which is within a factor of 2 of the achievable sum-DoF. [ABSTRACT FROM AUTHOR]

Although interference alignment (IA) can theoretically achieve the optimal degrees of freedom (DoFs) in the $K$ -user Gaussian interference channel, its direct application comes at the prohibitive cost of precoding over exponentially many signaling dimensions. On the other hand, it is known that practical one-shot IA precoding (i.e., linear schemes without symbol expansion) provides a vanishing DoFs gain in large fully connected networks with generic channel coefficients. In our previous work, we introduced the concept of cellular IA for a network topology induced by hexagonal cells with sectors and nearest-neighbor interference. Assuming that neighboring sectors can exchange decoded messages (and not received signal samples) in the uplink, we showed that linear one-shot IA precoding over $M$ transmit/receive antennas can achieve the optimal $M/2$ DoFs per user. In this paper, we extend this framework to networks with omni-directional (non-sectorized) cells and consider a limited practical scenario where users have 2 antennas, and base-stations have 2, 3, or 4 antennas. We provide linear one-shot IA schemes for the $2\times 2$ , $2\times 3$ , and $2\times 4$ cases, and show the achievability of 3/4, 1, and 7/6 DoFs per user, respectively. DoFs converses for one-shot schemes require the solution of a discrete optimization problem over a number of variables that grows with the network size. We develop a new approach to transform such optimization problem into a tractable linear program with significantly fewer variables. This approach is used to show that 3/4 DoFs per user are indeed optimal for one-shot schemes over large (extended) cellular network with $2\times 2$ links. [ABSTRACT FROM AUTHOR]

Interference alignment promises that, in Gaussian interference channels, each link can support half of a degree of freedom (DoF) per pair of transmit–receive antennas. However, in general, this result requires to precode the data bearing signals over a signal space of asymptotically large diversity, e.g., over an infinite number of dimensions for time-frequency varying fading channels, or over an infinite number of rationally independent signal levels, in the case of time-frequency invariant channels. In this paper, we consider a wireless cellular system scenario where the promised optimal DoFs are achieved with linear precoding in one-shot (i.e., over a single time-frequency slot). We focus on the uplink of a symmetric cellular system, where each cell is split into three sectors with orthogonal intrasector multiple access. In our model, interference is local, i.e., it is due to transmitters in neighboring cells only. We consider a noniterative local cooperation scheme where base stations pass to their neighbors their decoded messages such that interference from already decoded messages can be canceled. Therefore, for a given decoding order, the interference between sectors is described by a directed locally connected graph. The problem consists of maximizing the per-sector DoFs over all possible decoding orders and precoding schemes. In particular, we provide a decoding order and a one-shot interference alignment scheme able to achieve optimal per-sector DoFs, up to an additive gap due to boundary effects, that vanishes as the size of the network becomes large. Then, we extend our treatment by considering the case of intersector interference with joint processing of the three sector at each cell site. In order to avoid signaling schemes relying on the strength of interference, we further introduce the notion of topologically robust schemes, which are able to guarantee a minimum rate (or DoFs) irrespectively of the strength of the interfering links. Toward this end, we design a different decoding order and alignment scheme, which is topologically robust and still achieves the same optimum DoFs. Finally, we provide a new scheme for the downlink, based on local base station cooperation, where base stations pass to their neighbors a quantized version of their dirty-paper coded signals. For the proposed downlink scheme, we can prove a DoFs duality result showing that, for an appropriate choice of the precoding order and of the alignment beamforming vectors, it can achieve the same per-sector DoFs of the corresponding uplink schemes. [ABSTRACT FROM PUBLISHER]

In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter's data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters' points of view) and two multiple-access channels (from the receivers' points of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple-antenna broadcast subchannels or two noninterfering multiple-antenna multiple. access subchannels. The main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain (MG). It is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable MG. In particular, it is shown that in some specific cases, the achieved MG is the same as the MG of the system if full cooperation is provided either between the transmitters or between the receivers. In the second part of the paper, it is shown that by using mixed design schemes, rather than decomposition schemes, and taking the statistical properties of the interference terms into account, the power offset of the system can be improved. The power offset represents the horizontal shift in the curve of the sum-rate versus the total power in decibels. [ABSTRACT FROM AUTHOR]

In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine–Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the \(X\) channel. It is proved that the sum DoF of the \(K\) -user IC is \(({K}/{2})\) for almost all channel parameters. We also prove that the sum DoF of the \(X\) -channel with \(K\) transmitters and \(M\) receivers is \(({KM}/{K+M-1})\) for almost all channel parameters. [ABSTRACT FROM PUBLISHER]