In this paper, we develop and evaluate compressed representations of the channels between a massive MIMO base station and user terminals that can serve as attractive proxies in the context of various applications of interest. To create such compressed channel representations (CCRs), channel features are first extracted from wideband massive-MIMO channel data via appropriate preprocessing in the angular-delay domain. PCA-based and UMAP-based embedding algorithms are then applied to the extracted feature sets to generate the CCR embeddings. We evaluate CCRs in the context of two use cases - user localization and beam tracking - using neural networks. Our ray-tracing based simulation reveals that the proposed CCRs are attractive candidates for these tasks, in terms of not only computation and memory usage but also task performance.

We investigate the problem of wireless beam tracking on mmWave bands with the assistance of camera images. In particular, based on the user’ beam indices used and camera images taken in the trajectory, we predict the optimal beam indices in the next few time spots. To resolve this problem, we first reformulate the “ViWi” dataset in [1] to get rid of the image repetition problem. Then we develop a deep learning approach and investigate various model components to achieve the best performance. Finally, we explore whether, when, and how to use the image for better beam prediction. To answer this question, we split the dataset into three clusters - (LOS, light NLOS, serious NLOS)-like - based on the standard deviation of the beam sequence. With experiments we demonstrate that using the image indeed helps beam tracking especially when the user is in serious NLOS, and the solution relies on carefully-designed dataset for training a model. Generally speaking, including NLOS-like data for training a model does not benefit beam tracking of the user in LOS, but including light NLOS-like data for training a model benefits beam tracking of the user in serious NLOS.

For short distance traveling in crowded urban areas, bike share services is becoming popular owing to the flexibility and convenience. To expand the service coverage, one of the key tasks is to seek new service ports, which requires to well understand the underlying features of the existing service ports. In this paper, we propose a new model, named for Efficient and Semantic Location Embedding (ESLE)1, which carries both geospatial and semantic information of the geo-locations. To generate ESLE, we first train a multi-label model with a deep Convolutional Neural Network (CNN) by feeding the static map-tile images and then extract location embedding vectors from the model. Compared to most recent relevant literature, ESLE is not only much cheaper in computation, but also easier to interpret via a systematic semantic analysis. Finally, we apply ESLE to seek new service ports for NTT DOCOMO’s bike share services operated in Japan. The initial results demonstrate the effectiveness of ESLE, and provide a few insights that might be difficult to discover by using the conventional approaches.

Gains in area spectral efficiency have been recently demonstrated in networks of large-antenna arrays by means of fog massive MIMO operation and virtual sector-based processing. In this paper, we adopt such sector-based processing and operation to localize users in the network. We investigate the viability of some widely used supervised-learning methods in estimating user locations by observing across the fog massive MIMO network signals transmitted by the users. In particular, we evaluate linear regression (LR), weighted K-nearest neighbors (WKNN), and neural networks (NN) in the context of a network of massive-antenna remote-radio heads (RRHs) using simulations based on a spatially consistent channel model. As our simulations reveal, NN-based location estimators trained with user-sector channel gains could be a viable approach for providing user location information at the network side.

The decoupling of data and control planes in the forthcoming 5G wireless networks enables the efficient implementation of multitier architectures, where coverage and connectivity are guaranteed by top-tier macro-cells, and at the same time, high throughput and low latency are achieved locally by lower tiers in the hierarchy. This paper considers a new architecture for such lower tiers, dubbed fog massive multi-in multi-out (MIMO), where the user equipment (UE) nodes can connect to a “fog” of the densely deployed remote radio heads (RRHs) in a seamless, user-centric, and opportunistic manner. In the case of dense small cells, traditional cellular architectures inherently give rise to frequent handovers and pilot sequence re-assignments, which typically incur excessive protocol overhead and latency. In the proposed fog massive MIMO architecture, the UEs implicitly associate themselves with the most convenient RRHs in a completely autonomous manner. Each UE makes use of the uplink pilot sequences that contain equal-weight codewords and enable a novel “on-the-fly” pilot contamination control mechanism. We analyze the spectral efficiency and the outage probability of the proposed architecture via stochastic geometry, using some recent results on unique coverage in Boolean models, and provide a detailed comparison with the benchmark represented by massive MIMO cellular system with a genie-aided minimum-distance user-cell association. Our analysis, corroborated by extensive system simulation, reveals that there exists a “sweet spot” of the per pilot user load (number of users per pilot), such that the proposed system achieves a spectral efficiency close to that of the genie-aided cellular system. In these conditions, it is possible to achieve the low protocol overhead and low user RRH association latency promised by the fog massive MIMO at virtually no significant performance cost in terms of system spectral efficiency with respect to the cellular benchmark.

We investigate the viability of using machine-learning techniques for estimating user-channel features at a large-array base station (BS). In the scenario we consider, user-pilot broadcasts are observed and processed by the BS to extract angle-of-arrival (AoA) specific information about propagation-channel features, such as received signal strength and relative path delay. The problem of interest involves using this information to predict the angle-of-departure (AoD) of the dominant propagation paths in the user channels, i.e., channel features not directly observable at the BS. To accomplish this task, the data collected in the same propagation environment are used to train neural networks. Our studies rely on ray-tracing channel data that have been calibrated against measurements from Shinjuku Square, a famous hotspot in Tokyo, Japan. We demonstrate that the observed features at the BS side are correlated with the angular features at the user side. We train neural networks that exploit different combinations of measured features at the BS to infer the unknown parameters at the users. The evaluation based on standard statistical performance metrics suggests that such data-driven methods have the potential to predict unobserved channel features from observed ones.

We propose a novel scheme for estimating the large- scale gains of the channels between user terminals (UTs) and base stations (BSs) in a cellular system. The scheme leverages TDD operation, uplink (UL) training by means of properly designed non-orthogonal pilot codes, and massive antenna arrays at the BSs. Subject to Q resource elements allocated for UL training and using the new scheme, a BS is able to estimate the large- scale channel gains of K users transmitting UL pilots in its cell and in nearby cells, provided K ≤Q2. Such knowledge of the large-scale channel gains of nearby out-of-cells users can be exploited at the BS to mitigate interference to the out-of-cell users that experience the highest levels of interference from the BS. We investigate the large-scale gain estimation performance provided by a variety of non-orthogonal pilot codebook designs. Our simulations suggest that among all the code designs considered, Grassmannian line-packing type codes yield the best large-scale channel gain estimation performance.

This paper considers a new architecture underpinned by on-the-fly pilot contamination control, termed Fog massive MIMO, where the users are able to establish high-throughput and low-latency data links in a seamless and opportunistic manner, as they travel through a dense fog of high capacity Remote Radio Heads (RRHs). Utilizing some recent results on unique coverage in Boolean models, we analyze the spectral efficiency and outage probability of the proposed architecture via stochastic geometry. Our analysis, supported by extensive system simulation, reveals that there exists a “sweet spot” of the per-pilot user load (number of users per pilot), such that the proposed system achieves spectral efficiency close to that of the ideal cellular massive MIMO baseline, while exhibiting the simplicity and low-latency of completely user-centric operations.

We consider the recently proposed Coded Distributed Computing (CDC) framework [1]-[3] that leverages carefully designed redundant computations to enable coding opportunities that substantially reduce the communication load of distributed computing. We generalize this framework to heterogeneous systems where different nodes in the computing cluster can have different storage (or processing) capabilities. We provide the information-theoretically optimal data set placement and coded data shuffling scheme that minimizes the communication load in a cluster with 3 nodes. For clusters with K > 3 nodes, we provide an algorithm description to generalize our coding ideas to larger networks.

In this paper, we consider a device-to-device communication network in which K transmitter-receiver pairs are sharing spectrum with each other. We propose a novel but simple binary scheduling scheme for this network to maximize the average sum rate of the pairs. According to the scheme, each receiver predicts its Signal-to-Interference-plus-Noise Ratio (SINR), assuming all other user pairs are active, and compares it to a preassigned threshold to decide whether its corresponding transmitter to be activated or not. For our proposed scheme, the optimal threshold that maximizes the expected sum rate is obtained analytically for the two user-pair case and empirically in the general K user-pair case. Simulation results reveal that our proposed SINR-threshold scheduling scheme outperforms ITLinQ [1], FlashLinQ [2] and the method presented in [3] in terms of the expected sum rate (network throughput). In addition, the computational complexity of the proposed scheme is O(K), outperforming both ITLinQ and FlashLinQ that have O(K^2) complexity requirements. Moreover, we also discuss the application of our proposed new scheme into an operator-assisted cellular D2D heterogeneous network.

We consider a single-cell scenario involving a single base station (BS) with a massive array serving multi-antenna terminals in the downlink of a mmWave channel. We present a class of multiuser MIMO schemes, which rely on uplink training from the user terminals, and on uplink/downlink channel reciprocity. The BS employs virtual sector-based processing according to which, user-channel estimation and data transmission are performed in parallel over non-overlapping angular sectors. The uplink training schemes we consider are non-orthogonal, that is, we allow multiple users to transmit pilots on the same pilot dimension (thereby potentially interfering with one another). Elementary processing allows each sector to determine the subset of user channels that can be resolved on the sector (effectively pilot contamination free) and, thus, the subset of users that can be served by the sector. This allows resolving multiple users on the same pilot dimension at different sectors, thereby increasing the overall multiplexing gains of the system. Our analysis and simulations reveal that, by using appropriately designed directional training beams at the user terminals, the sector-based transmission schemes we present can yield substantial spatial multiplexing and ergodic user-rates improvements with respect to their orthogonal-training counterparts.

Technologies for millimeter wave (mmWave) communication are at the forefront of investigations in both industry and academia, as the mmWave band offers the promise of orders of magnitude additional available bandwidths to what has already been allocated to cellular networks. The much larger number of antennas that can be supported in a small footprint at mmWave bands can be leveraged to harvest massive-MIMO type beamforming and spatial multiplexing gains. Similar to Long-Term Evolution (LTE) systems, two prerequisites for harvesting these benefits are detecting users and acquiring user channel state information (CSI) in the training phase. However, due to the fact that mmWave channels encounter much harsher propagation and decorrelate much faster, the tasks of user detection and CSI acquisition are both imperative and much more challenging than in LTE bands. In this paper, we investigate the problem of fast user detection and CSI acquisition in the downlink of small cell mmWave networks. We assume Time Division Duplex (TDD) operation and channel-reciprocity based CSI acquisition. To achieve densification benefits we propose pilot designs and channel estimators that leverage a combination of aggressive pilot reuse with fast user detection at the base station and compressed sensing channel estimation. As our simulations show, the number of users that can be simultaneously served by the entire mmWave-band network with the proposed schemes increases substantially with respect to traditional compressed sensing based approaches with conventional pilot reuse.

Dense large-scale antenna deployments are one of the most promising technologies for delivering very large throughputs per unit area in the downlink (DL) of cellular networks. We consider such a dense deployment involving a distributed system formed by multi-antenna remote radio head (RRH) units connected to the same fronthaul serving a geographical area. Knowledge of the DL channel between each active user and its nearby RRH antennas is most efficiently obtained at the RRHs via reciprocity based training, that is, by estimating a user's channel using uplink (UL) pilots transmitted by the user, and exploiting the UL/DL channel reciprocity. We consider aggressive pilot reuse across an RRH system, whereby a single pilot dimension is simultaneously assigned to multiple active users. We introduce a novel coded pilot approach, which allows each RRH unit to detect pilot collisions, i.e., when more than a single user in its proximity uses the same pilot dimensions. Thanks to the proposed coded pilot approach, pilot contamination can be substantially avoided. As shown, such a strategy can yield densification benefits in the form of increased multiplexing gains per UL pilot dimension with respect to conventional reuse schemes and some recent approaches assigning pseudorandom pilot vectors to the active users.

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.

We characterize the degrees of freedom (DoFs) of a multiway relay wireless network consisting of four user nodes, each with M antennas, and one N-antenna relay node. Each user node sends one independent message to each of the other users, and there are no direct links between any two user nodes. For this network, we show that the symmetric DoF value per message is given by max(min((M/3), (N/7)), min(((2M)/7), (N/6))) normalized by space dimensions, i.e., piecewise linear depending on M and N alternatively. While the information theoretic DoF upper bound is established for every M and N antennas, the achievability relying on linear signal subspace alignment is established in the spatially normalized sense in general. In addition, by deactivating four messages to form a twoway relay MIMO X channel, we also present the DoF result max(min((M/2), (N/5)), min(((2M)/5), (N/4))) in a similar piecewise linear type. The key ingredient to these new results is to first establish the principle of beamforming design via linear dimension counting perspective, which is essentially the fundamental element for establishing both the DoF converse and the DoF achievability. Moreover, we also settle the feasibility of linear interference alignment that extends the feasibility framework from one-way one-hop to multiway relay interference networks.

We characterize the degrees of freedom (DoF) of a wireless network consisting of 4 user nodes, each with M antennas, and one N-antenna relay node. In this network, each user sends one independent message to each of the other users, and there are no direct links between any two users, i.e., all communication must pass through the relay node. For this network, we show that the symmetric DoF value per message is given by max(min(M/3, N/7), min(2M/7, N/6)) normalized by space dimensions, i.e., piecewise linear depending on M,N alternatively. While the information theoretic DoF converse is established for every M,N, the achievability relying on linear signal subspace alignment is established in the spatially-normalized sense in general. The central new insight to emerge from this work is the notion of inter-user signal subspace alignment incorporating the idea of network coding, which is the key to achieve the optimal DoF for multi-way relay interference networks. Moreover, this work also settles the feasibility of linear interference alignment that extends the feasibility framework from one-way to multi-way networks.

Starting from the elemental 2 × 2 × 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 × 2 × 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 × 2 × 2 × 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.

We show that the three-user MT× MRMultiple-Input Multiple-Output (MIMO) interference channel where each transmitter is equipped with MTantennas and each receiver is equipped with MRantennas has (M) d(M, N) =Δmin (M/2-1/κ, N/2+1/κ) degrees of freedom (DoF) normalized by time, frequency, and space dimensions, where =Δmin(MT, MR), N =Δmax(MT, MR), κ =Δ⌈M/N-M⌉. While the DoF outer bound of d(M, N) is established for every MT, MRvalue, the achievability of 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 qd(M, N) DoF are achievable for the three-user qMT × qMR 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 M or N being the bottleneck within each linear segment, whereas the other value contains some redundancy, i.e., it can be reduced without reducing the DoF. The corner points of these piecewise linear segments correspond to two sets, A={1/2, 2/3, 3/4, ...}and B={1/3, 3/5, 5/7, ...}. 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, i.e., either can be reduced without reducing the DoF. The set B 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, i.e., neither can be reduced without reducing the DoF. Because A and 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× MRMIMO interference channel, completely for all values of MT, MR. In particular, we show that the linear interference alignment problem (MT× MR, d)3(as defined in previous paper by Cenk et al.) is feasible if and only if d ≤ d(M, N). With the exception of the values M/N ∈ 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 ∈ 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 ∈ A settings.

We provide the degrees of freedom (DoF) characterization for the three-user MT× MRmultiple-input-multipleoutput (MIMO) interference channel (IC) with rank-deficient channel matrices, where each transmitter is equipped with MTantennas and each receiver with MRantennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks D1and D2, respectively. One important intermediate step for both the converse and achievability arguments is to convert the fully-connected rank-deficient channel into an equivalent partially-connected full-rank MIMO-IC by invertible linear transformations. As such, existing techniques developed for full-rank MIMO-IC can be incorporated to derive the DoF outer and inner bounds for the rank-deficient case. Our result shows that when the interfering links are weak in terms of the channel ranks, i.e., D1+ D2≤ min(MT, MR), zero forcing is sufficient to achieve the optimal DoF. On the other hand, when D1+ D2> min(MT, MR), a combination of zero forcing and interference alignment is in general required for DoF optimality. The DoF characterization obtained in this paper unifies several existing results in the literature.

A conventional relay causes a processing delay of at least one symbol duration relative to the direct paths between a source and a destination. This delay caused by using the conventional relay limits the degrees of freedom (DoF) gain in a wireless interference network. In this paper, it is shown that the exploitation of an instantaneous relay (relay-without-delay) improves DoF gain significantly for a two-user wireless network. Specifically, for two different message settings: the interference channel and the X channel, it is shown that a total of 3/2 and 5/3 DoF are achievable almost surely, respectively. The achievable schemes are inspired by the notion of aligned interference neutralization recently proposed for the layered two-user two-hop interference channel.

We show that the 3 user MT× MRMIMO interference channel where each transmitter is equipped with MTand each receiver is equipped with MRantennas has min (M/2-1/k, N/2+1/k) degrees of freedom (DoF) per user normalized by time, frequency, and space dimensions, where N = max(MT, MR), M = min(MT, MR), k = [M/N-M]. While the information theoretic DoF outer bound is established for every M, N value, the achievability, relying only on linear interference alignment, 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 the absence of spatial extensions, we can also show through examples how essentially the same alignment scheme may be applied over time or frequency extensions. The central new insight to emerge from this work is the notion of subspace alignment chains as DoF bottlenecks. The subspace alignment chains are instrumental both in identifying the extra dimensions provided by a genie to a receiver for the DoF outer bound, as well as constructing the optimal interference alignment schemes. In addition, our results also settle the question of feasibility of linear interference alignment for the 3 user MT× MRMIMO interference channel, for all values of MT, MR.

We explore the degrees of freedom (DoF) of the K >; 3 user MT× MRMIMO Gaussian interference channel where each transmitter is equipped with MTand each receiver is equipped with MRantennas. Expressing the DoF characterization as a function of the ratio γ = M/N, where M = min(MT, MR) and N = max(MT, MR), we find that when γ ≤ γo= K-1/K(K-2) = γo, the DoF value per user is piecewise linear depending on M and N alternately, similar to the DoF characterization for K = 3 which has been previously obtained. The regime γ >; γo, which is the dominant regime for K >; 3 users and is not encountered in the K = 3 user setting, is the main focus of this paper. Our DoF results in this regime are obtained through a novel “genie chains” approach, which is the main contribution of this work. It is a chain of mappings from genie signals provided to a receiver to the exposed signal spaces at that receiver, which then serve as the genie signals for the next receiver in the chain, until an acceptable genie with the required number of dimensions is obtained, essentially converting an information theoretic problem into a linear algebra problem.

We show that the 2 × 2 × 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.

We study the sum capacity of multiple unicasts in wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network). We explore the degrees of freedom (DoF) of wireless multihop X networks with a layered structure, allowing arbitrary number of hops and arbitrary connectivity within each hop. For the case when there are no more than two relay nodes in each layer, the DoF can only take values 1, 4/3, 3/2 or 2, based on the connectivity of the network, for almost all values of channel coefficients. When there are arbitrary number of relays in each layer, the DoF can also take the value 5/3. Achievability schemes incorporate linear forwarding, interference alignment and aligned interference neutralization principles. Information theoretic converse arguments specialized for the connectivity of the network are constructed based on the intuition from linear dimension counting arguments.

We consider a multi-pair two-way relay (TWR) network where the multi-antenna users of each pair exchange information via a multi-antenna relay. The interesting challenge is how to deal with the inter- user interference and explore the potential of multiple antennas concurrently. Beamforming methods in previous works are based on the criteria of zero forcing (ZF) and minimum mean square error (MMSE) to mitigate the inter-user interference. However, since the user already knows its own information, it is unnecessary to mitigate the intra-pair interference at the relay. In this paper, we propose a coordinated eigen beamforming (CEB) scheme, which maximizes the effective channel gain of each user in the sub-space nulling the inter-pair interference. The CEB scheme is implemented with an iterative optimization algorithm with limited iterations. Additionally, the power loading scheme is adopted after convergence to guarantee fairness among users. Simulation results indicate our scheme achieves near full diversity order within the sub-space, outperforming pervious works.

Fundamentally, benefits of Multiple Input Multiple Output (MIMO) in wireless systems rest on increasing the number of Degrees of Freedom (DoFs) that can be exploited for transmission. DoFs can be used to increase spectral efficiency and/or provide increased diversity. However, exploiting DoFs in MIMO often requires knowledge of Channel State Information (CSI) at the transmitter and/or receiver. Obtaining CSI creates overheads due to the required use of wireless resources for CSI-estimation pilots and/or CSI feedback. This can create a fundamental "dimensionality bottleneck" that limits the growth in spectral efficiency for some conventional MIMO systems. Recently a new class of techniques known as "Blind Interference Alignment" (BIA) has demonstrated the possibility to grow DoFs without many of the CSI overheads of conventional systems. BIA therefore has the potential to relieve the "dimensionality bottleneck". However, BIA can have limited applicability to many users in a cellular environment given that it requires a high Signal to Noise Ratio (SNR) to operate efficiently. By examining BIA, we present a method to reduce the SNR requirements and improve the application of BIA through power allocation and cluster-based transmission. We show that BIA can be applied successfully in cellular without the need for joint processing between base-stations, and can improve performance over conventional MIMO for even cell-edge users in some scenarios.

We explore the interplay between interference, cooperation and connectivity in heterogeneous wireless interference networks. Specifically, we consider a 4-user locally-connected interference network with pairwise clustered decoding and show that its degrees of freedom (DoF) are bounded above by 12/5. Interestingly, when compared to the corresponding fully connected setting which is known to have 8/3 DoF, the locally connected network is only missing interference-carrying links, but still has lower DoF, i.e., eliminating these interference-carrying links reduces the DoF. The 12/5 DoF outer bound is obtained through a novel approach that translates insights from interference alignment over linear vector spaces into corresponding sub-modularity relationships between entropy functions.

We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multiple-input single-output (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weingartenhave found inner and outer bounds on the DoF with 2 users. The bounds have a different character. While the inner bound collapses to unity as the number of states increases, the outer bound does not diminish with the increasing number of states beyond a threshold value. It has been conjectured that the outer bound is loose and the inner bound represents the actual DoF. In the complex setting (all signals, noise, and channel coefficients are complex variables), we solve a few cases to find that the outer bound—and not the inner bound—of Weingartenis tight. For the real setting (all signals, noise, and channel coefficients are real variables), we completely characterize the DoF, once again proving that the outer bound of Weingartenis tight. We also extend the results to arbitrary number of users. Second, we characterize the DoF of finite state scalar (single antenna nodes) compound$X$networks with arbitrary number of users in the real setting. Third, we characterize the DoF of finite state scalar compound interference networks with arbitrary number of users in both the real and complex setting. The key finding is that scalar interference networks and (real)$X$networks do not lose any DoF due to channel uncertainty at the transmitter in the finite state compound setting. The finite state compound MISO BC does lose DoF relative to the perfect CSIT scenario. However, what is lost is only the DoF benefit of joint processing at transmit antennas, without which the MISO BC reduces to an$X$network.

We propose a blind interference alignment scheme for the vector broadcast channel where the transmitter is equipped with M antennas and there are K receivers, each equipped with a reconfigurable antenna capable of switching among M preset modes. Without any knowledge of the channel coefficient values at the transmitters and with only mild assumptions on the channel coherence structure we show that MK/(M+K-1) degrees of freedom are achievable. The key to the blind interference alignment scheme is the ability of the receivers to switch between reconfigurable antenna modes to create short term channel fluctuation patterns that are exploited by the transmitter. The achievable scheme does not require cooperation between transmit antennas and is therefore applicable to the M×K X network as well. Only finite symbol extensions are used, and no channel knowledge at the receivers is required to null the interference.

It has been conjectured by Hø-Madsen and Nosratinia that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom regardless of the number of users. While several examples are known of constant channels that achieve more than 1 degree-of-freedom, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 degree-of-freedom is achievable. In this paper, we settle the Høst-Madsen-Nosratinia conjecture in the negative. We show that at least 1.2 degrees-of-freedom are achievable for all values of complex channel coefficients except for a subset of measure zero. For the class of linear beamforming and interference alignment schemes considered in this paper, it is also shown that 1.2 is the maximum number of degrees-of-freedom achievable on the complex Gaussian 3 user interference channel with constant channel coefficients, for almost all values of channel coefficients. To establish the achievability of 1.2 degrees-of-freedom we use the novel idea of asymmetric complex signaling - i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric. With asymmetric complex signaling, we also show that the 2 user complex Gaussian X channel with constant channel coefficients achieves the outer bound of 4/3 degrees-of-freedom, i.e., the assumption of time-variations/frequency-selectivity used in prior work to establish the same result, is not needed.