On the spatial degrees of freedom benefits of reverse TDD in multicell MIMO networks

In this paper we study the degrees of freedom (DoF) achieved by interference alignment (IA) for cellular networks in reverse time division duplex (R-TDD) mode, a new configuration associated to heterogeneous networks. We derive a necessary feasibility condition for interference alignment in the multi-cell R-TDD scenario, which is then specialized to the particular case of symmetric demands and antenna distribution. We show that, for those symmetric networks for which the properness condition holds with equality, R-TDD does not improve the DoF performance of conventional synchronous TDD systems. Nevertheless, our simulation results indicate that, in more asymmetric scenarios, significant DoF benefits can be achieved by applying the R-TDD approach.This work has been supported by the Ministerio de Economía y Competitividad (MINECO) of Spain under grant TEC2013-47141- C4-R (RACHEL project) and FPI grant BES-2014-069786

Power minimization in multi-tier networks with flexible duplexing

In this paper we present an algorithm to minimize transmit power in multiple-input multiple-output (MIMO) heterogeneous networks (HetNets) with flexible duplexing, a promising strategy that allows the coexistence of uplink and downlink cells within the same time and frequency resource block. First, the proposed algorithm minimizes transmit power for a given uplink/downlink (UL/DL) combination, and afterwards, the optimal solution out of the explored UL/DL combinations is selected. To reduce the computational cost of exploring all the UL/DL settings, we propose a hierarchical switching (HS) approach that considers a reduced subset of transmit directions. By means of Monte Carlo simulations, we show that the proposed technique provides significant power savings with respect to a conventional time-division duplex (TDD) scheme.This work has been supported by the MINECO of Spain and AEI/FEDER funds from the EU, under grant TEC2016-75067-C4-4-R (CARMEN project) and FPI grant BES-2014-069786

Statistical analysis of single-beam interference alignment schemes

In this work, we derive analytical approximate expressions for the user rates achievable by interference alignment (IA) algorithms in single-beam multiple-input multiple-output (MIMO) networks for a fixed channel realization. Unlike previous works that perform a large-system analysis in which the number of users, antennas, or streams is required to tend to infinity, in this paper we only require that the number of different IA solutions (precoders and decoders) for the given scenario is sufficiently high, which typically happens even for moderate-size feasible networks. Based on the assumption that the IA beamformers for a given channel realization are random vectors isotropically distributed on the complex unit sphere, we characterize the user rates by averaging over the (possible finite) set of IA solutions. Some simulation results show the accuracy of the proposed rate expressions.This work was supported by the Ministerio de Economía y Competitividad (MINECO), Spain, under project RACHEL (TEC2013-47141-C4-3-R) and FPI grant BES-2014-069786

Flexible duplexing for maximum downlink rate in multi-tier MIMO networks

In this paper, we propose an algorithm to maximize downlink rate performance in the context of multiple-input multiple-output (MIMO) Heterogeneous Networks (HetNets). Specifically, we evaluate the benefits of flexible duplexing, a promising strategy that consists in combining uplink and downlink cells within the same channel use. In order to handle intercell interference, we rely on the interference alignment (IA) technique, taking into account the impact of the channel estimation errors on the inter-cell interference leakage. Determining the best uplink/downlink configuration is a combinatorial problem, and therefore we consider several approaches to reduce the computational demands of the problem. First, we use a statistical characterization for the average rates achieved by IA in order to avoid the calculation of alignment solutions for all possible settings in the network. Additionally, we propose two hierarchical switching (HS) strategies so that only a subset among the total number of combinations is explored. As a performance baseline, we include in the comparison the conventional time division duplex (TDD) approach and the well-known minimum mean square error (MMSE) decoder. The obtained results show that downlink rates achieved by implementing flexible duplexing and applying inter-cell IA significantly outperform conventional TDD transmissions. Finally, the proposed hierarchical schemes are shown to obtain almost the same rates as exhaustive search with much lower computational cost.This work has been supported by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain under grant TEC2016-75067-C4-4-R (CARMEN), and FPI grant BES-2014-069786

Homotopy continuation for vector space interference alignment in MIMO X networks

In this paper we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for MIMO X networks (XN). The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the known solutions of a start system which can be trivially solved. The key observation leading to a simple start system is realizing that the inverse IA problem, i.e., finding the channels that satisfy the IA conditions given a set of precoders and decoders, is linear and, therefore, a convenient trivial system. Once the start system has been solved, standard prediction and correction techniques are applied to track the solution all the way to the target system. Our results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom (DoF) whereas alternating minimization techniques, which typically work well for the interference channel (IC), repeatedly fail for the XN. Further, the algorithm provides insights into the feasibility of alignment in MIMO X networks for which theoretical results are scarce.This work was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project COSIMA (TEC2010-19545-C04-03), project COMONSENS (CSD2008-00010, CONSOLIDER-INGENIO 2010 Program) and FPU grant AP2009-1105

A quaternion-based approach to interference alignment with Alamouti coding

Based on the representation of Alamouti space-time codewords as quaternions, this paper proposes a scheme that combines interference alignment (IA) with Alamouti signals. The proposed formulation allows for a separation of the space-time block coding (to gain spatial diversity) and the IA precoding (to reduce or ideally suppress interference). Although this separation is not necessarily optimal, the splitting of alignment precoding and Alamouti encoding is particularly convenient because it enables the independent optimization of the IA solution using quaternionic versions of standard alternating optimization techniques such as the maximum signal-to-interference-plus-noise algorithm. Some numerical simulations are included to compare the performance of the proposed quaternion IA+Alamouti algorithm with standard IA algorithms in the complex domain as well as with interference cancellation schemes at the receiver side.This work has been supported by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, under grants TEC2013-47141-C4-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN), and FPI grant BES-2014-06978

Homotopy continuation for spatial interference alignment in arbitrary MIMO X networks

In this paper, we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce.This work has been supported by the Ministerio de Economía y Competitividad (MINECO) of Spain, under grants TEC2013-47141-C4-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN), MTM2014-57590-P, and FPI grant BES-2014-069786

Interference alignment testbeds

Interference alignment has triggered high impact research in wireless communications since it was proposed nearly 10 years ago. However, the vast majority of research is centered on the theory of interference alignment and is hardly feasible in view of the existing state-of-the-art wireless technologies. Although several research groups have assessed the feasibility of interference alignment via testbed measurements in realistic environments, the experimental evaluation of interference alignment is still in its infancy since most of the experiments were limited to simpler scenarios and configurations. This article summarizes the practical limitations of experimentally evaluating interference alignment, provides an overview of the available interference alignment testbed implementations, including the costs, and highlights the imperatives for succeeding interference alignment testbed implementations. Finally, the article explores future research directions on the applications of interference alignment in the next generation wireless systems.Jacobo Fanjul's research has been supported by the Ministerio de Economía y Competitividad (MINECO) of Spain, under grants TEC2013-47141-C4-R (RACHEL project) and FPI grant BES-2014-069786. José A. García-Naya's research has been funded by the Xunta de Galicia (ED431C 2016–045, ED341D R2016/012, E0431 G/01), the Agencia Estatal de Investigación of Spain (TEC2013-47141-C4-1-R, TEC2015-69648-REOC, TEC2016-75067-C4-1-R), and ERDF funds of the EU (AEI/FEDER, UE). Hamed Farhadi's research has been funded by the Swedish Research Council (VR) under grant 2015–00500

Experimental evaluation of flexible duplexing in multi-tier MIMO networks

In this paper, we present an experimental evaluation of the performance benefits provided by flexible duplexing, an access technique that allows uplink and downlink cells to coexist within the same time-frequency resource blocks. In order to replicate a wireless multi-tier network composed of 1 macro-cell and 2 small cells, a measurement campaign has been conducted using an indoor wireless testbed comprised of a total of 6 multiple-input multiple-output (MIMO) software-defined radio (SDR) devices. Since each cell has a single active user, each uplink/downlink configuration can be identified with a different interference channel, over which interference alignment (IA) is used as an inter-cell interference management technique and compared to other existing methods. The obtained results show that flexible duplexing clearly outperforms the conventional time-division duplex (TDD) access approach, where all cells operate synchronized either in uplink or dowlink mode. Additionally, interference alignment consistently provides better results in most of the interference regimes when compared to minimum means quare error (MMSE)-based schemes. The impact of channel estimate quality on the different communication strategies is also studied. It is worth highlighting that the presented over-the-air (OTA) experiments represent the first implementation of IA with real-time precoding and decoding.The work of Jacobo Fanjul, Jesús Ibáñez and Ignacio Santamaria has been supported by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grant TEC2016-75067-C4-4-R (CARMEN), grant PID2019-104958RB-C43 (ADELE), and FPI grant BES-2014-069786. The work of José A. García-Naya has been funded by the Xunta de Galicia (ED431G2019/01), the Agencia Estatal de Investigación of Spain (TEC2016-75067-C4-1-R, RED2018-102668-T), and ERDF funds of the E.U. (AEI/FEDER, UE)

An experimental evaluation of broadband spatial IA for uncoordinated MIMO-OFDM systems

In this paper we present an experimental study on the performance of spatial Interference Alignment (IA) in broadband indoor wireless local area network scenarios that use Orthogonal Frequency Division Multiplexing (OFDM) according to the IEEE 802.11a physical-layer specifications. Experiments have been carried out using a wireless network testbed made up of six nodes equipped with Multiple-Input Multiple-Output (MIMO) radio interfaces. This setup allows the implementation of a 3-user MIMO interference channel. We have implemented different IA decoding schemes that operate either before or after the Fast Fourier Transform block. IA has been experimentally evaluated comparing both approaches to analyze its performance in synchronous and asynchronous transmissions. Our results indicate that spatial IA performs satisfactorily in practical broadband indoor scenarios in which wireless channels often exhibit relatively large coherence times.This work has been supported by the MINECO of Spain and Feder funds of the E.U. under grants CSD2008-00010 (COMONSENS project), TEC2013-47141-C4-R (RACHEL project) and FPU grant AP2010-21