A Distributed Numerical Approach to Interference Alignment and Applications to Wireless Interference Networks

Interference alignment (IA) is a linear precoding strategy that can achieve optimal capacity scaling at high SNR in interference networks. Most of the existing IA designs require full channel state information (CSI) at the transmitters, which induces a huge CSI signaling cost. Hence it is desirable to improve the feedback efficiency for IA and in this paper, we propose a novel IA scheme with a significantly reduced CSI feedback. To quantify the CSI feedback cost, we introduce a novel metric, namely the feedback dimension. This metric serves as a first-order measurement of CSI feedback overhead. Due to the partial CSI feedback constraint, conventional IA schemes can not be applied and hence, we develop a novel IA precoder/decorrelator design and establish new IA feasibility conditions. Via dynamic feedback profile design, the proposed IA scheme can also achieve a flexible tradeoff between the degree of freedom (DoF) requirements for data streams, the antenna resources and the CSI feedback cost. We show by analysis and simulations that the proposed scheme achieves substantial reductions of CSI feedback overhead under the same DoF requirement in MIMO interference networks.

Interference Alignment in Multi-user MIMO Systems

Multiple-input multiple-output (MIMO) wireless communication systems can achieve higher throughput through interference alignment. For a small number of users, determining the maximum possible degrees of freedom as well as the feasibility of interference alignment in MIMO systems is well studied. However, the issues of scheduling in systems employing interference alignment and serving a large number of users have received little attention so far. In this paper, we study the problem of joint scheduling, interference alignment, and packet admission control in MIMO wireless systems with the goal of maximizing system throughput subject to stability constraints. We formulate a stochastic network optimization problem and propose a scheduling and interference alignment (SIA) algorithm. In each time slot, SIA schedules some users among many competing ones to transmit data, and determines encoding and decoding matrices for the selected users. Packet admission control is performed in each time slot. In addition, we propose a heuristic semi-distributed algorithm (SDSIA), which has a lower computational complexity than the SIA algorithm. Via simulation, we evaluate the performance of SIA and SDSIA for different algorithm parameters and different numbers of users. We also compare the performance of SDSIA with other approaches which do not simultaneously exploit interference alignment and scheduling and find that the combination of these two techniques increases the achievable data rate dramatically.

The explosive demand for high data rates and the need ubiquitous wireless connectivity has led to the phenomenon of network densification, the deployment of large number of base station within a geographic area. Since the radio spectrum is limited, wireless transmissions need to share a common resource which results in interference. Interference in turn creates a bottleneck on the communication rate. Recently three breakthroughs have been made to increase the capacity of wireless networks while mitigating interference : multiple input multiple output (MIMO) beamforming, interference alignment (IA) and pattern reconfigurable antennas (PRA). While a great deal of progress has been made on understanding each individually, relatively little is known about how to use these techniques in combination to increase system performance. In this dissertation, we analyze and experimentally evaluate how these new technologies can be leveraged to enhance the rate performance of communication networks. Specifically, we address three problems: i) enhancing multi-user MIMO performance with PRA, ii) improving IA performance with PRA-based antenna selection, and iii) enabling practical blind IA with PRA. To understand the impact PRAs on MU-MIMO and IA, it is necessary to evaluate their performance through measurements. Simulation-based studies often reiterate over set of simplistic channel models and unrealistic assumptions. This dissertation focuses on a measurement-based evaluation approach. For each of these problems, a hardware testbed implementation and measurement methodology is developed for evaluating the performance of the aforementioned technologies through efficient and repeatable experiments. The first two major contributions of this dissertation focus on multi-user MIMO (MU-MIMO) and IA. While the theoretical rate gains of MU-MIMO and IA are substantial, the performance gains in practical systems and measured channels have been limited. One of the key limiting factors are spatially correlated user channels. In this work, we propose MU-MIMO and IA transmission schemes that leverage the pattern diversity provided by PRAs to mitigate the effects of spatial correlation in wireless channels. PRAs are capable of dynamically adjusting their radiation pattern, providing an additional degree of freedom that can be exploited to improve MU-MIMO and IA performance by treating the array configuration and radiation characteristics as additional components in the joint optimization of adaptive system parameters. We quantify the benefits of pattern diversity on the rate performance of MU-MIMO and IA systems through extensive measurements. Furthermore, we develop efficient antenna mode selection algorithms to realize those benefits without increasing the system complexity or overhead, making these techniques suitable for practical implementation. The third contribution of this dissertation focuses on a transmission technique known as blind IA. In contrast to MU-MIMO and conventional IA, blind IA is signaling scheme that suppresses interference in multi-user systems, without the knowledge of channel state information at the transmitter (CSIT). The key to performing IA without CSIT is the use of PRAs that are capable of dynamically switching among a fixed number of radiation patterns to introduce artificial fluctuations in the channel. In this dissertation, we develop a novel implementation of a blind IA system on a software defined radio platform where each of the receivers is equipped with a PRA. Our work provides the first experimental evaluation of PRA-based blind IA schemes and demonstrates significant gains in rate and reliability over traditional orthogonal transmission schemes such as TDMA.

We consider the application of interference alignment (IA) to the cellular case with constant MIMO channel coefficients. Neglecting the weakest interferers in the network, we introduce an algorithm to obtain a partially connected (in particular, L-interfering) network, over which the feasibility of IA can be analyzed simply. We consider the application of IA over the obtained L-interfering network, while the rest of the interference is treated as noise. We benchmark this technique through extensive Monte-Carlo simulations, and introduce an approximate, compact expression for the ergodic mutual information achievable in the considered network setting.

A fundamental problem arising in dense wireless networks is the high co-channel interference. Interference alignment (IA) was recently proposed as an effective way to combat interference in wireless networks. The concept of IA, though, is originated by the capacity study of interference channels and as such, its performance is mainly gauged under ideal assumptions, such as instantaneous and perfect channel state information (CSI) at all nodes, and homogeneous signal-to-noise ratio (SNR) users, i.e., each user has the same average SNR. Consequently, the performance of IA under realistic conditions has not been completely investigated yet. In this paper, we aim at filling this gap by providing a performance assessment of spatial IA in practical systems. Specifically, we derive a closed-form expression for the IA average sum-rate when CSI is acquired through training and users have heterogeneous SNR. A main insight from our analysis is that IA can indeed provide significant spectral efficiency gains over traditional approaches in a wide range of dense network scenarios. To demonstrate this, we consider the examples of linear, grid and random network topologies.

Interference alignment (IA) is an effective method that can eliminate interferences in wireless networks, and has been applied to spectrum sharing in cognitive radio (CR) networks recently. However, the availability of perfect network channel state information (CSI) is necessary for most existing IA schemes, which is not practical in general due to the realistic communication scenarios and deployment challenges. In this paper, we apply IA to cognitive relay networks under CSI mismatch where the variance of the CSI measurement error depends on signal-to-noise ratio (SNR). An adaptive Max-SINR IA algorithm has been introduced to improve the performance of the secondary network by using the knowledge of CSI error variance. Finally, we analyze the performance of the secondary network in terms of the end-to-end equivalent transmission rate and outage probability. Simulation results indicate that our proposed adaptive Max-SINR IA scheme can greatly improve the performance of the secondary network.

In wireless interference networks, orthogonal medium access techniques like time division multiple access (TDMA) and frequency division multiple access (FDMA) achieve merely one degree of freedom (DoF). However, by using interference alignment (IA) the achievable DoF can be linearly scaled up with the number of users. Nevertheless, this outperformance of IA heavily depends on the availability of perfect channel state information (CSI), which is not a realistic assumption in practice. Since under imperfect CSI, the performance of IA may become severely degraded, design of enhanced IA algorithms by relying on the availability of merely imperfect CSI is of particular interest. In this paper, we propose a least squares (LS)-based IA algorithm which adaptively designs the beamformers based on the knowledge of the channel estimation error variance, which is possible to be known in advance. Then, we compare the performance of the proposed scheme with interference leakage minimization algorithms. It is shown that under both perfect and imperfect CSI, the proposed LS-based IA outperforms interference leakage minimization algorithms.

Interference alignment (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition matches with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.

A transmission scheme based on the Alamouti code, which we call the Li-Jafarkhani-Jafar (LJJ) scheme, was recently proposed for the 2×2 X Network (i.e., two-transmitter (Tx) two-receiver (Rx) X Network) with two antennas at each node. This scheme was claimed to achieve a sum degrees of freedom (DoF) of 8 over 3 and also a diversity gain of two when fixed finite constellations are employed at each Tx. Furthermore, each Tx required the knowledge of only its own channel unlike the Jafar-Shamai scheme which required global CSIT to achieve the maximum possible sum DoF of 8 over 3. In this paper, we extend the LJJ scheme to the 2 × 2 X Network with four antennas at each node. The proposed scheme also assumes only local channel knowledge at each Tx. We prove that the proposed scheme achieves the maximum possible sum DoF of 16 over 3. In addition, we also prove that, using any fixed finite constellation with appropriate rotation at each Tx, the proposed scheme achieves a diversity gain of at least four.

Interference alignment is a promising technique to handle the interference in wireless networks. For a time-invariant channel, interference alignment for a scenario consisting of several pairs of nodes can be achieved using a number of single antenna relays. In the present work, a two time-slot transmission scheme which can be considered as a virtual MIMO interference channel is introduced. At the first time slot, every relay stores the received signal. During the second time-slot, it retransmits the received signal after a proper adjustment on both the amplitude and the phase of the signal. For a priori known transmit and receive filters, a closed form solution for the relays' scaling factors is obtained. The required number of relays can be reduced by adapting the transmit and receive filters to the channel. Also the transmit energies of the relays are analyzed. The performance of the proposed scheme is investigated using numerical simulations. The results show that the proposed schemes outperform the conventional schemes, e.g., in terms of the achieved sum rates at high SNRs.

Interference alignment (IA) is a potential solution to combat interference in a wireless network. It can also be extended to mitigate the harmful effects of adversarial jamming. Anti-jamming opportunistic IA (OIA) strategy jointly optimizes the transmission power and harvested energy of the adversarial IA wireless network in the presence of jammers. In anti-jamming OIA network, selected users transmit information at a given time slot while unselected users perform energy harvesting (EH). Selected users may also be allowed to perform EH whilst they are performing information transfer, using simultaneous information and power transfer technique. The total radio frequency energy received at the selected users is split into two parts based on the power splitting coefficient, one for information decoding and the other for energy harvesting. The total transmitted power of the network and power splitting coefficient are then jointly optimised by adopting a sub-optimal algorithm. This paper proposes the use of minimum interference leakage (MinIL) algorithm for formulation of anti-jamming OIA network and subsequent joint optimisation of power splitting and transmit power of the users in the network. The simulation results show that usage of MinIL algorithm reduces the total transmit power of the entire network for low jamming power levels.

Consider a MIMO interference channel whereby each transmitter and receiver are equipped with multiple antennas. The basic problem is to design optimal linear transceivers (or beamformers) that can maximize system throughput. The recent work [1] suggests that optimal beamformers should maximize the total degrees of freedom and achieve interference alignment in high SNR. In this paper we first consider the interference alignment problem in spatial domain and prove that the problem of maximizing the total degrees of freedom for a given MIMO interference channel is NP-hard. Furthermore, we show that even checking the achievability of a given tuple of degrees of freedom for all receivers is NP-hard when each receiver is equipped with at least three antennas. Interestingly, the same problem becomes polynomial time solvable when each transmit/receive node is equipped with no more than two antennas. Finally, we propose a distributed algorithm for transmit covariance matrix design, while assuming each receiver uses a linear MMSE beamformer. The simulation results show that the proposed algorithm outperforms the existing interference alignment algorithms in terms of system throughput.

Analyzing massive amounts of data using complex machine learning models requires significant computational resources. The conventional approach to such problems involves centralizing training data and inference processes in the cloud, i.e., in data centers. However, with the proliferation of mobile devices and increasing application of the Internet-of-Things (IoT) paradigm, very large amounts of data are collected at the edges of wireless networks, and due to privacy constraints and limited communication resources, it is undesirable or impractical to upload this data from mobile devices to the cloud for centralized learning. This problem can be solved by distributed learning at the network edge, by which edge devices collaboratively train a shared learning model using real-time mobile data. The avoidance of raw-data uploading not only helps to preserve privacy but may also alleviate network-traffic congestion and minimize latency. With that said, distributed training still requires a substantial amount of information exchange between devices and edge servers over wireless links. In the process, wireless impairments such as noise, interference, and imperfect knowledge of channel states can significantly slow down distributed learning (e.g., convergence speed) and degrades its performance (e.g., learning accuracy). This makes it crucial to optimize wireless network performance so as to support the efficient deployment of distributed learning algorithms. On the other hand, distributed learning algorithms provide a powerful tool-set for solving complex problems in wireless communication and networking. One important framework, called federated learning (FL), enables users to collaboratively learn a shared model while helping to preserve local data privacy. The application of FL can endow edge devices with capabilities of user behavior prediction, user identification, and wireless environment analysis. As another example, distributed reinforcement learning is capable of leveraging distributed computation power and data to solve complex optimization and control problems that arise in various use cases, such as network control, user clustering, resource management, and interference alignment. To cover this paradigm of distributed learning over wireless networks, this two-part Special Issue features papers dealing with two main research challenges: a) optimization of wireless network performance for efficient implementation of distributed learning in wireless networks, and b) distributed learning for solving communication problems and optimizing network performance.

A novel interference alignment (IA) scheme based on the errors-in-variables (EIV) mathematic model has been proposed to overcome the channel state information (CSI) estimation error for the MIMO interference channels. By solving an equivalently unconstrained optimization problem, the proposed IA scheme employing a weighted total least squares (WTLS) algorithm can obtain the solution to a constrained optimization problem for transmit precoding (TPC) matrices and minimizes the distortion caused by imperfect CSI according to the EIV model. It is shown that the design of TPC matrices can be realized through an efficient iterative algorithm. The convergence of the proposed scheme is presented as well. Simulation results show that the proposed IA scheme is robust over MIMO interference channels with imperfect CSI, which yields significantly better sum rate performance than the existing IA schemes such as distributed iterative IA, maximum signal-to-interference-plus-noise ratio (Max SINR), and minimum mean square error (MMSE) schemes.