Interference Alignment: From Degrees of Freedom to Constant-Gap Capacity Approximations

An interference alignment example is constructed for the deterministic channel model of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user interference channel. The deterministic channel example is then translated into the Gaussian setting, creating the first known example of a fully connected Gaussian <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user interference network with single antenna nodes, real, nonzero and constant channel coefficients, and no propagation delays where the degrees of freedom outerbound is achieved. An analogy is drawn between the propagation delay based interference alignment examples and the deterministic channel model which also allows similar constructions for the two-user <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> channel as well.

A linear shift deterministic 3-way channel with reciprocal channel gains is considered in this work. The 3-way channel is an extension of the 2-way channel introduced by Shannon. Here, a number of six messages is exchanged, one message from each user to the two other users. Each user operates in a full-duplex mode. We derive the capacity region of this 3-way channel w.r.t. the linear shift deterministic channel model. To this end, first, an outer bound is derived using cutset and genie-aided upper bounds. Then, it is noted that the outer bound bears a resemblance to the capacity region of a related linear shift deterministic Y-channel. Utilizing a Δ-Y transformation, the optimal scheme for the related Y- channel is modified in a way that achieves the outer bound of the 3-way channel. Mainly, the capacity achieving communication schemes are based on multi-way relaying by signal alignment, interference neutralization and backward decoding. We also consider a scheme which is based on interference alignment only. It turns out, that for the symmetric linear deterministic 3-way channel, this scheme is optimal. Thus, backward decoding and the resulting delays are avoided.

Real interference alignment is efficient in breaking-up a one-dimensional space over time-invariant channels into fractional dimensions. As such, multiple symbols can be simultaneously transmitted with fractional degrees-of-freedom (DoF). Of particular interest is when the one dimensional space is partitioned into two fractional dimensions. In such scenario, the interfering signals are confined to one sub-space and the intended signal is confined to the other sub-space. Existing real interference alignment schemes yield poor achievable rate at finite signal-to-noise ratio (SNR), which is of interest from a practical point of view. In this paper, we propose a radically novel nonlinear interference alignment technique, which we refer to as Interference Dissolution (ID). ID allows to break-up a one dimensional space into two fractional dimensions while achieving near-capacity performance for the entire SNR range. This is achieved by aligning signals by signals, as opposed to aligning signals by the channel. We introduce ID by considering a timeinvariant, point-to-point multiple-input single-output (MISO) channel. This channel has a one-dimensional space and offers one DoF. We show that, by breaking-up the one dimensional space into two sub-spaces, ID achieves a rate of two symbols per channel use while providing DoF for each symbol. We also propose a decoder and prove its optimality. We compare numerically the performance of ID in terms of the achievable rate performance to that of existing schemes and demonstrate ID's superiority.

We first consider a single hop wireless X network with $K$ transmitters and $J$ receivers, all with a single antenna. Each transmitter conveys an independent message for each receiver. The channel is assumed to have constant coefficients. We develop an interference alignment scheme for this setup and derive an achievable degrees of freedom (DoF) region. We show that in some cases, the derived region meets a previous outer bound, and hence, is the (exact) DoF region. For our achievability schemes, we divide each message into streams and use real interference alignment on the streams. Several previous results on the DoF region and total DoF for several special cases can be recovered from our result. Next, we consider a network model, such that each transmitter emits an arbitrary number of messages and each receiver can request an arbitrary subset of all emitted messages. We term this network the X network with multicast. We derive an achievability result for the DoF region of such networks, as well as an outer bound. Our achievability scheme is based on a novel extension of real interference alignment that enables us to achieve more points of the DoF region. This approach allows multiple messages from a single user to be aligned with other users’ messages. Finally, we discuss some points on the outer bounds that are not achievable with any of the alignment schemes that we present.

Existing work on cross-layer optimization for wireless networks adopts simple physical-layer models, i.e., treating interference as noise. In this paper, we adopt a deterministic channel model proposed in, a simple abstraction of the physical layer that effectively captures the effect of channel strength, broadcast and superposition in wireless channels. Within the Network Utility Maximization (NUM) framework, we study the cross-layer optimization for wireless networks based on this deterministic channel model. First, we extend the well-applied conflict graph model to capture the flow interactions over the deterministic channels and characterize the feasible rate region. Then we study distributed algorithms for general wireless multi-hop networks. The convergence of algorithms is proved by Lyapunov stability theorem and stochastic approximation method. Further, we show the convergence to the bounded neighborhood of optimal solutions with probability one under constant steps and constant update intervals. Our numerical evaluation validates the analytical results.

MIMO researches penetrate the network community due to recent advances in MIMO degree-of-freedom (DoF) frameworks. Independent from MIMO, Successive Interference Cancellation (SIC) is a powerful multi-user detection technology in physical layer, and Interference Alignment (IA) is a powerful technique for handling interference. Based on the understanding of the strengths and weaknesses of SIC and DoF, we propose mutual assistance by joint IA, SIC and DoF-based Interference Cancellation (DoF IC) to (i) conserve precious DoF resources through IA and SIC; (ii) meet strict SINR threshold criteria through IC and IA. In this paper, we develop the mathematical model to achieve the two ideas in a multi-hop MIMO network. Combined with scheduling and routing constraints, we developed a cross-layer optimization framework to the throughput maximization problem with joint IA and SIC for MIMO networks. Simulation results show that the join of IA and SIC can significantly conserve DoFs for IC and thereby improve the throughput.

We consider the additive white Gaussian noise (AWGN) cognitive fading interference channel consisting of one primary and multiple secondary transmitter-receiver pairs. The secondary transmitters have non-causal knowledge of the primary message. We find a tuple of achievable rates by utilizing the discrete superposition model (DSM), which is a simplified, deterministic channel model. The coding scheme devised for the DSM can be translated into a coding scheme for the AWGN model, where the rate achieved in the AWGN model is at most a constant gap below the rate achieved in the DSM. We then calculate the average throughput of the secondary pairs under the assumption of Rayleigh fading channels. The main result is that our scheme performs well in the weak interference regime. The sum-throughput increases with the number of secondary pairs.

Individual traffic management systems are considered as a solution of the problems caused by increasing road traffic. For bidirectional communication between roadside beacons and individual vehicles, a transmission system with a radio link operating at 5.8 GHz is a suitable medium. To study the link performance in multipath fading channels, a deterministic channel model was derived. Calculations, considering the radiation characteristics of the antennas as well as the reflectors 'motorhood' and 'road', are already confirmed by measurements. Since the mobile channel is in general composed of further reflectors, e.g. cars or trucks, the deterministic model was extended by including additional statistical distributed reflectors. The simulation results presented give information on the average power delay profile. Furthermore, the effect of polarization of beacon and the vehicle antenna on communications is discussed. >

This article provides a channel model which is suited for broadband indoor WLAN (wireless local area network) applications. Especially the communication within one room is addressed. These applications are characterized by no or very slow movements of the terminal in conjunction with high data rates requiring high bandwidths for transmission. Present WLAN systems offer data rates up to 108 Mb/s, multiple antenna systems (MIMO systems) are at the beginning of their introduction into the market. Upcoming demand for even higher data rates necessitating higher bandwidth efficiency is almost sure. This requires at first hand a full understanding of the channel in order to make best use of it. The article shows that the channel can be described best by a deterministic model, which needs only few dominant paths. This is underlined by channel sounder measurements and simple calculations. Making use of this deterministic channel model the article shows capacity improvements over a widespread Rayleigh fading model assumption.

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 in Multi-user MIMO Systems

We show that the three-user M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> × M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> Multiple-Input Multiple-Output (MIMO) interference channel where each transmitter is equipped with M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> antennas and each receiver is equipped with M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> antennas has (M) d(M, N) = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> min (M/2-1/κ, N/2+1/κ) degrees of freedom (DoF) normalized by time, frequency, and space dimensions, where = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> min(M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> ), N = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> max(M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> ), κ = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> ⌈M/N-M⌉. While the DoF outer bound of d(M, N) is established for every M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> value, 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 M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> × M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> MIMO interference channel, completely for all values of M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> . In particular, we show that the linear interference alignment problem (M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> × M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> , d) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> (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.

A spatio-temporal (ST) channel measurement carried out at 8.45 GHz is reported, which is purposed to determine the ST propagation characteristics in urban micro- and pico-cell environments. A wideband channel sounder and a directional parabolic antenna are employed to measure the ST channel parameters. A deconvolution technique is utilized and proved to be effective to obtain unambiguous spatial channel profiles. A random-phase-assisted hybrid 2D-3D ray-tracing model is used to predict the ST channel parameters and the statistical distribution of angular profiles. The verification between ray-tracing and measurement demonstrated that ray-tracing approaches are appropriate for deterministic ST channel modeling in urban micro- and pico-cell environments.

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.

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.