Spatial Interference Alignment Research Articles

Spatial Interference Alignment with Limited Precoding Matrix Feedback in a Wireless Multi-User Interference Channel for Smart Grids

Cellular communication provides an efficient, flexible, long-lived, and reliable communication technology for smart grids to improve the automated analysis, demand response, adoptive control, and coordination between the generator and consumers. With the expansion of wireless networks and the increase of access devices, interference has become a major problem that limits the performance of cellular wireless communication systems for smart grids. Spatial interference alignment (IA) is an effective method to eliminate interference and improve the capacity of wireless communication networks. This paper provides the sufficient conditions of spatial interference alignment operating with limited precoding matrix feedback for a K-user MIMO interference channel. Each receiver feeds the matrix index of the transmitting precoder back to the corresponding transmitter through an interference-free and error-free link. We calculated the number of feedback bits required to achieve the maximum theoretical multiplexing gain for the spatial interference alignment schemes considered and demonstrate the feasibility of spatial interference alignment under the limited feedback constraint investigated. It is shown that in order to maintain the same spatial multiplexing gain as that of the idealized scheme relying on perfect channel state information, the number of feedback bits per receiver scales as Nd≥di(M−di)log2SNR, where M and di denote the number of transmit (receive) antennas and the number of data steams for user i. Finally, the analytical results were verified by simulations for practical interference alignment schemes relying on limited precoding matrix feedback indices.

Secure Degrees of Freedom Region of Static and Time-Varying Gaussian MIMO Interference Channel

We consider the two-user multiple-input multiple-output (MIMO) interference channel with confidential messages (ICCM). We determine the exact secure degrees of freedom (s.d.o.f.) region for the symmetric case of $M$ antennas at both transmitters and $N$ antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the interference channel with no secrecy constraints, and vector extensions of the secrecy penalty and role of a helper lemmas. For the achievability, we first show that the s.d.o.f. region is a four-vertex polytope. For the sum s.d.o.f. point, we propose a novel achievable scheme for the $2 \times 2$ ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any $M$ and $N$ by proper vector space operations. We achieve the other non-trivial extreme polytope points by employing one of the transmitters as a deaf helper for assisting the secure transmission of the other user. We present simplified achievable schemes for the special case of time-varying MIMO ICCM. The achievable schemes, in this case, make use of the time-varying nature of the channel to construct vector-space alignment counterpart of the real interference alignment used in the static channel case.

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.

CSIT Sharing for Spatial Interference Alignment Using Limited Capacity Backhaul

Cellular systems that employ time division duplexing (TDD) transmission are good candidates for implementation of interference alignment (IA) in the downlink since channel reciprocity enables the estimation of the channel state by the base stations (BS) in the uplink phase. However, the interfering BSs need to share their channel estimates via backhaul links of finite capacity. A quantization scheme is proposed which reduces the amount of information exchange (compared to conventional methods) required to achieve IA in such a system. The scaling (with the transmit power) of the number of bits to be exchanged between the BSs that is sufficient to preserve the multiplexing gain of IA is derived. Furthermore, assuming that the BSs have accurate estimates of their outgoing channels, new methods are proposed to further improve the performance of the network in a distributed manner.

Experimental evaluation of interference alignment for broadband WLAN systems

In this paper, we present an experimental study on the performance of spatial interference alignment (IA) in indoor wireless local area network scenarios that use orthogonal frequency division multiplexing (OFDM) according to the physical-layer specifications of the IEEE 802.11a standard. Experiments have been carried out using a wireless network testbed capable of implementing a 3-user MIMO interference channel. We have implemented IA decoding schemes that can be designed according to distinct criteria (e.g., zero-forcing or MaxSINR). The measurement methodology has been validated considering practical issues like the number of OFDM training symbols used for channel estimation or feedback time. In case of asynchronous users, a time-domain IA decoding filter is also compared to its frequency-domain counterpart. We also evaluated the performance of IA from bit error ratio measurement-based results in comparison to different time-division multiple access transmission schemes. The comparison includes single- and multiple-antenna systems transmitting over the dominant mode of the MIMO channel. Our results indicate that spatial IA is suitable for practical indoor scenarios in which wireless channels often exhibit relatively large coherence times.

Interference Alignment With Asymmetric Complex Signaling on MIMO X Channels

It is known that with conventional spatial interference alignment, i.e., linear interference alignment without symbol extension, the achievable Degrees of freedom (DoF) of MIMO X channels is no more than ⌊D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">outer</sub> ⌋, where D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">outer</sub> denotes the outer bound of DoF of MIMO X Channels. In this paper, we propose a spatial interference alignment and zero-forcing framework in combination with asymmetric complex signaling, which can achieve the DoF of 1/2⌊2D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">outer</sub> ⌋ for arbitrary number of antennas on each terminal. Note that 1/2⌊2D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">outer</sub> ⌋ is equal to or larger than ⌊D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">outer</sub> ⌋. The result shows that the technique of asymmetric complex signaling, which was originally proposed for single-antenna systems, can be useful for MIMO channels, in particular when symbol extensions are not allowed.

Exploiting Spatial Interference Alignment and Opportunistic Scheduling in the Downlink of Interference-Limited Systems

In this paper, we analyze the performance of single-stream and multistream spatial multiplexing (SM) systems employing opportunistic scheduling in the presence of interference. In the proposed downlink framework, every active user reports the postprocessing signal-to-interference-plus-noise power ratio (post-SINR) or the receiver-specific mutual information (MI) to its own transmitter using a feedback channel. The combination of scheduling and multiantenna receiver processing leads to substantial interference suppression gain. Specifically, we show that opportunistic scheduling exploits the spatial interference alignment (SIA) property inherent to a multiuser system for effective interference mitigation. We obtain bounds for the outage probability and the sum outage capacity for single-stream and multistream SM employing real or complex encoding for a symmetric interference channel (SIC) model. The techniques considered in this paper are optimal in different operating regimes. We show that the sum outage capacity can be maximized by reducing the SM rate to a value less than the maximum allowed value. The optimal SM rate depends on the number of interferers and the number of available active users. In particular, we show that the generalized multiuser SM (MU SM) method employing real-valued encoding provides a performance that is either comparable or significantly higher than that of MU SM employing complex encoding. A combination of analysis and simulation is used to describe the tradeoff between the multiplexing rate and the sum outage capacity for different antenna configurations.