Interference Alignment and the Degrees of Freedom for the K User Interference Channel

While the best known outerbound for the K user interference channel states that there cannot be more than K/2 degrees of freedom, it has been conjectured that in general the constant interference channel with any number of users has only one degree of freedom. In this paper, we explore the spatial degrees of freedom per orthogonal time and frequency dimension for the K user wireless interference channel where the channel coefficients take distinct values across frequency slots but are fixed in time. We answer five closely related questions. First, we show that K/2 degrees of freedom can be achieved by channel design, i.e. if the nodes are allowed to choose the best constant, finite and nonzero channel coefficient values. Second, we show that if channel coefficients can not be controlled by the nodes but are selected by nature, i.e., randomly drawn from a continuous distribution, the total number of spatial degrees of freedom for the K user interference channel is almost surely K/2 per orthogonal time and frequency dimension. Thus, only half the spatial degrees of freedom are lost due to distributed processing of transmitted and received signals on the interference channel. Third, we show that interference alignment and zero forcing suffice to achieve all the degrees of freedom in all cases. Fourth, we show that the degrees of freedom $D$ directly lead to an $\mathcal{O}(1)$ capacity characterization of the form $C(SNR)=D\log(1+SNR)+\mathcal{O}(1)$ for the multiple access channel, the broadcast channel, the 2 user interference channel, the 2 user MIMO X channel and the 3 user interference channel with M>1 antennas at each node. Fifth, we characterize the degree of freedom benefits from cognitive sharing of messages on the 3 user interference channel.Comment: 30 pages. Revision extends the 3 user proof to K user

Interference alignment for the MIMO interference channel

We study vector space interference alignment for the MIMO interference channel with no time or frequency diversity, and no symbol extensions. We prove both necessary and sufficient conditions for alignment. In particular, we characterize the feasibility of alignment for the symmetric three-user channel where all users transmit along d dimensions, all transmitters have M antennas and all receivers have N antennas, as well as feasibility of alignment for the fully symmetric (M=N) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a K-user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.Comment: 16 pages, 7 figures, final submitted versio

Interference management techniques in large-scale wireless networks

In this thesis, advanced interference management techniques are designed and evaluated for large-scale wireless networks with realistic assumptions, such as signal propagation loss, random node distribution and non-instantaneous channel state information at the transmitter (CSIT). In the first part of the thesis, the Maddah-Ali and Tse (MAT) scheme for the 2-user and 2-antenna base station (BS) broadcast channel (BC) is generalised and optimised using the probabilistic-constrained optimisation approach. With consideration of the unknown channel entries, the proposed optimisation approach guarantees a high probability that the interference leakage power is below a certain threshold in the presence of minimum interference leakage receivers. The desired signal detectability is maximised at the same time and the closed-form solution for the receiving matrices is provided. Afterwards, the proposed optimisation approach is extended to the 3-user BC with 2-antenna BS. Simulation results show substantial sum rate gain over the MAT scheme, especially with a large spatial correlation at the receiver side. In the second part, the MAT scheme is extended to the time-correlated channels in three scenarios, in which degrees of freedom (DoF) regions as well as achievability schemes are studied: 1) 2-user interference channel (IC) using imperfect current and imperfect delayed CSIT; 2) K-user BC with K-antenna BS using imperfect current and perfect delayed CSIT; 3) 3-user BC with 2-antenna BS using imperfect current and perfect delayed CSIT. Notably, the consistency of the proposed DoF regions with the MAT scheme and the ZF beamforming schemes using perfect current CSIT consents to the optimality of the proposed achievability schemes. In the third part, the performance of the ZF receiver is evaluated in Poisson distributed wireless networks. Simple static networks as well as dynamic networks are studied. For the static network, transmission capacity is derived whereby the receiver can eliminate interference from nearby transmitters. It is shown that more spatial receive degrees of freedom (SRDoF) should be allocated to decode the desired symbol in the presence of low transmitter intensity. For the dynamic network, in which the data traffic is modelled by queueing theory, interference alignment (IA) beamforming is considered and implemented sequentially. Interestingly, transmitting one data stream achieves the highest area spectrum efficiency. Finally, a distance-dependent IA beamforming scheme is designed for a generic 2-tier heterogeneous wireless network. Second-tier transmitters partially align their interferences to the dominant cross-tier interference overheard by the receivers in the same cluster. Essentially, the proposed IA scheme compromises between enhancing the signal-to-interference ratio and increasing the multiplexing gain. It is shown that acquiring accurate distance knowledge brings insignificant throughput gain compared to statistical distance knowledge. Simulation results validate the derived expressions of success probabilities as well as throughput, and show that the distance-dependent IA scheme significantly outperforms the traditional IA scheme in the presence of path-loss effect

MIMO Interference Alignment Over Correlated Channels with Imperfect CSI

Interference alignment (IA), given uncorrelated channel components and perfect channel state information, obtains the maximum degrees of freedom in an interference channel. Little is known, however, about how the sum rate of IA behaves at finite transmit power, with imperfect channel state information, or antenna correlation. This paper provides an approximate closed-form signal-to-interference-plus-noise-ratio (SINR) expression for IA over multiple-input-multiple-output (MIMO) channels with imperfect channel state information and transmit antenna correlation. Assuming linear processing at the transmitters and zero-forcing receivers, random matrix theory tools are utilized to derive an approximation for the post-processing SINR distribution of each stream for each user. Perfect channel knowledge and i.i.d. channel coefficients constitute special cases. This SINR distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate, but also permits a realistic comparison of IA with other transmission techniques. More specifically, IA is compared with spatial multiplexing and beamforming and it is shown that IA may not be optimal for some performance criteria.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Signal Processin

Interference Alignment for Cognitive Radio Communications and Networks: A Survey

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Interference alignment (IA) is an innovative wireless transmission strategy that has shown to be a promising technique for achieving optimal capacity scaling of a multiuser interference channel at asymptotically high-signal-to-noise ratio (SNR). Transmitters exploit the availability of multiple signaling dimensions in order to align their mutual interference at the receivers. Most of the research has focused on developing algorithms for determining alignment solutions as well as proving interference alignment’s theoretical ability to achieve the maximum degrees of freedom in a wireless network. Cognitive radio, on the other hand, is a technique used to improve the utilization of the radio spectrum by opportunistically sensing and accessing unused licensed frequency spectrum, without causing harmful interference to the licensed users. With the increased deployment of wireless services, the possibility of detecting unused frequency spectrum becomes diminished. Thus, the concept of introducing interference alignment in cognitive radio has become a very attractive proposition. This paper provides a survey of the implementation of IA in cognitive radio under the main research paradigms, along with a summary and analysis of results under each system model.Peer reviewe