The emergence of interference alignment (IA) as a degrees-of-freedom optimal strategy motivates the need to investigate whether IA can be leveraged to aid conventional network utility maximization algorithms, which are typically only capable of finding locally optimal solutions. To test the usefulness of IA in this context, this paper proposes a two-stage optimization framework for the downlink of a G -cell multi-antenna network with K users/cell. The first stage of the proposed framework focuses on nulling interference from a set of dominant interferers using IA, while the second stage optimizes transmit and receive beamformers to maximize a network-wide utility using the IA solution as the initial condition. Further, this paper establishes a set of new feasibility results for partial IA that can be used to guide the number of dominant interferers to be nulled in the first stage. Through simulations on specific topologies of a cluster of base stations, it is observed that the impact of IA depends on the choice of the utility function and the presence of out-of-cluster interference. In the absence of out-of-cluster interference, the proposed framework outperforms straightforward optimization when maximizing the minimum rate, while providing marginal gains when maximizing sum rate. However, the benefit of IA is greatly diminished in the presence of significant out-of-cluster interference.

This paper investigates the symmetric degrees of freedom (DoF) of multiple-input multiple-output (MIMO) cellular networks with G cells and K users per cell, having N antennas at each base station and M antennas at each user. In particular, we investigate techniques for achievability that are based on either decomposition with asymptotic interference alignment or linear beamforming schemes and show that there are distinct regimes of (G,K,M,N) , where one outperforms the other. We first note that both one-sided and two-sided decomposition with asymptotic interference alignment achieve the same DoF. We then establish specific antenna configurations under which the DoF achieved using decomposition-based schemes is optimal by deriving a set of outer bounds on the symmetric DoF. Using these results, we completely characterize the optimal DoF of any G-cell network with single-antenna users. For linear beamforming schemes, we first focus on small networks and propose a structured approach to linear beamforming based on a notion called packing ratios. Packing ratio describes the interference footprint or shadow cast by a set of transmit beamformers and enables us to identify the underlying structures for aligning interference. Such a structured beamforming design can be shown to achieve the optimal spatially normalized DoF (sDoF) of two-cell two-user/cell network and the two-cell three-user/cell network. For larger networks, we develop an unstructured approach to linear interference alignment, where transmit beamformers are designed to satisfy conditions for interference alignment without explicitly identifying the underlying structures for interference alignment. The main numerical insight of this paper is that such an approach appears to be capable of achieving the optimal sDoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition, and a significant portion of sDoF elsewhere. Remarkably, polynomial identity test appears to play a key role in identifying the boundary of the achievable sDoF region in the former case.

This paper proposes a linear beamforming strategy for interference alignment in multiple-input multiple-output (MIMO) cellular networks. In particular, we consider a network consisting of G mutually interfering cells with K users/cell, having N antennas at each base station (BS) and M antennas at each user - a (G, K, M, N) network. We develop an unstructured approach to designing linear beamformers for interference alignment where transmit beamformers are designed to satisfy conditions for interference alignment without explicitly identifying the underlying structures for alignment. Specifically, the transmit beamformers in the uplink are required to satisfy a certain number of random linear vector equations in order to constrain the number of dimensions occupied by interference at each BS. The conceptual simplicity and the fact that no customization to a given network is needed makes this method applicable to a broad class of cellular networks. The key observation made in this paper is that such an approach appears to be capable of achieving the optimal DoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition-based schemes for interference alignment, and a significant portion of the DoF elsewhere. Remarkably, polynomial identity test plays a key role in identifying the scope and limitations of such a technique.

In this paper we investigate the spatially-normalized degrees of freedom (sDoF) of 2-cell, multiple-input multiple-output (MIMO) cellular networks with three users per cell having M antennas at each user and N antennas at each base-station. We characterize the optimal sDoF/user for all values of M and N and show that the optimal sDoF is a piecewise linear function, with either M or N being the bottleneck. We assume all channels to be generic, and establish achievability through linear transmit beamforming strategies. We introduce the notion of packing ratio that describes the interference footprint or shadow cast by a set of transmit beamformers. Through this notion, we reinterpret the alternating behavior of the optimal sDoF and attribute it to the availability of sets of transmit beamformers with certain packing ratios. We also derive a new DoF outer bound when 5 over 9 ≤ M over N ≤ 3 over 4.

This paper proposes an algorithm to compute the transmit beamformers for linear interference alignment for the MIMO interference channel and the MIMO interfering multiple-access/broadcast channel without symbol extensions. We first formulate the interference alignment problem as a rank minimization problem with linear constraints, then approximate the matrix rank by the nuclear norm. We further propose the use of an iterative reweighted nuclear norm approach and show that adaptive reweighting can significantly improve the algorithm's ability to find aligned beamformers. Simulation results show that the proposed algorithm is able to provide more interference-free dimensions and also converges faster than a previously proposed rank-constrained rank-minimization approach for interference alignment.

This paper characterizes the spatially-normalized degrees of freedom of a 2-cell, 2-user/cell MIMO cellular networks with M antennas at each user and N antennas at each base-station. We show that the optimal DoF is a piecewise linear function, with either M or N being the bottleneck. Denoting the ratio M/N as γ, we show that the network has redundant dimensions in both M and N when γ ϵ {1/2,1} and that the network has no redundancy when γ ϵ {1/4, 2/3, 3/2}. We also show that not all proper systems are feasible and that the only set of feasible proper systems that lie on the proper-improper boundary are those with γ ϵ {1/4, 2/3, 3/2}. We make comparisons between the DoF achievable using strategies such as time sharing between users or cells and discuss their implications on user scheduling in such networks.

In this paper we study the effect of receiver phase noise on single carrier frequency division multiple access (SC-FDMA). We show that common phase error rotates all the symbols by a certain angle and that the higher order frequency components of phase noise result in inter-carrier interference, or ICI and draw parallels to orthogonal frequency division multiple access (OFDMA). We then study the effect of phase noise on the performance of linear receivers that are often used in practice. In particular, we show that the amount of ICI affecting the sub-carriers depends closely on the allocation of sub-carriers among different users and prove that the performance of linear receivers in the presence of receiver phase noise deteriorates much more in the case of interleaved SC-FDMA than in the case of localized SC-FDMA. We identify the association of the significant phase noise components with the components of multi-user interference to be the fundamental reason behind the performance gap between interleaved and localized SC-FDMA.

We study the effect of receiver phase noise (PHN) on single carrier frequency division multiple access (SC-FDMA). We show that in the case of SC-FDMA, common phase error (CPE) rotates all the symbols by a certain angle, while the higher order frequency components of PHN result in inter-carrier interference (ICI). We then study the effect of PHN on the performance of linear receivers used in the detection of SC-FDMA/OFDMA symbols. In particular, we show that the amount of ICI affecting the sub-carriers depends closely on the allocation of sub-carriers amongst different users and further show that the performance of linear receivers in the case of interleaved SC-FDMA deteriorates much more than in the case of localized SC-FDMA in the presence of receiver PHN.

This paper addresses the issue of blind estimation of common phase error (CPE) in OFDM systems affected by phase noise (PHN). Common approaches to blind CPE detection detect the symbols, and estimate the phase noise in an iterative manner. An important assumption that these decision-directed algorithms make is that a majority of the symbols detected in the first iteration, while ignoring the presence of phase noise, have been detected correctly. This assumption fails to hold under scenarios of high CPE and leads to a premature error floor. In this paper we dispense with the assumption that most of the symbols have been detected correctly and instead associate with each symbol a certain probability of having been detected correctly. Through the introduction of an auxiliary binary variable that indicates whether the right decision on a symbol has been made or not, we design a new algorithm to estimate CPE. This algorithm is robust to high CPE scenarios and is able to lower the error floor seen at high SNRs.

The performance of iterative decoding of low density parity check (LDPC) codes over binary erasure channels can be completely characterized by the study of stopping sets. Therefore, the burst erasure correction capability of a given LDPC code can be readily quantified by searching for stopping sets within consecutive bit nodes. In this work we study the optimal permutation of the bit nodes that will result in the maximum possible burst erasure correction capability for a given LDPC code. Noting that this is essentially a combinatorial optimization problem that is highly likely to be NP-hard, we adopt a simulated annealing based approach for finding the optimal permutation. We present bounds based on stopping sets that limit the burst erasure correction capability. As part of our results, we provide interleavers that greatly improve the burst erasure correction capability of protograph quasi-cyclic LDPC codes used in the WiMax standard.