Linear Interference Alignment Research Articles

BIA for the K-User Interference Channel Using Reconfigurable Antenna at Receivers

In this paper, we consider the problem of data transmission for ${K}-$ user interference channel (IC) with no channel state information (CSI) at transmitters. Each pair of transceivers with the aid of a particular precoder and a switching pattern structure tries to place its desired signal in a subspace which is linearly independent of interference signals. We show that if the channel values are known only to the receivers, the sum degrees-of-freedom (DoF) of the linear interference alignment (IA) with reconfigurable antenna at receivers is $\frac {{ { Kr}}}{ {r}^{2}- {r}+ {K}}$ , where $ {r} = \left \lceil{ {\frac {\sqrt {1+4 {K}}-1}{2}} }\right \rceil $ . For previous methods when $3 \leq {K} \leq 10^{4}$ , the number of solvable problems to achieve maximum sum DoF is less than 2% of different cases while in our work there is not any limitation on the number of users. In comparison with the previous related works in our proposed method, there is no limit on the number of users and the reception modes. The result indicates that the maximum sum DoF for the ${K}-$ user IC with asymptotically large values of K is $\frac {\sqrt { {K}}}{2}$ . Thus, the sum DoF of such networks using the reconfigurable antenna at receivers grows sublinearly with the number of users, whereas it grows linearly in the case where transmitters have access to CSI.

Performance Analysis of Multi-Cell Full-Duplex Cellular Networks

We analyze the performance of a cellular network, where Poisson point process distributed half-duplex (HD) downlink (DL) and uplink (UL) users are served by multiple full-duplex (FD) base stations (BSs). To address the surge in interference in the network due to the simultaneous operation in time and frequency of the FD BSs, we (a) adopt a self-interference cancellation scheme at each BS, and (b) apply linear interference alignment in each cell to cancel the intra-cell interference. Further, to better capture the distribution of the FD BSs, we model the BSs as a Matérn hard-core point process, in which a minimum distance is imposed between points. The performance of both UL and DL users is analyzed by deriving general expressions and closed-form approximations for the outage probability and throughput. Next, simulations are carried out for both macro and micro cell environments under both FD and HD operations with respect to various network parameters. Our results reveal several fundamental characteristics and the necessary conditions required for the successful deployment of such networks.

Achievable Degrees of Freedom of Relay-Aided MIMO Cellular Networks Using Opposite Directional Interference Alignment

In this paper, we propose an interference alignment (IA) scheme for the multiple-input multiple-output (MIMO) uplink cellular network with the help of a relay which operates in half-duplex mode. The proposed scheme only requires global channel state information (CSI) knowledge at the relay, with no transmitter beamforming and time extension at the user equipment (UE), which differs from conventional IA schemes for cellular networks. We derive the feasibility condition of the proposed scheme for the general cellular network configuration and analyze the degrees-of-freedom (DoF) performance of the proposed IA scheme while providing a closed-form beamformer design at the relay. Extensions of the proposed scheme to downlink and full-duplex cellular networks are also proposed in this paper. The DoF performance of the proposed scheme is compared to those of linear IA scheme and relay-aided interference management scheme for a cellular network with no time extension. It is also shown that advantages similar to those in the uplink case can be obtained for the downlink case through the duality of a relay-aided interfering multiple-access channel (IMAC) and an interfering broadcast channel (IBC). Furthermore, the proposed scheme for a full-duplex cellular network is shown to have advantages identical to those of a number of proposed half-duplex cellular cases.

Interference Alignment in Multi-Hop Cognitive Radio Networks under Interference Leakage

In this work, we examine the interference alignment (IA) performance of a multi-input multi-output (MIMO) multi-hop cognitive radio (CR) network in the presence of multiple primary users. In the proposed architecture, it is assumed that linear IA is adopted at the secondary network to alleviate the interference between primary and secondary networks. By doing so, the secondary source can communicate with the secondary destination via multiple relays without causing any interference to the primary network. Even though linear IA can suppress the interference in CR networks considerably, interference leakages may occur due to a fast fading channel. To this end, we focus on the performance of the secondary network for two different cases: (i) the interference is perfectly aligned; (ii) the impact of interference leakages. For both cases, closed-form expressions of outage probability and ergodic capacity are derived. The results, which are validated by Monte Carlo simulations, show that interference leakages can deteriorate both system performance and the diversity gains considerably.

Achieving Optimal Degrees of Freedom for an Interference Network with General Message Demand

The concept of degrees of freedom (DoF) has been adopted to resolve the difficulty of studying the multi-user wireless network capacity regions. Interference alignment (IA) is an important technique developed recently for quantifying the DoF of such networks. In the present study, a single-hop interference network with K transmitters and N receivers is taken into account. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. Using the linear IA techniques, the optimal DoF assignment has been analyzed. Assuming generic channel coefficients, it has been shown that the perfect IA cannot be achieved for a broad class of interference networks. Analytical evaluation of DoF feasibility for general interference channels (IFCs) is complicated and not available yet. Iterative algorithm designed to minimize the leakage interference at each receiver is extended to work with general IFCs. This algorithm provides numerical insights into the feasibility of IA, which is not yet available in theory.

Linear Interference Alignment in Full-Duplex MIMO Networks With Imperfect CSI

In this paper, we consider a system where full-duplex (FD) base-stations (BSs) communicate with half-duplex (HD) downlink (DL) and uplink (UL) users in a multi-user multi-cell network, where all nodes are equipped with multiple antennas. The introduction of FD BSs offers potential to increase spectral efficiency, however, it also causes a surge in the number of interference links compared with the HD network counterpart. Here, we apply linear interference alignment (IA) to manage interference in this network under imperfect channel state information (CSI). First, we characterize the performance losses incurred with respect to the achievable sum rate and degrees of freedom (DoFs). Results show that the general trend in performance loss is mainly determined by how the error scales with the signal-to-noise ratio (SNR). In particular, full UL and DL DoF can be achieved even under imperfect CSI when the channel error is at least inversely proportional to SNR. Moreover, in such cases the sum rate loss is always finite, and either goes to zero or is upper bounded by a derived value. Second, we design two linear IA algorithms applicable to the system under consideration. These are based on minimizing the mean square error (MMSE) and maximizing the signal-to-interference-plus-noise ratio, and consider statistical knowledge of the CSI error for added robustness. The proposed algorithms follow specific design principles that distribute the different interference components amongst the various beamformers and result in unitary receivers and precoders. In addition, we show that under certain conditions both designs result in identical beamforming solutions, even though the MMSE algorithm has lower computational complexity. Finally, we also derive the proper condition for IA feasibility in the multi-cell system under consideration.

The Feasibility of Interference Alignment for MIMO Interfering Broadcast—Multiple-Access Channels

The feasibility conditions of interference alignment (IA) are analyzed for interfering broadcast-multiple-access channels in which one cell operates as downlink but the other cell operates as uplink. Under a general multiple-input and multiple-output antenna configuration, a necessary condition and a sufficient condition for one-shot linear IA are established, i.e., linear IA without symbol or time extension. In various example networks of interest, the optimal sum degrees of freedom (DoFs) are characterized by the derived necessary condition and sufficient condition. For symmetric DoF within each cell, a sufficient condition is established in a more compact expression, which yields the necessary and sufficient condition for a class of symmetric DoFs. An iterative construction of transmit and receive beamforming vectors is further proposed, which provides a specific beamforming design satisfying one-shot IA. Simulation results demonstrate that the proposed IA not only achieves larger DoF, but also significantly improves the sum rate over the single-cell operation in the practical signal-to-noise ratio regime.

Non‐cooperative interference alignment for multicell multiuser MIMO uplink channels

Linear interference alignment (IA) is considered a promising interference management technique for future cellular networks. However, its application to practical cellular networks still faces many challenges, two of which are the overhead of sharing global channel state information (CSI) and the cost of signalling dimensionality. These two challenges are resolved in this study via a new linear IA scheme that not only prevents global CSI sharing but also keeps the number of signalling dimensions manageable. While making linear IA more applicable, the proposed scheme provides comparable degrees of freedom to the existing IA schemes in symmetric multicell multiuser multiple-input multiple-output (MIMO) uplink channels.

Joint Mode Selection and Interference Management in Device-to-Device Communications Underlaid MIMO Cellular Networks

This paper considers a device-to-device (D2D) communications underlaid multiple-input multiple-output cellular network and studies D2D mode selection from a previously unexamined perspective. Since D2D mode selection affects the network interference profile and vice versa, a joint D2D mode selection and interference management is desired but challenging. In this paper, we propose a holistic approach to this problem with interference-free considerations. We adopt the degrees-of-freedom (DoFs) as the mode-selection criterion and exploit the linear interference alignment technique for interference management. We analyze the achievable sum DoF of the potential D2D users according to their mode selections, and derive the probabilistic sum-rate relations between the proposed DoF-based mode selection scheme and the common received-signal-strength-index-based mode selection scheme in Poisson point process networks. Simulation illustrates the theoretical insights and shows the advantages of the proposed DoF-based mode selection scheme over conventional mode selection schemes from various perspectives. The proposed scheme presents a promising proposal for D2D mode selection in 5G communications.

On Analytical Achievable Rate for MIMO Linear Interference Alignment with Imperfect CSI

This paper studies the impact of channel error on the achievable rate of symmetrical K-user multiple-input multiple-output linear interference alignment (IA) networks. The upper and lower bounds of the achievable sum rate are derived analytically with the assumption of orthonormal transmit precoders and receive filters designed from imperfect channel state information (CSI) over both the uncorrelated and correlated channels. For uncorrelated channels, quite tight lower and upper bounds are obtained. The impact of channel error on the degrees of freedom (DoF) and the DoF persistence conditions are also investigated. Results show that the DoF of IA networks persists only if the channel error decreases in an order higher than the signal-to-noise ratio. For correlated channel, the lower and upper bounds for one realization of IA are derived. The derived upper bound can be used to characterize the achievable rate approximately. Simulation results indicate that the achievable rate of IA network is influenced significantly by CSI uncertainty. The obtained analytical bounds provide an intuitive way to show the impact of channel error on the achievable rate and thus can help practical systems deign.

Beyond One-Way Communication: Degrees of Freedom of Multi-Way Relay MIMO Interference Networks

We characterize the degrees of freedom (DoFs) of a multiway relay wireless network consisting of four user nodes, each with $M$ antennas, and one $N$ -antenna relay node. Each user node sends one independent message to each of the other users, and there are no direct links between any two user nodes. For this network, we show that the symmetric DoF value per message is given by $\max (\min (({M}/{3}),({N}/{7})),\min ((({2M})/{7}),({N}/{6})))$ normalized by space dimensions, i.e., piecewise linear depending on $M$ and $N$ alternatively. While the information theoretic DoF upper bound is established for every $M$ and $N$ antennas, the achievability relying on linear signal subspace alignment is established in the spatially normalized sense in general. In addition, by deactivating four messages to form a two-way relay MIMO $X$ channel, we also present the DoF result $\max (\min (({M}/{2}),({N}/{5})),\min ((({2M})/{5}),({N}/{4})))$ in a similar piecewise linear type. The key ingredient to these new results is to first establish the principle of beamforming design via linear dimension counting perspective, which is essentially the fundamental element for establishing both the DoF converse and the DoF achievability. Moreover, we also settle the feasibility of linear interference alignment that extends the feasibility framework from one-way one-hop to multiway relay interference networks.

Interference Alignment for Multicell Multiuser MIMO Uplink Channels

This paper proposes a linear interference alignment (IA) scheme, which can be used for uplink channels in a general multicell multiuser multiple-input-multiple-output (MIMO) cellular network. The proposed scheme aims to align interference caused by signals from a set of transmitters into a subspace that is established by the signals from only a subset of those transmitters, thereby effectively reducing the number of interfering transmitters. The total degrees of freedom (DoF) achievable by the proposed scheme is given in closed-form expression, and a numerical analysis shows that the proposed scheme can achieve the optimal DoF in certain scenarios and provides a higher total DoF than other related schemes in most cases.

On Feasibility Conditions for Linear Interference Alignment over Cognitive Interference Channel: A DoF Analysis with Diversity Tradeoff

ABSTRACTIn a multiple-antennas cognitive radio network, the rate of the primary link is maximized by water-filling power allocation along the spatial directions associated with the singular values of primary channel matrix. Due to transmitter power constraint, even when the primary user occupies the entire spectrum, some spatial opportunities remain that can be utilized by secondary users. This scheme is called opportunistic interference alignment (OIA). The feasibility issue of OIA in a general symbol-extended system considering the diversity tradeoff, in particular, is the topic that is considered in this paper. An outer bound on the achievable degrees of freedom and also a necessary condition on the feasibility of a multiuser OIA network are presented analytically. In the remaining parts of the paper, the diversity and rate tradeoff is considered. In order to achieve diversity, it is assumed that the paired nodes utilize a space-time coder before the OIA pre-coder. A closed-form relation is presented that relates the minimum achievable diversity to interference alignment quality and code rate.

Cellular Interference Alignment: Omni-Directional Antennas and Asymmetric Configurations

Although interference alignment (IA) can theoretically achieve the optimal degrees of freedom (DoFs) in the $K$ -user Gaussian interference channel, its direct application comes at the prohibitive cost of precoding over exponentially many signaling dimensions. On the other hand, it is known that practical one-shot IA precoding (i.e., linear schemes without symbol expansion) provides a vanishing DoFs gain in large fully connected networks with generic channel coefficients. In our previous work, we introduced the concept of cellular IA for a network topology induced by hexagonal cells with sectors and nearest-neighbor interference. Assuming that neighboring sectors can exchange decoded messages (and not received signal samples) in the uplink, we showed that linear one-shot IA precoding over $M$ transmit/receive antennas can achieve the optimal $M/2$ DoFs per user. In this paper, we extend this framework to networks with omni-directional (non-sectorized) cells and consider a limited practical scenario where users have 2 antennas, and base-stations have 2, 3, or 4 antennas. We provide linear one-shot IA schemes for the $2\times 2$ , $2\times 3$ , and $2\times 4$ cases, and show the achievability of 3/4, 1, and 7/6 DoFs per user, respectively. DoFs converses for one-shot schemes require the solution of a discrete optimization problem over a number of variables that grows with the network size. We develop a new approach to transform such optimization problem into a tractable linear program with significantly fewer variables. This approach is used to show that 3/4 DoFs per user are indeed optimal for one-shot schemes over large (extended) cellular network with $2\times 2$ links.

Degrees of Freedom of MIMO Cellular Networks: Decomposition and Linear Beamforming Design

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.

On Degrees of Freedom Region of Three-User MIMO Interference Channels

Degrees of freedom (DoF) region of three-user interference channels is studied in this paper. The outer-bound of sum DoF of three-user interference channels was derived based on subspace alignment chain, but the complete DoF region remains unknown. In this paper, an outer-bound of DoF region of three-user interference channels is first derived. Then, a linear interference alignment scheme based on spatial beamforming is proposed that can achieve all integer DoF inside the region. As a result, the region can be seen as both the sufficient and necessary condition for the feasibility of linear interference alignment based on spatial beamforming in three-user interference channels. Moreover, the achievability of fractional DoF inside the outer bound DoF region is also addressed with the proposed beamforming scheme in combination with symbol extension.

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.

On feasibility of linear interference alignment for single‐input–single‐output multi‐frequency interference channel

This study explores the feasibility of linear interference alignment (IA) for a ( M × M , 1) K system with multi-frequency independent channels. The authors prove that number of users K ≤ 2 M - 2 is a necessary condition for ( M × M , 1) K multi-frequency IA system, which is less than that of ( M × M , 1) K multiple-input-multiple-output system (i.e. K ≤ 2 M - 1). The conclusion can be extended to all cases with the diagonal channel matrix. They also reveal that the traditional frequency division multiplexing method is inefficient in spectrum utilisation. They apply max-SINR (signal to interference plus noise ratio) and iterative IA algorithms and the author's simulation results verify that IA algorithms work well in ( M × M , 1) 2M-2 IA system.

Subspace Alignment Chains and the Degrees of Freedom of the Three-User MIMO Interference Channel

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.

Degrees of Freedom Characterization: The 3-User SISO Interference Channel with Blind Interference Alignment

We characterize the degrees of freedom (DoF) of the 3-user Gaussian interference channel where each transmitter is equipped with a single conventional antenna and each receiver is equipped with one multi-mode antenna. By assuming that the channel is unknown to the transmitters and only known to the receivers, we show that by using linear blind interference alignment (BIA) with antenna switching at the receivers only, the sum DoF are 6/5. The new insight behind this result is that any vector of a user aligned at one unintended receiver cannot be aligned at the other unintended receiver. This is the first complete characterization of the sum DoF when using BIA over the Gaussian Interference Channel. The DoF result under the temporal correlated channels is also discussed.