Upper Bounds of Interference Alignment Degree of Freedom

Interference alignment allows multiple users to share the same frequency and time resource in a wireless communications system. At present, two performance bounds, in terms of degree of freedom, have been proposed. One is for infinite-dimension extension and the other is for MIMO systems. This paper provides an understanding of the MIMO bound by examining its proofs and shows that it does not apply to a more practical case: MIMO-OFDM. Several approaches are proposed in searching for DoF bounds for systems such as finite-dimension time extension and MIMO-OFDM systems

The Degrees of Freedom of MIMO Interference Channels without State Information at Transmitters

This paper fully determines the degree-of-freedom (DoF) region of two-user interference channels with arbitrary number of transmit and receive antennas and isotropic fading, where the channel state information is available to the receivers but not to the transmitters. The result characterizes the capacity region to the first order of the logarithm of the signal-to-noise ratio (SNR) in the high-SNR regime. The DoF region is achieved using random Gaussian codebooks independent of the channel states. Hence the DoF gain due to beamforming and interference alignment is completely lost in absence of channel state information at the transmitters (CSIT).Comment: second revisio

Interference Networks with No CSIT: Impact of Topology

We consider partially-connected $K$-user interference networks, where the transmitters have no knowledge about the channel gain values, but they are aware of network topology (or connectivity). We introduce several linear algebraic and graph theoretic concepts to derive new topology-based outer bounds and inner bounds on the symmetric degrees-of-freedom (DoF) of these networks. We evaluate our bounds for two classes of networks to demonstrate their tightness for most networks in these classes, quantify the gain of our inner bounds over benchmark interference management strategies, and illustrate the effect of network topology on these gains.Comment: Accepted for Publication in IEEE Transactions on Information Theor

Interference Channels with Coordinated Multi-Point Transmission: Degrees of Freedom, Message Assignment, and Fractional Reuse

Coordinated Multi-Point (CoMP) transmission is an infrastructural enhancement under consideration for next generation wireless networks. In this work, the capacity gain achieved through CoMP transmission is studied in various models of wireless networks that have practical significance. The capacity gain is analyzed through the degrees of freedom (DoF) criterion. The DoF available for communication provides an analytically tractable way to characterize the capacity of interference channels. The considered channel model has K transmitter/receiver pairs, and each receiver is interested in one unique message from a set of K independent messages. Each message can be available at more than one transmitter. The maximum number of transmitters at which each message can be available, is defined as the cooperation order M. For fully connected interference channels, it is shown that the asymptotic per user DoF, as K goes to infinity, remains at 1/2 as M is increased from 1 to 2. Furthermore, the same negative result is shown to hold for all M > 1 for any message assignment that satisfies a local cooperation constraint. On the other hand, when the assumption of full connectivity is relaxed to local connectivity, and each transmitter is connected only to its own receiver as well as L neighboring receivers, it is shown that local cooperation is optimal. The asymptotic per user DoF is shown to be at least max {1/2,2M/(2M+L)} for locally connected channels, and is shown to be 2M/(2M+1) for the special case of Wyner's asymmetric model where L=1. An interesting feature of the proposed achievability scheme is that it relies on simple zero-forcing transmit beams and does not require symbol extensions. Also, to achieve the optimal per user DoF for Wyner's model, messages are assigned to transmitters in an asymmetric fashion unlike traditional assignments where message i has to be available at transmitter i.Comment: Submitted to IEEE Transactions on Information Theor

On the Scaling of Interference Alignment Under Delay and Power Constraints

Future wireless standards such as 5G envision dense wireless networks with large number of simultaneously connected devices. In this context, interference management becomes critical in achieving high spectral efficiency. Orthogonal signaling, which limits the number of users utilizing the resource simultaneously, gives a sum-rate that remains constant with increasing number of users. An alternative approach called interference alignment promises a throughput that scales linearly with the number of users. However, this approach requires very high SNR or long time duration for sufficient channel variation, and therefore may not be feasible in real wireless systems. We explore ways to manage interference in large networks with delay and power constraints. Specifically, we devise an interference phase alignment strategy that combines precoding and scheduling without using power control to exploit the diversity inherent in a system with large number of users. We show that this scheme achieves a sum-rate that scales almost logarithmically with the number of users. We also show that no scheme using single symbol phase alignment, which is asymmetric complex signaling restricted to a single complex symbol, can achieve better than logarithmic scaling of the sum-rate.Comment: Shorter version to appear in ISIT 201

Degrees-of-Freedom of the MIMO Three-Way Channel with Node-Intermittency

The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region and sum-DoF. We devise a non-adaptive encoding scheme based on zero-forcing, interference alignment and erasure coding, and show its DoF region (and thus sum-DoF) optimality for non-intermittent 3WCs and its sum-DoF optimality for (node-)intermittent 3WCs. However, we show by example that in general some DoF tuples in the intermittent 3WC can only be achieved by adaptive schemes, such as decode-forward relaying. This shows that non-adaptive encoding is sufficient for the non-intermittent 3WC and for the sum-DoF of intermittent 3WCs, but adaptive encoding is necessary for the DoF region of intermittent 3WCs. Our work contributes to a better understanding of the fundamental limits of multi-way communication systems with intermittency and the impact of adaptation therein

The DoF Region of the Multiple-Antenna Time Correlated Interference Channel with Delayed CSIT

We consider the time-correlated multiple-antenna interference channel where the transmitters have (i) delayed channel state information (CSI) obtained from a latency-prone feedback channel as well as (ii) imperfect current CSIT, obtained e.g. from prediction on the basis of these past channel samples. We derive the degrees of freedom (DoF) region for the two-user multiple-antenna interference channel under such conditions. The proposed DoF achieving scheme exploits a particular combination of the space-time alignment protocol designed for fully outdated CSIT feedback channels (initially developed for the broadcast channel by Maddah-Ali et al, later extended to the interference channel by Vaze et al. and Ghasemi et al.) together with the use of simple zero-forcing (ZF) precoders. The essential ingredient lies in the quantization and feedback of the residual interference left after the application of the initial imperfect ZF precoder. Our focus is on the MISO setting albeit extensions to certain MIMO cases are also considered.Comment: 30 pages, 2 figures, with detailed proof of Theorem

On the Degree of Freedom for Multi-Source Multi-Destination Wireless Network with Multi-layer Relays

Degree of freedom (DoF) region provides an approximation of capacity region in high signal-to-noise ratio (SNR) regime, while sum DoF gives the scaling factor. In this correspondence, we analyse the DoF region and sum DoF for unicast layered multi-hop relay wireless networks with arbitrary number of source/destination/relay nodes, arbitrary number of hops and arbitrary number of antennas at each node. The result is valid for quite a few message topologies. We reveal the limitation on capacity of multi-hop network due to the concatenation structure and show the similarity with capacitor network. From the analysis on bound gap and optimality condition, the ultimate capacity of multi-hop network is shown to be strictly inferior to that of single-hop network. Linear scaling law can be established when the number of hops is fixed. At cost of channel state information at transmitters (CSIT) for each component single-hop network, our achievable scheme avoids routing and simplifies scheduling.Comment: 15 pages, 2 figure

On the Degrees of Freedom of the Symmetric Multi-Relay MIMO Y Channel

In this paper, we study the degrees of freedom (DoF) of the symmetric multi-relay multiple-input multiple-output (MIMO) Y channel, where three user nodes, each with M antennas, communicate via K geographically separated relay nodes, each with N antennas. For this model, we establish a general DoF achievability framework based on linear precoding and post-processing methods. The framework poses a nonlinear problem with respect to user precoders and post-processors, as well as relay precoders. To solve this problem, we adopt an uplink-downlink asymmetric strategy, where the user precoders are designed for signal alignment and the user post-processors are used for interference neutralization. With the user precoder and post-processor designs fixed as such, the original problem then reduces to a problem of relay precoder design. To address the solvability of the system, we propose a general method for solving matrix equations. This method is also useful to the DoF analysis of many other multiway relay networks. Together with the techniques of antenna disablement and symbol extension, an achievable DoF of the symmetric multi-relay MIMO Y channel is derived for an arbitrary setup of (K, M, N). We show that, for K >= 2, the optimal DoF is achieved for M/N in [0, max{sqrt(3K)/3,1}) and [(3K+sqrt(9K^2-12K))/6,infinity). We also show that the uplink-downlink asymmetric design proposed in this paper considerably outperforms the conventional approach based on uplink-downlink symmetry.Comment: 30 pages, 5 figures, submitted to IEEE Trans. Wireless Communicatio

Secure Degrees of Freedom of Multi-user Networks: One-Time-Pads in the Air via Alignment

We revisit the recent secure degrees of freedom (s.d.o.f.) results for one-hop multi-user wireless networks by considering three fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian multiple access wiretap channel, and Gaussian interference channel with secrecy constraints. We present main enabling tools and resulting communication schemes in an expository manner, along with key insights and design principles emerging from them. The main achievable schemes are based on real interference alignment, channel prefixing via cooperative jamming, and structured signalling. Real interference alignment enables aligning the cooperative jamming signals together with the message carrying signals at the eavesdroppers to protect them akin to one-time-pad protecting messages in wired systems. Real interference alignment also enables decodability at the legitimate receivers by rendering message carrying and cooperative jamming signals separable, and simultaneously aligning the cooperative jamming signals in the smallest possible sub-space. The main converse techniques are based on two key lemmas which quantify the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs; and the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. These two lemmas when applied according to the unique structure of individual networks provide tight converses. Finally, we present a blind cooperative jamming scheme for the helper network with no eavesdropper channel state information at the transmitters that achieves the same optimal s.d.o.f. as in the case of full eavesdropper channel state information.Comment: To appear in Proceedings of the IEEE, special issue on Physical Layer Security and its Applications. arXiv admin note: text overlap with arXiv:1404.7478, arXiv:1209.537