Optimal Sum Degrees Of Freedom Research Articles

Revisiting Degrees of Freedom of Full-Duplex Systems with Opportunistic Transmission: An Improved User Scaling Law.

It was recently studied how to achieve the optimal degrees of freedom (DoF) in a multi-antenna full-duplex system with partial channel state information (CSI). In this paper, we revisit the DoF of a multiple-antenna full-duplex system using opportunistic transmission under the partial CSI, in which a full-duplex base station having M transmit antennas and M receive antennas supports a set of half-duplex mobile stations (MSs) having a single antenna each. Assuming no self-interference, we present a new hybrid opportunistic scheduling method that achieves the optimal sum DoF under an improved user scaling law. Unlike the state-of-the-art scheduling method, our method is designed in the sense that the scheduling role between downlink MSs and uplink MSs is well-balanced. It is shown that the optimal sum DoF of is asymptotically achievable provided that the number of MSs scales faster than , where SNR denotes the signal-to-noise ratio. This result reveals that, in our full-duplex system, better performance on the user scaling law can be obtained without extra CSI, compared to the prior work that showed the required user scaling condition (i.e., the minimum number of MSs for guaranteeing the optimal DoF) of . Moreover, the average interference decaying rate is analyzed. Numerical evaluation is performed to not only validate our analysis but also show superiority of the proposed method over the state-of-the-art method.

On the DoF Region for the Asymmetric MIMO Two-Way X Relay Channel

In this paper, we study the degrees of freedom (DoF) region for the multiple-input multiple-output two-way X relay channel with asymmetric antenna setting. In this channel model, there are two groups of source nodes, each group contains two source nodes, every source node in one group exchanges independent messages with every source node in another group via a common relay node, and each node has a different number of antennas. First, we derive an outer bound of the DoF region by using the cut-set theorem and the genie-message approach. Then, we obtain an inner bound of the DoF region by proposing a new transmission scheme that collectively utilizes antenna deactivation, pairwise signal alignment, cyclic signal alignment, and generalized signal alignment techniques. In the case of symmetric data exchange, our inner bound coincides with the outer bound, and thus, our proposed transmission strategy is optimal. We also obtain the optimal sum DoF for the special case, where the source nodes within a same group are equipped with the same number of antennas. This paper provides new insights for the study of more complicated relay networks.

Cognitive Blind Interference Alignment for Macro-Femto Networks

We propose a cognitive blind interference alignment (BIA) scheme for macro-femto two-tier networks where the users are equipped with a single reconfigurable antenna. The proposed scheme fully cancels the intracell interference in both the upper and lower tiers. Moreover, it provides the optimal Degrees of Freedom (DoF) in the macro-tier while the lower tier subject to inter-tier interference achieves non-zero DoF. To do so, the proposed scheme relies on a topology management scheme where the users belong to the macro-tier if and only if they can optimally treat the interference caused by the transmission at the femto-tier as noise. The proposed scheme does not require any channel state information at the transmitter or data sharing between the macro- and femto-tiers. An outer bound of the DoF is derived for the considered macro-femto network. It is demonstrated that the proposed scheme can attain the outer bound subject to optimal sum DoF for the macro-tier. Furthermore, compared to previous approaches, cognitive BIA can achieve better sum rates for macro-femto networks for femtocells subject to different levels of inter-tier interference.

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.

Optimal DoF Region for the Asymmetric Two-Pair MIMO Two-Way Relay Channel

In this paper, we study the optimal degrees of freedom (DoF) region for the two-pair MIMO two-way relay channel (TWRC) with asymmetric antenna setting, where two pairs of users exchange information with the help of a common relay. Each user $i$ is equipped with $M_i$ antennas, for $i=1,2,3,4$, and the relay is equipped with $N$ antennas. First, we derive an outer bound of the DoF region by using the cut-set theorem and the genie-message approach. Then, we propose a new transmission scheme to achieve the outer bound of the DoF region. Due to the asymmetric data exchange, where the two users in each pair can communicate a different number of data streams, we not only need to form the network-coded symbols but also need to process the additional asymmetric data streams at the relay. This is realized through the joint design of relay compression matrix and source precoding matrices. After obtaining the optimal DoF region, we study the optimal sum DoF by solving a linear programming problem. From the optimal DoF region of this channel, we show that in the asymmetric antenna setting, some antennas at certain source nodes are redundant and cannot contribute to enlarge the DoF region. We also show that there is no loss of optimality in terms of the sum DoF by enforcing symmetric data exchange, where the two users in each pair are restricted to communicate the same number of data streams.

A MIMO Relay With Delayed Feedback Can Improve DoF in $K$- User MISO Interference Channel With No CSIT

This paper studies the impact of a multiple-input-multiple-output (MIMO) relay on the K-user multiple-input-single-output (MISO) interference channel (IC) when the relay has delayed feedback (i.e., delayed channel state information (CSI) or delayed channel output feedback) from each receiver, yet each transmitter has no knowledge about CSI. We first develop a new relay-aided retrospective interference alignment (r-RIA) and characterize the optimal sum degrees of freedom (DoFs) for the K-user MISO IC with a MIMO relay by providing a new matching outer bound. It is shown that the sum DoF does not decrease, even in the absence of direct links between transmitters and receivers, as long as K is sufficiently large. We next show that a MIMO relay can provide a sum-DoF gain in the K-user MISO IC with delayed feedback to the relay in the absence of CSI at transmitter (CSIT), whereas relaying is shown to be not useful with instantaneous CSIT from the DoF perspective.

Achieving Full DoF in Heterogeneous Parallel Broadcast Channels With Outdated CSIT

We consider communication over heterogeneous parallel channels, where a transmitter is connected to two users via two parallel channels: a MIMO broadcast channel (BC) and a noiseless rate-limited multicast channel. We characterize the optimal degrees of freedom (DoF) region of this setting when the transmitter has delayed channel state information (CSIT) regarding the MIMO BC. Our results show that jointly coding over the two channels strictly outperforms simple channel aggregation and can even achieve the instantaneous CSIT performance with completely outdated CSIT on the MIMO BC in the sum DoF sense; this happens when the multicast rate of the second channel is larger than a certain threshold. The main idea is to send information over the MIMO BC at a rate above its capacity and then use the second channel to send additional side information to allow for reliable decoding at both receivers. We call this scheme a two-phase overload-multicast strategy. We show that such a strategy is also sum DoF optimal for the K-user MIMO BC with a parallel multicast channel when the rate of the multicast channel is high enough and can again achieve the instantaneous CSIT performance (optimal sum DoF) with completely outdated CSIT. For the regime where the capacity of the multicast channel is small, we propose another joint coding strategy which is sum DoF optimal.

Degrees of Freedom of Millimeter Wave Full-Duplex Systems With Partial CSIT

The degrees of freedom (DoF) of $L$ -path poor scattering full-duplex (FD) systems is studied in which a FD base station having $M$ transmit antennas and $M$ receive antennas supports a set of half-duplex mobile stations (MSs). Assuming no self-interference, a hybrid scheduling is proposed achieving the optimal sum DoF with partial channel state information at the transmitter side as the number of MSs increases. In particular, the proposed scheme combines a zero-forcing beamforming for uplink and a random transmit beamforming for downlink with opportunistic scheduling. It is shown that the optimal sum DoF of $2M$ is asymptotically achievable as long as the number of MSs scales faster than ${\sf{snr}}^{\min\left(M-1,L\right)+M}$ , where ${\sf{snr}}$ denotes the signal-to-noise ratio.

The Feasibility of Interference Alignment for Full-Duplex MIMO Cellular Networks

The feasibility condition of interference alignment (IA) for full-duplex (FD) multiple-input multiple-output (MIMO) cellular networks is considered. A necessary condition and a sufficient condition on the IA feasibility are established, characterizing the optimal sum degrees of freedom (DoF) for a broad class of network topologies. The necessary and sufficient condition is shown specially for a class of symmetric network topologies. The results demonstrate that FD operation at the base station with appropriate IA is able to improve the sum DoF than the conventional half-duplex operation.

전이중 셀룰라 시스템의 간섭 제어에 관한 최근 연구 동향

This review paper introduces recent results on interference management for full-duplex cellular systems. Interference management techniques for uplink-downlink cellular networks are frist introduced, which are closely related to those for full-duplex cellular systems. Self-interference suppression method for full-duplex radios and the corresponding modeling of full-duplex cellular systems are then explained. Even if self-interference is perfectly suppressed, there exists a new source of interference between full-duplex users for full-duplex cellular systems. Therefore, management of such user-to-user interference is of crucially importance to improve the capacity of full-duplex cellular systems. Recently, new interference management techniques for achieving the optimal sum degrees of freedom of full-duplex cellular systems have been proposed. In this review paper, these optimal interference management techniques are mainly introduced.

Degrees of Freedom for a MIMO Gaussian $K$-Way Relay Channel: Successive Network Code Encoding and Decoding

This paper studies a network information flow problem for a multiple-input multiple-output (MIMO) Gaussian wireless network with K users and a single intermediate relay having M antennas. In this network, each user sends a multicast message to all other users while receiving K-1 independent messages from the other users via an intermediate relay. This network information flow is termed a MIMO Gaussian K-way relay channel. For this channel, it is shown that the optimal sum degrees of freedom (sum-DoF) is KM/K-1, assuming that all nodes have global channel knowledge and operate in full-duplex. A converse argument is derived by cut-set bounds. The achievability is shown by a repetition coding scheme with random beamforming in encoding and a zero-forcing method combined with self-interference cancelation in decoding. Furthermore, under the premise that all nodes have local channel state information at the receiver only and operate in half-duplex mode, it is shown that a total K/2 DoF is achievable when M=K-1. The key to showing this result is a novel encoding and decoding scheme, which creates a set of network code messages with a chain structure during the multiple access phase and performs successive interference cancelation using side-information for the broadcast phase. One major implication of the derived results is that efficient exploitation of the transmit message as side-information leads to an increase in the sum-DoF gain in a multiway relay channel with multicast messages.

Degrees of Freedom of Multi-Hop MIMO Broadcast Networks with Delayed CSIT

We study the sum degrees of freedom (DoF) of a class of multi-layer relay-aided MIMO broadcast networks with delayed channel state information at transmitters (CSIT). In the assumed network a K-antenna source intends to communicate to K single-antenna destinations, with the help of N-2 layers of K full-duplex single-antenna relays. We assume identical and independent fading channels on every hop. Two practical delayed CSIT feedback scenarios are studied. If the source can obtain the CSI feedback signals from all layers, we prove the optimal sum DoF of the network to be \frac{K}{1+\frac{1}{2}+…+\frac{1}{K}}. If the CSI feedback is only within each hop, we show that when K=2 the optimal sum DoF is \frac{4}{3}, and when K≥ 3 the sum DoF \frac{3}{2} is achieved asymptotically.