Achievable Sum Degrees Of Freedom Research Articles

Degrees of Freedom of a K-User Interference Channel in the Presence of an Instantaneous Relay.

In this paper, we study the degrees of freedom (DoF) of a frequency-selective K-user interference channel in the presence of an instantaneous relay (IR) with multiple receiving and transmitting antennas. We investigate two scenarios based on the IR antennas’ cooperation ability. First, we assume that the IR receiving and transmitting antennas can coordinate with each other and that the transmitted signal of each transmitting antenna can depend on the received signals of all receiving antennas, and we derive lower and upper bounds for the sum DoF of this model. In an interference alignment scheme, we divide receivers into two groups called clean and dirty receivers. We design our scheme such that a part of the messages of clean receivers can be de-multiplexed at the IR. Thus, the IR can use these message streams for an interference cancellation at the clean receivers. Next, we consider an IR, the antennas of which do not have coordination with each other and where the transmitted signal of each transmitting antenna depends only on the received signal of its corresponding receiving antenna. We also derive lower and upper bounds for the sum DoF for this model of IR. We show that the achievable sum DoF decreases considerably compared with the coordinated case. In both of these models, our schemes achieve the maximum K sum DoF if the number of transmitting and receiving antennas is more than a finite threshold.

Cache-Aided Retrospective Interference Alignment in Wireless Broadcast Channels

In this paper, we investigate joint retrospective interference alignment (RIA) and caching schemes for multiple-input single-output (MISO) broadcast channels (BC) with delayed channel state information at the transmitter (CSIT). By exploiting the cached content, we propose one sophisticated cache-aided RIA scheme to cancel the interference. Importantly, our scheme takes the number of symbols in a packet into account, as different number of symbols in a packet result in different system configuration, which may have significant impact on the design of the transmission scheme and achievable degrees of freedom (DoF). Furthermore, we present two theorems to quantify the achievable sum DoF of the proposed cached-aided RIA scheme for different system configuration. Moreover, the system configuration of the existing cache-aided RIA scheme with mixed CSIT can be treated as a special case in our paper. And also our scheme can simultaneously support more users than the existing cache-aided RIA scheme with mixed CSIT to invoke zero forcing (ZF) precoding, which limits the number of users simultaneously supported.

On the Degrees-of-Freedom for Relay-Aided MIMO Interference Channels With Partial and Delayed CSI

This letter shows that a multi-antenna relay using only partial and delayed channel state information (CSI) helps mitigate interference effects for multi-input multi-output interference channels when no CSI is available at transmitters. To this end, we present a novel relay-aided interference alignment, which comprises of two phases: 1) side-information learning and 2) overheard equation swapping via a relay. Leveraging the proposed scheme, we show that the achievable sum-degrees of freedom (sum-DoF) is equal to 2min(R, M)N/(min(R, M) + N) if min(R, M) > N where M, N, and R are the number of antennas at transmitter, receiver, and relay, respectively. One major implication of this result is that using the outdated CSI at the relay is sufficient to attain the optimal sum-DoF achieved with perfect CSI knowledge, provided that the number of antennas at the relay is larger than that of transmit and receive antennas.

Linear Network Coded Wireless Caching in Cloud Radio Access Network

This paper investigates a cache-aided cloud radio access network (C-RAN), comprising a central unit, K base stations (BSs) each with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> antennas, and M users each with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> antennas, where each BS and user have local caches to store some popular contents from the central unit. For this cache-aided network, we propose the linear network coded (NC) wireless caching that consists of linear wireless network coding assisted cache placement phase and signal-space alignment (SSA) enabled content delivery phase. In the cache placement phase, we design a joint NC caching function at the BSs to store linear combinations of messages from the central unit, as a form of linear wireless network coding. In the content delivery phase, we design the SSA pattern based on the NC caching to guide the precoding designs at BSs. Then, each user can reliably decode its requested messages by receiver shaping and reverse NC operation. The primary contribution of this work is to achieve the coding gain induced by the integration of linear wireless network coding and SSA, which has been not exploited in the field of wireless coded caching. In particular, to deal with high temporal variability of user requests, we show that the proposed cache placement is invariant to different user requests in the worst-case caching, without any shared caching messages at different BSs. Furthermore, we verify that the proposed scheme is also compatible with the insufficient caching scenario at the BSs. In addition, we analyze the achievable sum degrees of freedom (DoF) for the proposed caching network. Both analytical and numerical results verify that the proposed caching scheme achieves a higher sum DoF than the existing related works.

A Cross Time Slot Partial Interference Alignment Scheme in Two-Cell Relay Heterogeneous Networks

The interference of a two-cell two-hop multi-input–multi-output (MIMO) heterogeneous network where the cell-center user (CCU) coexists with the cell-edge user (CEU) is complex to characterize and costly to suppress. In downlink, the CEU is assumed to be served by a half-duplex relay with amplify-and-forward mode. To suppress the intra-cell and inter-cell interference, a cross time slot partial interference alignment (TPIA) scheme, which aligns the interference terms generated in different sub-time slots to the same subspace, is proposed in this paper. Furthermore, the feasibility condition of antenna configuration is analyzed. Simulation results indicate that the TPIA scheme outperforms other existing conventional techniques in achievable sum degrees of freedom and sum-rate performance.

Cache-Assisted Broadcast-Relay Wireless Networks: A Delivery-Time Cache-Memory Tradeoff

An emerging trend of next generation communication systems is to deploy caches at network edges to reduce file delivery latency. To investigate this aspect, we study the fundamental limits of a cache-aided broadcast-relay wireless network consisting of one central base station, $M$ cache-equipped transceivers and $K$ receivers from a latency-centric perspective. We use the normalized delivery time (NDT) to capture the per-bit latency at high signal-to-noise ratio (SNR). The objective is to jointly design the cache placement and file delivery in order to minimize the NDT. To this end, we establish two converse results and two achievability schemes. The first converse result is restricted to one-shot delivery schemes, while the second excludes this restriction. Similarly, the first achievable scheme is a general NDT-optimal one-shot scheme that synergistically exploits both multicasting and distributed zero-forcing opportunities. With respect to the second converse result, this scheme performs well for various parameter settings, particularly at higher cache sizes. The second scheme, effective at lower cache sizes, designs beamformers to facilitate both subspace interference alignment and zero-forcing. Exploiting both schemes, we are able to characterize the optimal tradeoff between cache storage and latency in networks satisfying $K+M\leq 4$ . The tradeoff illustrates that the NDT is the preferred choice to capture the latency of a system rather than the commonly used sum degrees of freedom (DoF). In fact, our optimal tradeoff refutes the popular belief that increasing cache sizes translates to increasing the achievable sum DoF. As such, we discuss cases where increasing cache sizes decreases both the delivery time and the achievable DoF.

Cooperative Communication for Cognitive Satellite Networks

A cooperative cognitive radio for satellite networks is considered, in which the primary network is a satellite network and the secondary network is a cellular network. Due to the lack of multipath in a satellite environment, the channel matrices of the satellite network are assumed to be rank-deficient, which implies that the capacity cannot be increased in proportion to the number of antennas. To overcome the rank deficiency, we propose a novel cooperative transmission strategy where the base station or mobile users in the cellular network both help the communication of the satellite network and transmit and receive their own streams. Not only does the secondary network carefully adjust the number of transmitted streams to avoid causing interference to the primary network beyond a certain threshold; it also provides alternative signal paths for the primary network, thereby effectively increasing the channel ranks of the primary network. We obtain both the achievable sum degrees of freedom (DoFs) and the sum rate under the proposed scheme, and we also derive upper bounds on the sum DoF. Using the analytical and numerical analysis, we show that our scheme significantly improves the overall system throughput compared with the satellite network alone, without cognitive access.

New Achievable Sum Degrees of Freedom in Half-Duplex Single-Antenna Multi-User Multi-Hop Networks

We investigate the achievable sum degrees of freedom (DoF) in a class of single-antenna multi-user multi-hop relay networks. The networks consist of multiple information sources and destinations, without direct signal propagation link between them, so that multiple layers of relays are deployed to assist in information delivery. We consider the situation that relays are unable to shield their receptions from the harmful self-interference and from the interference generated by other relays. Hence, ideal full-duplex relaying is not applicable. Utilizing half-duplex decode-and-forward relays, a cluster successive relaying (CSR) transmission scheme is adopted to conduct message transmission. The CSR scheme divides each layer of relays into two successively activated relay clusters to compensate the extra channel consumption demanded by the half-duplex operation. We propose two interference alignment strategies to deal with the interference issues. By properly clustering the relays in each layer, we find the asymptotically achievable sum DoF, subject to time-varying and frequency-selective fading, respectively. These results can lead to new lower bounds for the available DoF in the considered class of multi-user multi-hop networks.

Degrees of Freedom of Full-Duplex Cellular Networks With Reconfigurable Antennas at Base Station

Full-duplex (FD) cellular networks are considered in which an FD base station (BS) simultaneously supports a set of half-duplex (HD) downlink (DL) users and a set of HD uplink (UL) users. The transmitter and the receiver of the BS are equipped with reconfigurable antennas, each of which can choose its transmit or receive mode from several preset modes. Under the no self-interference assumption arisen from an FD operation at the BS, the sum degrees of freedom (DoF) of FD cellular networks is investigated for both no channel state information at the transmit side (CSIT) and the partial CSIT. In particular, the sum DoF is completely characterized for the no CSIT model and an achievable sum DoF is established for the partial CSIT model, which improves the sum DoF of the conventional HD cellular networks. For both no CSIT and partial CSIT models, the results show that the FD BS with reconfigurable antennas can double the sum DoF even in the presence of user-to-user interference as both the numbers of DL and UL users and preset modes increase. It is further demonstrated that such DoF improvement indeed yields the sum rate improvement at the finite and operational signal-to-noise ratio regime.

Achievable Sum DoF of the K-User MIMO Interference Channel with Delayed CSIT

This paper considers a $K$-user multiple-input-multiple-output (MIMO) interference channel (IC) where 1) the channel state information obtained by the transmitters (CSIT) is completely outdated, and 2) the number of transmit antennas at each transmitter, i.e., $M$, is greater than the number of receive antennas at each user, i.e., $N$. The usefulness of the delayed CSIT was firstly identified in a $K$-phase Retrospective Interference Alignment (RIA) scheme proposed by Maddah-Ali et al for the Multiple-Input-Single-Output Broadcast Channel, but the extension to the MIMO IC is a non-trivial step as each transmitter only has the message intended for the corresponding user. Recently, Abdoli et al focused on a Single-Input-Single-Output IC and solved such bottleneck by inventing a $K$-phase RIA with distributed overheard interference retransmission. In this paper, we propose two $K$-phase RIA schemes suitable for the MIMO IC by generalizing and integrating some key features of both Abdoli's and Maddah-Ali's works. The two schemes jointly yield the best known sum Degrees-of-Freedom (DoF) performance so far. For the case $\frac{M}{N}{\geq}K$, the achieved sum DoF is asymptotically given by $\frac{64}{15}N$ when $K{\to}\infty$.

전 이중 다중 안테나 셀룰라 네트워크의 간섭 정렬 타당성

The feasibility condition of interference alignment (IA) for full-duplex (FD) multiple-input multipleoutput (MIMO) cellular networks is considered. The necessary and sufficient condition on the IA feasibility is established, characterizing the achievable sum degrees of freedom (DoF). The results demonstrate that FD operation with appropriate IA is able to improve the sum DoF on the conventional half-duplex operation.

Retrospective Interference Alignment for the Two-Cell MIMO Interfering Multiple Access Channel

In this paper, we propose a new retrospective interference alignment for two-cell multiple-input multiple-output (MIMO) interfering multiple access channels (IMAC) with $M$ receive antennas per base station (BS) and $K$ users per cell each with $N$ transmit antennas. The key idea of the retrospective IA lies in interference-purification during phase 1 and 2, and interference-repetition during phase 3. On the basis of the proposed method, we show that the achievable sum degrees of freedom (sum-DoF) is equal to $2M\left(\left\lceil\frac{2M}{N}\right\rceil+1\right)/\left(2\left\lceil\frac{2M}{N} \right\rceil+1\right)$ if $K\le M and $\min\{2KN,M\}$ if $NK \le M$ with completely delayed channel state information at the transmitters (CSIT) . It is shown that having delayed CSIT can strictly increase the sum-DoF compared to the case with no CSIT for cellular networks, especially for uplink scenarios.

Multi-User Multi-Hop Relay Networks: Transmission Schemes and Degrees of Freedom

We study the achievable sum degrees of freedom (DoF) in wireless single-antenna multi-user multi-hop relay networks. In most existing works targeting this problem, it is assumed that relays operate in perfect full-duplex fashion and can also shield their receptions from the transmissions of other relays in the same and rear layers. In practice, such ideal assumptions are normally hard to realize. And a naive adoption of half-duplex operation in relays may result in significantly inefficient use of available radio resources. We propose spectrally-efficient transmission schemes to address this issue. A lower-bound to the networks' available DoF (i.e., optimally achievable sum DoF) hence can be attained. Our results indicate that besides providing information delivery paths, relays can also bring DoF gain over single-hop networks, even when relay interference issues are taken into consideration. This lower-bound would approach the upper-bound of the available DoF, if each relay layer deploys more nodes. When the number of relays in every layer is infinitely large, the exact available DoF is identified, which shows that handling interference issues through distributed signal processing and half-duplex operation across multiple layers of terminals may not negatively affect DoF performance, compared with ideal full-duplex and multi-antenna networks.

On the Achievable Degrees of Freedom of Two-Cell Multiuser MIMO Interference Networks

In this paper, we study the sum degrees of freedom (DoF) of an uplink two-cell multiuser MIMO interference network with asymmetric number of users in the cells. The achievable DoF is devised based on a two-dimensional space-time spreading code framework with linear precoding/decoding design and finite channel extension. The derivation of the achievable DoF is shown related to a rank minimization problem, which corresponds to the minimization of the dimension of the interference subspace. The problem is solved by the proposed grouping algorithm (GA) based on aligning interfering signals into a low-dimensional subspace as a group and attaining the minimum number of groups. The achievable sum DoF derived based on the proposed GA is shown to be greater than prior arts and achieves the theoretic upper bound in several cases. We also give a closed-form expression of the maximum achievable sum DoF when there is the maximum number of admissible users in the considered finite diversity environment.

Degrees of Freedom of Two-Hop MISO Broadcast Networks With Mixed CSIT

We consider a downlink two-hop MISO broadcast network with a 2-antenna source communicating to 2 single-antenna destinations, via 2 single-antenna relays. We investigate spectrally efficient transmission and the associated achievable sum degrees of freedom (DoF) with mixed channel state information at the transmitter (CSIT), which consists of perfect delayed CSIT and imperfect instantaneous CSIT. When the variance of the estimation error of the instantaneous CSIT lies on level of O(P−α) for the transmission power P and some α ∈ [0, 1], we show that the sum DoF 4−2α over 3−2α ∈ [4 over 3, 2] can be achieved by a novel interference alignment (IA) scheme. The result shows that rather than exploiting only delayed or imperfect instantaneous CSIT, the transmission design taking advantages of both can achieve higher sum DoF.

Cooperative Relaying for the Rank-Deficient MIMO Relay Interference Channel

Rank-deficient multiple-input multiple-output (MIMO) relay interference channel (IC) is investigated in which K source-destination pairs communicate with the help of N relays. For the K-user rank-deficient MIMO IC with no relays, an achievable sum degrees of freedom (DoF) is upper bounded by Krds, where rds denotes the rank of each point-to-point channel matrix. However, if relays assist the communication, we show that there can be significant improvement on the DoF compared to the case where there is no relay. The proposed cooperative relaying uses relays not only for increasing ranks of desired channel matrices but also nullifying inter-user interference.