Distributed MIMO multiway relaying: Joint signal alignment and interference neutralization

It was shown recently that the 2-user interference channel with a cognitive relay (IC-CR) has full degrees of freedom (DoF) almost surely, that is, 2 DoF. The purpose of this work is to check whether the DoF of the K-user IC-CR, consisting of K user pairs and a cognitive relay, follow as a straight forward extension of the 2-user case. As it turns out, this is not the case. The k-user IC-CR is shown to have 2K/3 DoF if K > 2 for the when the channel is time varying, achievable using interference alignment. Thus, while the basic k-user IC with time varying channel coefficients has 1/2 DoF per user for all K, the k-user IC-CR with varying channels has 1 DoF per user if K = 2 and 2/3 DoF per user if K > 2. Furthermore, the DoF region of the 3-user IC-CR with constant channels is characterized using interference neutralization, and a new upper bound on the sum-capacity of the 2-user IC-CR is given.

This paper studies the achievable degrees of freedom (DoF) for multi-user multiple-input multiple-output (MIMO) two-way relay channels, where there are K source nodes, each equipped with M antennas, one relay node, equipped with N antennas, and each source node exchanges independent messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary information exchange pattern, the considered channel model is a unified one. It includes several existing channel models as special cases: 1) K-user MIMO Y channel; 2) multi-pair MIMO two-way relay channel; 3) generalized MIMO two-way X relay channel; and 4) L-cluster MIMO multiway relay channel. Previous studies mainly considered the achievability of the DoF cut-set bound 2N at the antenna configuration N <; 2M by applying signal alignment for network coding. This paper aims to investigate the achievability of the DoF cut-set bound K M for the case N 2M. To this end, we first derive tighter DoF upper bounds for three special cases of the considered channel model. Then, we propose a new transmission framework, generalized signal alignment (GSA), to approach these bounds. The notion of GSA is to form network-coded symbols by aligning every pair of signals to be exchanged in a compressed subspace at the relay. A necessary and sufficient condition to construct the relay compression matrix is given. We show that using GSA, the new DoF upper bound is achievable when: 1) N/m ∈ (0, 2+ 4/{K(K-1)}]∪[K-2, +∞) for the K-user MIMO Y channel; 2) N/M ∈ (0,2 +4/K]∪[K - 2, +∞) for the multi-pair MIMO two-way relay channel; and 3) N/M ∈ (0, 2+ 8/K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ]∪[K-2, +∞) for the generalized MIMO two-way X relay channel. We also provide the antenna configuration regions for the general multi-user MIMO two-way relay channel to achieve the total DoF KM.

We apply signal alignment (SA), a wireless communication technique that enables physical layer network coding (PNC) in multi-input multi-output (MIMO) wireless networks. Through calculated precoding, SA contracts the perceived signal space at a node to match its receive capability, and hence facilitates the demodulation of linearly combined data packets. PNC coupled with SA (PNC-SA) has the potential of fully exploiting the precoding space at the senders, and can better utilize the spatial diversity of a MIMO network for higher system degrees-of-freedom (DoF). PNC-SA adopts the idea of `demodulating a linear combination' from PNC. The design of PNC-SA is also inspired by recent advances in IA, though SA aligns signals not interferences. We study the optimal precoding and power allocation problem of PNC-SA, for SNR (singal-to-noise-ratio) maximization at the receiver. The mapping from SNR to BER is then analyzed, revealing that the DoF gain of PNC-SA does not come with a sacrifice in BER. We then design a general PNC-SA algorithm in larger systems, and demonstrate general applications of PNC-SA, and show via network level simulations that it can substantially increase the throughput of unicast and multicast sessions, by opening previously unexplored solution spaces in multi-hop MIMO routing.

This paper studies a new symmetric two-user Gaussian interferencechannel (IC) in heterogeneous networks where twotransmitter-receiver pairs are underlaid with one primarytransmitter-receiver pair. When underlay transmitters must restricttheir transmission to guarantee target degrees of freedom (DoF) of aprimary receiver, the achievable DoF of the underlay receivers inheterogeneous networks is investigated. Either transmit power ortransmission time is regulated to secure the target DoF of a primaryreceiver and their effects on the achievable DoF are analyzed for thesimple Han-Kobayashi scheme. Our analytical results show that theachievable DoF of the underlay two-user IC is substantiallydifferent from that of a conventional two-user IC due to the imposedrestriction on the underlay users. It is also shown that jointdecoding capability at the primary receiver using common codebookrelaxes the restriction imposed on the underlay users and henceimproves the achievable DoF of the underlay receivers.

The achievable degrees of freedom (DOF) in an interference relay channel are examined. We highlight some differences between two relaying strategies in two different setups. Namely, we study the DOF achieved using interference alignment and interference cancellation in a cognitive relay setup and in a half-duplex relay setup. The difference between the two setups is causality, which leads to a difference in the achievable DOF. We show that 3/2 DOF are achievable almost surely in a 3-user complex Gaussian interference relay channel with quasistatic channel coefficients and with one antenna at each node. This result holds for both the cognitive as well as for the more practical half-duplex non-cognitive relay. However, while this is achieved in the cognitive relay setup using one symbol duration, it needs two symbol extensions in the half-duplex case. On the other hand, we show that in the cognitive case, interference cancellation performs better than interference alignment, since it achieves 2 DOF almost surely. Moreover, interference cancellation achieves full, i.e. K DOF for a family of K-user interference channels with a cognitive relay. Interestingly, for the half-duplex setup the outcome is swapped. Here, interference alignment outperforms interference cancellation, since the latter achieves less than 3/2 DOF almost surely in the 3 user case.

The achievable degree of freedom (DoF) boosting has been demonstrated on a single-input single-output (SISO) X channel by using outdated and instantaneous channel state information at transmitter (CSIT) synergistically, in contrast to that of using completely outdated CSIT. However, the means by which the DoF gain can be obtained in a multiple-input multiple-output (MIMO) system remains unclear. This paper proposes an interference alignment scheme with synergistic CSIT for MIMO X channel. We show that the achievable DoF is greater than the optimal DoF obtained with outdated CSIT, and that achievable DoF equals to the optimal value with outdated CSIT and transmitter cooperation.

We investigate the three-user MIMO Gaussian broadcast channel with i.i.d. fading and the same number of antennas at each receiver, and with the delayed channel state information at the transmitter (CSIT). We obtain achievability results on the degrees of freedom (DoF) of this channel and also show that our achievable DoF is tight for some ranges of transmit-receive antenna ratio. It is observed that when the number of antennas at the transmitter is strictly greater than that at each receiver, the DoF with delayed CSIT lies strictly between the DoF with perfect CSIT and DoF with no CSIT.

In this paper, we investigate asymmetric signal space alignment (ASSA) for the multi-pair two-way relaying (TWR) network, which consists of three pairs of single-antenna users and a two-antenna common access relay. In this particular scenario, the traditional signal space alignment (SSA) scheme has to rely on symbol extension for the reason of insufficient spatial dimensions. Moreover, the naive zero-forcing (ZF) based scheme only achieves 1 degrees of freedom (DOF). By utilizing ASSA, the DOF of 1.5 can be obtained without symbol extension. In addition, in order to further improve the sum rate, a joint beamforming optimization (JBO) algorithm is presented, which jointly optimizes the beam vectors of the users and relay. In consideration of the case with more than three pairs of users, we also propose a semi-orthogonal aligned user-pair scheduling (SAUS) method, which not only facilitates the ASSA scheme, but also harvests the multiuser diversity (MuD) to enhance the performance.

This paper investigates how multiuser dimensions can effectively be exploited for target degrees of freedom (DoF) in interfering broadcast channels (IBC) consisting of K-transmitters and their user groups. First, each transmitter is assumed to have a single antenna and serve a singe user in its user group where each user has receive antennas less than K. In this case, a K-transmitter single-input multiple-output (SIMO) interference channel (IC) is constituted after user selection. Without help of multiuser diversity, K-1 interfering signals cannot be perfectly removed at each user since the number of receive antennas is smaller than or equal to the number of interferers. Only with proper user selection, non-zero DoF per transmitter is achievable as the number of users increases. Through geometric interpretation of interfering channels, we show that the multiuser dimensions have to be used first for reducing the DoF loss caused by the interfering signals, and then have to be used for increasing the DoF gain from its own signal. The sufficient number of users for the target DoF is derived. We also discuss how the optimal strategy of exploiting multiuser diversity can be realized by practical user selection schemes. Finally, the single transmit antenna case is extended to the multiple-input multiple-output (MIMO) IBC where each transmitter with multiple antennas serves multiple users.

We consider vector space interference alignment strategies over the $K$-user interference channel and derive an upper bound on the achievable degrees of freedom as a function of the channel diversity $L$, where the channel diversity is modeled by $L$ real-valued parallel channels with coefficients drawn from a non-degenerate joint distribution. The seminal work of Cadambe and Jafar shows that when $L$ is unbounded, vector space interference alignment can achieve $1/2$ degrees of freedom per user independent of the number of users $K$. However wireless channels have limited diversity in practice, dictated by their coherence time and bandwidth, and an important question is the number of degrees of freedom achievable at finite $L$. When $K=3$ and if $L$ is finite, Bresler et al show that the number of degrees of freedom achievable with vector space interference alignment is bounded away from $1/2$, and the gap decreases inversely proportional to $L$. In this paper, we show that when $K\geq4$, the gap is significantly larger. In particular, the gap to the optimal $1/2$ degrees of freedom per user can decrease at most like $1/\sqrt{L}$, and when $L$ is smaller than the order of $2^{(K-2)(K-3)}$, it decays at most like $1/\sqrt[4]{L}$.

In wireless interference networks, orthogonal medium access techniques like time division multiple access (TDMA) and frequency division multiple access (FDMA) achieve merely one degree of freedom (DoF). However, by using interference alignment (IA) the achievable DoF can be linearly scaled up with the number of users. Nevertheless, this outperformance of IA heavily depends on the availability of perfect channel state information (CSI), which is not a realistic assumption in practice. Since under imperfect CSI, the performance of IA may become severely degraded, design of enhanced IA algorithms by relying on the availability of merely imperfect CSI is of particular interest. In this paper, we propose a least squares (LS)-based IA algorithm which adaptively designs the beamformers based on the knowledge of the channel estimation error variance, which is possible to be known in advance. Then, we compare the performance of the proposed scheme with interference leakage minimization algorithms. It is shown that under both perfect and imperfect CSI, the proposed LS-based IA outperforms interference leakage minimization algorithms.

The degrees of freedom (DoF) of the $K$-user multiple-input multiple-output (MIMO) interference channel are studied when perfect, but delayed channel state information is available at the transmitter side (delayed CSIT). Recent works have proposed schemes that achieve increasing DoF values, but at the cost of long communication delays. This work proposes three linear precoding strategies, formulated in such a way that the achievable DoF can be derived as a function of the transmission delay, thus elucidating its achievable DoF-delay trade-off. All strategies are based on the concept of interference alignment, and built upon three main ingredients: delayed CSIT precoding, user scheduling, and redundancy transmission. In this respect, the interference alignment is realized by exploiting delayed CSIT in order to align the interference at the non-intended receivers along the space-time domain. Finally, the latter part of this work settles that all the proposed strategies work also for constant channels, except for SISO. In such a case, the schemes can be made feasible by resorting to asymmetric complex signaling concepts. This conclusion removes the time-varying channels assumption unnecessarily common along all the literature on delayed CSIT.

Joint signal alignment precoding and physical network coding for heterogeneous networks

This paper investigates the degrees of freedom (DoF) of the L-cluster LT-user MIMO multi-way relay channel. A DoF upperbound is derived by providing users with carefully designed genie information, and properly enhancing the received signal of one of the users. For the L-cluster LT-user MIMO multi-way relay channel in the symmetric setting, conditions under which the DoF upperbound can be achieved using either multiple access transmission or signal space alignment are established, demonstrating that the newly derived upperbound is the first tight DoF upperbound for the general MIMO multi-way relay channel. Additionally, this new upperbound proves the optimality of the achievable DoF for several special cases of the MIMO multi-way relay channel obtained in previous works. The results provide the insight that, with fixed spatial dimension at the relay, increasing the number of users and clusters cannot provide any DoF gain. In addition, it is observed that allowing three or more users to share the spatial dimension of the relay cannot provide any DoF gain.

In this paper, we study the degrees of freedom (DoF) of cellular networks in which a base station with full-duplex operation simultaneously communicates to multiple half-duplex mobile stations. The half-duplex mobile stations are assumed to either communicate with the base station in the uplink or downlink. For such networks, inter-terminal interference needs to be taken into account to achieve the potential gain that doubles the throughput of conventional half-duplex cellular networks. We provide an achievable total DoF for such networks and show that having full-duplex operation at the base station only can indeed double the DoF when the number of mobile stations is sufficiently greater than the number of antennas at the base station. The key idea is to utilize the full DoF for the uplink transmission, while minimizing the inter-terminal interference via interference alignment. The downlink communication rate is then carefully chosen to occupy the remaining DoF at the receiving mobile stations.