Asymmetric signal space alignment for multi-pair two-way relaying network

MIMO relay channel signal transmission in transformed signal subspace

In this letter, we consider a new interference alignment (IA) strategy for single-input single-output interference broadcast channels with constant channel coefficients. First, we show that 1.5 degrees of freedom (DOF) is achievable for 3-cell case by utilizing asymmetric complex signaling (AC) and multiuser diversity without symbol extension. It is also investigated that the achievable DOF varies with the user scaling condition and ω(√(SNR)) is required for guaranteeing the DOF of 1.5. To improve the sum-rate performance, user scheduling algorithms combined with the beamforming techniques are suggested which outperform the conventional IA schemes. After introducing an exhaustive scheduling algorithm which shows optimal sum-rate, a simplified scheduling method is also proposed which reduces both scheduling metric computations and the search size.

We study the degrees of freedom (DoF) of a distributed multi-input multi-output (MIMO) multiway relay channel (mRC) where two pairs of users, each equipped with M antennas, exchange messages in a pairwise manner with the help of two separated relay nodes, each with N antennas. We establish a general framework to derive achievable DoF based on linear signal processing. We show that, to achieve a certain DoF, a joint design of the user transmit beamforming, relay precoding, and user receive beamforming is required. We propose novel signal alignment techniques to reduce the number of linearly independent equations required for interference neutralization. Then, the original joint transceiver and relay design problem boils down to a problem solely on the design of the relay precoders. Based on recent developments on solving linear matrix systems, we determine the solution to the relay design problem and derive the corresponding achievable DoF. Our analysis reveals that the DoF of the considered network is achieved for equation, which is broader than the existing results by covering an extra range of M over N ∈ (1, 2).

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 investigates the physical layer security issue in an amplify-and-forward (AF) multi-input multi-output (MIMO) two-way relay assisted cognitive radio (CR) nonorthogonal multiple access (NOMA) network, where the simultaneous wireless information and power transfer (SWIPT) technology is employed to improve network energy efficiency. We consider the scenario that a pair of primary users and two pairs of secondary users (SUs) exchange information via a MIMO two-way relay, where the edge SU of each SU pair is untrusted and tries to wiretap the central SU’s information. For ensuring security, we aim to maximize the sum achievable secrecy rate (SASR) by jointly optimizing the power allocation at all users, power splitting factor and relay beamforming subject to the quality of service (QoS), energy harvesting and transmit power constraints. The formulated optimization problem is highly nonconvex due to coupling variables, thus it is challenging to solve. An effective path-following (PF)-based algorithm is proposed, which is proven to converge to a stationary point. Theoretical and simulation results show that the proposed PF-based algorithm has lower complexity than the state-of-art algorithm. To further reduce complexity, we proposed a zero-forcing (ZF)-based scheme. Numerical simulations show that the proposed PF-based algorithm achieves the same SASR as the state-of-art algorithm with moderate complexity, while the proposed ZF-based scheme strikes a good balance between performance and complexity.

In this paper, we propose a simple yet effective beamforming technique for multiple-input-multiple-output (MIMO) multipair two-way relay channels. Two key ingredients in our technique are adoption of signal space alignment (SSA) for transmit and receive beamforming and amplify-and-forward (AF) relay beamforming using advanced zero-forcing (ZF) technique. From the sum-rate analysis on MIMO multipair two-way relay channels, we show that the proposed method achieves multiplexing gain proportional to the number of user pairs.

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 cognitive radio networks, primary users can share some licensed spectrums with secondary users in exchange for cooperation. In this study, an overlay scenario is investigated where a secondary node provides two-way relaying service to a pair of primary users and thus is allowed to transmit its own messages by using some licensed spectrums. Orthogonal channelisation is assumed for the two-way relay channel to form a number of parallel subchannels. Hence, the licensed spectrums can be partitioned between primary and secondary signals transmitted by the relay in the broadcast phase. Moreover, subchannels in the two phases of two-way relaying can be permutated to further improve performance. The authors seek to maximise achievable data rate of secondary transmission subject to data rate requirements of the two primary users under individual power constraints. The joint spectrum partition, subchannel permutation, and power allocation problem is formulated into a mixed combinatorial programming problem, which is then transformed into a solvable form and finally yield an asymptotically optimal solution through dual decomposition method. They further prove that the solution to the relaxed problem is exactly the same as that to the original problem. Numerical results demonstrate performance gain of the proposed algorithm.

Interference alignment (IA) with symbol extensions in the quasi-static flat-fading K-user multipleinput multiple-output (MIMO) interference channel (IC) is considered in this paper. In general, long symbol extensions are required to achieve the optimal fractional degrees of freedom (DOF). However, long symbol extensions over orthogonal dimensions produce structured (diagonal or block diagonal) channel matrices from transmitters to receivers. Most of existing approaches are limited in cases where the channels have some special structures, because they align the interference without preserving the dimensionality of the desired signal explicitly. To overcome this common drawback of most existing IA algorithms, two novel iterative algorithms for IA with symbol extensions are proposed. The first algorithm designs transceivers for IA based on the mean square error (MSE) criterion which minimizes the total MSE of the system while preserving the dimensionality of the desired signal. The novel IA algorithm is a constrained optimization problem which can be solved by Lagrangian method. Its convergence is proven as well. Utilizing the reciprocity of alignment, the second algorithm is proposed based on the maximization of the multidimensional case of the generalized Rayleigh Quotient. It maximizes each receiver’s signal to interference plus noise ratio (SINR) while preserving the dimensionality of the desired signal. In simulation results, we show the superiority of the proposed algorithms in terms of four aspects, i.e., average sum rate, the fraction of the interfering signal power in the desired signal subspace, bit error rate (BER) and the relative power of the weakest desired data stream.

We study a downlink distributed MIMO system where a central unit (CU) broadcasts messages to $K^{\prime }$ users through $K$ distributed BSs. The CU is connected to the BSs via $K$ independent rate-constrained fronthaul (FH) links. The distributed BSs collectively serve the users through the air. We propose a new network coding based distributed MIMO broadcasting scheme, using reverse compute-and-forward and signal-space alignment. At the CU, a network coding generator matrix is employed for pre network coding of the users’ messages. The network coded messages are forwarded to the BSs, where the FH rate-constraint determines the actual number of network-coded messages forwarded to the BSs. At the BSs, linear precoding matrices are designed to create a number of bins , each containing a bunch of spatial streams with aligned signal-spaces. At each user, post physical-layer network coding is employed to compute linear combinations over the NC messages with respect to the bins, which reverses the prenetwork coding and recovers the desired messages. We derive an achievable rate of the proposed scheme based on the existence of NC generator matrix, signal-space alignment precoding matrices, and nested lattice codes. Improved rate and degrees of freedom over existing interference alignment and compress-and-forward schemes are shown. Numerical results demonstrate the performance improvement, e.g., by as much as 70% increase in throughput over benchmark schemes.

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.

In order to gain new insights into multiple-input–multiple-output (MIMO) interference networks, the optimality of $\sum _{k=1}^{K} M_{k}/2$ (half the cake per user) degrees of freedom is explored for a $K$ -user MIMO interference channel where the cross-channels have arbitrary rank constraints, and the $k$ th transmitter and receiver are equipped with $M_{k}$ antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have $M$ antennas; and by Tang et al., of full rank interference channels where the $k$ th user pair has $M_{k}$ antennas. The broader outcome of this paper is a novel class of replication-based outer bounds for arbitrary rank-constrained MIMO interference networks where replicas of existing users are added as auxiliary users and the network connectivity is chosen to ensure that any achievable scheme for the original network also works in the new network. The replicated network creates a new perspective of the problem, so that even simple arguments such as user cooperation become quite powerful when applied in the replicated network, giving rise to stronger outer bounds, than when applied directly in the original network. Remarkably, the replication-based bounds are broadly applicable not only to MIMO interference channels with arbitrary rank-constraints, but much more broadly, even beyond Gaussian settings.

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.

The multiple-input-multiple-output (MIMO) interference channel (IC) is considered with constant channel coefficients, N transmit and receive antennas at each user, and coordinated multipoint (CoMP) transmission, in which each message is jointly transmitted by Mt successive transmitters. It is shown that the degrees of freedom with CoMP transmission using a two-stage scheme involving both zero forcing and interference alignment can be significantly greater than without CoMP transmission. In particular, all K users can achieve d degrees of freedom almost surely if d ≤ ⌊(2N)/(K - M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> + 1)⌋ and M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> ≤ K - 2. Additionally, the first M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> - 1 users can achieve d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> degrees of freedom, and the last K - M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> + 1 users can achieve d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> degrees of freedom almost surely if d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ≤ ⌊(2N)/(K -M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> +1)⌋, M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> ≤ K - 2, and d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> + (K - M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> + 1) d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ≤ 2N. Next, the analysis of the constant MIMO IC with CoMP transmission is applied to the development of iterative algorithms to design transmit and receive vectors analogous to those without CoMP transmission. The degrees of freedom analysis is shown through simulations to provide a good guideline for choosing how many beams each user should send for the iterative algorithms. Furthermore, it is seen in the numerical results that CoMP transmission can result in greatly improved convergence speed for the iterative interference alignment algorithms.

In this paper, we consider transceiver design for multiuser cellular two-way relay network (cTWRC), where a multi-antenna base station (BS) exchanges information with multiple single-antenna mobile stations (MSs) with the help of a multi-antenna relay station (RS). We propose a low complexity two-way relaying scheme for cTWRC via signal space alignment. In our scheme, the precoders at the BS and MSs are jointly designed that the two data streams delivered to and from the same MS fall in the same spatial direction at the RS. With such signal space alignment, interference-free physical-layer network coding can be performed at the relay. We analyze the end-to-end sum bit error rate (BER) performance of the proposed scheme and investigate the optimal power allocation at the BS and RS to improve the BER performance. Numerical results demonstrate that our scheme is superior to the existing amplify-and-forward based signal alignment schemes.