This letter proposes a scheme for the backward transmission of the propagation-delay based three-user X channel, which is reciprocal to the forward transmission. The given scheme successfully delivers 10 expected messages in 6 time-slots by cyclic interference alignment without loss of degrees of freedom, which supports efficient bidirectional transmission between the two ends of the three-user X channel.

To obtain a full picture of potential applications for propagation-delay based X channels, it is important to obtain all feasible schemes of cyclic interference alignment including the encoder, channel instance, and decoder. However, when the dimension goes larger, theoretical analysis about this issue will become tedious and even impossible. In this letter, we propose a computer-aided solution by searching the channel space and the scheduling space, which can find all feasible schemes in details. Examples are given for some typical X channels. Computational complexity is further analyzed.

Compared with the unicast scenario, X channels with multicast messaging can support richer transmission scenarios. The transmission efficiency of the wireless multicast X channel is an important and open problem. This article studies the degrees of freedom of a propagation-delay based multicast X channel with two transmitters and arbitrary receivers, where each transmitter sends K different messages and each receiver desires K - 1 of them from each transmitter. The cyclic polynomial approach is adopted for modeling and analysis. The DoF upper bound is analyzed and shown to be unreachable. Then a suboptimal scheme with one extra time-slot cycle is proposed, which uses the cyclic interference alignment method and achieves a DoF of K - 1. Finally, the feasibility conditions in the Euclidean space are derived and the potential applications are demonstrated for underwater acoustic and terrestrial radio communications.

Interference alignment (IA) in temporal domain is important in the case of single-antenna vehicle communications. In this paper, perfect cyclic IA based on propagation delay is extended to the K×2 X channels with two receivers and arbitrary transmitters K≥2, which achieves the maximal multiplexing gain by obtaining the theoretical degree of freedom of 2K/(K+1). We deduce the alignment and separability conditions, and propose a general scheme which is flexible in setting the index of time-slot for IA at the receiver side. Furthermore, the feasibility of the proposed scheme in the two-/three- Euclidean space is analyzed and demonstrated.

For the three-user X channel, its degree of freedom (DoF) 9/5 has been shown achievable theoretically through asymptotic model with infinite resources, which is impractical. In this article, we explore the propagation delay (PD) feature among different links to maximize the achievable DoF with the minimum cost. Since perfect interference alignment (IA) is impossible for 9 messages within 5 time-slots, at least one extra time-slot should be utilized. By the cyclic polynomial approach, we propose a scheme with the maximum achievable DoF of 5/3 for 10 messages within 6 time-slots. Feasibility conditions in the Euclidean space are also deduced, which demonstrates a quite wide range of node arrangements.

In this paper, we propose to use a strategy for the two-user Gaussian X channel with limited receiver cooperation in the general case consisting of two parts: 1) the transmission scheme where the superposition coding is used and 2) the cooperative protocol where the two-round strategy based on quantize-map-and-forward (QMF) is employed. We image that a Gaussian X channel can be considered as a superposition of two Gaussian interference channels based on grouping of the sent messages from each transmitter to the corresponding receivers. Finally, we give an achievable rate region for the general case of this channel.

In this paper, we propose a new interference alignment (IA) scheme that jointly designs the linear transmitter and receiver for the 2-user MIMO X channel system, using minimum total mean square error criterion, subject to each transmitter power constraint. We show that transmitters and receivers under such criteria could be realized through a joint iterative algorithm. Considering the imperfection of channel state information (CSI), we also extend the minimum mean square error interference alignment schemes for the MIMO X channel with CSI estimation error. A robust iterative algorithm which is insensitve to CSI estimation error is proposed. Simulation results are also provided to demonstrate the proposed algorithm.