Propagation Delay Based Cyclic Interference Alignment for X Channels With Two Transmitters

Propagation delay based cyclic interference alignment design is proposed for general X channels with two transmitters and K receivers. From the basic case with K=3 to the general case with arbitrary K, the transmit polynomial and the PD feature of the channels are given. The corresponding receive polynomials are deduced, which show that perfect cyclic IA has been performed in K+1 time-slots to obtain the optimal degrees of freedom 2K/(K+1). Furthermore, the feasibility analysis of node placement in the Euclidean space is provided, which demonstrates the wide application scope from underwater acoustic to terrestrial radio communications.

I. Introduction

The X channel (XC) has attracted increasing attentions in recent years due to its message transmission capability between full connected links. It was shown that with transmitters and receivers, the single antenna XC has the degrees of freedom (DoF) of by [1]. Interference alignment (IA) is the key technology to achieve this DoF, which can be implemented in many forms such as IA through antenna domain [2], [3] for the XC.