Degrees-of-freedom for the 4-user SISO interference channel with improper signaling

Abstract

It has been recently shown that for the 3-user singleinput single-output (SISO) interference channel with constant channel coefficients, a maximum of 1.2 degrees-of-freedom (DoF) are achievable using linear interference alignment schemes when improper (a.k.a. asymmetric) Gaussian signaling is applied. In this paper, we study the 4-user SISO interference channel and provide inner and outer bounds for the total number of DoF achievable for this channel. We prove that at least 4 3 DoF are achievable for the 4-user channel using also linear interference alignment techniques and improper signaling. A simple converse proof shows that no more than 8 5 DoF are achievable for this scheme. Simulation results seem to indicate that the inner bound is in fact tight for this channel, and serve to illustrate the sumrate improvement with respect to time division multiple access (TDMA) techniques.

Improper Gaussian Signaling Scheme for the Z-Interference Channel

“…4 that improper Gaussian signaling outperforms the proper Gaussian counterpart in the strong interference regime, especially when the interference link gain |h 12 | is large. Although proper Gaussian signaling is also able to avoid performance degradation from excessive interference by letting S 2 to remain silent when the interference link gain |h 12 | is large, the extra dimension provided by improper Gaussian signaling is generally superior for the system sum-rate. This is achieved by adjusting the interference and the desired signal to be orthogonal to each other, hence eliminating the influence of the interference while still allowing S 2 to transmit.…”

“…This higher achievable DoF using improper signaling is due to its ability to control the interference signal dimension, and it is one form of interference alignment [11]. The DoF results have also been extended to IC with larger number of users, such as 4-user IC, which is shown to have 4/3 DoF per user [12]. Beyond the DoF analysis for IC, [13] showed that improper signaling with widely linear receiver in point-to-point Multiple Input Multiple Output (MIMO) channels can reduce the bit error rate as compared to proper signaling.…”

On the Superiority of Improper Gaussian Signaling in Wireless Interference MIMO Scenarios

“…The same applies in the Gaussian MIMO interference channel (IC), where IGS has been shown to: i) obtain larger degrees of freedom, i.e. slope of the sumrate as a function of the signal-to-noise ratio (SNR) at the high SNR regime, [3][5] [13] and ii) improve the known achievable rates when interference is treated as noise under certain MIMO configurations [4][14] [15] and under coexistence of linear and widely linear transceivers in MIMO systems [16] [17]. In addition, the positive benefits of IGS have been reported in terms of achievable rates [18] and outage probabilities [19] for underlay cognitive radio systems.…”

Information-Theoretic Analysis of a Family of Improper Discrete Constellations

“…They considered a single-antenna three-user interference channel with constant channel extensions and showed that the number of degrees of freedom (DoF), which is the number of interference-free signals that can be transmitted, was larger when users transmit improper signals as opposed to proper ones. Similar DoF results were derived for the four-user interference channel in [14]. After that, a number of new works has emerged, and the payoffs of improper signaling have been revealed for different multiuser scenarios such as the interference channel [3][4][5]15], Z-interference channel [6,[16][17][18], broadcast channels with linear precoding [19,20], underlay and overlay cognitive radio networks [7,8,21] and relay channels [22,23].…”