Improper Gaussian Signaling on the Two-User SISO Interference Channel

Abstract

On a single-input-single-out (SISO) interference channel (IC), conventional non-cooperative strategies encourage players selfishly maximizing their transmit data rates, neglecting the deficit of performance caused by and to other players. In the case of proper complex Gaussian noise, the maximum entropy theorem shows that the best-response strategy is to transmit with proper signals (symmetric complex Gaussian symbols). However, such equilibrium leads to degrees-of-freedom zero due to the saturation of interference.With improper signals (asymmetric complex Gaussian symbols), an extra freedom of optimization is available. In this paper, we study the impact of improper signaling on the 2user SISO IC. We explore the achievable rate region with noncooperative strategies by computing a Nash equilibrium of a non-cooperative game with improper signaling. Then, assuming cooperation between players, we study the achievable rate region of improper signals. We propose the usage of improper rank one signals for their simplicity and ease of implementation. Despite their simplicity, rank one signals achieve close to optimal sum rate compared to full rank improper signals. We characterize the Pareto boundary, the outer-boundary of the achievable rate region, of improper rank one signals with a single real-valued parameter; we compute the closed-form solution of the Pareto boundary with the non-zero-forcing strategies, the maximum sum rate point and the max-min fairness solution with zero-forcing strategies. Analysis on the extreme SNR regimes shows that proper signals maximize the wide-band slope of spectral efficiency whereas improper signals optimize the high-SNR power offset. Index Terms-asymmetric complex signaling, improper signaling, SISO, interference channel

Information-Theoretic Analysis of a Family of Improper Discrete Constellations

“…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]. More recently, in [24], the authors showed the advantages of improper signaling in a multiuser scenario where a point-to-point link coexists with a multiple access channel.…”

“…In more complex interference-limited scenarios, such as the interference channel, transmitting proper Gaussian signals is in general suboptimal, so assuming this input distribution in such cases is not theoretically justified. As a matter of fact, recent works have shown that, when treating interference as noise, a higher transmitted rate may be achieved in interference-limited networks by transmitting improper Gaussian signals, which are correlated with their complex conjugate [2][3][4][5][6][7][8].…”

Decentralized widely linear precoding design for the MIMO interference channel

“…As transmit and receive filters in (11) cannot be solved analytically, we can follow a block coordinate descent approach to find a local optimum to problem (P 0 ) in (8) by alternate optimization of transmit and receive filters in (11). This procedure is fully centralized, nevertheless, a decentralized approach could be derived if every BS had knowledge of (8) is equivalent to define the following problem to be solved at each k-th BS:…”

“…where function k g -stands for the impact of the k-th BS over the MSE of the UEs associated to the neighboring BSs, which depends on k  and k Γ defined in (10) as: (13) (6), each k-th BS can solve problem (P 0,k ) in (13) with alternate optimization between transmit and receive filters in (11). Compared to the decentralized procedure presented in [5] for the proper Gaussian signaling case, when improper Gaussian signaling is used two interfering cost matrices are required ( k  and k Γ ).…”

Interference MAC: Impact of improper Gaussian signaling on the rate region Pareto boundary

“…For instance, improper signaling was proposed in [14] as a means to improve the degrees 2 of freedom (DoF) in the 3-user IC. In comparison, for the 2-user IC improper signaling does not enhance the DoF, yet improper signaling is useful in the low and moderate SNR (signal to noise power ratio) regime, as it improves the signalto-interference-plus-noise ratio (SINR) as shown in [15], [16]. In these papers, the authors show that the rate region of the 2-user IC is improved by Gaussian improper signaling compared to Gaussian proper signaling.…”