Transmit Optimization With Improper Gaussian Signaling for Interference Channels

Abstract

Abstract-This paper studies the achievable rates of Gaussian interference channels with additive white Gaussian noise (AWGN), when improper or circularly asymmetric complex Gaussian signaling is applied. For the Gaussian multiple-input multiple-output interference channel (MIMO-IC) with the interference treated as Gaussian noise, we show that the user's achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex Gaussian signaling in terms of the users' transmit covariance matrices, and an additional term, which is a function of both the users' transmit covariance and pseudo-covariance matrices. The additional degrees of freedom in the pseudocovariance matrix, which is conventionally set to be zero for the case of proper Gaussian signaling, provide an opportunity to further improve the achievable rates of Gaussian MIMO-ICs by employing improper Gaussian signaling. To this end, this paper proposes widely linear precoding, which efficiently maps proper information-bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo-covariance matrices. In particular, for the case of twouser Gaussian single-input single-output interference channel (SISO-IC), we propose a joint covariance and pseudo-covariance optimization algorithm with improper Gaussian signaling to achieve the Pareto-optimal rates. By utilizing the separable structure of the achievable rate expression, an alternative algorithm with separate covariance and pseudo-covariance optimization is also proposed, which guarantees the rate improvement over conventional proper Gaussian signaling.

Impact of improper Gaussian signaling on hardware impaired systems

“…The transformation in (3) represents a widely linear transformation of x 0 [10]. The widely linear transformation of PGS results in IGS which can be verified by finding˜ 2 xIQI that is found from˜…”

“…IGS is a generalized complex Gaussian scehme that is appropriately described by the variance as well as the pseudovariance in contrast to its counterpart traditional Gaussian scheme, known as proper Gaussian signaling (PGS) sceheme, which is only described by its variance [10]. Hence, IGS offers additional degrees of design freedom pertinent to its circularly asymmetric characteristics.…”

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

“…The semidefinite relaxation (SDR) is then solved efficiently by interior point methods (i.e., barrier methods [20]). Note that, the optimal solution of SDR may not satisfy the rank constraints of the original problem and we need to determine an approximate solution by the so-called Gaussian randomization process [16]. By numerical evaluation, we demonstrate that under both weak and strong interference, improper signaling improves the Pareto boundary compared to proper signaling.…”

“…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.…”

Information-Theoretic Analysis of a Family of Improper Discrete Constellations

“…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].…”