Abstract
In this paper, the impact of improper Gaussian signaling is studied for an underlay cognitive radio (CR) scenario comprised of a primary user (PU), which has a rate constraint, and a secondary user (SU), both single-antenna. We first derive expressions for the achievable rate of the SU when it transmits proper and maximally improper Gaussian signals (assuming that the SU is solely limited by the CR constraint). These expressions depend on the channel gains to and from the SU through a single variable. Thereby, we observe that improper signaling is beneficial whenever the SU rate is below a threshold, which depends on the signal-to-noise ratio (SNR) and rate requirement of the PU. Furthermore, we provide bounds on the achievable gain that also depend only on the PU parameters. Then, the achievable rate is studied from a statistical viewpoint by deriving its cumulative distribution function considering a constant received SNR at the PU. In addition, we specialize this expression for the Z interference channel, for which the expected achievable rate is also derived. Numerical examples illustrate our claims and show that the SU may significantly benefit from using improper signaling.
Highlights
Improper or asymmetric complex signals arise when the real and imaginary parts of the transmitted symbols are correlated and/or have unequal power [1]
The achievable rate region of the 2-user single-input single-output (SISO)-interference channel (IC) was shown to be enlarged by the use of improper signaling in [5] and [6], and these results were extended to the K-user multiple-input multiple-output (MIMO) IC in [7]
We have considered a simple scenario, where a single-antenna primary user (PU) shares the spectrum with a single-antenna secondary user (SU) in an underlay fashion
Summary
Improper or asymmetric complex signals arise when the real and imaginary parts of the transmitted symbols are correlated and/or have unequal power [1]. The first work showing the benefits of improper signaling for such scenarios was [3], where the authors studied the degreesof-freedom (DoF), i.e., the number of parallel data streams, of the 3-user single-input single-output (SISO) interference channel (IC) with constant channel extensions They proved that the use of improper signaling allows to achieve 1.2 DoF, as opposed to 1 DoF achieved by traditional proper signaling schemes. In our recent work [13], we proved that when the SU performance is only limited by the PU rate constraint, and whenever improper signaling is advantageous, transmitting maximally improper signals (i.e., the real and imaginary parts are fully correlated) is optimal Motivated by this result, in this paper we further analyze the maximally improper setting and study the impact of the PU parameters (signal-to-noise ratio -SNR- and rate constraint) on the potential gain achieved by improper signaling. The obtained results reveal interesting insights into improper signaling for this scenario, which we illustrate with several numerical examples
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