Spectrally-efficient SIMO relay-aided underlay communications: An exact outage analysis

International audienceIn this paper, we carry out an exact outage analysis for a secondary (unlicensed) system operating under a strict primary (licensed) system outage constraint. We focus on single-user singleinput multiple-output (SIMO) secondary communications where the direct link is being assisted by a cluster of single-antenna decodeand-forward (DF) relay nodes acting in a half-duplex selective-andincremental relaying mode. Firstly, we derive a transmit power model for the secondary system where the source and relays adapt their transmit power based on: 1) a perfect acquisition of the underlying interference channel state information (I-CSI), and 2) an interference constraint that is either fixed or proportional to the primary system outage probability. Secondly, the cumulative distribution functions (CDF)s of the received signal-to-noise ratio (SNR) at the secondary receiving nodes are devised in a recursive and tractable closed-form expressions. These statistics are used to derive the exact end-to-end secondary system outage probability. The analytical and simulation results are then compared and interestingly shown to perfectly match, while revealing that with a moderate number of primary and secondary receive antennas, the secondary system spectral efficiency is amply enhanced as opposed to being severely degraded in the single receive antenna case

Exact Outage Probability Analysis for Relay-aided Underlay Cognitive Communications

International audienceIn a spectrum sharing underlay context, we investigatethe exact derivation of the outage probability for relay-aided cognitiveradio communications. To give more degrees of freedom to thesecondary system in acquiring a targeted quality-of-service (QoS)under the primary system interference constraint, the secondary linkis assisted by a set of relays acting in a two-hop decode-and-forwardselective relaying mode. By means of the cumulative distributionfunctions of the received signal-to-noise ratio (SNR) at the secondaryreceiver, we derive the end-to-end outage probability of the secondarysystem in its closed form. The analytical and simulation results arethen compared and interestingly shown to perfectly match over theentire interference threshold region

TAS Strategies for Incremental Cognitive MIMO Relaying: New Results and Accurate Comparison

In this paper, we thoroughly elaborate on the impact different transmit-antenna selection (TAS) strategies induce in terms of the outage performance of incremental cognitive multiple-input multiple-output (MIMO) relaying systems employing receive maximum-ratio combining (MRC). Our setup consists of three multi-antenna secondary nodes: a transmitter, a receiver and a decode-and-forward (DF) relay node acting in a half-duplex incremental relaying mode whereas the primary transmitter and receiver are equipped with a single antenna. Only a statistical channel-state information (CSI) is acquired by the secondary system transmitting nodes to adapt their transmit power. In this context, our contribution is fourfold. First, we focus on two TAS strategies that are driven by maxim

W1,NW^{1,N} versus C1C^1 local minimizer for a singular functional with Neumann boundary condition

Let $\Omega\subset\R^N,$ be a bounded domain with smooth boundary. Let $g:\R^+\to\R^+$ be a continuous on $(0,+\infty)$ non-increasing and satisfying $$c_1=\liminf_{t\to 0^+}g(t)t^{\delta}\leq\underset{t\to 0^+}{\limsup} g(t)t^{\delta}=c_2,$$ for some $c_1,c_2>0$ and $00$ is a constant. Consider the singular functional $I: W^{1,N}(\Omega)\to \R$ defined as \begin{eqnarray*} &&I(u) \eqdef\frac{1}{N}\|u\|^N_{W^{1,N}(\Omega)}-\int_{\Omega}G(u^+)\,{\rm d} x -\int_{\Omega}F(x,u^+) \,{\rm d} x\nonumber\\ && -\frac{1}{q+1}||u||^{q+1}_{L^{q+1}(\partial\Omega)} \nonumber \end{eqnarray*} where $F(x,u)= \int_0^sf(x,s)\,{\rm d}s$, $G(u)=\int_0^s g(s)\,{\rm d}s$. We show that if $u_0\in C^1(\overline{\Omega})$ satisfying u_0\geq \eta \mbox{dist}(x,\partial\Omega), for some $0<\eta$, is a local minimum of $I$ in the $C^1(\overline{\Omega})\cap C_0(\overline{\Omega})$ topology, then it is also a local minimum in $W^{1,N}(\Omega)$ topology. This result is useful %for proving multiple solutions to the associated Euler-lagrange equation ${\rm (P)}$ defined below. to prove the multiplicity of positive solutions to critical growth problems with co-normal boundary conditions

Existence and non-existence of solutions for a singular problem with variable potentials

The purpose of this article is to prove some existence and nonexistence theorems for the inhomogeneous singular Dirichlet problem $$- \Delta_p u = \frac{\lambda k(x)}{u^\delta}\pm h(x) u^q.$$ For proving our results we use the sub and super solution method, and monotonicity arguments