In the presence of multiple primary users (PUs), the exact outage probability of partial amplify-and-forward (AF) relay selection in the spectrum-sharing relay networks is investigated. To gain more insight, a simple and accurate outage probability approximation is also derived in the high signal-to-noise ratio (SNR) region. It is shown that, at high SNR, the outage probability is affected only by the channel gain ratio between relay-destination links to relay-PU links, regardless of the number of relays. Moreover, when more PUs are present, it causes outage performance degradation on the secondary system. Finally, simulation results are presented to verify the analysis.Introduction: Recently, spectrum sharing cognitive relay networks have been investigated as an effective technology to improve spectral efficiency of the secondary user (SU). There have been active studies on spectrum sharing cognitive relay networks [1][2][3][4][5]. In [1], the exact outage probability of cognitive dual-hop amplify-and-forward (AF) relay networks is derived. By taking the direct link into consideration, the work in [2] presents the exact outage probability of cognitive AF relay networks with selection combination deployed. In [3], a tight lower bound on the outage probability of cognitive relay networks with relay selection is obtained. With maximum transmit power limits, the exact outage probability of cognitive selection decode-and-forward (DF) relay networks is derived in [4]. However, all the works above focus on analysing the performance of cognitive relay networks with a single primary user (PU). When multiple PUs are present, the transmit powers of the SU would be subject to additional constraints resulting in an outage performance degradation. In the presence of multiple PUs, the outage probability and ergodic capacity of cognitive relay networks over Nakagami-m fading are investigated in [5]. However, the work in [5] just considers the cognitive relay network equipped with a single DF relay.In this Letter, extending the system model of [1] to multiple relays and multiple PUs, we analyse the outage performance of partial AF relay selection in cognitive relay networks. We derive an exact closed-form expression for the outage probability of cognitive relay networks. To gain more insight, an asymptotic expression is also presented, which is very tight with the exact outage probability in the high signal-tonoise ratio (SNR) regime.

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This paper describes interferometry measurement of the film profiles of sliding elastohydrodynamic lubrication (EHL) contacts with spin. In the custom-made EHL test rig, spin motion is introduced through adjusting the center offset of the ball-on-disc contact with respect to the disc rotation axis. A parameter, spin ratio S sp , is employed to represent the spin level, which is defined as the ratio of the Hertzian contact radius to the center offset. Experimental results show that with spin the film shape is obviously skewed, and the film thicknesses at the two side lobes are no longer the same; therefore, the symmetry of the classical horseshoe film shape is lost. The film thickness dependences on entrainment speeds are significantly influenced by the spin ratio S sp , and high spin ratios induce high speed indices. At a fixed spin ratio S sp , with increasing sliding speeds the film thickness difference between the two side lobes becomes large, and the horseshoe film shape is more distorted. When applied loads are raised, more spin is introduced, film thickness decreases, and film shape is obviously twisted.

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