The relentlessly increasing number of small-sized devices with limited powering and computational capabilities requires the adoption of new approaches to spectrum access. In this paper, we analyze an underlay cooperative cognitive wireless system based on available statistical channel state information (CSI) that is applicable to the cognitive system with limited computational resources due to its low complexity. We considered the scenario where the primary and the cognitive network coexist in the same spectrum band, under the constraints of interference threshold and maximal tolerable outage permitted by the primary user. The communication in the secondary decode-and-forward (DF) relaying system is established via a self-sustainable relay, which harvests energy from both cognitive and primary transmitters. The closed-form expressions for the outage probability of the cognitive network are derived, which are valid for both time-switching relaying (TSR) and power-splitting relaying (PSR) protocols. We analyze the influence of both cognitive and primary systems as well as the impact of channel parameters on the cognitive system outage performance. The derived analytical results are corroborated by an independent simulation method.