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On the premise of satisfying the speed and acceleration constraints of the UAV, the energy efficiency (EE) of the relaying system is maximized by jointly optimizing the UAV\u2019s trajectory and the individual transmit power levels of the source and the UAV relay. The initial joint optimization problem is non-convex and cannot be solved directly. Therefore, the joint optimization problem is decomposed into two sub-problems which are solved by applying the successive convex approximation technique and the Dinkelbach\u2019s algorithm. On this basis, an efficient iterative algorithm is proposed to tackle the joint optimization problem through the block coordinate descent technique. Simulation results demonstrated that by conducting the proposed algorithm, the flight trajectory of the UAV and the individual transmit power levels of the nodes can be flexibly adjusted according to the system conditions, and the proposed algorithm contributes to the higher EE compared with the benchmark schemes.<\/jats:p>","DOI":"10.1186\/s13638-023-02304-w","type":"journal-article","created":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T03:21:50Z","timestamp":1694575310000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Energy efficiency maximization for UAV-enabled amplify-and-forward relaying via joint power and trajectory optimization"],"prefix":"10.1186","volume":"2023","author":[{"given":"Lili","family":"Guo","sequence":"first","affiliation":[]},{"given":"Shibing","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1324-8051","authenticated-orcid":false,"given":"Xiaodong","family":"Ji","sequence":"additional","affiliation":[]},{"given":"Senyi","family":"Shi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,9,13]]},"reference":[{"issue":"3","key":"2304_CR1","doi-asserted-by":"publisher","first-page":"5508","DOI":"10.1109\/JIOT.2019.2903165","volume":"6","author":"M Liu","year":"2019","unstructured":"M. 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