{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:17:01Z","timestamp":1761581821283,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004826","name":"Beijing Municipal Natural Science Foundation","doi-asserted-by":"publisher","award":["4172024"],"award-info":[{"award-number":["4172024"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The simultaneous wireless information and power transfer (SWIPT) technique has been considered as a promising approach to prolong the lifetime of energy-constraint wireless sensor networks (WSNs). In this paper, a multiple-input multiple-output (MIMO) full-duplex (FD) bidirectional wireless sensor network (BWSN) with SWIPT is investigated. Based on minimum total mean-square-error (total-MSE) criterion, a joint optimization problem for source and relay beamforming and source receiving subject to transmitting power and harvesting energy constraints is established. Since this problem is non-convex, an iterative algorithm based on feasible point pursuit-successive convex approximation (FPP-SCA) is derived to obtain a local optimum. Moreover, considering the scenarios in which source and relay nodes equipped with the same and different numbers of antennas, a low-complexity diagonalizing design-based scheme is employed to simplify each non-convex subproblem into convex problems and to reduce the computational complexity. Numerical results of the total-MSE and bit error rate (BER) are implemented to demonstrate the performance of the two different schemes.<\/jats:p>","DOI":"10.3390\/s19081827","type":"journal-article","created":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T07:58:09Z","timestamp":1555487889000},"page":"1827","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Joint Source-Relay Optimization for MIMO Full-Duplex Bidirectional Wireless Sensor Networks with SWIPT"],"prefix":"10.3390","volume":"19","author":[{"given":"Dan","family":"Liu","sequence":"first","affiliation":[{"name":"Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0562-4539","authenticated-orcid":false,"given":"Zhigang","family":"Wen","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqing","family":"Liu","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shan","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junwei","family":"Zou","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3647","DOI":"10.1109\/TWC.2013.072313.121949","article-title":"Performance Analysis and Optimization for Energy-Efficient Cooperative Transmission in Random Wireless Sensor Network","volume":"12","author":"Li","year":"2013","journal-title":"IEEE Trans. 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