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We show that the optimal relay amplifying matrices have a beamforming structure. Exploiting the structure of relay matrices, an iterative joint source and relay matrices optimization algorithm is developed to minimize the mean-squared error (MSE) of the signal waveform estimation at the destination using the PG approach. The performance of the proposed algorithm is demonstrated through numerical simulations.<\/jats:p>","DOI":"10.1186\/1687-1499-2014-151","type":"journal-article","created":{"date-parts":[[2014,9,15]],"date-time":"2014-09-15T11:05:16Z","timestamp":1410779116000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Joint source and relay design for MIMO multi-relay systems using projected gradient approach"],"prefix":"10.1186","volume":"2014","author":[{"given":"Apriana","family":"Toding","sequence":"first","affiliation":[]},{"given":"Muhammad RA","family":"Khandaker","sequence":"additional","affiliation":[]},{"given":"Yue","family":"Rong","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,9,15]]},"reference":[{"key":"970_CR1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1109\/TIT.2004.839487","volume":"51","author":"B Wang","year":"2005","unstructured":"Wang B, Zhang J, H\u00f8st-Madsen A: On the capacity of MIMO relay channels. 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