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However, this method is often not practical due to two important shortcomings: it requires channel state information at the transmitter and the computation of the SVD of the channel matrix is generally too complex. To deal with these issues, we propose a method for establishing an SVD beamforming link without requiring feedback of actual channel or SVD coefficients to the transmitter. Concretely, our method takes advantage of channel reciprocity and a power iteration algorithm (PIA) for determining the precoding and decoding singular vectors from received preamble sequences. A low-complexity version that performs no iterations is proposed and shown to have a signal-to-noise-ratio (SNR) loss within 1\u00a0dB of the bit error rate of SVD beamforming with least squares channel estimates. The low-complexity method significantly outperforms maximum ratio combining diversity and Alamouti coding. We also show that the computational cost of the proposed PIA-based method is less than the one of using the Golub\u2013Reinsch algorithm for obtaining the SVD. The number of computations of the low-complexity version is an order of magnitude smaller than with Golub\u2013Reinsch. This difference grows further with antenna array size.<\/jats:p>","DOI":"10.1186\/s13638-021-02026-x","type":"journal-article","created":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T08:03:27Z","timestamp":1625904207000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A low-complexity channel training method for efficient SVD beamforming over MIMO channels"],"prefix":"10.1186","volume":"2021","author":[{"given":"Felipe","family":"Kettlun","sequence":"first","affiliation":[]},{"given":"Fernando","family":"Rosas","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3068-096X","authenticated-orcid":false,"given":"Christian","family":"Oberli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,10]]},"reference":[{"key":"2026_CR1","doi-asserted-by":"publisher","unstructured":"J.M. Kahn, R.H. Katz, K.S.J. 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