A low-complexity channel training method for efficient SVD beamforming over MIMO channels

Singular value decomposition (SVD) beamforming is an attractive tool for reducing the energy consumption of data transmissions in wireless sensor networks whose nodes are equipped with multiple antennas. 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 dB 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–Reinsch algorithm for obtaining the SVD. The number of computations of the low-complexity version is an order of magnitude smaller than with Golub–Reinsch. This difference grows further with antenna array size