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.

奇异值分解 (SVD) 波束成形是一种有吸引力的工具，用于降低无线传感器网络中数据传输的能耗，其节点配备多个天线。然而，由于两个重要的缺点，这种方法通常不实用：它需要发射机处的信道状态信息，并且信道矩阵的 SVD 计算通常过于复杂。为了解决这些问题，我们提出了一种无需将实际信道或 SVD 系数反馈给发射机即可建立 SVD 波束成形链路的方法。具体来说，我们的方法利用信道互易性和功率迭代算法 (PIA) 来从接收到的前导序列中确定预编码和解码奇异向量。提出了一种不执行迭代的低复杂度版本，并显示其信噪比 (SNR) 损失与使用最小二乘信道估计的 SVD 波束成形的误码率相差 1 dB 以内。低复杂度方法明显优于最大比率组合分集和 Alamouti 编码。我们还表明，所提出的基于 PIA 的方法的计算成本低于使用 Golub-Reinsch 算法获得 SVD 的方法。低复杂度版本的计算数量比 Golub-Reinsch 小一个数量级。这种差异随着天线阵列尺寸的增加而进一步增大。低复杂度方法明显优于最大比率组合分集和 Alamouti 编码。我们还表明，所提出的基于 PIA 的方法的计算成本低于使用 Golub-Reinsch 算法获得 SVD 的方法。低复杂度版本的计算数量比 Golub-Reinsch 小一个数量级。这种差异随着天线阵列尺寸的增加而进一步增大。低复杂度方法明显优于最大比率组合分集和 Alamouti 编码。我们还表明，所提出的基于 PIA 的方法的计算成本低于使用 Golub-Reinsch 算法获得 SVD 的方法。低复杂度版本的计算数量比 Golub-Reinsch 小一个数量级。这种差异随着天线阵列尺寸的增加而进一步增大。