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A new two-way multiple-input multiple-output (MIMO) channel sounding method for enabling a transmitter and a receiver both to have complete knowledge of the channel between them is presented. The key idea is that when the transmitter sends out its training signal, the receiver repeats, or ldquoechoes,rdquo its received signal back to that transmitter. From this round-trip training signal, together with the usual one-way incoming training signal from the receiver, the transmitter is able to recover its own outgoing channel fading coefficients for all transmit/receive pairs of antenna elements. The two-stage, weighted least squares problem to estimate the incoming and outgoing channel response matrices is solved. The method applies to FDD and TDD channels, and is suitable for wireless networks with relays. A second contribution of this paper is to propose another new training step, called naturally channel-matched beamforming (NCMB). This step actively uses the physical channel to match the transmit and receive beamformers, instead of relying on uncoordinated beamformer estimates at the transmit and receive ends. When we create parallel virtual channels, by spatial precoding with singular modes of the channel matrix, this training step directly matches each pair of right and left singular vectors used to beamform, adjusting the receive vector to optimize the virtual link gain for the pair. Evidence for a ridge in the gain surface over beamformer pairs is given, which would explain the near-ideal gains obtained from the channel-matching step. We also show how to optimize the link gains while constraining these pairs to ensure low interchannel interference (ICI). Simulation results show that the echo-MIMO method for the case of channel-matched maximal ratio transmission/combining (MRT/MRC) approaches the performance of the ideal beamformers based on perfect channel estimates, especially for the case of no fewer transmit antennas than receive antennas. In this case, echo- - -MIMO outperforms a quantized MRT/MRC codebook feedback method.