A method of antenna selection training for a transceiver device having a plurality of antennas, the method comprising: searching potential channel estimation sub-matrices within a full-dimensional matrix corresponding to the full-dimensional description of a multiple-input, multiple-output, MIMO, channel between a plurality of receiving antennas (18A-18M) and a plurality of transmission antennas (14A-14N), wherein the full dimensional matrix has components associated with a row dimension having a number of rows equal to the number of receiving antennas and a column dimension having a number of columns equal to the number of transmission antennas, and wherein each potential channel estimation sub-matrix has components associated with a row dimension having a number of rows equal to a number of receive chains and a column dimension having a number of columns equal to a number of transmit chains to be used to transmit spatial data streams; wherein the number of receive chains is less than the number of receiving antennas and/or the number of transmit chains is less than the number of transmission antennas; right-multiplying each potential channel estimation sub-matrix with a spatial spreading matrix to form respective channel estimation sub-matrices that account for the spatial spreading matrix, wherein the spatial spreading matrix has components associated with a row dimension having a number of rows equal to the number of transmit chains and a column dimension having a number of columns equal to the number of spatial data streams to be transmitted, wherein the number of spatial streams is less than a minimum of the number of transmit chains and the number of receive chains; selecting one of the formed channel estimation sub-matrices that account for the spatial spreading matrix based on channel sounding information transmitted over different antenna subsets and an optimality criterion; and selecting a subset of the antennas corresponding to the selected channel estimation sub-matrix that account for the spatial spreading matrix. searching potential channel estimation sub-matrices within a full-dimensional matrix corresponding to the full-dimensional description of a multiple-input, multiple-output, MIMO, channel between a plurality of receiving antennas (18A-18M) and a plurality of transmission antennas (14A-14N), wherein the full dimensional matrix has components associated with a row dimension having a number of rows equal to the number of receiving antennas and a column dimension having a number of columns equal to the number of transmission antennas, and wherein each potential channel estimation sub-matrix has components associated with a row dimension having a number of rows equal to a number of receive chains and a column dimension having a number of columns equal to a number of transmit chains to be used to transmit spatial data streams; wherein the number of receive chains is less than the number of receiving antennas and/or the number of transmit chains is less than the number of transmission antennas; right-multiplying each potential channel estimation sub-matrix with a spatial spreading matrix to form respective channel estimation sub-matrices that account for the spatial spreading matrix, wherein the spatial spreading matrix has components associated with a row dimension having a number of rows equal to the number of transmit chains and a column dimension having a number of columns equal to the number of spatial data streams to be transmitted, wherein the number of spatial streams is less than a minimum of the number of transmit chains and the number of receive chains; selecting one of the formed channel estimation sub-matrices that account for the spatial spreading matrix based on channel sounding information transmitted over different antenna subsets and an optimality criterion; and selecting a subset of the antennas corresponding to the selected channel estimation sub-matrix that account for the spatial spreading matrix.