The control circuitry is, in some implementations, configured to determine the portion of the LTF mapping matrix by concatenating a portion of a fixed matrix with a zero matrix. A position of the portion of the fixed matrix in the portion of the LTF mapping matrix corresponds to the spatial stream and the fixed matrix associated with a standard LTF mapping matrix. In some embodiments, the LTF mapping matrix is an R-matrix representative of a training matrix for determining carrier phase error accumulated over the transmitted HE-LTF symbols, and the transmitter is further configured to transmit HE-LTF symbols mapped by the R-matrix over one or more pilot tones in the wireless channel. For HE-LTF symbols mapped by the R-matrix transmitted over the pilot tone, the control circuitry is configured to assemble the HE-LTF symbols mapped by the R-matrix by aligning the portion of the fixed matrix within a subset of rows of the R-matrix for application, at the receiver, of an inverse of the fixed matrix and a pseudo inverse of a channel response matrix to the R-matrix to obtain carrier phase error associated with the spatial stream.

In some implementations, the LTF mapping matrix is a P-matrix representative of a training matrix for determining at least a channel estimate of the spatial stream. The transmitter is further configured to transmit HE-LTF symbols mapped by the P-matrix over one or more data tones in the wireless channel. For HE-LTF symbols mapped by the P-matrix transmitted over the data tone, the control circuitry is configured to assemble the HE-LTF symbols mapped by the P-matrix by interleaving the portion of the fixed matrix diagonally for application, at the receiver, of an inverse of the fixed matrix at the position of the portion of the fixed matrix in the P-matrix to determine the channel estimate of the spatial stream after receiving a subset of the transmitted HE-LTF symbols.