Embodiments described herein provide a system for transmitting high efficiency long term training field (HE-LTF) symbols for multiple wireless spatial streams over a wireless channel. An advanced P-matrix design is used to construct HE-LTF symbols that are processed by a receiver such that channel properties such as channel estimates or carrier phase error are determined prior to receiving all HE-LTF symbols. Tone multiplexing of wireless spatial stream is also used to transmit multiple spatial streams based on an assignment of sets of spatial streams to sets of tones available for transmission, increasing the throughput of the transmission system. The advanced P-matrix design and tone multiplexing are used in combination to achieve calculate channel properties before receiving all HE-LTF symbols while minimizing power fluctuation among the high efficiency short training field symbol and the HE-LTF symbols.