Reduced Training Overhead for WLAN MU-MIMO Channel Feedback with Compressed Sensing

The WLAN packet format has a short training field (STF) for synchronization followed by a long training field (LTF) for channel estimation. To enable MIMO channel estimation, the LTF is repeated as many times as the number of spatial streams. For MU-MIMO, the CSI feedback in the 802.11ac/ax requires the access point (AP) to send a null data packet (NDP) where the HT/VHT/HE LTF is repeated as many times as the number of transmit antennas $N_{t}$. With each LTF being 4$\mu$s long in case of VHT and 12$\mu$s to 16$\mu$s long in case of High Efficiency WLAN (HEW), the length of NDP grows linearly with increasing $N_{t}$. Furthermore, the station (STA) with $N_{r}$ receive antennas needs to expend significant processing power to compute SVD per tone for the $N_{r}\times N_{t}$ channel matrix for generating the feedback bits, which again increases linearly with $N_{t}\cdot N_{r}$. To reduce the training and feedback overhead, this paper proposes a scheme based on Compressed Sensing that allows only a subset of tones per LTF to be transmitted in NDP, which can be used by STA to compute channel estimates that are then sent back without any further processing. Since AP knows the measurement matrix, the full dimension time domain channel estimates can be recovered by running the L1 minimization algorithms (OMP, CoSAMP). AP can further process the time domain channel estimates to generate the SVD precoding matrix.