We propose CSIApx, a very fast and lightweight method to compress the CSI of Wi-Fi networks. CSIApx is based on our finding that any sinusoid can be approximated very well by a set of base sinusoids on constant frequencies.
In Wi-Fi, the CSI for an antenna pair is a vector of complex numbers, representing the channel coefficients of the OFDM subcarriers. The CSI is needed to calculate the modulation parameters, such as for Multi-User Multiple-Input-Multiple-Output (MU-MIMO). In Wi-Fi, the CSI is typically measured at the receiver and is transmitted back to the sender, which requires significant overhead. For example, on a 20 MHz channel with 64 subcarriers, the full CSI for a single antenna pair has 64 complex numbers, and for 9 antenna pairs, 576. Although Wi-Fi does not use all subcarriers, the feedback for 9 antenna pairs still may exceed 1000 bytes. The Wi-Fi standard defines options to compress the CSI, such as reducing the quantization accuracy or the number of subcarriers in the feedback, or using the Given's rotation on the V matrix after the Singular Value Decomposition (SVD) of the CSI matrix. However, these methods either reduce the accuracy of the CSI, or only achieve modest compression ratios. For example, a 3 by 3 complex V matrix can only be compressed into 6 real numbers, at a compression ratio of 3.
CSIApx approximates the CSI vector as the linear combination of a small number of base sinusoids on constant frequencies, and uses the complex coefficients of the base sinusoids as the compressed CSI. While it is well-known that the CSI vector can be represented as the linear combination of sinusoids, fixing the frequencies of the sinusoids is the key novelty of CSIApx, which is guided by our mathematical finding that almost any sinusoid can be approximated by a set of base sinusoids on constant frequencies. CSIApx enjoys very low computation complexity, because key steps in the compression can be pre-computed due to the constant frequencies of the base sinusoids. We extensively test CSIApx with both experimental and synthesized Wi-Fi channel data, and the results confirm that CSIApx can achieve very good compression ratio with little loss of accuracy..