On the theoretical aspect, we have proved a strong result which serves as the foundation of this project, that is, a sinusoid can be approximated as a linear combination of base sinusoids on constant frequencies and the approximation error decays exponentially fast as the number of base sinusoids increases. This result basically explains the main theoretical question of this project, and has been used to guide the design options in a number of practical problems.
On the practical aspect, we expect our results on CSI compression and estimation to have profound impact on the design and real-world performance of wireless networks such as Wi-Fi and cellular networks. Our patented CSI compression algorithm, CSIApx, achieves higher compression ratio, lower distortion, and lower computation complexity than the existing CSI compression algorithm. With high compression ratio, more frequent CSI feedbacks can be obtained, and more efficient data transmission options, such as MU-MIMO, can be enabled or enjoy lower error ratio. Our CSI estimation algorithm, ParEst, achieves much higher accuracy than existing algorithms in challenging cases when the transmitter has multiple antennas. ParEst can be used for CSI estimation in a number of scenarios, such as 5G MIMO uplink and Grant Free channels, and improve the performance of the network.