Statistical Sparse Channel Modeling for Measured and Simulated Wireless Temporal Channels

Time-domain wireless channels are generally modeled by Tapped Delay Line (TDL) model and its variants. These models are not effective for channel representation and estimation when the number of multipath taps is large. Compressive sensing (CS) provides a powerful tool for sparse channel modeling and estimation. Most of the research has been focusing on sparse channel estimation, while sparse channel modeling (SCM) is rarely considered for centimetre-wave channels. In this paper, we investigate statistical sparse channel modeling, using both measured and simulated channels over a frequency range of 6 to 8.5 GHz. We first introduce the triple equilibrium principle to explore the trade-off between sparsity, modeling accuracy, and algorithm complexity in SCM, and provide a methodology for characterizing the sparsity of time-domain channels using single-measurement-vector compressive sensing algorithms. Using mainly the selected wavelet dictionary and various CS reconstruction (aka recovery) algorithms, we then present comprehensive statistical sparse channel models, including channel sparsity, magnitude decaying profile, sparse coefficient distribution and atomic index distribution. Connections between the parameters of conventional TDL and sparse channel models are mathematically established. We also propose three methods for generating simulated channels from the developed sparse channel models, which validates their effectiveness.