A Two-Stage Approach for the Estimation of Doubly Spread Acoustic Channels

In this paper, the estimation of doubly spread acoustic channels is investigated. By parameterizing the amplitude variation and delay variation of each path with polynomial approximation, this paper derives a mathematical model for the discrete-time channel input-output relationship tailored to single-carrier block transmissions. Based on the mathematical model, the channel estimation problem is transformed into estimation of the low-dimensional parameter sets (amplitude, delay, Doppler scale) that characterize the channel. A two-stage sparse channel estimation technique is then developed, which estimates the delay and Doppler scale sequentially. Compared to the one-stage joint estimation, the two-stage estimation approach greatly reduces the number of candidates on the delay-Doppler scale grid searched by the orthogonal matching pursuit (OMP) algorithm, that is, the dictionary size is reduced dramatically. As a result, the computational complexity is much lower. Further, the two-stage approach demonstrated higher levels of accuracy in computer simulations and led to better detection performance when applied to experimental data.