Robust sparse underwater acoustic channel estimation method via projected ℓ₁-ℓ₂ Optimization

By exploiting the intrinsic sparse structure of the underwater acoustic channel, we adopt ℓ_l-ℓ₂ optimization criterion, which incorporates least squares with the penalized ℓ₁ minimization to reduce noise effects while inducing channel sparsity. However, the estimate of channel parameters might not be in the feasible region. Therefore, we then define convex sets and utilize convex projection as a supplement to ℓ₁-ℓ₂ optimization method to further improve the estimation accuracy. In addition, we elaborate matrix multiplications of the ℓ₁-ℓ₂ solution into vector computation efficiently implemented by FFT. Simulation results show that the proposed method outperforms some conventional channel estimation techniques in low SNR scenarios, and it can resolve multipath effectively even when SNR equals -5dB.