First Arrival Detection for Sparse Multipath Channel

Since most components of sparse multi-path channel (SMPC) are zero, impulse response of SMPC can be recovered from a short training sequence and its non-zero entries can be detected from a short training sequence. In this paper, we use 1-bit measurements, which preserve only the sign information of the random measure, to detect the first arrival of sparse channel. Although it is possible to detect using the classical compressive sensing approach by treating the 1-bit measurement as ± 1 measurement values, in this paper we reformulate the problem to a convex problem. In order to mitigate inter-atom interference (IAI), a sensing dictionary is used. The simulation results demonstrate that the percentage of first arrival of SMPC by the proposed method is significantly better than the classical compressive sensing method that use the quantized 1-bit measurement and better than that doesn´t use a sensing dictionary.