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An Application of Second-Order Reed-Muller Codes for Multiple Target Localization in Wireless Sensor Networks

Compressive sensing is a new signal processing technique for efficient reconstruction of an n-dimensional signal from m (m n) measurements. Most of compressive sensing researches are based on randomization, while research on deterministic sampling is essential for practical implementation. In this paper, we study m × n deterministic binary sensing matrices using second-order Reed-Muller codes, which satisfy a statistically restricted isometry property with reduced complexity for an application of multiple target localization in wireless sensor networks. We formulate multiple target locations as a sparse matrix, then exploit received signal strength information to recover noisy information using the deterministic sensing matrices and greedy algorithms to locate each target. The simulation results show that our scheme also achieves high accuracy in terms of localization errors when compared to traditional approaches with the random sensing matrices. Keywords—wireless sensor network; multiple target localization; compressive sensing; deterministic sensing matrix; Reed-Muller codes.