Sparse Reconstruction OFDM Delay Estimation Algorithm Based on Bayesian Automatic Relevance Determination

Considering the problem of Orthogonal Frequency Division Multiplexing (OFDM) signal delay estimation with only a Single Measurement Vector (SMV) in a complex environment, a sparse reconstruction time delay estimation algorithm based on Bayesian Automatic Relevance Determination (BARD) is proposed. The Bayesian framework is used to start from the perspective of further mining useful information, and asymmetric Automatic Relevance Determination(ARD) priori is introduced to integrate into the parameter estimation process, which improves the accuracy of time delay estimation under SMV and low Signal-to-Noise Ratio (SNR) conditions. Firstly, a sparse real-domain representation model is constructed based on the estimated frequency domain response of the OFDM signal physical layer protocol data unit. Then, probability hypothesis for the noise and sparse coefficient vectors are made in the model, and Automatic Relevance Determination (ARD) prior is introduced. Finally, according to the Bayesian framework, the Expectation Maximization (EM) algorithm is used to solve the hyperparameters to estimate the delay. The simulation experiments show that the proposed algorithm has better estimation performance and is closer to the Cramer-Rao Bound (CRB). At the same time, based on the Universal Software Radio Peripheral (USRP), the effectiveness of the proposed algorithm is verified by the actual signal.