Channel estimation in OFDM systems with virtual subcarriers using DPSS

In practical Orthogonal Frequency Division Multiplexing (OFDM) systems, due to the presence of virtual subcarriers, the OFDM input-output relation is ill-conditioned in the Fourier basis. Therefore, an unbiased estimator does not exist and regularization methods, generally used to estimate the channel, provide biased time domain estimates. To estimate exact channel sparsity, we propose an unbiased estimator in discrete prolate spheroidal sequences (DPSS) basis. We theoretically show that our estimates recover exact sparsity information as the SNR increases.