Incorporation of prior knowledge into sparse time dispersive OFDM channel estimation via weighted atomic norm minimisation

A new estimator for sparse time dispersive channels in pilot aided orthogonal frequency division multiplexing (OFDM) systems is developed by considering prior knowledge on channel time dispersions. The authors propose a weighted atomic norm minimisation (WANM) in order to incorporate the prior information into the estimator. The dual of the WANM is then converted to a tractable semidefinite programming using positive trigonometric polynomial theory. After solving the dual problem, the channel response is identified by solving a least squares approach. In this work, they assume that time dispersions associated delays can take any value with a mild minimum separation condition on the normalised interval [0, 1). The performance of the new estimator is compared with conventional approaches. With respect to the pilot number and signal to noise ratio (SNR), simulation results reveal that the proposed estimator performs superior to that of traditional methods. It is shown that both a lower SNR and number of pilots are required to achieve the same mean square error reported in previous works.