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Subspace-based phase noise estimation in OFDM receivers

In this paper, we consider the problem of channel and phase noise estimation for an orthogonal frequency division multiplexing (OFDM) radio link. We solve this problem by first investigating the subspace in which the phase noise spectral vector lies and then exploiting this information during estimation. Building upon earlier works, the phase noise spectral estimate is obtained by minimizing a homogeneous quadratic cost function and the channel estimate in turns depends on the obtained phase noise estimate. We show that, at infinite signal-to-noise ratio, the true phase noise spectral estimate lies in the null space of the matrix associated with the cost function. We utilize this knowledge by imposing constraints that adhere to this null space when minimizing the cost function. In addition, we also propose constraints based on knowledge of the covariance matrix of the phase noise process. Through simulations, we demonstrate lower phase noise mean-square error (MSE) and consequently lower channel MSE when incorporating the subspace information.