On complexity-reduced implementation of multi-dimensional Wiener Interpolation Filtering

The Wiener Interpolation Filter is commonly used to reconstruct a stochastic process from noisy samples. We focus on the case of a multi-dimensional stochastic process and the practical example of application of the filter for estimation of mobile radio propagation channels at a wireless receiver. We show that computational complexity of the implementation can be considerably reduced by exploiting two properties: first, multidimensional Wiener filtering is in general non-separable, while upsampling for interpolation is separable if the sample structure is a lattice - so it is beneficial to separate the two steps. Second, Wiener filtering can be implemented using spectral shaping of partially overlapping multidimensional blocks (fast convolution, overlap-add or overlap-save method). We discuss performance and complexity of the application to estimate the time-variant channel transfer function in OFDM (2D channel correlation) and MIMO-OFDM (3D channel correlation) transmission, for varying channel autocorrelation values (WSSUS model) and filter kernel sizes.