Asymptotic Capacity Results for Non-Stationary Time-Variant Channels Using Subspace Projections

In this paper we deal with a single-antenna discrete-time flat-fading channel. The fading process is assumed to be stationary for the duration of a single data block. From block to block the fading process is allowed to be non-stationary. The number of scatterers bounds the rank of the channels covariance matrix. The signal-to-noise ratio (SNR), the user velocity, and the data block-length define the usable rank of the time-variant channel subspace. The usable channel subspace grows with the SNR. This growth in dimensionality must be taken into account for asymptotic capacity results in the high-SNR regime. Using results from the theory of time-concentrated and band-limited sequences we are able to define an SNR threshold below which the capacity grows logarithmically. Above this threshold the capacity grows double-logarithmically. Index Terms Non-coherent capacity, non-stationary time-variant channel, Slepian basis expansion, Fourier basis expansion, prolate spheroidal sequences. I