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Cyclic water-filling for additive wide-sense cyclostationary Gaussian noise channel

In this paper, we derive the capacity of a continuous-time band-limited channel corrupted by an additive wide-sense cyclostationary (WSCS) proper-complex Gaussian noise, and find the jointly optimal signaling and reception scheme to asymptotically achieve the capacity. Unlike a wide-sense stationary (WSS) noise, a WSCS noise has a structure that can be exploited in the noise suppression. Such a noise is often encountered when co-channel interference generated by linearly modulated codeword symbols from a Gaussian codebook is present in the frequency band of interest. The problem is formulated as a variational problem to find the optimal correlation function of the channel input, and the solution is obtained in the frequency domain by using the vectorized Fourier transform (VFT) and the matrix-valued PSD (MV-PSD) technique. It turns out that the optimal solution distributes the transmit power over the frequency band in a water-filling-like way that results in a WSCS, not WSS, signal as the channel input. Numerical results show that this cyclic water-filling (CWF) scheme performs significantly better than the ordinary water-filling scheme that ignores the spectral correlation of the WSCS noise.