Capacity of Second-Order Cyclostationary Complex Gaussian Noise Channels

Abstract

In this paper, we derive the capacity of a continuous-time, single-input single-output (SISO), frequency-selective, band-limited, linear time-invariant (LTI) channel, whose output is corrupted by a second-order cyclostationary (SOCS) complex Gaussian noise. By using a pair of invertible, linear-conjugate linear time-varying operators called a properizing FREquency SHift (p-FRESH) vectorizer and a p-FRESH scalarizer, it is shown that, whether the complex noise is proper or improper, the SISO channel can always be converted to an equivalent multiple-input multiple-output (MIMO) LTI channel whose output is now corrupted by a proper-complex vector wide-sense stationary noise. A variational problem is then formulated in the frequency domain to find the optimal input distribution that maximizes the throughput of the equivalent MIMO channel. It turns out that the optimal input to the SISO channel, obtained through a procedure similar to the water filling, is an SOCS complex Gaussian random process with the same cycle period as the noise. It is shown that this procedure, named cyclic water filling, significantly outperforms ordinary water filling by effectively utilizing the spectral correlation of the cyclostationary noise.