Optimal signaling in second-order cyclostationary Gaussian jamming environment

In this paper, we derive the capacity-achieving transmission scheme for a continuous-time single-input single-output (SISO) band-limited channel corrupted by a second-order cyclostationary (SOCS) Gaussian jamming signal. Such an interference is encountered when a real or a complex Gaussian random sequence is linearly modulated and transmitted to jam the frequency band of interest. It is shown that an invertible linear-conjugate linear time-varying operator called a properizing FREquency SHift (p-FRESH) vectorizer can always convert the SISO channel into an equivalent multiple-input multiple-output (MIMO) linear time-invariant channel, whose output is now corrupted by a proper-complex vector wide-sense stationary (WSS) Gaussian jamming signal regardless of the propriety of the SOCS random process input. 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 capacity of the SISO channel is achieved by an SOCS Gaussian random process input with the same cycle period as the jamming signal. Numerical results show that the throughput of the channel can be significantly improved by exploiting the correlation structure of the SOCS Gaussian jamming signal.