Capacity of an Orthogonal Overlay Channel

In this paper, the design of a selfless overlay system is considered for a frequency-selective bandlimited linear time-invariant channel already occupied by a legacy system. It is assumed that the transmitted signal by the legacy system is well modeled by a zero-mean second-order cyclostationary (SOCS) Gaussian random process. It is also assumed that the legacy receiver employs a linear-conjugate linear (LCL) filter to capture possible impropriety of the signal. Our objective is to maximize the throughput of the overlay system under the constraint that no interfering signal component is observed at the output of the legacy LCL filter sampled at a uniform rate. A relevant problem of deriving the constrained capacity of a discrete-time vector Gaussian noise channel is first examined. Then, it is shown that the optimal input to the overlay channel must be a zero-mean SOCS Gaussian random process. Using these results, the optimization problem is formulated in the frequency domain, and the procedure named orthogonal cyclic water filling (O-CWF) is derived to find the optimal channel input distribution. Numerical results are provided to show that the proposed selfless overlay scheme enables reliable communication even over a channel fully occupied by a legacy system.