Asymptotic Analysis of CP-SC-FDE and UW-SC-FDE in Additive Cyclostationary Noise

In this paper, linear minimum mean-squared error (LMMSE) frequency domain equalizers (FDEs) are considered for single-carrier (SC) block transmission over additive wide- sense cyclostationary (WSCS) noise. Using the theory of asymptotically equivalent sequences of matrices, it is shown that the mean-squared error (MSE) of cyclic prefix (CP) appended SC- FDE and that of the unique word (UW) appended SC-FDE converge to the same limit as the block length tends to infinity. The closed-form expression of the limit is also derived. Unlike SC-FDEs in additive white Gaussian noise, the computational complexity of the FDEs are as high as that of the time domain equalizers in the presence of the WSCS noise. So, suboptimal SC- FDEs with much lower computational complexity are proposed that achieve the asymptotic MSE of the LMMSE SC-FDEs as the block length tends to infinity. Numerical results are also provided.