Sum-MSE Gain of DFT-Based Channel Estimator Over Frequency-Domain LS One in Full-Duplex OFDM Systems

In this paper, we make an investigation on the sum-mean-square-error (Sum-MSE) performance gain in full-duplex orthogonal frequency-division multiplexing (OFDM) systems in the presence of colored interference-plus-noise (IPN). This gain is defined as the ratio of Sum-MSE of frequency-domain least-square (LS) channel estimator to that of DFT-based LS one. The closed-form formula of the gain is derived. And, its simple upper and lower bounds are given using inequalities of matrix eigenvalues. The exact value of Sum-MSE gain depends heavily on the correlation factor of the IPN covariance matrix. More importantly, we also find that the Sum-MSE performance gain grows from 1 to <inline-formula><tex-math notation="LaTeX">$N/L$</tex-math></inline-formula> as the correlation factor gradually decreases from 1 to 0, where <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula> denote the number of total subcarrier and the length of cyclic prefix, respectively. Also, via theoretical analysis, the exact Sum-MSE gain degenerates into 1 and <inline-formula><tex-math notation="LaTeX">$N/L$</tex-math></inline-formula> in two extreme scenarios: fully-correlated and white, respectively. The former 1 means there is no performance gain, while the latter <inline-formula><tex-math notation="LaTeX">$N/L$</tex-math></inline-formula> corresponds to the maximum Sum-MSE performance gain achievable. Numerical simulation further validates the above results. Additionally, the derived lower bound is shown to be closer to the exact value of Sum-MSE gain compared to the upper bound.