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In this paper, we make an investigation on the sum-mean-square-error(sum-MSE) performance gain achieved by DFT-based least-square (LS) channelestimator over frequency-domain LS one in full-duplex OFDM system in thepresence of colored interference and noise. The closed-form expression of thesum-MSE performance gain is given. Its simple upper and lower bounds arederived by using inequalities of matrix eigen-values. By simulation andanalysis, the upper lower bound is shown to be close to the exact value of MSEgain as the ratio of the number N of total subcarriers to the cyclic prefixlength L grows and the correlation factor of colored interference increases.More importantly, we also find that the MSE gain varies from one to N/L as thecorrelation among colored interferences decreases gradually. According totheoretical analysis, we also find the MSE gain has very simple forms in twoextreme scenarios. In the first extreme case that the colored interferencesover all subchannels are fully correlated, i.e., their covariance matrix is amatrix of all-ones, the sum-MSE gain reduces to 1. In other words, there is noperformance gain. In the second extreme case that the colored-interferencecovariance matrix is an identity matrix, i.e, they are mutually independent,the achievable sum-MSE performance gain is N/L. A large ratio N/L will achievea significant sum-MSE gain.

Sum-MSE performance gain of DFT-based channel estimator over frequency-domain LS one in full-duplex OFDM systems with colored interference