### Abstract

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 <formula><tex>$N/L$</tex></formula> as the correlation factor gradually decreases from 1 to 0, where <formula><tex>$N$</tex></formula> and <formula><tex>$L$</tex></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 <formula><tex>$N/L$</tex></formula> in two extreme scenarios: fully-correlated and white, respectively. The former 1 means there is no performance gain, while the latter <formula><tex>$N/L$</tex></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.

Original language | English |
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Journal | IEEE Systems Journal |

DOIs | |

Publication status | Accepted/In press - 12 Jul 2018 |

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### Keywords

- Channel estimation
- Covariance matrices
- Frequency division multiplexing
- Frequency-domain analysis
- full duplex (FD)
- least squares (LSs)
- Linear matrix inequalities
- OFDM
- orthogonal frequency-division multiplexing (OFDM)
- Performance gain
- sum-MSE performance gain
- upper/lower bound

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*IEEE Systems Journal*. https://doi.org/10.1109/JSYST.2018.2850934