Blind Frequency Synchronization in OFDM via Diagonality Criterion

In this paper, we address the problem of blind carrier frequency offset (CFO) estimation in orthogonal frequency-division multiplexing (OFDM) systems in the case of frequency-selective channels. CFO destroys the orthogonality between the carriers leading to nondiagonal signal covariance matrices in frequency domain. The proposed blind method enforces a diagonal structure by minimizing the power of nondiagonal elements. Hence, the orthogonality property inherent to OFDM transmission with cyclic prefix is restored. The method is blind since it does not require a priori knowledge of the transmitted data or the channel, and does not need any virtual subcarriers. A closed-form solution is derived, which leads to accurate and computationally efficient CFO estimation in multipath fading environments. Consistency of the estimator is proved and the convergence rate as a function of the sample size is analyzed as well. To assess the large sample performance, we derive the Cramer-Rao bound (CRB) for the blind CFO estimation problem. The CRB is derived assuming a general Gaussian model for the OFDM signal, which may be applied to both circular and noncircular modulations. Finally, simulation results on CFO estimation are reported using a realistic channel model

I Nomenclature

Scalar , column vector , matrix .

Transpose of , conjugate transpose of .

Hermitian square-root of , inverse of .

element of matrix .

Identity matrix of size .

matrix filled with ones.

matrix filled with zeros.

diagonal matrix with on the main diagonal.

E

Expectation operator.

Trace operator, elementwise conjugation.

Frobenius norm.

Kronecker product, Hadamard product.

, mod

Proportional to, modulo operator.

vec

Stacks columns of a matrix on top of each other.

Real part, imaginary part.

Argument of a complex number.

if , if .

i.i.d.

Independent and identically distributed.

w.p. 1

Convergence with probability one.