For and in, we use the Frobenius inner product, and the Frobenius norm, where "tr" denotes the trace operation of a square matrix.
The operator d i a g ( a ) denotes a diagonal matrix with elements given by a. Trace(a) denotes the trace operation of matrix a.
Furthermore, trace and E represent the trace and the expectation operations of matrix A, respectively.
Notation E ( A ) and Tr(A) denote the expectation and trace operation of matrix A, respectively.
Secondly, the proposed method needs only fast Fourier transform (FFT) operation instead of the inversion operation of a large dimensional matrix.
In comparison with conventional LMMSE channel estimation, the proposed channel estimation method does not require statistical knowledge of the channel in advance and avoids the inverse operation of a large dimension matrix by using the FFT operation.
It is noted that the estimation of the LMMSE matrix requires only points FFT operation and circle shifting operation, which reduce the computational complexity significantly compared with the conventional LMMSE estimator since it requires the inverse operation of a large dimension matrix.
In comparison with the conventional LMMSE channel estimation, the proposed channel estimation method does not require the statistic knowledge of the channel in advance and avoids the inverse operation of a large dimension matrix by using the fast Fourier transform (FFT) operation.
Lleft(lambda, t,mathrm{R},Lambda right)=mathrm{t}mathrm{r}left EP{E}^{mathrm{T}}right)+mathrm{t}mathrm{r}left(Lambda left({R}^{mathrm{T}}R-{I}_3right)right)= min, (8 where tr denotes trace operation of matrix, Λ is a symmetric Lagrangian multiplier matrix, and P represents the weight matrix that every point has an isotropic weight and is independent of each other.
