Concatenating these vectors yields a matrix, called
circulant matrix, which can be expressed as
Then, transform the convolution based on
circulant matrix in linear system.
In [16], an orthogonal
circulant matrix transform (OCT) based precoding scheme is proposed, which achieves a relatively flat signal-to-noise ratio (SNR) profile over the signal bandwidth and alleviates significant BER degradation at high frequency carriers.
First, we embed Toeplitz matrix [T.sub.K] into a 2K x 2K
circulant matrix [C.sub.2N] as follows [18, 19]:
where [mathematical expression not reproducible] is an N x N
circulant matrix, with the first columns [mathematical expression not reproducible], and [mathematical expression not reproducible] are circular complex white Gaussian noise with zero mean and covariance matrix [mathematical expression not reproducible] that is allocated to the relay training, that is, [mathematical expression not reproducible] is allocated to the amplified received data, where 0 < [gamma] < 1.
together with the rank-2[n.sub.x] primary
circulant matrix C, that is, the
circulant matrix whose first row has second element one and all other elements zero, allows constructing a banded matrix
The results of Table 2 show that the method has a higher performance than traditional Toeplitz or
Circulant matrix method.
are special Toeplitz matrices as each column of a
circulant matrix is a circulant shift of its preceding column.
One can obtain the same description Q = [D.sup.T]D, where D is also a
circulant matrix,