circulant matrix


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circulant matrix

[′sər·kyə·lənt ′mā‚triks]
(mathematics)
A matrix in which the elements of each row are those of the previous row moved one place to the right.
References in periodicals archive ?
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.
The circulant matrix [a] can be diagonalized by [V] as shown in Equation (18), where [[V].sup.H] is the Hermitian matrix of [V].
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 matrix C is chosen as Strang's circulant matrix ([C.sub.s]), R.
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,