In a symmetric matrix, the symbol "*" is used to denote the term that is induced by symmetry.
Let (R^{n}) be the n-dimensional Euclidean space, (R^{n times m}) represents the set of (n times m) real matrix, the symbol * denotes the elements below the main diagonal of a symmetric block matrix, (A > 0) means that A is a real symmetric positive definitive matrix, I denotes the identity matrix with appropriate dimensions.
where is the time-domain channel matrix, denotes the precoder matrix, represents the symbol vector consisting of the multiplexed pilot and data symbols, and stands for the noise vector, which is assumed to be uncorrelated with the data symbols.
In order to estimate the channel matrix, the symbols are transmitted from each antenna.
The symbol stands for an zero matrix and the symbol stands for the vector.
The values of (varPhi^0) at the integers are obtained by finding the 1-eigenvector of the matrix D. Since the symbol function H is a matrix polynomial of degree 3, the support((varPhi^0 )) is contained in [0,3].
where (5). is the equivalent crosscorrelation matrix of the symbols as seen at the receiver.
For a matrix A, the symbols A ∗,A T, and A H denote the complex conjugation, transpose, and conjugate transpose respectively.
For an (mtimes n) matrix A, the symbols (mathscr{M} (boldsymbol{A})), (boldsymbol{A}'), (boldsymbol{A}^) and (boldsymbol{A}^) denote the column space, the transpose, the generalized inverse and Moore Penrose inverse of A, respectively.
Our aim is to find the necessary as well as sufficient conditions a spectral data must satisfy so that the corresponding matrix polynomial is the symbol function of a compactly supported, symmetric multiscaling function (varPhi (x)).
