RVs, and the superscript T denotes the matrix transpose operation.
The number of time snapshots is equated to L. The superscript "T" represents matrix transpose operation.
Denote the modulated data symbols in one slot as (textbf {s} = [s_{1}, cdots, s_{N_{s}}]^{T} in {mathcal S}^{N_{s}}), where ({mathcal S}) is the modulation alphabet set, A T is the matrix transpose operation, and N s is the number of data symbols in one slot.
Thus, S m and T k can be expressed as: S m = x 1, m, x 2, m, …, x K, m T T k = x k, 1, x k, 2, …, x K, M T, where the superscript T denotes the matrix transpose operation.
Omitting some mathematical derivations, the baseband COQAM signal, for a block of size MK, can be expressed in a matrix form as s MK × 1 COQAM = diag G MK × K ′ E MK × M W M × M A M × K ′ T, where T denotes the matrix transpose operation and diag corresponds to the extraction of the diagonal elements of a matrix.
where = is the received sample vector at the th hydrophone with denoting matrix transpose operation, (4). is the matrix obtained with the th pilot sequence, and =, =, and = are the phase drift matrix, the fading coefficient vector, and the noise vector, respectively.
It is shown that the inverse transform of the proposed PROJT is conveniently obtained by the reciprocal of each elements of the forward matrix and transpose operation.
where denotes the matrix-vector transpose operation.
is matrix stack operator, is matrix transpose, is Hermitian operation, is complex conjugate, denotes the trace of a matrix, is Frobenius norm, ( is vector norm), denotes the Kronecker product, denotes identity matrix, and defines new symbols.
The notation T means the operation of matrix transpose.
Let tr denote the transpose operation for matrices.
