As an example of complex matrix operations decomposition, Fig. 4 shows the required operators to perform 2×2 complex matrix multiplication operation.
where × is matrix multiplication operation, and H t is a transpose of the H matrix. 4. The operator precedence relation.
Since multiplication operation of the unitary matrices of relay terminals given in the optimal training scheme is equivalent to circular shifting operation, the complex matrix multiplication operation in the relay terminals can be avoided.
Furthermore, the Chu sequence is employed as the training sequence at the source terminal to achieve the minimum MSE estimation performance while avoid the complex matrix multiplication operation at the relay terminals.
In addition, the Chu sequence is employed as the training sequence to achieve the minimum MSE estimation performance while avoid the complex matrix multiplication operation at the relay terminals.
With the same matrix representation, the quotient matrix of the frequency-domain symbols is provided {left({mathbf{D}}_{div}right)}_{mu, n}={left({mathbf{D}}_{Rx}right)}_{mu, n}/{left({mathbf{D}}_{Tx}right)}_{mu, n}={overrightarrow{k}}_R^Tcdot {overrightarrow{k}}_D (28 with T being the matrix transpose operation and being the matrix multiplication operation.
There are a number of basic operations that can be applied to modify matrices, called matrix addition, scalar multiplication, transposition, matrix multiplication, row operations, and submatrix.
The OrthoMCL uses matrix multiplication, the operation with the minimal complexity n ω, where the exponent ω is a parameter.
The GAMP algorithm transforms a multiple integral nonlinear problem into a linear problem, so the computational complexity in each iteration mainly depends on the simple matrix multiplication and addition operations in formula (10)–(16).
