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This slide shows the equation of the detection process, where X is the transmitted signal vector, Y is the received signal vector, H is the channel transfer matrix, N and N' are complex noise vectors.
With respect to this equation, please observe that the multiplication of both sides by H Hermitian transpose converts the R-by-T system to a T-by-T system, which is less expensive to solve.
The estimation of X through the solution of this linear system is the most computationally demanding portion of the receiver algorithm for reasonably high values of T.
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