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Text: This joint optimization problem is extended in [8] to complex-baseband quadrature amplitude modulation (QAM) of a WSS complex-valued **data** symbol sequence. Under the linear MMSE (LMMSE) optimality criterion and the average transmit power constraint, the jointly optimal transmit and receive waveforms are derived for use over an additive WSCS noise channel. It is well known that a WSCS noise model is better than a WSS model for the case in which data-like QAM interferences are present as well as an ambient Gaussian noise [1]. In contrast to the previous results only with an additive WSS noise, the optimal waveforms are shown in general to have nonzero spectral values on a frequency interval whose length is greater than that of the generalized Nyquist interval. This is because, unlike a WSS random process, a WSCS random process possesses non-zero correlation in the frequency domain among the components that are spaced integer multiples of the symbol rate apart [9]. To exploit such spectral correlation of the WSCS random process, a vectorized Fourier transform (VFT) technique is employed in [8]. This technique is motivated by the harmonic series representation [9] of a WSCS random process, and the use of that representation for joint Tx and Rx optimizations in cyclostationary interference and noise has been examined in [10] and [11].<|eot_id|><|start_header_id|>assistant<|end_header_id|>

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