In this study, it is mathematically shown that the detector inputs obtained using the matched filters in the Quadrature Amplitude Modulation (QAM) receiver are the same expressions as those obtained using the integrators if a rectangular pulse is used in the transmitter and the channel is Additive White Gaussian Noise (AWGN). Under the assumption that there is a perfect synchronization between the transmitter and the receiver. QAM is intensively used at the present time for the data transmission on subchannels in orthogonal frequency-division multiplexing (OFDM) communication systems such as digital subscriber lines (DSLs) modems, wireless local area networks (WLANs) and cellular wireless communication systems (e.g. 4G LTE). Cyclic-prefix OFDM is deployed in 4G LTE systems and the rectangular pulse is used in the time domain to shape all subcarriers of OFDM.

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Abstract:In this study, the classical phase-locked loop (PLL) and Costas loop are investigated together. How the synchronization is obtained by the carrier recovery from the sinusoidal reference signal is mathematically shown with some assumptions and presented. It is concluded from this paper that Costas loop produces about half of the error signal produced by the PLL in the locked-stateoperation. This result may affect the decision whether the Costas loop will be used more frequently in the phase coherent communication systems in the future.