In this paper, we extend our recent work and further demonstrate and analyze a single-carrier short-reach direct-detect transceiver and two modulation formats, dual-polarization pulse amplitude modulation 4 plus 4-phase modulation (DP-PAM4+4PM) and DP-PAM4+3PM, for intradata center applications delivering 504 and 462 Gb/s, respectively. To the best of the authors’ knowledge, this is the first demonstration of a transceiver delivering half a terabit per second on a single carrier with direct detection at a BER of 1.8 $\times\, 10^{\mathbf {-3}}$ , below the threshold of hard-decision FEC of 6.69% overhead. We thoroughly detail the receiver digital signal processing that leverages the performance of this transceiver and formats. We derive the adaptation of all filters and coefficients that are updated using the stochastic gradient descent algorithm. Even if the transceiver and formats are meant to be operated in the O-band, we present several performance results in the C-band, where chromatic dispersion is large. We present the performance of the 504 Gb/s single carrier over varying received signal powers and for three different MIMO/MISO filters lengths, and show that the required received power decreases by as much as 2.4 dB when 10 neighboring symbols are included in the DSP compared to 4. We also demonstrate that, when operated in the C-band, the DP-PAM4+4PM format delivers 448 Gb/s of error-free data payload over 500 m and DP-PAM4+3PM delivers 400 Gb/s of error-free payload over 1 km, independently of the state of polarization of the received signal. Finally, we experimentally compare at 84 GBaud the BER degradation of the PAM4- $\hat{x}$ , PAM4- $\hat{y}$ , and PM tributaries of the DP-PAM4+4PM and DP-PAM4+3PM formats from 0 to 1 km, demonstrating much worst degradation of the PAM4 bearing phase modulation caused by phase to intensity conversion via chromatic dispersion.
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