Multi-stage detector for bipolar PAM with direct detection

Bipolar pulse amplitude modulation (BPAM) can improve power efficiency by leveraging the bipolar optical field. However, the maximum likelihood (ML) detection for BPAM grows exponentially in complexity as the modulation order and channel memory length increase. In this paper, we propose what we believe to be a novel multi-stage detector for BPAM to eliminate multi-level impairments while maintaining tolerable complexity. A key innovation of the multi-stage detector is the extension of sign estimation to general shaping pulses using the Viterbi algorithm. The detector effectively decouples and compensates for the signal impairments from the transmitter, the polarity loss of square-law detection, and the receiver in a sequential multi-stage process. In a 1-km C-band transmission experiment using 50-Gbaud BPAM-8 signals, the proposed detector achieves a bit-error ratio (BER) below 2.2 × 10^-2 (the 20% soft-decision forward error correction (SD-FEC) threshold) across a range of roll-off factors. As a comparison, conventional ML detection fails to recover the signal due to the impractical computational complexity. These results demonstrate the effectiveness of our multi-stage detector in addressing current limitations.