An optimized method of modulation and demodulation via BMOCZ for non-coherent short packet communications

In non-coherent short packet communications (SPCs) based on binary modulation on conjugate-reciprocal zeros (BMOCZ), noise interference and channel zero distribution critically degrade the bit error rate (BER) performance. This paper proposes a systematic modulation–demodulation optimization framework by decoupling these two interference sources. For noise mitigation, we derive a zero-constellation radius based on noise bound (ZRNB) through rigorous theoretical analysis under the maximum noise tolerance criterion. To address channel zero interference, two novel detection algorithms are proposed: a region-division root-finding minimal distance (RDRFMD) detector and a zero-rejudgment root-finding minimal distance (ZRRFMD) detector. A dynamic optimization strategy is further introduced: at low signal-to-noise ratio (SNR), ZRNB combined with RDRFMD prioritizes noise suppression for robust detection; at high SNR, a zero-constellation radius based on Euclidean distance (ZRED) integrated with ZRRFMD focuses on channel zero interference mitigation. Simulations show that ZRNB achieves a maximum performance gain of 0.6 dB over the original BMOCZ at BER of $10^{-3}$ without channel zero interference, while the proposed method attains a significant 8 dB performance improvement at BER of $10^{-1}$ under random channel zero distribution.