Learning Zero Constellations for Binary MOCZ in Fading Channels

In this work, we propose two methods to design zero constellations for binary modulation on conjugate-reciprocal zeros (BMOCZ). In the first approach, we treat constellation design as a multi-label binary classification problem and learn the zero locations for a direct zero-testing (DiZeT) decoder. In the second approach, we introduce a neural network (NN)-based decoder and jointly learn the decoder and zero constellation parameters. We show that the NN-based decoder can directly generalize to flat-fading channels, despite being trained under additive white Gaussian noise. Furthermore, the results of numerical simulations demonstrate that learned zero constellations outperform the canonical, Huffman BMOCZ constellation, with the proposed NN-based decoder achieving large performance gain at the expense of increased computational complexity.

A Smooshed BMOCZ Zero Constellation for CFO Estimation Without Channel Coding

In this study, we propose a new binary modulation on conjugate-reciprocal zeros (BMOCZ) zero constellation, which we call smooshed binary modulation on conjugate-reciprocal zeros (SBMOCZ), to address carrier frequency offset (CFO)-induced zero rotation without depending on channel coding. In our approach, we modify the phase mapping of Huffman BMOCZ by shrinking the angle between adjacent zeros, except for the first and last, to introduce a gap in the zero constellation. By discerning the gap location in the received polynomial, the receiver can estimate and correct the phase rotation. We demonstrate the error rate performance of SBMOCZ relative to Huffman BMOCZ, showing that SBMOCZ addresses a CFO-induced rotation at the cost of a modest performance reduction compared to Huffman BMOCZ in the absence of a CFO. Finally, we compare SBMOCZ to Huffman BMOCZ using a cyclically permutable code (CPC), showing a 4 dB bit error rate (BER) improvement in a fading channel, while demonstrating comparable performance across other simulations.

Fourier-Domain CFO Estimation Using Jutted Binary Modulation on Conjugate-Reciprocal Zeros

In this work, we propose jutted binary modulation on conjugate-reciprocal zeros (J-BMOCZ) for non-coherent communication under a carrier frequency offset (CFO). By introducing asymmetry to the Huffman BMOCZ zero constellation, we exploit the identical aperiodic auto-correlation function of BMOCZ to derive a Fourier-domain metric for CFO estimation. Unlike the existing methods for Huffman BMOCZ, which require a cyclically permutable code (CPC) for pilot-free CFO correction, J-BMOCZ enables the estimation of a CFO without the use of pilots or channel coding. Through numerical simulations in additive white Gaussian noise and fading channels, we show that the bit error rate (BER) loss of J-BMOCZ under a CFO is just 1 dB over Huffman BMOCZ without a CFO. Furthermore, the results show that coded J-BMOCZ achieves better BER performance than Huffman BMOCZ with a CPC.