arXiv:2610.35177v1 Announce Type: new Abstract: Modulation on conjugate-reciprocal zeros (MOCZ) is a promising candidate for blind short-packet communication (SPC) in future wireless systems; however, its performance is sensitive to timing and frequency synchronization errors. In this paper, we propose a novel scheme named multi-radius binary MOCZ (MR-BMOCZ). This method introduces a new root placement strategy that enhances diversity in the autocorrelation domain. The resulting structure enhances the autocorrelation properties of the transmitted waveform, leading to improved timing offset (TO) estimation. Moreover, the multi-radius construction distributes the signal energy over a larger set of radii, hence reducing the peak-to-average power ratio (PAPR). The resulting waveform also exhibits a distinctive spectral structure that is exploited for carrier frequency offset (CFO) estimation and correction, yielding lower normalized mean square error (NMSE) compared with BMOCZ-based schemes. Simulation results over additive white Gaussian noise (AWGN) and fading channels demonstrate that MR-BMOCZ achieves superior synchronization performance while maintaining comparable bit error rate (BER) and block error rate (BLER) performance. Consequently, the proposed scheme offers a synchronization oriented extension of BMOCZ for robust non-coherent SPC.