Generalized Dynamic Codebook Design for Non-Coherent Short-Packet Communications: Radius Control and Placement of Complex-Conjugate Reciprocal Zero Pairs

Modulation on Conjugate-Reciprocal Zeros (MOCZ) is a non-coherent communication scheme designed for the reliable transmission of short data packets over unknown wireless multipath channels. Unlike traditional methods that require channel estimation or training sequences, MOCZ encodes information into the zeros of the transmitted signal’s z-transform, enabling the receiver to decode data without prior channel knowledge. To support multiple users, the Multi-User MOCZ (MU-MOCZ) scheme was introduced, employing time-division multiplexing (TDM). However, the use of a fixed codebook for all users in MU-MOCZ can degrade performance due to variations in channel zero distributions. This paper extends previous work by introducing a dynamic codebook design for MU-MOCZ. The design incorporates a rotation parameter into the angular positions of zero-pairs, allowing the transmitter to adjust the codebook to each user’s unique channel conditions and optimize performance. Simulation results demonstrate significant improvements in bit error rate (BER), throughput, and packet delivery ratio (PDR) compared to the fixed codebook MU-MOCZ scheme.