Recent Study on Periodic Binary Signals with Zero Cross Correlation Based on Walsh Sequences

This study considers periodic binary signals coded using Walsh orthogonal functions. Binary coded
signals are used in modern communication, telemetric and optical systems. For periodic signals, it is
shown that groups of signals that do not have mutual frequency components exist for each Walsh
system with size N = 2n (n = 1, 2, 3,...). These groups of periodic signals have zero cross correlation
(CC) or zero multiple access interference (MAI). Ensembles of periodic signals with zero MAI can be
created from these groups of signals. The maximum number of binary signals in these ensembles is
defined by the number of groups and is equal to n+1. Signals with zero MAI are orthogonal in the
time domain when a time shift is present between them and can be separated without tight
synchronization. Examples of separating filters are presented. Applying this principle to radio signals
enables the creation of n+1 independent radio frequency signals. These signals can be separated on
the receiver side without a tight synchronization between them. The results of this study can be used
in asynchronous CDMA communication, telemetric networks (e.g. Wireless Body Area Networks
(WBANs), Wireless Sensor Networks (WSNs)), and optical systems.