The Use of Genuine Two-Phase Perfect Code for Increased Fiber Sensing Performance

In optical sensing systems, such as fiber-optic sensors and lidar systems, pulse compression is a technique employed to enhance both the temporal/spatial resolution and system sensitivity. These goals are accomplished by transmitting a specific code, and correlating the received echos with a stored version of the code, resulting in a strong and narrow peak, albeit accompanied by sidelobes. Normally, the lower the sidelobes (with respect to the peak) the better the code. Perfect Periodic Autocorrelation (PPA) is a property of certain codes, whose periodic autocorrelation function is identically zero for all out-of-phase shifts. The Legendre code is a popular two-valued PPA code which exhibits the PPA property only when applied with a specific, complex, two-phase alphabet, suggested by S.W. Golomb. Alternatively, the binary version of the Legendre code, although easier to implement, exhibits only a near-perfect periodic autocorrelation with a finite sidelobe level: the longer the code the lower the sidelobe level. This paper investigates, for the first time, the application of complex-valued Legendre PPA codes, comparing their performance to that of a real-valued quasi-PPA one. Configurations studies via both simulation and experiment are dual-path and random multi-path interferometers. In the case of a single reflector, an improvement of 31 dB in Peak to Side-Lobe Ratio (PSLR) is achieved, whereas, for multiple reflectors, involving the cumulative effect of many sidelobes, a 7.5 dB improvement was obtained, solely by using the genuine two-phase values of the Legendre codes instead of their antipodal (± 1) version. These observations can benefit code-driven fiber-based sensing systems in sidelobe level limited scenarios.