Analysis of Doppler Effect on the Pulse Compression of Different Codes Emitted by an Ultrasonic LPS

Abstract

This work analyses the effect of the receiver movement on the detection by pulse compression of different families of codes characterizing the emissions of an Ultrasonic Local Positioning System. Three families of codes have been compared: Kasami, Complementary Sets of Sequences and Loosely Synchronous, considering in all cases three different lengths close to 64, 256 and 1,024 bits. This comparison is first carried out by using a system model in order to obtain a set of results that are then experimentally validated with the help of an electric slider that provides radial speeds up to 2 m/s. The performance of the codes under analysis has been characterized by means of the auto-correlation and cross-correlation bounds. The results derived from this study should be of interest to anyone performing matched filtering of ultrasonic signals with a moving emitter/receiver.

Improvement of high‐voltage impulses in track circuits with Kasami and LS codes

“…32 From this point of view, as shown in Figures 14-17, except for the 71-bit LS code, all the other types of sequences have good performance. This condition implies that the correlation maximum can be detected more easily among sidelobes, as well as the transmitted signal can be distinguished from noise.…”

“…In some previous works, it has been experimentally stated that the limit for these 2 bounds θ AC and θ CC should be 0.5. 32 From this point of view, as shown in Figures 14-17, except for the 71-bit LS code, all the other types of sequences have good performance. Although the 63-bit Kasami sequences have better performance than the other ones in general, the 15-bit Kasami and 19-bit LS codes still show a stable performance in bad noise conditions.…”

Diseño de esquemas de modulación para un sistema de posicionamiento local ultrasónico codificado con secuencias Zadoff-Chu

“…El movimiento del receptor produce un ensanchamiento o compresión de la señal emitida a medida que se aleja o se acerca al emisor, este efecto es modelado asumiendo una frecuencia de muestreo virtual f s para la señal emitida [8], dada por:…”

“…Además, la señal suele estar limitada por el ancho de banda disponible en el canal, y más específicamente por los transductores empleados.La codificación de la señal a emitir permite mejorar el desempeño del sistema y mitigar los efectos comentados anteriormente. Como alternativa a códigos pseudo-aleatorios tradicionales [7,8], las secuencias Zadoff-Chu (ZC) proporcionan un buen rendimiento en sistemas de medida de distancia con ultrasonido, sobretodo si se encuentran afectados por el efecto Doppler [5]. Las secuencias ZC son polifásicas de valores complejos, con amplitud unitaria constante, y auto-correlación (AC) cero para desplazamientos no nulos.…”

Easily-Deployable Acoustic Local Positioning System Based on Auto-Calibrated Wireless Beacons

“…Several families of sequences have been studied for these systems, for instance, gold codes, Complementary Sequence Sets (CSS), and LS (Loosely Synchronized) codes. However, in a recent work [26], it has been demonstrated that not all of these families are equally resilient to adverse effects such as multi-access, multipath, and Doppler shift. Kasami sequences are known to represent a good compromise between the good cross-correlation values and the slow degradation of these properties associated with the movement of the receiver.…”