Sample reduction during signal detection using difference sets and almost difference sets

Abstract

Wide signal bandwidths typically require receivers performing signal detection to collect very large quantities of data. However, in applications with limited size, weight and power (SWAP) requirements, reducing the amount of data becomes important for proper operation. Most existing sample reduction approaches rely on reconstruction algorithms to compensate for the missing data, but these are often computationally complex. Therefore, in this work sample reduction without reconstruction is considered. This work proposes an approach to discarding samples prior to detection using difference sets (DSs) and almost difference sets (ADSs) – exploiting their sidelobe and cyclic properties – to minimise the negative impact on detection performance. Included are mathematical analyses, simulations, and experiments with practical data evaluating the effects of this technique on the detection performance. This work demonstrates that while the lack of a reconstruction algorithm does introduce interference, this is reduced when using DSs and ADSs compared to when samples are discarded at random, and the use of these sets allows predictions about performance to be made beforehand using only the set parameters. Additionally, the proposed technique performs much faster than detection with reconstruction, while having a reasonable decrease in detection performance.