Blind Source Separation of Instantaneous Mixture of Delayed Sources Using High-Order Taylor Approximation

Abstract

This paper deals with the problem of blind source separation (BSS), where observed signals are a mixture of delayed sources. In reference to a previous work, when the delay time is small such that the first‐order Taylor approximation holds, delayed observations are transformed into an instantaneous mixture of original sources and their derivatives, for which an extended second‐order blind identification (SOBI) approach is used to recover sources. Inspired by the results of this previous work, we propose to generalize its first‐order Taylor approximation to suit higher‐order approximations in the case of a large delay time based on a similar version of its extended SOBI. Compared to SOBI and its extended version for a first‐order Taylor approximation, our method is more efficient in terms of separation quality when the delay time is large. Simulation results verify the performance of our approach under different time delays and signal‐to‐noise ratio conditions, respectively.

Co‐channel interference cancellation based on BSS for multi‐satellite MIMO communication systems with FFR

“…Furthermore, the relationship between the observation signals and their derivatives and the source signals and their derivatives is established, and the first‐order Taylor expansion was used to approximate the delay mixing model, which realized the separation of the mixed signals without increasing the number of observation signals 37 . By deducing the order of Taylor extended approximate delay mixing model from first‐order to higher‐order, the separation accuracy of the algorithm is improved 38 …”

“…37 By deducing the order of Taylor extended approximate delay mixing model from first-order to higher-order, the separation accuracy of the algorithm is improved. 38 Although the delay mixing model can be converted into an extended dimensional instantaneous mixing model by Taylor expansion, the above work does not consider its application in multi-satellite MIMO communication systems. In multi-satellite MIMO communication systems, the relative positions of satellites and earth stations, the frequency points where BSS is performed, and the data transmission rate of single user all have an impact on the separation performance.…”