The objective of this project is on the development of signal processing tasks on-board the satellite payload of a Geostationary (GEO) or Medium Earth Orbit (MEO) satellite. In the considered scenario, digitized wideband signals are channelized and routed through the satellite payload. However, Nyquist rate processing for wideband signals is difficult due to their bandwidth and also due to the possible requirement on process multiple wideband signals simultaneously. Towards envisaging a feasible on-board digital processing, the use of sparse processing techniques and array processing techniques need to be investigated. Motivated by this, the project focusses on the development of novel sparse techniques to mitigate inter and intra-system interferences and their implementation on-board the satellite. Exploiting sparsity for the selection of lower number of feeds and applying sparse array processing techniques will provide power and cost-efficient precoding, thus enabling flexibility on-board the satellite. A sparse synthetic aperture array formulation for the interference signals will be formulated in order to apply array signal processing techniques to detect and recover the positions of the interferers on-board the satellite. While on-board processing is being actively considered by industry, it provides significant research challenges while incorporating key techniques.