This paper addresses the design of a custom digital signal processing receiver and companion frame format for a 56 GBaud coherent optical Dual-Polarization Quadrature Phase- Shift Keying GEO feeder link. The selected algorithms combine standard practice from both coherent optical fiber and RF satellite communications. Robust blind algorithms are used in the first stages, followed by data-aided algorithms for subsequent fine carrier and phase recovery. A simplified blind equalizer architecture is proposed for fast and robust polarization demul- tiplexing, based on a modified constant-modulus algorithm. Our simulations demonstrate the possibility to establish links at an electrical SNR as low as -6 dB, in the presence of realistic values of system impairments, using less than 5% signaling overhead.