Ice shelves fringe much of the Antarctic continent, and, despite being up to 2 km thick, are vulnerable to climate change. Owing to their role in helping to control the ice sheet contribution to sea level change there is great interest in measuring the rate at which they are melting into the ocean. This study describes the development and deployment of an ice-penetrating phase-sensitive FMCW radar, sufficiently robust and with sufficiently low-power consumption to be run through the Antarctic winter as a standalone instrument, yet with the stability and mm-precision needed to detect the very slow changes in ice shelf thickness in this exceptionally demanding environment. A number of elegant processing techniques are described to achieve reliable, high-precision performance and results presented on field data obtained from the Larsen-C ice shelf, Antarctica.