  The high-k ($7 \lesssim k_{\bot} \rho_i \lesssim 11$) wavenumber spectrum of
density fluctuations has been measured for the first time in MAST [B. Lloyd et
al, Nucl. Fusion 43, 1665 (2003)]. This was accomplished with the first
implementation of Doppler backscattering (DBS) for core measurements in a
spherical tokamak. DBS has become a well-established and versatile diagnostic
technique for the measurement of intermediate-k ($k_{\bot} \rho_i \sim 1$, and
higher) density fluctuations and flows in magnetically confined fusion
experiments. A novel implementation with 2D steering was necessary to enable
DBS measurements in MAST, where the large magnetic field pitch angle presents a
challenge. We report on the scattering considerations and ray tracing
calculations used to optimize the design and present data demonstrating
measurement capabilities. Initial results confirm the applicability of the
design and implementation approaches, showing the strong dependence of
scattering alignment on toroidal launch angle. We also present comparisons of
DBS plasma velocity measurements with charge exchange recombination and beam
emission spectroscopy measurements, which show reasonable agreement over most
of the minor radius, but imply large poloidal flows approaching the magnetic
axis in a discharge with an internal transport barrier. The 2D steering is
shown to enable high-k measurements with DBS, at $k_{\bot}>20\
\mathrm{cm}^{-1}$ ($k_{\bot} \rho_i>10$) for launch frequencies less than 75
GHz; this capability is used to measure the wavenumber spectrum of turbulence
and we find $|n(k_{\bot})|^2 \propto k_{\bot}^{- 4.7 \pm 0.2}$ for $k_{\bot}
\rho_i \approx 7-11$, which is similar to the expectation for the turbulent
kinetic cascade of $|n(k_{\bot})|^2 \propto k_{\bot}^{- 13/3}$.
