A novel multichannel Doppler backscattering system has been designed and tested for application on the DIII-D [J. L. Luxon, Fusion Sci. Technol. 48, 828 (2005)] and National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] fusion plasma devices. Doppler backscattering measures localized intermediate wavenumber (k(perpendicular)rho(i) approximately 1-4,k(perpendicular) approximately 2-15 cm(-1)) density fluctuations and the propagation velocity of turbulent structures. Microwave radiation is launched at a frequency that approaches a cutoff layer in the plasma and at an angle that is oblique to the cutoff layer. Bragg backscattering occurs near the cutoff layer for fluctuations with k(perpendicular) approximately -2k(i), where k(i) is the incident probe wave vector at the scattering location. The turbulence propagation velocity can be determined from the Doppler shift in the return signal together with knowledge of the scattering wavenumber. Ray tracing simulations are used to determine k(perpendicular) and the scattering location. Frequency modulation of a voltage-controlled solid state microwave source followed by frequency multiplication is used to create an array of finely spaced (Delta f=350 MHz) frequencies spanning 1.4 GHz. The center of the array bandwidth is tunable within the range of approximately 53-78 GHz. This article details the system design, laboratory tests, and presents initial data from DIII-D plasmas.