We introduce a new optical frequency domain reflectometry (OFDR) system and processing method that utilize negative beat frequencies for the first time. The new approach enables efficient use of the available system bandwidth and facilitates distributed sensing with the maximum allowable update rate for a given fiber length. This is achieved by using a coherent optical-communications-type receiver that detects both the in-phase (I) and quadrature (Q) components of the backscatter field. The I and Q components are digitally combined to produce a complex backscatter signal whose Fourier transform is not necessarily symmetric. Judicious processing of the complex backscatter signal maps the reflection profile of one half of the sensing fiber to positive beat-frequencies and the profile of the other half to negative beat-frequencies. The new approach was tested via comprehensive computer simulations and experiment.