Long processing time and, in certain cases, restricted ability to detect moving targets are seen as the shortcomings of the moving target detection by focusing technique. The detection ability reduces significantly when Normalized Relative Speeds (NRS) with respect to the speed of the platform are approximated or equal to one. This paper propose solutions for such problems. Local Backprojection (LBP) replaces Global Backprojection (GBP) in the focusing approach of the detection method to save the processing time and a space-time processing technique, namely Displaced Phase Center Antenna (DPCA) is used to pre-process multi-channel SAR data to strengthen detection ability. Simulation results demonstrates a fast- and reliable detection achieved with these proposals.