In this work, we propose a new positron annihilation lifetime spectrum measuring method for pulsed positrons. The spatially arranged positron burst detection system is based on a state-of-the-art calcium-doped LYSO crystal and silicon photomultiplier array, with readout by a multichannel fast waveform digitizing DRS4 chip; this system simultaneously provides high detection efficiency and decent timing resolution. The positron burst generation signal serves as the starting trigger and the timing signal of all the detector channels is the stopping signal, so that the time spread distribution is the lifetime spectrum. The current system has 2048-channel modularized crystals coupled to 2048-channel 3 x 3 m(2) silicon photomultipliers. All analog signals from the detectors are digitized separately before implementing digital constant fraction discrimination by a field-programmable gate array. The performance of the single-channel detector was investigated and optimized by improving the silicon photomultiplier readout electronics and the light collection of the scintillator. Preliminary results showed that the best coincidence timing resolution by two identical, 5 mm long, single LYSO detectors was 84 ps and that the measurement was double the 511 keV coincidence of a Na-22 source.