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GNSS (Global Navigation Satellite System) signal reception in indoor environments is susceptible to spatial fading and signal attenuation. An antenna array utilizing spatial diversity can be implemented to improve detection performance which reduces the required fading margin. However for the typical handheld GNSS receiver, constrained to a single antenna, spatial processing gain is possible only if the antenna is physically translated as the signal is being captured by the receiver. This is equivalent to realizing a spatially distributed synthetic array (SA) antenna. An investigation of the indoor detection performance of a GNSS receiver based on SA processing with optimized combining algorithms is made and compared with the detection performance of the equivalent static antenna. The processing gain achievable through spatial combining of a synthetic antenna is considered from a general theoretical perspective and validated with an extensive set of experimental measurements satisfying statistical significance criteria. The performance of the proposed method is theoretically analyzed in terms of the probability of false alarm (PFA) and probability of detection (PD). It is shown that the significant processing gain resulting from randomly moving the antenna relative to a stationary position can be large, exceeding 10 dB in practically encountered usage cases for a GNSS handset.