We consider the scenario where each sensor in a sensor network observes an instantaneous linear mixture of multiple sources in a sensing field. A portion of sensors transmit their observations to a fusion center simultaneously, through channels with different gains. Due to the bandwidth constraint of links, the sensors' observations are quantized before transmission. A multiple-access interference (MAI) model is therefore adopted to measure the quality of the links under two cases. The fusion center uses a fast independent component analysis (Fast ICA) algorithm with pre-whitening to extract the sources, based on the received data from the transmitting sensors. The performance of source extraction is evaluated by numerical simulations. The results show that the second case is better regarding the impact of MAI on the performance.