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We minimize average transmit power with finite-rate feedback for coherent communications in a wireless sensor network (WSN), where sensors communicate with a fusion center using adaptive modulation and coding over a wireless fading channel. By viewing the coherent WSN setup as a distributed space-time multiple-input single-output (MISO) system, we present optimal distributed beamforming and resource allocation strategies when the full (F-) channel state information at the transmitters (CSIT) is available through a feedback channel. We also develop optimal adaptive transmission policies and design optimal quantizers for the finite-rate feedback case where the sensors only have quantized (Q-) CSIT, or, each sensor has F-CSIT of its own link with the FC but only Q-CSIT of other sensors. Numerical results confirm that our novel finite-rate feedback-based strategies achieve near-optimal power savings based on even a small number of feedback bits.