For energy management in wireless sensor networks, only the sensors with most informative measurements are activated to operate. How to select sensors that make good tradeoff between performance and energy consumption is what many researchers are focusing on. Existing solutions assume analog data model, i.e., the data from sensors collected by a center node, called fusion center, are analog measurements. In practical application, due to limitations of energy of sensors and bandwidth of wireless channel, original measurements are usually compressed before being transmitted to the fusion center. In addition, transmitted signals are usually distorted by wireless channel effects, therefore it is possible that the received data are corrupted with errors. In this thesis, we consider two compressive techniques: one-bit quantization and multi-bit quantization. In one-bit quantization, an indicator message is generated in a sensor according to whether the original measurement is larger than a threshold or not. In multi-bit quantization, the original measurements are quantized to multiple bits and only the most significant bits are reserved. The indicators or the most significant bits are then transmitted through realistic wireless channel to the fusion center for it to process. By these ways, the transmitted signals are digital, and they may flip into opposite values by the effects of wireless channels. For one-bit quantization case, we develop a sensor selection approach, based on convex programming. For multi-bit quantization, we extend the sensor selection to bit allocation and propose a novel algorithm to determine the number of bits to transmit for each sensors, which is also based on convex programming. In both cases we consider the effects of wireless channels, which are characterized as bit error rate. Particularly, for the multi-bit quantization, numerical results show that the bit allocation can further reduce the cost that we defined compared with existing solutions where transmitted data are assumed to be analog.