Maximum average entropy-based quantization of local observations for distributed detection

In a wireless sensor network, multilevel quantization is necessary in order to find a compromise between the smallest possible power consumption of the sensors and the detection performance at the fusion center (FC). The general methodology is using distance measures such as J-divergence and Bhattacharyya distance in this quantization. This work proposes a different approach which is based on maximizing the average output entropy of the sensors under both hypotheses and utilizes it in a Neyman-Pearson criterion based distributed detection scheme in order to detect a point source. The receiver operating characteristics of the proposed maximum average entropy (MAE) method in quantizing sensor outputs was obtained for multilevel quantization both when the sensor outputs are available error-free at the FC and when non-coherent M-ary frequency shift keying communication is used for transmitting MAE based multilevel quantized sensor outputs over a Rayleigh fading channel. The simulation studies show the success of the MAE both in the cases of isolated error-free fusion and in the case where the effect of the wireless channel is incorporated. As expected the performance gets better as the level of quantization increases and with six-level quantization it approaches the performance of non-quantized data transmission.