Optimal power allocation for M-ary distributed detection in the presence of channel uncertainty

We consider a wireless sensor network (WSN), consisting of several sensors and a fusion center (FC), which is tasked with detecting M known signals in Gaussian noise. Sensors make M-ary decisions and transmit their digitally modulated decisions over orthogonal fading channels to the FC. Considering two coherent and non-coherent systems, we study how to distribute the total transmit power among the sensors such that J-divergence at the FC is maximized, subject to cumulative and individual transmit power constraints. To fairly compare the two systems, we consider the cost of channel estimation for coherent systems via introducing trade off between pilot and data transmission. We develop power allocation schemes and provide the optimal fusion rule for both systems. Our numerical results show that, the coherent system does not necessarily outperform the non-coherent system, when the cost of channel estimation (required transmit power for pilot) is considered. In particular, when the total transmit power is low (and the effect of channel estimation is more severe) the non-coherent system outperforms the coherent one. The proposed power allocation schemes for the coherent system allow us to reduce the total transmit power consumption up to 80%, compared with uniform power allocation.