Relative robustness of detection to detector threshold by joint optimization in WSN over fading MAC and with non-identical sensor SNRs

A fading Multiple Access Channel (MAC) between distributed sensors and multiple antennas yields incoherent fusion in Wireless Sensor Networks. With limited on-board energy, an overall sensor power constraint is not only reasonable and desirable but indeed, inevitable. With unknown/varying channel gain envelope, Uniform Power Allocation (UPA) to sensors is suboptimal. The problem is compounded if, as in this paper, we permit non-identical sensor observation Signal-to-Noise Ratios (SNR). With Optimal Power Allocation (OPA) that jointly accounts for sensor SNRs and fading MAC, we bring out the dependence of detection probability and false alarm rate on detector threshold. We demonstrate through simulations that for enhanced performance, compared to UPA, OPA is more robust to detector threshold. We show that the additional computational effort with OPA over UPA is justified not merely by a relative sensor on-board energy saving and longevity but also by a commensurate robust performance.