Attacks on Sensor Network Parameter Estimation With Quantization: Performance and Asymptotically Optimum Processing

Parameter Estimation via Unlabeled Sensing Using Distributed Sensors

“…It can be shown that with σ 2 w being zero, equation (13) holds, which is consistent with the results obtained in [9].…”

“…Remark 3 It seems that K does not have effect on (13). This is not true because the variance of y (i) is proportional to 1/K.…”

“…Suppose that the channels between sensors and fusion center may be not error free [12] or sensors suffer from attack [13,14]. For example, if the channel coefficient between sensors and fusion center is Rayleigh distributed, and hard decision is adopted at the fusion center, then the channel can be described by a probability transition matrix [12].…”

“…(6), let y (i) and h (i) be the ascending order of y and h, i.e., y (0) ≤ y (1) ≤ · · · ≤ y (N −1) and h (0) ≤ h (1) ≤ · · · ≤ h (N −1) . If for any y (i) ≤ y (j) and h (i) ≤ h (j) , equation (13) …”

“…Remark 2 Note that if both y (i) + y (j) ≥ 2h (i) θ ≥ 0 and θ ≥ 0 are satisfied, or if both y (i) + y (j) ≤ 2h (j) θ ≤ 0 and θ ≤ 0 are satisfied, equation (13) holds, which implies that sorting according to h or −h is optimal.…”