Optimization based on network size and bandwidth: Consider a variation of the second method described in Exercise 2, wherein each sensor sends only a fraction f of measurements to the fusion center....

Optimization based on network size and bandwidth: Consider a variation of the second method described in Exercise 2, wherein each sensor sends only a fraction f of measurements to the fusion center. (a) Derive expressions for the detection probability and total network traffic T (fnM) when a fraction f of measurements are sent from each sensor. (b) Derive conditions for optimal f and N for the criterion function wpN + wb T (fnM) + wp pD (fnN), which is a weighted sum of physical parameter N, network traffic parameter T (.), and performance parameter pD (.).