Consider a hexagonal cellular system where base stations have been mounted in the middle of the cells. Each base station uses an omni-directional antenna and an equivalent isotropically radiated transmit power Pt. We have a total of 90 channels available and are aiming at 30 channels/cell. The required SIR for good signal quality is γt = 8 dB and the propagation path loss exponent is α = 4. The transmitted power at the base station has been adjusted such that the SNR at the border of the cell is 10 dB. 

a) Considering the downlink, compute the outage probability of this cellular system. 

b) Determine the required extra power margin needed that ensures full coverage (zero outage probability)