Mission Design for the CubeSat OUFTI-1

CHAPTER 10to reach the receiver passing through the free space. The losses on this way arecalled space loss:L s [W ] =Sλ( )RIP [W ]22EIRP [W ] = 4π λ4πSd = =2 4πd( ) 2 c(10.4)4πdfwhere RIP is the Received Isotropic Power, λ the wavelength and S thepower per unit area at distance d.Passing in decibel, we have:L s [dBW ] = 20log (c) − 20log (4π) − 20log (d) − 20log (f) == 147.55 − 20log (d) − 20log (f)(10.5)The space loss contains the hypothesis of free-space propagation: in reality,the signal pass through the atmosphere and we would have therefore to take intoaccount the attenuation due to atmosphere and rain. As these attenuations areimportant only for high frequency wave (mainly in the SHF band and higher),they are practically are null in our case.Once the signal is received by the receiving antenna, its gain G R should beadded.In digital communications, the received energy-per-bit E b is equal to the receivedpower times the bit duration:E b = P R − 10log(R) (10.6)where P R = RIP + G R is the received power and R the data rate.The noise spectral density, N 0 , can be expressed as:N 0 = 10log(k) + 10log(T s) (10.7)where k = 1.38 · 10 −23 is the Boltzmann’s constant and T s the system noisetemperature.Hence, the total received noise is:where B is the bandwidth.N = N 0 + 10log(B) (10.8)Using the above mentioned equations, we can obtain the parameters we werelooking for:• the radio of received energy-per-bit to noise-densityE bN 0= EIRP + L s + G R − 10log(k) − 10log(T s) − 10log(R) (10.9)Galli Stefania 100 University of Liège