e homodyne structure seems preferable. For this reason, up to now we will assume Aw = 0. In this case, the electronics front end reduces to a baseband filter fixing the electrical bandwidth Be 22 Rs of the receiver, Rs being the symbol rate, not differently from the case of a direct detection receiver. The photocurrents in the homodyne receiver have the following expressions: Telecommunication Networks (9.34) where R is the photodiodes responsivity, which is assumed to be the same for all the photodiodes PL is the LO power, which can be written as PL(t) = PLO [1 + r(t)] if the LO RIN r(t) has to be considered (see Chapter 5) nj(t) is the shot noise component coming from the jth receiver p;(t) is the thermal noise component coming from the jth receiver If the coherent receiver has to work with the best performances, the LO power has to be much higher both of the incoming signal power and of the so-called "thermal" power. The thermal power is defined as the optical power that would cause a photocurrent with a power equal to the thermal noise power. The second condition is generally easily realized, while the first could impose limita- tions on the amplification of the receiver preamplifier. In these conditions, Equation 9.34 can be simplified as =2RPL[Sj(t)+nj(t)]+nj(t) (9.35) Moreover, due to the fact that a complex electronic processing has to be performed after fil- tering, we will assume that all electronics functions will be performed via digital circuits. This requires a sampling of the baseband signal before filtering at a sufficiently high sam- pling rate. On the ground of the experience in electronic compensation, we will assume that five samples per pulse are sufficient to allow effective electronic processing and we will assume a sampling rate R 22 5Rs. This means that in order to work at 100 Gbit/s with a 64-4QAM, the sampling rate has to be about 83 GHz, a very challenging speed, but probably within the reach of very high speed complementary metal-oxide-semiconductor (C-MOS) 22nm application-specific i