 noise, O2 (Steele, Walker, & Walker, 1991). Receiver manufacturers optimize the value of Mapd to achieve a balance between the sensitivity enhancement that an APD can offer and the additional noise that results from the impact ionization process, on which its operation depends. Inspection of equation 6.21 reveals that, when there is a good extinction ratio, it is pos- sible to achieve a high Q value by minimizing all of the noise sources (so that O1 and are low) and/o by increasing the power of the 1s (so that I 1 is high). Another way of saying this is that, once we have done everything to minimize the noise, the only way of achieving acceptably high Q values (and hence lower BERs) is to augment the incident optical power. Consequently, even when the transmitter offers a high extinction ratio, all of the noise sources in equation 6.24 impose a power penalty, Equation 6.24 can be used in various ways to substitute into equation 6.21 and therefore to deduce the BER. In an unamplified system the noise of the 0 bits is given by of oz owing to the fact that there is neither RIN nor shot noise at the instants when the transmitter is turned off. However, this does not apply for the 1s, SO we must use . The noise on the 1s and 0s can be visualized in terms of Figure 6.14, in which the two Gaus- sian curves have different widths. When we use equation 6.21, in which the transmitter has a high extinction ratio, Q = R Pinc-1/(01+00). It follows that the 1s must have a higher incident power, Pinc-1 to achieve the same BER in the presence of RIN than they would require in an ideal RIN-free transmit- ter. Therefore, we can specify a RIN penalty, Srin. Fortunately, the RIN can be a relatively small contributor to the BER in many unamplified systems with high-quality transmitters. Optical Preamplifiers Optical preamplifiers, as shown schematically in Part C of Figure 6.5, are key elements in high-capacity and long-span optical communications systems. Sometimes the amplifier, such as an EDFA, is constructed as a constituent elem