In Section 4.11 we studied the eye diagram of a quaternary (M 4) PAM baseband transmission system under both noisy and band-limited conditions. In that experiment, the channel was assumed linear. In a strictly linear system with truly random data, all the eye openings would be identical. In practice, however, it is often possible to discern asymmetries in the eye pattern, which are caused by nonlinearities in the communication channel. In this experiment, we study the effect of a nonlinear channel on the openings of an eye pattern. Specifically, we repeat the computer experiment pertaining to the noiseless eye pattern of Figure a for M = 4, but this time assume that the channel is nonlinear with the following input-output relation: x (t) s (t) + as2 (t), where s (t) is the channel input and x (t) is the channel output, and a is a constant.

(i). Do the experiment for a = 0, 0.05, 0.1, 0.2.

(ii). Hence., explain how varying a affects the shape of the eye pattern.