Page 150 - Phase-Locked Loops Design, Simulation, and Applications

PLL PERFORMANCE IN THE PRESENCE OF NOISE Ronald E. Best 94
only the fundamental is transmitted. The received signal is therefore a sine wave. For an
arbitrary sequence of bits, the waveform gets more complex of course, but the transitions
still look like “sine waves,” and the received signal must be considered “analog.”
In every communication link, the transmitted signal picks up noise. Noise can be
generated in every amplifier and in repeaters, but it also can be created by crosstalk from
other channels, from atmospheric noise and many other sources. However it is generated,
all that noise is added algebraically to the (analog) data signal. This is sketched by Fig.
4.1 for the trivial case where the data signal is a bit stream of the form 10101010 …
Many types of additive noise exist. The most common is called AWGN (added white
Gaussian noise). The term “Gaussian” characterizes the amplitude distribution of the
signal, saying that the probability density function of the noise amplitude is normally
distributed (a Gauss function). The term “white” refers to the spectrum of noise and
says that within the so-called noise bandwidth of the channel, every frequency interval df
contains the same noise power dP —meaning dP /df is constant. The noise
n n

Figure 4.1 Added noise to information signal. (a) Shows a very simple signal (a
sequence of binary 101010 …). (b) A random noise signal. (c) The sum of
both.