Wireless Network Design: Optimization Models and Solution ...

2 Introduction to Wireless Communications 17
The bandwidth of the signal is defined as the range of positive frequencies that
are transmitted. It can easily be seen that the bandwidth of sp(t) equals twice the
bandwidth of s(t); this process is referred to as double sideband modulation. Clearly,
this process is wasteful in bandwidth.
One way to use the bandwidth more efficiently is to use a complex signal
constellation u(t) instead of a real s(t). Thus the transmitted passband signal is
now u(t)e− j2π fct + u∗ (t)e j2π fct where u∗ (t) is the complex conjugate of u(t).
Examples of such complex constellation are the quadrature amplitude modulation
(QAM) signals given in Figure 2.5. The error performance of QAM signals can
be derived in a manner similar to that for PAM signals and is given by [34]
�� �
3log2 (M)SNRbit
Pe ≤ 4Q
. (2.7)
M − 1
It turns out that for high SNR and large values of M this upper bound is quite tight.
The probability of error versus SNR for QAM is given in Figure 2.4.
Fig. 2.4 Probability of symbol error with specific PAM and QAM schemes.