Wireless Network Design: Optimization Models and Solution ...

14 Dinesh Rajan
ping (FH) CDMA, and orthogonal frequency division multiplexing (OFDM), are
covered in Sections 2.5.2.1, 2.5.2.2, and 2.5.2.3, respectively. Finally, we discuss
several advanced wireless transceiver techniques in Section 2.6.
Due to the wide range of topics involved in the design of wireless systems, in
this chapter, we discuss only the key results and the underlying intuition. Detailed
mathematical proofs and derivations of the main results are omitted due to space
constraints; relevant references are provided as appropriate. To stay in focus we
only consider the transmission of digital data. As and when possible, we provide
performance metrics that can be easily used by network designers to ensure that
desired quality of service guarantees are provided by their designs.
2.2 Digital Modulation in Single User Point-to-point
Communication
Consider the transmission of digital data at rate R bits per second. Let Ts denote the
symbol period in which M bits are transmitted. Then, R = M/Ts. The information
sequence to be transmitted is denoted by a sequence of real symbols {In}. This
sequence could be the output of the channel coding block shown in Figure 2.2. A
traditional modulation scheme consists of transmitting one of 2 M different signals
every Ts seconds. In orthogonal modulation the signal s(t) is given as
s(t) = ∑ n
Inqn(t), (2.1)
where qn(t) form a set of orthonormal pulses, i.e. � qi(t)q j(t)dt = δi− j, where δm is
the Kronecker delta function which is defined as follows: δ0 = 1, and δm = 0,m �= 0.
In many traditional modulation schemes these orthonormal waveforms are generated
as time-shifts of a basic pulse p(t). Examples of p(t) include the raised cosine
and Gaussian pulse shapes. For example, in pulse-amplitude modulation (PAM), the
transmit signal s(t) equals
s(t) = ∑ n
Inp(t − nTs). (2.2)
In (2.2) for a 2-PAM system, In ∈ {−A,+A}, where the amplitude A is selected to
meet average and peak power constraints at the transmitter. Similarly, for a 4-PAM
system In ∈ {−3A,−A,+A,+3A}.
Consider the transmission of data through an ideal additive white Gaussian
noise (AWGN) channel, in which the received signal, r(t) is given by,
r(t) = s(t) + n(t), (2.3)
where input signal s(t) has an average power constraint P and the noise n(t) has a
constant power spectral density of N0/2. The additive noise channel is one of the
simplest and most widely analyzed channel. In practical systems, the noise at the