Resource Allocation in OFDM Based Wireless Relay Networks ...

1.3 Basics of the Optimization Theory
to its much higher processing efficiency. Finally, CP is inserted before actual data
transmission. The receiver section performs the reverse operation of the transmitter.
It removes CP and then transforms the signal back to frequency domain using fast
Fourier transform (FFT). The block diagram of a typical OFDM transceiver is shown
in Fig. 1.3.
1.3 Basics of the Optimization Theory
The design of wireless systems often involve the optimization of an objective subject
to certain resource constraints. An optimization problem with arbitrary equality and
inequality constraint can be written as [13]
min
x
f o (x) (1.1)
subject to f i (x) ≤ 0, 1 ≤ i ≤ m,
h i (x) = 0, 1 ≤ i ≤ p,
where x is the optimization variable, f o is the objective function, f 1 , ......, f m are
the m inequality constraint functions, and h 1 , ......, h p are the p equality constraint
functions.
The optimization problems could be grouped into different classes depending
on the nature of the objective function and the constraint functions. The problem
is called linear programming if the objective and all constraint functions are linear.
The linear programming problems can be solved effectively using the well known
Dantzig’s simplex method, the criss-cross algorithm, and the recently developed
interior point methods [13]. The problem is called non-linear optimization if the
objective and/or constraint functions are non-linear and non-convex [14].
The convex optimization theory gives an easy solution if the problem is,
or can be transformed into, convex problem.
optimization problem if the objective function f o
A problem is called a convex
and the inequality constraint
functions f 1 , ......, f m are convex and the equality constraint functions h 1 , ......, h m are
affine. Convex optimization problems can be optimally solved either in closed form
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