orthogonal Archives

Understanding an OFDM transmission

Let us try to understand simulation of a typical Orthogonal Frequency Division Multiplexing (OFDM) transmission defined per IEEE 802.11a specification.

Orthogonal pulses
In a previous post (here ), we have understood that the minimum frequency separation for two sinusoidals with arbitrary phases to be orthogonal is $\frac{1}{T}$ , where $T$ is the symbol period.

In Orthogonal Frequency Division Multiplexing, multiple sinusoidals with frequency separation $\frac{1}{T}$ is used. The sinusoidals used in OFDM can be defined as (Refer Sec6.4.2 in [DIG-COMM-BARRY-LEE-MESSERSCHMITT]:

$g_k(t) = \frac{1}{\sqrt{T}}e^{\frac{j2\pi kt}{T}}w(t)$ , where

$k=0,1,\ldots,K-1$ correspond to the frequency of the sinusoidal and

$w(t)=u(t)-u(t-T)$ is a rectangular window over $[0\ T)$ .

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Minimum frequency spacing for having orthogonal sinusoidals

In this post, the objective is to figure out the minimum separation between two sinusoidals having frequencies $f_1$ , $f_2$ of duration $T$ each to be orthogonal. Let the phase difference between the sinusoidals is $\phi$ where $\phi$ can take any value from $0$ to $2\pi$ (Refer Example 4.3 [DIG-COMM-SKLAR]).

For the two sinuosidals to be orthogonal,

$\int_0^Tcos(2\pi f_1 t+\phi)cos(2 \pi f_2t)dt = 0$

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