## Notion of Orthogonality in LTE

Notion of Orthogonality in LTE, sub-carriers are separated in the frequency domain to avoid interference between the sub-channels.

In FDM, the sub-carriers are separated in the frequency domain to avoid interference between the sub-channels
It results in a loss of spectrum efficiency because the frequency guard band can not be used to send data.
The OFDM allows one to remove the frequency guard band.
Benefit: There are more sub-carriers, so more symbols are sent at the same time. The orthogonality brings a better spectrum efficiency.
In OFDM, the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each other, meaning that cross-talk between the sub-channels is eliminated and inter-carrier guard bands are not required. This greatly simplifies the design of both the transmitterand the receiver; unlike conventional FDM a separate filter for each sub-channel is not required.

The orthogonality requires that the sub-carrier spacing is Vf = k/(TU) Hertz, where TU seconds is the useful symbol duration (the receiver side window size), and k is a positive integer, typically equal to 1. Therefore, with N sub-carriers, the total passband bandwidth will be B ? N(delta)Vf (Hz).

That leads to the representation of a sub-carrier.
The duration of the symbol depends on the width of the sub-carrier.
•  It is inversely proportional. The shorter the symbol, the wider the sub-carrier and vice-versa.
•  The frequency center of the sub-carrier is linked to the frequency of the carrier.
• The inter-channel (or inter sub-carrier) interferences are cancelled because they are located in a such way that when there is the peak for a given sub-carrier, the adjacent subcarriers are null.
OFDM allows high density of carriers, without generating Inter-Channel Interference (ICI).

BASIC IDEA : The channel bandwidth is divided into multiple subchannels to reduce ISI and frequency-selective fading.
A single wideband signal is transformed into multiple narrow band signals transmitted on orthogonal subcarriers
• One single stream at high rate
• Each symbol occupies the whole bandwidth
• Very short symbol duration to ensure high rate