# DFT-s-OFDM

DFT-s-OFDM stands for Discrete Fourier Transform spread Orthogonal Frequency Division Multiplexing. It's a modulation and multiplexing technique used primarily in wireless communication systems like the IEEE 802.16 WiMAX standard.

Let's break down DFT-s-OFDM into its constituent parts:

**OFDM (Orthogonal Frequency Division Multiplexing)**:- OFDM is a modulation technique that divides a high-rate data stream into multiple parallel lower-rate streams, each transmitted over its own subcarrier.
- The advantage of OFDM is its ability to mitigate the effects of multipath propagation and frequency-selective fading. This is achieved because the symbols transmitted on different subcarriers experience different frequency-selective fading characteristics. Hence, while some subcarriers might suffer from fading, others might not, thus improving the overall system performance.
- In OFDM, subcarriers are orthogonal to each other, meaning that they do not interfere with one another. This orthogonality is maintained through the use of the Inverse Fast Fourier Transform (IFFT) at the transmitter and the Fast Fourier Transform (FFT) at the receiver.

**DFT-s (Discrete Fourier Transform spread)**:- DFT-s-OFDM incorporates the concept of spreading using the Discrete Fourier Transform (DFT). This spreading is used to achieve a few goals:
- It helps in reducing the peak-to-average power ratio (PAPR) of the transmitted signal. OFDM signals can suffer from high PAPR, which can lead to nonlinear distortions in the transmitter's power amplifier. By spreading the signal using DFT, the peaks of the signal are reduced, thus making it more amplifier-friendly.
- DFT spreading also aids in reducing the sensitivity of the system to frequency and time synchronization errors.

- Mathematically, the spreading can be represented as:

�[�]=����(�[�]×�[�])*x*[*n*]=*IDFT*(*X*[*k*]×*S*[*k*])

where:

�[�]*x*[*n*] is the time-domain signal.

�[�]*X*[*k*] is the original OFDM symbol in the frequency domain.

�[�]*S*[*k*] is a spreading sequence.

- DFT-s-OFDM incorporates the concept of spreading using the Discrete Fourier Transform (DFT). This spreading is used to achieve a few goals:
**Key Aspects**:**PAPR Reduction**: By spreading the signal using DFT, the peak amplitudes of the OFDM symbols are reduced, leading to a decrease in the PAPR. This reduction is beneficial for the power amplifier efficiency and linearity.**Improved Synchronization**: The DFT spreading sequence can provide better performance against synchronization errors, both in frequency and time domains.**Flexibility**: The use of DFT spreading provides flexibility in designing the spreading sequences, allowing for specific performance enhancements based on system requirements.

**Implementation**:- In practical systems, the DFT-s-OFDM modulation scheme is implemented by first generating the OFDM symbols in the frequency domain. These symbols are then spread using a spreading sequence obtained from the DFT operation. At the receiver, the process is reversed by applying the Inverse DFT to despread the signal and recover the original OFDM symbols for demodulation.

DFT-s-OFDM is a modulation scheme that combines the advantages of OFDM with the benefits of DFT spreading. It helps in reducing PAPR, improving synchronization, and offering flexibility in system design for enhanced performance in wireless communication systems.