Orthogonal frequency-division multiplexing (OFDM) is a powerful digital modulation technique used in modern wireless communication systems. It divides high-rate data streams into multiple low-rate substreams, each modulated onto separate orthogonal subcarriers, enabling efficient transmission over frequency-selective channels.

OFDM offers high spectral efficiency, robustness against multipath fading, and simplified channel equalization. However, it faces challenges like high peak-to-average power ratio and sensitivity to carrier frequency offset. OFDM finds applications in Wi-Fi, LTE, digital TV broadcasting, and powerline communication.

Overview of OFDM

• Orthogonal frequency-division multiplexing (OFDM) is a digital multi-carrier modulation scheme that is widely used in modern wireless communication systems and is an essential part of the Advanced Signal Processing course
• OFDM divides a high-rate data stream into multiple parallel low-rate substreams, each modulated onto a separate orthogonal subcarrier, enabling efficient transmission over frequency-selective channels

Key principles

Orthogonality

• Orthogonality refers to the mathematical property where the inner product of two signals is zero, allowing multiple signals to be transmitted simultaneously without interfering with each other
• In OFDM, subcarriers are chosen to be orthogonal to each other, ensuring that they do not interfere with one another even though their spectra overlap
  • This is achieved by selecting subcarrier frequencies that are integer multiples of the inverse of the symbol duration

Frequency-division multiplexing

• Frequency-division multiplexing (FDM) is a technique where the available bandwidth is divided into non-overlapping frequency subchannels, each carrying a separate signal
• OFDM extends the concept of FDM by allowing the subcarriers to overlap in the frequency domain while maintaining orthogonality
  • This results in a more efficient use of the available spectrum compared to traditional FDM systems

OFDM transmitter

Serial-to-parallel conversion

• The high-rate serial data stream is first converted into multiple parallel low-rate substreams
  • This process reduces the symbol rate on each subcarrier, making the system more resistant to intersymbol interference (ISI) caused by multipath propagation

Modulation using IFFT

• The parallel substreams are modulated onto orthogonal subcarriers using an inverse fast Fourier transform (IFFT) operation
  • The IFFT efficiently generates the time-domain OFDM signal by mapping the data symbols onto the orthogonal subcarriers in the frequency domain

Cyclic prefix insertion

• To combat ISI and maintain orthogonality between subcarriers, a cyclic prefix (CP) is added to each OFDM symbol
  • The CP is a copy of the last portion of the OFDM symbol appended to the beginning of the symbol
• The CP acts as a guard interval, ensuring that the delayed copies of the OFDM symbol due to multipath propagation do not interfere with the next symbol

Parallel-to-serial conversion

• After the CP insertion, the parallel OFDM symbols are converted back into a serial stream for transmission over the channel
  • This process generates the final time-domain OFDM signal to be transmitted over the wireless medium

OFDM receiver

Serial-to-parallel conversion

• The received serial OFDM signal is first converted into parallel streams, separating the OFDM symbols for further processing

Cyclic prefix removal

• The CP is removed from each received OFDM symbol, eliminating the effects of ISI and ensuring that the subcarriers remain orthogonal
  • The removal of the CP is crucial for maintaining the orthogonality between subcarriers and enabling simple equalization in the frequency domain

Demodulation using FFT

• The parallel OFDM symbols are demodulated using a fast Fourier transform (FFT) operation
  • The FFT converts the time-domain OFDM signal back into the frequency domain, recovering the original data symbols transmitted on each subcarrier

Parallel-to-serial conversion

• The demodulated parallel data streams are then converted back into a high-rate serial data stream
  • This process reconstructs the original transmitted data from the received OFDM symbols

Channel estimation and equalization

• To compensate for the effects of the wireless channel, channel estimation and equalization techniques are employed
  • Pilot symbols, known to both the transmitter and receiver, are used to estimate the channel response at the receiver
• The estimated channel response is then used to equalize the received signal, mitigating the effects of channel distortion and ensuring accurate data recovery

Advantages of OFDM

High spectral efficiency

• OFDM achieves high spectral efficiency by allowing the subcarriers to overlap in the frequency domain while maintaining orthogonality
  • This results in a more efficient use of the available bandwidth compared to traditional FDM systems, where the subchannels are non-overlapping

Robustness against multipath fading

• OFDM is inherently robust against multipath fading, which is a common challenge in wireless communication systems
  • By dividing the high-rate data stream into multiple low-rate substreams, OFDM reduces the impact of ISI caused by multipath propagation
• The use of a cyclic prefix further enhances the system's resilience to multipath fading by eliminating the interference between OFDM symbols

Simplified channel equalization

• OFDM simplifies the channel equalization process by enabling equalization in the frequency domain
  • The orthogonality of subcarriers allows for simple one-tap equalization, where each subcarrier can be equalized independently
• This is in contrast to single-carrier systems, where complex time-domain equalization techniques are required to combat the effects of the wireless channel

Flexibility in resource allocation

• OFDM offers significant flexibility in terms of resource allocation and adaptive modulation
  • The system can dynamically allocate different numbers of subcarriers and modulation schemes to different users based on their channel conditions and quality of service requirements
• This adaptability enables OFDM to efficiently utilize the available resources and optimize the system performance for various scenarios

Challenges in OFDM

Peak-to-average power ratio (PAPR)

• One of the main challenges in OFDM is the high peak-to-average power ratio (PAPR) of the transmitted signal
  • The PAPR arises from the coherent addition of multiple subcarriers, which can result in large peak values in the time-domain OFDM signal
• High PAPR requires the transmitter's power amplifier to have a large linear operating range, which reduces its efficiency and increases the cost of the system
  • Various PAPR reduction techniques, such as clipping, coding, and selective mapping, are employed to mitigate this issue

Sensitivity to carrier frequency offset

• OFDM is sensitive to carrier frequency offset (CFO), which can occur due to mismatches between the transmitter and receiver oscillators or Doppler shift in mobile environments
  • CFO destroys the orthogonality between subcarriers, leading to inter-carrier interference (ICI) and degrading the system performance
• Accurate frequency synchronization techniques, such as the use of pilot symbols and feedback loops, are essential to mitigate the impact of CFO in OFDM systems

Synchronization issues

• Synchronization is crucial in OFDM systems to maintain the orthogonality between subcarriers and prevent inter-symbol interference
  • Both time and frequency synchronization are required to ensure proper operation of the OFDM system
• Timing synchronization involves identifying the start of each OFDM symbol and aligning the receiver's sampling clock accordingly
  • This is typically achieved using techniques such as correlation-based synchronization or the use of synchronization symbols
• Frequency synchronization, as mentioned earlier, is necessary to combat the effects of carrier frequency offset and maintain orthogonality between subcarriers

OFDM system design considerations

Subcarrier spacing and symbol duration

• The choice of subcarrier spacing and symbol duration is a crucial design consideration in OFDM systems
  • Subcarrier spacing determines the frequency separation between adjacent subcarriers and affects the system's robustness to CFO and Doppler spread
• Symbol duration, which is inversely related to subcarrier spacing, impacts the system's tolerance to multipath delay spread and the required CP length
  • A longer symbol duration provides better resilience to delay spread but may increase the system's sensitivity to CFO and Doppler spread

Cyclic prefix length

• The cyclic prefix length is another important design parameter in OFDM systems
  • A longer CP provides better protection against ISI and ensures the maintenance of orthogonality between subcarriers
• However, a longer CP also reduces the system's spectral efficiency, as it consumes a portion of the available bandwidth without carrying useful information
  • The CP length must be chosen to strike a balance between the system's robustness and spectral efficiency, considering the expected channel conditions and delay spread

Modulation schemes

• The choice of modulation schemes for the subcarriers in OFDM systems depends on various factors, such as the desired data rate, error performance, and channel conditions
  • Common modulation schemes used in OFDM include quadrature phase-shift keying (QPSK), quadrature amplitude modulation (QAM), and phase-shift keying (PSK)
• Higher-order modulation schemes, such as 16-QAM or 64-QAM, offer higher data rates but are more sensitive to channel impairments and require a higher signal-to-noise ratio (SNR) for reliable operation
  • Adaptive modulation techniques can be employed to dynamically adjust the modulation scheme for each subcarrier based on the channel conditions, optimizing the system performance

Pilot allocation for channel estimation

• Pilot symbols, known to both the transmitter and receiver, are essential for channel estimation in OFDM systems
  • Pilots are typically inserted in the frequency domain, occupying specific subcarriers, and are used to estimate the channel response at the receiver
• The allocation of pilot symbols involves determining the number, location, and power of the pilots within the OFDM symbol
  • A higher number of pilots improves the accuracy of channel estimation but reduces the available bandwidth for data transmission
• The pilot allocation scheme must be designed to provide a balance between channel estimation accuracy and spectral efficiency, considering the expected channel conditions and the system's requirements

Applications of OFDM

Wireless communication systems

• OFDM is widely used in various wireless communication systems, such as:
  • IEEE 802.11a/g/n/ac/ax (Wi-Fi)
  • IEEE 802.16 (WiMAX)
  • 3GPP Long Term Evolution (LTE) and 5G New Radio (NR)
• These systems leverage the advantages of OFDM, such as high spectral efficiency and robustness against multipath fading, to provide high-speed wireless data transmission

Digital television broadcasting

• OFDM is employed in digital television broadcasting standards, including:
  • Digital Video Broadcasting - Terrestrial (DVB-T)
  • Advanced Television Systems Committee (ATSC) 3.0
• OFDM enables efficient and robust transmission of high-quality video and audio content over terrestrial broadcast channels, which are often subject to multipath propagation and interference

Powerline communication

• OFDM is used in powerline communication (PLC) systems, which utilize existing electrical power lines for data transmission
  • PLC systems, such as HomePlug and G.hn, employ OFDM to combat the frequency-selective and noisy nature of powerline channels
• OFDM's robustness against multipath fading and its ability to adapt to channel conditions make it well-suited for PLC applications

Optical wireless communication

• OFDM has found applications in optical wireless communication systems, such as visible light communication (VLC) and free-space optical (FSO) communication
  • In VLC systems, OFDM is used to modulate data onto the intensity of light emitted by LEDs, enabling high-speed data transmission using visible light
• FSO systems employ OFDM to combat atmospheric turbulence and scintillation effects, which can severely degrade the performance of single-carrier modulation schemes

Advanced topics in OFDM

Multiple-input multiple-output (MIMO) OFDM

• MIMO-OFDM combines the benefits of MIMO technology with OFDM to further enhance the capacity and reliability of wireless communication systems
  • MIMO systems employ multiple antennas at both the transmitter and receiver to exploit spatial diversity and multiplexing gains
• MIMO-OFDM leverages the orthogonality of subcarriers to simplify the MIMO processing and enable efficient exploitation of the spatial domain
  • This combination results in improved spectral efficiency, increased capacity, and enhanced robustness against channel impairments

Adaptive resource allocation

• Adaptive resource allocation techniques in OFDM systems aim to optimize the allocation of subcarriers, power, and modulation schemes based on the channel conditions and user requirements
  • These techniques leverage the flexibility of OFDM to dynamically adapt the transmission parameters to the time-varying nature of wireless channels
• Adaptive subcarrier allocation involves assigning subcarriers to users based on their channel quality, maximizing the overall system throughput
  • Power allocation techniques, such as water-filling, distribute the available transmit power among the subcarriers to optimize the system performance
• Adaptive modulation allows the system to adjust the modulation scheme for each subcarrier based on the channel conditions, ensuring reliable communication while maximizing the data rate

OFDM with index modulation

• OFDM with index modulation (OFDM-IM) is an emerging technique that aims to improve the spectral efficiency and energy efficiency of OFDM systems
  • In OFDM-IM, the subcarrier indices are used as an additional dimension for conveying information, alongside the conventional modulation symbols
• By selecting a subset of subcarriers to be active and modulating information onto their indices, OFDM-IM can achieve higher spectral efficiency and reduced PAPR compared to traditional OFDM
  • This technique exploits the sparsity in the frequency domain and introduces a trade-off between spectral efficiency and error performance

Filterbank multicarrier (FBMC) vs OFDM

• Filterbank multicarrier (FBMC) is an alternative multicarrier modulation scheme that aims to address some of the limitations of OFDM
  • FBMC employs a per-subcarrier filtering approach, where each subcarrier is filtered by a well-localized prototype filter
• This filtering operation reduces the out-of-band emissions and provides better spectral containment compared to OFDM, which relies on a rectangular window in the time domain
  • FBMC systems can achieve higher spectral efficiency and reduced sensitivity to synchronization errors compared to OFDM
• However, FBMC also introduces additional complexity in terms of filter design and implementation, and may require more advanced equalization techniques compared to the simple one-tap equalization in OFDM
  • The choice between FBMC and OFDM depends on the specific application requirements, such as spectral efficiency, complexity, and compatibility with existing standards