INTRODUCTION
Optical OFDM
Orthogonal frequency division multiplexing (OFDM) is a highly efficient multi-carrier modulation technique widely used in various communication standards Its advantages have led to its implementation in both wired and wireless networks, including wireless LANs like HIPERLAN/2 and IEEE 802.11a/g, as well as in technologies such as WiMax (IEEE 802.16), Digital Subscriber Line (DSL), and Digital Audio and Video Broadcast (DAB, DVB).
Orthogonal Frequency Division Multiplexing (OFDM) has recently emerged as a preferred physical interface in optical communications, despite its established use in other communication standards The transition to optical systems has faced challenges due to fundamental differences between conventional OFDM and typical optical systems In traditional OFDM, signals are bipolar and convey information through the electrical field, while optical systems utilize unipolar signals that transmit information via the intensity of the optical signal.
Advancements in silicon technology, driven by Moore's law, along with the rising demand for higher data rates over long fiber distances, have led to the emergence of Orthogonal Frequency Division Multiplexing (OFDM) in optical communications.
For optical communications, OFDM has demonstrated resilience to transmission impairments arising from fiber polarization mode dispersion and chromatic dispersion
OFDM can effectively mitigate dispersion-induced impairments as long as the delay spread from chromatic dispersion is shorter than the cyclic prefix interval This capability is significant because, as data rates rise, chromatic dispersion escalates with the square of the data rate, whereas polarization mode dispersion (PMD) increases linearly.
At high data rates, the computational demands of electronic dispersion compensation for serial modulation formats can be impractical, especially in access networks Additionally, OFDM offers a significant advantage by enhancing spectral efficiency through the use of higher modulation formats.
Leveraging the benefits of OFDM in the optical domain, this technology has shown significant research potential across various applications in core, metro, and access networks.
The research about Optical OFDM is mainly classified into two main categories: coherent detection [8] and direct detection [9, 10] according to their underlying techniques and applications
Coherent detection systems utilize coherent mixing between the incoming optical OFDM signal and a local oscillator for signal detection While coherent optical OFDM (CO-OFDM) offers exceptional sensitivity and spectral efficiency, it is also vulnerable to polarization mode dispersion (PMD) However, the advantages of CO-OFDM come with significant installation costs, which include narrow line-width laser sources, local oscillators, 90-degree optical hybrids, and additional signal processing for phase and frequency offset estimations.
In IM/DD optical OFDM systems, signals are transmitted using intensity modulation and received via square law detection DDO-OFDM offers compatibility with low-cost DFB lasers with megahertz-level line-width, eliminating the need for local oscillators and optical hybrids while avoiding phase and frequency offset estimation, thus simplifying implementation As a result, DDO-OFDM presents a viable alternative for optical transmission, balancing installation complexity with transmission performance This technology is emerging as a leading candidate for next-generation optical networks, including passive optical networks and optical transport networks.
IM/DD Optical OFDM offers advantages over coherent optical OFDM, particularly in terms of reduced complexity and straightforward configuration, thanks to its use of simple direct detection This approach not only simplifies system design but also enhances tolerance to fiber dispersion, making IM/DD optical OFDM a promising option for cost-sensitive optical access networks However, it faces challenges such as high peak-to-power ratio (PAPR) and chromatic dispersion (CD), which can lead to distortion in electrical and optical devices and introduce nonlinear effects in fiber transmission Therefore, it is crucial to address the transmission limits of IM/DD optical OFDM under conditions of high PAPR and chromatic dispersion to ensure effective performance.
This thesis explores three algorithms and techniques aimed at reducing high Peak-to-Average Power Ratio (PAPR) to mitigate fiber nonlinearity effects It emphasizes high spectral efficiency in Intensity Modulation with Direct Detection (IM/DD) optical Orthogonal Frequency Division Multiplexing (OFDM) over Single-Mode Fiber (SMF) links, proposing new experimental setups to enhance performance.
Thesis organization
This thesis follows a consistent structure, with each chapter starting with an introduction that outlines its objectives and content, and concluding with a summary that highlights the key contributions made within the chapter.
The organization of this thesis is given as follows:
This chapter provides an overview of OFDM modulation, covering its fundamental mathematical modeling and the components of both transmitters and receivers It includes a brief review of Optical OFDM, highlighting the essential optical components utilized in these systems Additionally, the chapter describes the two primary variants of optical OFDM: coherent optical OFDM and IM/DD optical OFDM.
This chapter introduces an innovative technique utilizing a novel spreading code to effectively reduce the high Peak-to-Average Power Ratio (PAPR) in Intensity Modulation with Direct Detection (IM/DD) optical Orthogonal Frequency Division Multiplexing (OFDM) The proposed system demonstrates a significant reduction in fiber nonlinearity compared to the original system An experimental setup is outlined to validate the theoretical findings.
To enhance the received sensitivity of optical OFDM systems, we introduce a novel hybrid approach that combines carrier interferometry codes with a companding technique to minimize Peak-to-Average Power Ratio (PAPR) and mitigate component nonlinearity Experimental results indicate a significant improvement in component nonlinearity as the fiber launch power increases.
This chapter introduces a novel approach to reduce Peak-to-Average Power Ratio (PAPR) in the IM/DD OOFDM system, emphasizing a new binary particle swarm optimization (NBPSO) method combined with dummy sequence insertion (DSI) This innovative technique not only effectively lowers PAPR but also simplifies the overall system complexity, enhancing performance in IM/DD optical communications.
OFDM system without any side information Experimental demonstration show better performance
This chapter summarizes the thesis and gives new directions for future work.
OPTICAL OFDM SYSTEM
Introduction
The rising demand for high data rates has significantly contributed to the adoption of Orthogonal Frequency Division Multiplexing (OFDM) in optical networks This trend has led to the development of various innovative solutions for next-generation networks OFDM offers several inherent benefits, including high spectral efficiency, straightforward channel and phase estimation, and strong resilience to delay.
This chapter provides a comprehensive overview of optical OFDM systems, starting with the fundamental concepts of OFDM and exploring its historical context and various applications It details the essential components of OFDM and discusses its advantages and disadvantages The integration of OFDM in optical communications is examined, focusing on optical transmission links and the relevant optical and electrical devices utilized in detection processes, including coherent and direct detection methods Additionally, a comparison between coherent optical OFDM and IM/DD optical OFDM is presented, highlighting the distinctions between these two approaches.
OFDM review
2.2.1 History of OFDM and its applications
The historical evolution of Orthogonal Frequency Division Multiplexing (OFDM) is illustrated in Figure 2.1, highlighting its theoretical foundations and practical applications across various communication systems The concept of utilizing orthogonal frequencies for transmission was first introduced in a 1966 patent by Chang from Bell Labs Subsequently, the idea of generating these orthogonal signals through Fast Fourier Transform (FFT) techniques emerged, paving the way for advancements in communication technology.
The cyclic prefix (CP), introduced in 1980, is a crucial component of most practical Orthogonal Frequency Division Multiplexing (OFDM) systems Key developments in the field include significant research breakthroughs by Telatar and Foschini on multiple antenna systems, which spurred further investigation into OFDM technology While the capacity enhancements of multiple-input–multiple-output (MIMO) systems are not inherently tied to any specific modulation scheme, OFDM's effectiveness in mitigating dispersion and its scalability make it increasingly relevant for practical wireless applications since the mid-1980s.
1980s Cimini of Bell Labs published a paper on OFDM for mobile communications in
In 1987, French researchers Lassalle and Alard explored the use of Orthogonal Frequency Division Multiplexing (OFDM) for radio broadcasting, emphasizing the significance of integrating forward error correction (FEC) with OFDM, which led to the term Coded OFDM (C-OFDM) among broadcast engineers Meanwhile, Stanford's Cioffi and colleagues pioneered the application of OFDM in wireline communications, showcasing its effectiveness as a modulation technique for digital subscriber loop (DSL) applications.
Orthogonal Frequency Division Multiplexing (OFDM) serves as the foundation for numerous telecommunications standards, including wireless local area networks (LAN), fixed wireless communications, and television broadcasting worldwide In DSL applications, OFDM is referred to as discrete multi-tone (DMT), as it operates without modulating the baseband signal onto a carrier frequency Recently, the application of OFDM in optical communications has gained traction, with a growing body of research exploring its theoretical and practical performance across various optical systems, such as radio over fiber wireless, signal mode optical fiber, multimode optical fiber, plastic optical fiber, and real-time optical systems.
The Orthogonal Frequency Division Multiplexing (OFDM) system is a type of multi-carrier modulation similar to frequency division multiplexing (FDM), where each modulated carrier utilizes only a portion of the overall bandwidth In this system, high data rate information is split into N lower-rate parallel streams, with each stream modulating a distinct subcarrier simultaneously Consequently, if the total data rate is R_s, then each parallel stream operates at a data rate of R_s/N, leading to an increase in the symbol duration for each stream by a factor of N.
Modern communication systems are increasingly utilizing technologies that are significantly more tolerant to inter-symbol interference (ISI), as they operate with symbol durations that are much longer than the channel delay spread This capability is essential for achieving high data rates while efficiently conserving limited spectrum resources.
The Orthogonal Frequency Division Multiplexing (OFDM) system relies on the orthogonality of its subcarriers A collection of subcarriers, represented by s_n(t) = e^(j(2πf_nt)), where n ranges from -N/2 + 1 to N/2 and 0 ≤ t ≤ T, is considered orthogonal in the time domain if a specific mathematical condition is satisfied.
S t S t S t S t dt e dtT (2.1) Where k,l is the Kronecker delta defined by:
In order for the orthogonality to exist between the subcarriers, the following conditions are necessary:
The frequency of each subcarrier must be chosen such that each subcarrier has an integer number of cycles within the OFDM symbol duration
The difference in the number of cycles per OFDM symbol for adjacent subcarriers must be one
For these two conditions to be met, the frequency separation between adjacent subcarriers has to be the inverse of the OFDM symbol duration T
Figure 2.2 shows the conceptual diagram of multicarrier modulation transmission system Data symbol is transmitted into N parallel channels with different frequencies
At the receiver, an analogue low-pass filter is used to recover the individual subcarriers
LPF Output exp( 2 j f t o ) exp( 2 j f t 1 ) exp( 2 j f N 1 t )
Figure 2.2 Diagram conceptual of Multicarrier transmission, S/P: serial-to-parallel, P/S:
Parallel - to - serial, LPF: Low - Pass Filter.
In Frequency Division Multiplexing (FDM) systems, guard bands are essential to prevent interference between subcarriers and to facilitate accurate demodulation through filtering However, the inclusion of these guard bands leads to reduced spectral efficiency Orthogonal Frequency Division Multiplexing (OFDM) is a specialized form of FDM that utilizes orthogonal subcarriers, enhancing performance in the frequency domain.
In OFDM, the spectra of the subcarriers are overlap, resulting in saving of bandwidth
Figure 2.3: OFDM Spectrum versus FDM spectrum
1 Mathematical representation of an OFDM signal
The complex envelope of an OFDM signal, ignoring the cyclic prefix, can be represented mathematically as:
In an OFDM system, the transmitted complex symbol \( a_{n,k} \) on the \( n \)th subcarrier at the \( k \)th signaling interval is represented as \( g_n(t-kT) \), where \( T \) denotes the OFDM symbol period and \( N_{sc} \) indicates the total number of subcarriers.
For each OFDM symbol, the n th recovered complex symbol, â n,k at the k th signaling interval is given by:
In equation (2.5), the received OFDM signal, denoted as r(t), undergoes a complex conjugation process represented by the superscript “*.” This equation illustrates that the recovery of each complex symbol is achieved by multiplying the OFDM symbol with the complex conjugate of the specific subcarrier and then integrating the result over the signaling interval.
An OFDM system can be implemented in both continuous and discrete time, utilizing a bank of oscillators—one for each subcarrier—in its continuous-time version At the transmitter, the incoming information stream is mapped into symbols based on the chosen modulation format, such as n-PSK or n-QAM, and then processed through a serial-to-parallel conversion block Each parallel output modulates its respective subcarrier through multiplication, while ensuring that adjacent subcarrier frequencies differ by 1/T to maintain orthogonality At the receiver, the original transmitted symbols are retrieved by correlating the received signal with the same subcarriers The representation of OFDM symbols with four subcarriers in both the frequency and time domains is illustrated in Figure 2.4.
As we can see in Figure 2.4, the spectra of the subcarriers are sinc-shaped and overlap, where the sinc function is defined as: sin( ) sin ( ) x c x x
Figure 2.4: OFDM symbol with four subcarriers: (a): Frequency domain, (b): Time domain
In an OFDM system, each subcarrier exhibits notable side lobes across a frequency range that encompasses multiple other subcarriers, as illustrated in figure 2.4 (a) The signal maintains mathematical orthogonality throughout one OFDM symbol period, meaning that the peak of each subcarrier's spectrum aligns with the zero points of the spectra of other subcarriers This orthogonality is crucial for minimizing interference and optimizing signal integrity within the system.
Therefore, compared with others multicarrier Modulation scheme, OFDM is better in low complexity and high spectral efficiency
The discrete-time implementation of Orthogonal Frequency Division Multiplexing (OFDM) adapts the principles of the continuous-time model for digital applications, utilizing the Discrete Fourier Transform (DFT) and its inverse, the Inverse Discrete Fourier Transform (IDFT) This innovative approach to OFDM modulation and demodulation was initially introduced by Weinstein and Ebert in 1971.
The DFT is defined on the N-long complex sequence x=(x j , 0≤j≤N ) as [34] :
The IDFT is defined as:
The transmitted OFDM signal, F(x), can be understood as a straightforward N-point IDFT of the information symbol, x n However, due to the extensive complex multiplications required for DFT and IDFT computations, OFDM modulation and demodulation are performed more efficiently using the Inverse Fast Fourier Transform (IFFT) and the Fast Fourier Transform (FFT) This approach significantly reduces the number of complex multiplications, decreasing it from N² to (N/2) log2(N) with the radix-2 algorithm, and from N² to (3/8) N log2(N-2) with the radix-4 algorithm.
The discrete-time implementation of OFDM is less complex than the oscillator-based approach, as it allows for easy modulation and demodulation of multiple orthogonal subcarriers using IFFT and FFT, eliminating the need for a large oscillator bank Figure 2.5 illustrates the block diagram of an OFDM system, which includes an OFDM transmitter, an OFDM receiver, and the communication channel.
Optical OFDM
This section delves into the Optical OFDM system, exploring its various components and highlighting its two primary variants: Coherent Optical OFDM and IM/DD Optical OFDM.
After that, a comparison will be made between these two techniques of detection in order to present their advantages and disadvantages
This section outlines the essential optical components in an optical transmission system, where both electrical and optical signal paths are involved Optical transmitters facilitate the conversion from electrical to optical signals, while optical receivers perform the reverse conversion Optical fibers act as the primary medium for transporting these signals from the source to the destination, although they do cause attenuation during transmission To enhance signal quality, optical amplifiers like Erbium-doped fiber amplifiers (EDFAs) are employed Additionally, optical modulators, often used alongside semiconductor lasers, impose the information signal The optical receiver's role is to terminate the light-wave path, converting the optical signal back to the electrical domain using a photo-detector, thus allowing for the recovery of the transmitted data.
Optical Ampliier Optical Fiber Optical Fiber
Figure 2.10: Typical optical transmission Link
Optical transmitters play a crucial role in generating optical signals, typically through semiconductor lasers, and launching modulated signals into optical fibers This process can be achieved via direct or external modulation However, direct modulation of semiconductor lasers can lead to frequency chirp, which becomes problematic at high transmission data rates due to pulse broadening Consequently, external modulation, which includes semiconductor lasers and Mach-Zehnder modulators (MZMs), is preferred for better optical modulation performance In this thesis, external modulation is employed, where semiconductor lasers are biased with a DC voltage to ensure continuous wave operation.
Laser technology, or light amplification by stimulated emission of radiation, generates a powerful beam of coherent light with specific frequencies In optical communication, there are three primary types of lasers utilized.
Distributed Feedback Laser (DFB): these kinds of lasers operates at longer wavelength (1310 or 1550 nm windows) They are high cost and edge emitters
Vertical Cavity Surface Emitting Laser (VCSEL): these laser are predominantly multi transversal mode and low cost They operate at
Fabry Perot Laser (FP): they operate at longer wavelength (1310 or
1550 nm windows) with multiple longitudinal modes They are edge- emitters and moderated cost between VCSEL and DFB lasers
A dual-electrode Mach-Zehnder modulator (DE-MZM), constructed from Lithium Niobate (LiNbO3) and featuring two Y-junctions, operates by splitting incoming light at the first Y-junction into two paths The electro-optical properties of the modulator allow for phase modulation of the light in each arm based on the application of an electrical field to the electrodes Without an electrical field, both arms maintain the same phase, resulting in maximum light intensity at the output When an electrical field is applied, it induces a phase difference that can lead to either constructive or destructive interference Specifically, if the phase difference reaches π, total destructive interference occurs, marking the DE-MZM's "off" state In contrast, a single-electrode MZM modulates only one arm with voltage Assuming an ideal extinction ratio and neglecting insertion loss, the output electrical field at the second Y-branch can be expressed in relation to the input optical field when the D.C offset voltage for maximum transmission is considered to be zero.
(2.15) where V is the half-wave voltage (the voltage at which there’s complete suppression of the MZM output V=V 1 -V 2 )
If a DC bias voltage is applied to one of the electrodes of the MZM while the other DC terminal is grounded The output electrical field E out (t) can be as [65] :
The equation (2.16) describes the Bessel function of the first kind of order n, where the parameter ε is defined as the ratio of V DC to V π, θ represents the phase angle of the RF signal, and ω RF is the angular frequency of the RF signal Additionally, ω c denotes the center angular emission frequency of the input optical field in semiconductor lasers According to equation (2.8), the optical signal produced at the output of the Mach-Zehnder modulator (MZM) is a Double Sideband with Carrier (DSB-C) signal, consisting of the optical carrier at the laser's center emission frequency ω c and various sidebands at multiples of the modulating RF frequency ω RF The DC bias voltage influences the suppression of the optical carrier and either the even or odd-order optical sidebands, allowing for flexible signal generation in optical communications.
C signal, the two arms of the MZM are driven by two RF signals with equal amplitude but out of phase by
Optical fibers are essential for optical transmission systems, effectively transporting signals from source to destination Their low-loss characteristics and vast bandwidth enable high-speed signal transmission over long distances, minimizing the need for regeneration Research indicates that optical fibers exhibit three low attenuation regions: the first at 800 nm with 2.5 dB/Km, the second at 1300 nm with 0.5 dB/Km, and the third at 1550 nm with an impressive 0.2 dB/Km Bandwidth can be quantified in terms of wavelength or frequency, providing insights into the fiber's performance capabilities.
The relationship between the speed of light (c), wavelength (λ), and bandwidth (Δf and Δλ) is described by the equation Δf ≈ c/Δλ In the 1300 nm and 1550 nm transmission windows, the usable bandwidth, defined as the range where the loss in dB/km is within a factor of 2 of its minimum, is approximately 35 THz Fiber optics generally fall into two categories based on the mode of propagation: single mode fiber (SMF) and multimode fiber (MMF), as illustrated in Figure 2.12.
Figure 2.12: Multi-Mode Fiber versus Single Mode Fiber
Multimode fiber, characterized by the propagation of multiple light modes, features a larger core that allows for the use of cost-effective light sources like light-emitting diodes (LEDs) However, its primary drawback is the occurrence of intermodal dispersion, which can affect signal quality.
Single-mode fiber (SMF) allows only one mode of light to be transmitted, effectively eliminating intermodal dispersion and enabling longer transmission distances Due to its small core size, SMF requires a semiconductor laser to generate high-intensity light energy for efficient long-distance transmission.
An optical amplifier is designed to restore signal power levels without converting between electrical and optical formats Optical signals experience degradation over distance, necessitating the use of these amplifiers to maintain signal integrity.
Optical amplifiers use the principle of stimulated emission The amplification gain
The gain (G) of an optical amplifier is defined as the ratio of output power (P out) to input power (P in), expressed as G = P out / P in There are two primary types of optical amplifiers: semiconductor laser amplifiers and doped-fiber amplifiers, with the latter being the most commonly used due to their effective doping methods.
Erbium, the 24th element on the periodic table, plays a crucial role in the technology of Erbium-Doped Fiber Amplifiers (EDFAs), which are extensively utilized in telecommunications These conventional EDFAs primarily function within the frequency range of 1530 to 1570 nm By substituting the appropriate values in the equation, it is determined that they offer a usable bandwidth of approximately 5 THz.
Figure 2.13: Principle of optical Amplifier
The purpose of optical receivers is to convert back the optical signal in an electrical form and to recover the transmitted data
In optical communication networks, the fundamental direct detection device is the photodiode, which absorbs photons from incoming optical signals and converts them into electrical signals Photodiodes can be categorized into five main types: p-i-n photodiodes, p-n photodiodes, avalanche photodiodes (APD), and metal-semiconductor-metal photodiodes (MSM) The p-n photodiode features a reverse-biased p-n junction, while the p-i-n photodiode includes an intrinsic region situated between the p and n junctions The APD is an enhanced version of the p-i-n photodiode, designed to operate under very high reverse bias conditions.
This section describes different channel impairments, including fiber attenuation, insertion losses, chromatic dispersion, PMD, and fiber nonlinearities
Attenuation in optical fiber refers to the reduction of signal power as it travels over a distance, described by the equation dP/dz=αP, where α represents the power attenuation coefficient in dB/km For an optical fiber with a length of L kilometers, the optical power received after this distance can be characterized by the effects of attenuation.
P out=P inexp(-αL) (2.18) where P in is power launched in to fiber
A PAPR REDUCTION SCHEME BASED ON A NEW SPREADING
Introduction
Orthogonal Frequency Division Multiplexing (OFDM) has garnered significant interest among researchers for its effectiveness in overcoming transmission impairments and its high spectral efficiency in optical communication There are two primary variants of Optical OFDM based on receiver configuration: intensity modulator and direct detection (IM/DD) optical OFDM, and coherent detection optical OFDM Studies indicate that IM/DD optical OFDM holds great potential as a cost-effective solution for metropolitan area networks (MANs), access networks, and local area networks (LANs).
The IM/DD configuration is favored for its straightforward setup, requiring only a single photodiode to convert optical signals back to electrical signals, making it less complex and more tolerant to fiber chromatic dispersion (CD) and polarization mode dispersion (PMD) When compared to Direct Detection systems, coherent optical OFDM offers superior sensitivity and spectral efficiency, primarily due to the inclusion of an optical local oscillator in the coherent detection process.
90 o optical hybrids, the high-speed analog/digital convertor and the digital signal processing [72] are needed These devices increase the complexity and the cost of the system [73, 74]
The IM/DD Optical OFDM system is cost-effective due to its simple receiver configuration; however, it faces challenges, primarily high Peak-to-Average Power Ratio (PAPR), which can lead to nonlinear effects during high optical launch power transmission To enhance the system's tolerance to optical intensity modulators, DACs/ADCs, and fiber nonlinearity, PAPR reduction techniques are essential Various methods have been proposed to mitigate PAPR in optical OFDM systems, including Partial Transmission Sequence (PTS), Selective Mapping (SLM), coding schemes, conventional clipping and filtering using FFT/IFFT, Bayesian clipping recovery, nonlinear companding transforms, Hadamard transform, and Carrier Interferometry codes (CI) While these techniques aim to reduce PAPR, they each come with their own set of disadvantages.
Principle of new spreading code
Conventional clipping leads to both in-band and out-of-band distortion, increasing the system's bit error rate (BER) In contrast, the Bayesian clipping recovery scheme enhances system performance by leveraging a priori information regarding sparsity rate and noise variance, although it requires side information While companding techniques outperform conventional clipping, they fail to maintain a constant envelope for OFDM signals due to BER limitations Additionally, the Selective Mapping (SLM) and Partial Transmit Sequence (PTS) methods suffer from high computational complexity and bandwidth expansion The CI code, a type of spreading code, significantly improves BER performance but only rearranges the original data and does not support user requirements.
To mitigate nonlinear distortion in electrical and optical devices as well as transmission fiber, we introduce and experimentally validate a peak to average power ratio (PAPR) reduction scheme utilizing a novel spreading code in direct detection optical OFDM systems This innovative spreading code features high auto-correlation and low cross-correlation, enabling the support of 2N+1 users Consequently, this allows for the transmission of 2N+1 users or data symbols over just N sub-carriers, effectively conserving bandwidth.
Our experimental results show that new spreading code is able to provide better performance in terms of both PAPR reduction and BER for OFDM systems
This chapter is structured into three main sections: Section 3.2 outlines the principles behind the new spreading code, Section 3.3 presents the experimental setup and results, and Section 3.4 offers the concluding remarks.
3.2 Principle of new spreading code
3.2.1 OFDM transmitter with new spreading code
In traditional Orthogonal Frequency Division Multiplexing (OFDM), each data symbol is individually modulated onto its own subcarrier for transmission However, the new spreading OFDM system enhances this process by multiplying each data symbol by a spreading code C(k,n), allowing the symbol to be distributed across all subcarriers In this system, 'n' represents the subcarrier index, while 'k' denotes the data index or symbol-k, as illustrated in Figure 3.1.
Figure 3.1:The transmitter of OFDM system with new spreading code
In traditional OFDM system, the base-band OFDM signal is given as:
(3.1) where d is the data symbol, f is the carrier spacing of IFFT, and N is the number of subcarriers
The signal of new spreading code for real data (d={-1,1}) can be expressed as:
(3.2) where C(k,i) are coefficients of new spreading code, where K=2N+1, and C (k,n) structure for N sub-carriers are written by
With CI codes [43] , where K=N, and C(k,n) structures for N subcarriers are written by:
The new spreading code, as shown in Eq (3.3), supports 2N+1 symbols or users with N sub-carriers, effectively optimizing bandwidth usage.
The PAPR of the OFDM signal with new spreading code can be expressed as:
The expectation E{ã} is represented as (3.5), where the variance σ² is equivalent to E{|S(t)|²} due to the zero mean of the symbols The Peak-to-Average Power Ratio (PAPR) statistics of an OFDM signal can be expressed through its complementary cumulative distribution function (CCDF) Specifically, the CCDF of PAPR indicates the probability that the PAPR of the OFDM symbols surpasses a specified threshold, denoted as PAPR₀ This relationship can be articulated mathematically for an OFDM signal.
3.2.2 OFDM receiver with new spreading code
Figure 3.2 shows the receiver of OFDM system with new spreading code
Figure 3.2: The receiver of OFDM system with new spreading code
The received signal R(t) is processed through the FFT module to transform it into the frequency domain This signal is then equalized using coefficient H i Subsequently, the equalized signals undergo de-spreading with complex conjugate codes C * (k,n) Finally, a hard decision device is utilized to produce the final decision dˆ k.
In this experiment, the channel estimation and the synchronization symbol are realized by using training sequence (TS)
The proposed TS method closely resembles Park's approach, utilizing Chen's synchronization technique, which extracts only the sign bit from the ADC captured sample This synchronization is achieved through straightforward XNOR and bit summation operations, with the timing metric defined accordingly.
(3.8) where t(n) is the transmitted training sequence of length N t = N+N cp , N is the size of
In the context of IFFT, the cyclic prefix length is denoted as N cp, while r(n) represents the received signal The sign bit extractor, indicated by sign[.], outputs a bit '0' for positive input values and a bit '1' for negative inputs Additionally, the XNOR operator is represented by ⊙, and V signifies a threshold value.
Channel estimation is performed using Chen’s method, which allows for the estimation of channel information on even subcarriers by utilizing frequency-domain interpolation from two adjacent odd subcarriers This process enables the retrieval of the even channel response through linear interpolation between the odd subcarriers.
(3.9) where H even(i) denotes the channel response on the i th sub-carrier with even index,
H odd(i-1) and H odd (i+1) are the channel response for two adjacent odd subcarriers
Experimental setup and results
Figure 3.3 illustrates the experimental setup for the IM/DD optical OFDM transmission system, which involves four distinct signals The new spreading code is modulated using BPSK, while both the CI codes and the original signal employ 4QAM modulation Detailed parameters of the experimental setup can be found in Table 1.
The experimental setup for the IM-DD OOFDM transmission system incorporates various essential components, including an external cavity laser (ECL), an attenuator (ATT), and a polarization controller (PC) It utilizes a digital to analog converter (DAC) and an arbitrary waveform generator (AWG) to generate OFDM signals, which are then modulated by a Mach–Zehnder modulator (MZM) The system is further enhanced by an erbium doped fiber amplifier (EDFA) to boost signal strength, while a photodiode (PD) and a low pass filter (LPF) facilitate signal detection and processing Finally, a real-time digital storage oscilloscope (TDS) and an analog to digital converter (ADC) are employed for accurate signal analysis and measurement.
Pseudo-random binary sequences (PRBS) are transformed into parallel data using a serial-to-parallel (S/P) converter, with 393 parallel signals for new spreading-OFDM with 512 subcarriers, 201 for new spreading-OFDM with 256 subcarriers, and 100 for both CI-OFDM and original OFDM This parallel data is subsequently mapped to BPSK modulation for the new spreading code, while CI code and original OFDM utilize 4QAM modulation.
The process begins with the dissemination of phase codes C (k,n), as outlined in Section 2.1 Following this, guard intervals (GI) and Hermitian constraints are incorporated before the signal is processed through an Inverse Fast Fourier Transform (IFFT) block The IFFT generates a complex-valued waveform in the time domain, after which a cyclic prefix (CP) is added to reduce inter-symbol interference (ISI).
Table 3.1: The parameters of experiment
OFDM (New spreading) FFT size 256/512
Training sequence (TS) Training sequence 1
Fiber Fiber length (km) 70km
Attenuation (dB/km) Dispersion (ps/nm/km) Dispersion slope (ps/nm 2 /km) Effective area (um 2 ) n 2 (m 2 /w) SNR (dB)
Wavelength Range (nm) 1200 to 1600 Auxiliary Out Bandwidth(MHz) 0.1 to 1500
A training sequence (TS) is implemented for effective channel estimation and symbol synchronization in the transmission of electrical base-band OFDM signals, which are generated offline using MATLAB and uploaded to a commercial arbitrary waveform generator (AWG) operating at a sample rate of 2.5 GSamples/s and a peak-to-peak voltage of 2V An external cavity laser (ECL) produces a continuous wave (CW) light at a wavelength of 1556.26 nm with a linewidth of 100 kHz and an output power of 14.5 dBm, while the optical OFDM signals post-modulation via a Mach-Zehnder modulator (MZM) exhibit an output power of -2 dBm These signals are amplified by an erbium-doped fiber amplifier (EDFA) to a fiber launch power of 2.75 dBm before being transmitted over 70 km of single-mode fiber (SMF), with a tunable attenuator (ATT) employed to adjust the optical signal power At the receiving end, the optical OFDM signals are converted to electrical signals using a PIN photodiode (PD-83446A) and captured by a Tektronix TDS684B real-time oscilloscope at a rate of 10 Gsamples/s, allowing for subsequent offline processing through a MATLAB-based OFDM receiver.
The electrical signal from the real-time oscilloscope undergoes resampling and synchronization before being processed through a serial-to-parallel converter, where CP is eliminated Subsequently, the waveforms are transformed into OFDM subcarriers using Fast Fourier Transform (FFT).
In the frequency-domain, each channel is estimated by TS so as to compensate the distortion, then de-new spreading code Each BPSK channel is demodulated to produce
In our study, we utilized N parallel data channels, which were subsequently transformed into a single data channel through a parallel-to-serial converter Ultimately, we evaluated the Bit Error Rate (BER) performance of four distinct types of Orthogonal Frequency Division Multiplexing (OFDM) signals.
Figure 3.4 illustrates the complementary cumulative distribution function (CCDF) in relation to the peak-to-average power ratio (PAPR) of OFDM signals Notably, at a CCDF of 10^-4, the PAPR of the new spreading-OFDM signal utilizing BPSK shows significant improvements of 1.5 dB and 4.6 dB when compared to the CI-OFDM signal using 4QAM and the original 4QAM signal, respectively.
The experimental results show that the new spreading code makes signal more stable than CI code and original system Thus, it can decreasingly produces nonlinear noises
The new spreading signal with 512 subcarriers exhibits a slightly higher Peak-to-Average Power Ratio (PAPR) compared to the version with 256 subcarriers, highlighting differences in performance between the nonlinear components, CI code, and the original system.
Figure 3.4: CCDF versus PAPR of OFDM signals
The net bit rate with 256 subcarriers is about 1.726 Gbit/s in the BPSK-modulated OOFDM system (RBPSK-NEW256 = 256 x 201/((496 + 288 x 257) x 0.4 ) = 1.726)
The net bit rate with 256 subcarriers is about 1.718 Gbit/s in the 4QAM-modulated OOFDM system (R 4QAM-CI256 = R4QAM-OFDM256 = 256 x 200/((496 + 288 x 257) x 0.4)
The net bit rate with 512 subcarriers is about 1.693 Gbit/s in the BPSK-modulated OOFDM system (RBPSK-NEW512 = 256 x 393/((496 + 576 x 257) x 0.4) = 1.693)
Figure 3.5 illustrates the Bit Error Rate (BER) performance comparison among 4QAM CI signals, original 4QAM signals, and BPSK new spreading signals, evaluated at a fiber launch power of 2.75 dBm over a 70 km stretch of Single-Mode Fiber (SMF) At a BER of 10^-3 with 256 subcarriers, the received optical power levels are approximately -26 dBm for BPSK new spreading signals, -25.4 dBm for 4QAM CI signals, and -23.9 dBm for original 4QAM signals.
The experimental results indicate that the Bit Error Rate (BER) performance can be enhanced using the new spreading signal, despite the RBPSK-NEW256/R4QAM-OFDM256 ratio being 1.005 Additionally, the received sensitivity optical power of the BPSK new spreading signal shows improvements of 0.6 dB and 2.1 dB when compared to the 4QAM CI signal and the original 4QAM signal, respectively.
Figure 3.5: BER curves of OFDM signals
The experimental results also show that, at the BER of 10 -3 , the received optical power is about -26.2, and -26 dBm for the BPSK new spreading signal with subcarrier of 512 and 256, respectively
This result proves that new spreading code with low cross correlation and has better orthogonality property proportional to the high number of subcarrier.
NEW HYBRID METHOD FOR PAPR REDUCTION BASED ON
Introduction
Building on the PAPR reduction technique discussed in Chapter 3, this chapter continues to explore a novel hybrid method that combines carrier interferometry codes and companding techniques for enhancing optical direct detection in orthogonal frequency division multiplexing systems.
For long transmission distances in IM/DD Optical OFDM systems, it is essential to increase the launch power; however, this can lead to excessive nonlinear noise Therefore, it is crucial to implement strategies to reduce high Peak-to-Average Power Ratio (PAPR).
This chapter introduces an innovative hybrid approach aimed at minimizing fiber nonlinearity by addressing the high Peak-to-Average Power Ratio (PAPR) in Intensity Modulation with Direct Detection (IM/DD) optical Orthogonal Frequency Division Multiplexing (OFDM) systems The proposed method combines a joint companding technique with coding schemes to enhance performance Specifically, a nonlinear companding scheme is implemented at the transmitter, ensuring that there is no expanding at the receiver This companding process utilizes a-law and linear algorithms to maintain the output power consistent with the original signal.
Our experimental results show that this hybrid method is able to offer better performance in terms of both PAPR reduction and BER for OFDM systems
This chapter is structured as follows: Section 4.2 outlines the principles of the hybrid method, while Section 4.3 presents the experimental setup and results Finally, Section 4.4 offers concluding remarks.
Principle of hybrid method
This section reviews CI codes and companding techniques aimed at reducing the Peak-to-Average Power Ratio (PAPR) of Orthogonal Frequency Division Multiplexing (OFDM) signals It also outlines the structure of a hybrid method used in the Intensity Modulation with Direct Detection (IM/DD) optical OFDM transmission system.
The OFDM transmitter with CI codes, as illustrated in Figure 4.1(a), employs a CI-OFDM system where each parallel data symbol is modulated across all N carriers This approach ensures the reparability of each parallel data symbol through the use of strategically chosen phase offsets.
Figure 4.1: Structure of OFDM with CI codes
This paper expands upon the CI-OFDM architecture previously discussed in Ref [43], which only considered BPSK modulation We investigate its functionality with 4QAM constellations, as proposed by Wu et al [86] and Ali et al [87] The signal incorporating CI codes, consisting of N different codes, is formulated as follows.
(4.1) where d is the data symbol, f is the carrier spacing of IFFT, and N is the number of subcarriers
C(k,i) are coefficients of CI codes C(k,n) structures for N subcarriers are
The PAPR of the CI-OFDM signal can be defined as
The expectation operation, denoted as E{●}, reveals that E{|S(t)|^2} equals the variance σ², given that the symbols have a zero mean The statistics of the Peak-to-Average Power Ratio (PAPR) for an OFDM signal can be expressed through its complementary cumulative distribution function (CCDF).
CCDF of PAPR is defined as the probability that the PAPR of the OFDM symbols exceeds a given threshold PAPR0 The CCDF for an OFDM signal is expressed as
The OFDM receiver, illustrated in Figure 4.1(b), processes the received signal r(t) by transforming it into the frequency domain using FFT The resulting signal is then de-spread with complex conjugate codes C*(k,n) and combined Ultimately, a hard decision device is utilized to generate the final decision dˆ(k).
Figure 4.2 illustrates the relationship between the CCDF and PAPR of OFDM signals, highlighting a significant reduction in PAPR by 3.1 dB when using CI codes compared to the original OFDM at a CCDF of 10^-4.
In this section, we review the companding technique for PAPR reduction of OFDM signal The traditional à-law companding algorithm was first proposed by Wang et al
In traditional companding techniques for speech processing, Orthogonal Frequency Division Multiplexing (OFDM) signals are compressed at the transmitter and expanded at the receiver This process enhances the amplitudes of smaller signals while maintaining the levels of larger signals, effectively optimizing the overall signal quality.
To enhance power, we amplify small signals by applying linear companding to OFDM signals, ensuring that the signals maintain equal average power as referenced.
[55] The signal S out at the end of transmitter using à-law companding [58] can be expressed as
(S ) ln(1 | S / A |) ln(1 ) in in out
(4.5) where S in is the output signal after N-point IFFT, here is the signal of CI codes, à is the companding coefficient, and A is the peak amplitude of the signal S in
According to Wang et al [55] , when N sufficiently large, with Taylor’s series,
The average power of the companded signal is amplified by the coefficient K, which is defined as K = à /ln (à + l) To maintain the signal power at a constant level, a linear companding method is employed by multiplying by a constant coefficient K’ = 1/K Consequently, the signal at the transmitter's output undergoes this transformation.
(S ) ln(1 | S / A |) S' out A sgn in in
From Eq (4.6), when à increases, the reduction rate of the peak power is decreasing But, if à is big, BER performance will be reduced, so à must be chosen a small value [82, 88, 89]
In this paper, we choose the à is 2 such as Ref [82, 88, 89]
Hou et al [76] suggest that a system without expansion at the receiver exhibits superior Bit Error Rate (BER) performance Therefore, this paper adopts a nonlinear companding scheme that utilizes à-law companding at the transmitter while omitting de-companding at the receiver.
The nonlinear companding scheme significantly enhances the Peak-to-Average Power Ratio (PAPR) by 2.8 dB compared to the original OFDM system at a CCDF of 10^-4, particularly when the parameter α is set to 2.
4.2.3 The structure of hybrid method
This paper presents a hybrid method for reducing Peak-to-Average Power Ratio (PAPR) by employing CI codes alongside a nonlinear companding scheme The first approach involves transmitting each bit across N carriers using innovative CI phase codes, while the second method applies variable attenuation to the signal based on its amplitude.
Figure 4.3 shows the principle of our proposed an IM-DD optical OFDM transmission system with hybrid method
Figure 4.3: Principle of the intensity-modulation direct-detection (IM/DD) optical OFDM transmission system with hybrid method LD: laser diode, PC: polarization controller,
IM: intensity modulation, OA: optical amplifier, PD: photodiode
At the transmitter side, the pseudorandom binary sequence (PRBS) data undergoes conversion into parallel data through an S/P converter This parallel data is then mapped onto a 4QAM format and spread using CI phase codes before passing through an N IFFT block, which generates a complex-valued time domain waveform comprising all subcarriers Following the IFFT, the OFDM symbols are processed through a nonlinear companding scheme and a cyclic prefix (CP) is added to reduce inter-symbol interference (ISI) A digital-to-analog converter (DAC) creates the electrical baseband OFDM signal, which is enhanced by a training sequence (TS) for channel estimation and symbol synchronization Finally, the DAC-driven electrical baseband OFDM signal modulates the optical carrier of a laser diode (LD), and the resulting optical OFDM signal is amplified by an optical amplifier (OA) for transmission over single mode fiber (SMF).
At the receiver side, the electrical signal generated by the photodiode is converted into a digital signal through an ADC This digital signal is then processed by a serial-to-parallel converter, followed by the transformation of waveforms into OFDM subcarriers using FFT.
In the frequency domain, each channel is estimated using time synchronization (TS) to correct for distortions caused by optical and electrical paths, followed by the de-spreading of CI codes Subsequently, each 4QAM channel is demodulated, resulting in N parallel data channels, which can then be combined into a single data channel using a parallel-to-serial converter.
Experimental setup and result
Figure 4.4 illustrates the experimental setup for the IM/DD optical OFDM transmission system, which utilizes three signal types: standard OFDM signals, those enhanced with CI codes, signals employing only the companding technique, and those utilizing the proposed hybrid method Detailed parameters of the experimental configuration are provided in Table 1.
The OFDM signal, generated offline using Matlab, is uploaded to a commercial arbitrary waveform generator (AWG) with a sample rate of 2.5 GSamples/s and a peak-to-peak voltage of 2V, featuring a pseudorandom pattern length of 51200 An external cavity laser (ECL) produces a continuous wave (CW) light at a wavelength of 1556.26 nm, with a linewidth of 100 kHz and an output power of 14.5 dBm After passing through a Mach-Zehnder modulator (MZM), the optical OFDM signals have an output power of approximately 3 dBm and are amplified by an erbium-doped fiber amplifier (EDFA) before being transmitted over 100 km of single-mode fiber (SMF) The optical signals are converted to electrical wave signals using a PIN photodiode (PD-83446A) and subsequently sampled and recorded by a TDS-6804B oscilloscope The received waveforms are processed with a Matlab program to evaluate the peak-to-average power ratio (PAPR) and bit error rate (BER) performance.
Table 4.1: The parameters of experiment
Attenuation (dB/km) 0.19 Dispersion (ps/nm/km)
Dispersion slope (ps/nm 2 /km) Effective area (um 2 ) n 2 (m 2 /w) SNR (dB)
AWG(AWG710) Sample rate (GSa/s) 2.5
PD(83446A) Wavelength range (nm) 1200 to 1600
Auxiliary out bandwidth (MHz) 0.1 to 1500
EDFA Wave length range (nm) 1530-1560
The IM-DD OFDM transmission system is implemented using a hybrid method, incorporating key components such as an attenuator (ATT), external cavity laser (ECL), polarization controller (PC), Mach-Zehnder modulator (MZM), Erbium doped fiber amplifier (EDFA), photodiode (PD), real-time/digital storage oscilloscope (TDS), and low pass filter (LPF).
The net bit rate of 4QAM OFDM signal is about 1.718 Gbit/s (R4QAM%6 x 200/((496 + 288 x 257) x 0.4) =1.718)
Figure 4.5 illustrates the Bit Error Rate (BER) performance comparison among the original OFDM signal, companding signal, CI signal, and hybrid signal at a fiber launch power of 3 dBm over a 100 km length of Single-Mode Fiber (SMF), with a parameter value of à = 2 At a BER of 10^-4, the received optical power levels for the hybrid signal, CI signal, companding signal, and original OFDM signal are approximately -25.8, -24.2, -24, and -22.1 dBm, respectively The findings indicate that the hybrid method (à=2) offers superior BER performance compared to the other methods Additionally, the proposed hybrid approach enhances the received sensitivity optical power by 1.6 dBm compared to CI codes, 1.8 dBm against the companding technique, and 3.7 dBm relative to the original OFDM signal.
Figure 4.5: BER curves of OFDM signals at 3 dBm launch power after transmission over 100km SMF, when à =2
Figure 4.6: BER curves of OFDM signals at 6 dBm launch power after transmission over 100 km SMF, when à =2
Figures 4.6 and 4.7 illustrate the Bit Error Rate (BER) performance comparison among the original OFDM signal, companding signal, CI signal, and hybrid signal at a parameter value of α = 2, with fiber launch powers of 6 dBm and 9 dBm after transmission over 100 km of Single Mode Fiber (SMF) At a BER of 10^-4, with a fiber launch power of 6 dBm, the received optical powers are approximately -26.6 dBm for the hybrid method, -24.9 dBm for CI codes, -24.6 dBm for the companding technique, and -22.4 dBm for the original OFDM signal When the fiber launch power is increased to 9 dBm, the received optical powers are about -27.6 dBm for the hybrid method, -25.7 dBm for CI codes, -25.2 dBm for the companding technique, and -22.6 dBm for the original OFDM signal.
Figure 4.7: BER curves of OFDM signals at 6 dBm launch power after transmission over 100 km SMF, when à =2
The analysis of Figures 4.5, 4.6, and 4.7 indicates that an increase in optical fiber launch power enhances the receiver sensitivity of optical OFDM signals Notably, the hybrid method demonstrates superior receiver sensitivity compared to other signal types.
Figure 4.8 illustrates the Bit Error Rate (BER) performance of optical OFDM signals at a received power of -26 dBm after being transmitted over 100 km of Single-Mode Fiber (SMF) The hybrid method demonstrates superior BER performance compared to the original method, which exhibits the poorest results As the launch power increases, the BER of the hybrid method decreases more rapidly than that of other techniques Notably, the BER at 9 dBm is lower than at 3 dBm, indicating that nonlinearity effects are negligible.
Figure 4.8: BER via launch power of OFDM signals after transmission over 100 km SMF, when à =2.