Orthogonal Chirp Division Multiplexing Research Articles

Wide-sense stationary discrete-time random processes: Analyses in the discrete-Fresnel and discrete-frequency domains

This article investigates the expectation and autocorrelation functions of random processes in the discrete-Fresnel and the discrete-frequency domains, originating from wide-sense stationary (WSS) random processes in the discrete-time domain. Through mathematical deduction, it is demonstrated that WSS random processes in the discrete-time domain exhibit the same expectation and autocorrelation functions as transformed to the discrete-Fresnel domain. In contrast, this property is not observed in the discrete-frequency domain. White, pink, and brown random processes are considered to illustrate these behaviors in the discrete-Fresnel and discrete-frequency domains. Furthermore, this study numerically compares data communication systems based on single-carrier with cyclic prefix, orthogonal chirp-division multiplexing, and orthogonal frequency-division multiplexing schemes, which are respectively designed in the discrete-time, discrete-Fresnel, and discrete-frequency domains. The numerical results show that orthogonal chirp-division multiplexing and single-carrier with cyclic prefix schemes achieve comparable communication performance under any additive noise modeled by a wide-sense stationary random process, regardless of the chosen linear equalization or the absence of it.

Polar coded SCMA-OCDM based on chaotic scrambled SLM

In this work, the polar coded sparse code multiple access (SCMA) scheme based on chaotic scrambled selective mapping (CS_SLM) is proposed for future passive optical networks (PONs). The original bits are coded by polar and mapped into constellation symbols by sparse code. Then orthogonal chirp division multiplexing (OCDM) modulation is adopted which has better anti-interference ability than orthogonal frequency division multiplexing (OFDM). At the receiver, the joint iterative detection and decoding for polar and SCMA is used to further improve the BER performance. The CS_SLM is helpful to improve the reliability and security, while keeping high spectral efficiency of SCMA-OCDM modulation. A 49.42 Gb/s coded SCMA-OCDM PON over 2 km seven-core fiber is demonstrated in the experiment. The results show that the SCMA-OCDM scheme gets a receiver sensitivity of 0.8 dB at a bit error rate (BER) of 3.8 × 10−3, compared with SCMA-OFDM. Because of peak to average power ratio (PAPR), the polar coded SCMA-OCDM based on CS_SLM is compared with clipping and filtering (CAF) method, about 2.08 dB receiver sensitivity gain is obtained when BER is lower than 10−5. The polar coded SCMA-OCDM based on CS_SLM also takes security into the consideration, due to the downlink broadcasting of PON. It can be a promising candidate for the next generation PONs.

Chaos key enhanced physical layer secure transmission method based on the convolutional long short-term memory neural network

In this paper, we propose a method for training a key-enhanced chaotic sequence using the convolutional long short term memory neural network (CLSTM-NN) for secure transmission. This method can cope with the potential security risk posed by the degradation of chaotic dynamics when using chaotic model encryption in traditional secure transmissions. The simulation results show that the proposed method improves the key space by 1036 compared to traditional chaotic models, reaching 10241. The method was applied to orthogonal chirp division multiplexing (OCDM). To demonstrate the feasibility of the proposed scheme, we conducted transmission experiments of encrypted 16 quadrature amplitude modulation (QAM) OCDM signals at a speed of 53.25 Gb/s over a 2 km length of 7-core optical fiber and test different encryption schemes. After key enhancements, the overall number of keys in the system can increase from 18 to 105.The results show that there is no significant difference between the bit error rate (BER) performance of the encryption method proposed in this paper and the traditional encryption method. The maximum performance difference between the different systems does not exceed 1 dBm. This fact proves the feasibility of the proposed scheme and provides new ideas for the next generation of secure transmission.

Image Super Resolution-Based Channel Estimation for Orthogonal Chirp Division Multiplexing on Shallow Water Underwater Acoustic Communications.

Orthogonal chirp division multiplexing (OCDM) offers a promising modulation technology for shallow water underwater acoustic (UWA) communication systems due to multipath fading resistance and Doppler resistance. To handle the various channel distortions and interferences, obtaining accurate channel state information is vital for robust and efficient shallow water UWA communication. In recent years, deep learning has attracted widespread attention in the communication field, providing a new way to improve the performance of physical layer communication systems. In this paper, the pilot-based channel estimation is transformed into a matrix completion problem, which is mathematically equivalent to the image super-resolution problem arising in the field of image processing. Simulation results show that the deep learning-based method can improve the channel distortion, outperforming the equalization performed by traditional estimator, the performance of Bit Error Rate is improved by 2.5 dB compared to the MMSE method in OCDM system. At the 7.5 to 20 dB region, it achieves better bit error rate performance than OFDM systems, and the bit error rate is reduced by approximately 53% compared to OFDM when the SNR value is 20, which is very useful in shallow water UWA channels with multipath extension and severe time-varying characteristics.

Channel Estimation for Multiple-Input Multiple-Output Orthogonal Chirp-Division Multiplexing Systems

In multiple-input multiple-output (MIMO) systems, channel estimation is of crucial importance to guarantee reliable recovery of ultra-high-speed MIMO signals. This paper proposes a novel channel estimation algorithm for the emerging MIMO-based orthogonal chirp-division multiplexing (OCDM) systems by utilizing the unique features of OCDM signals. In the proposed algorithm, a set of pilot signals is designed based on the Fresnel basis, which is essentially a family of orthogonal linear chirps. The pilots are assigned to different antennas for transmission occupying the same time slot and bandwidth. According to the convolution-preservation theorem of the Fresnel transforms, the transfer matrices of MIMO-OCDM systems can be readily estimated at the receiver without any inter-antenna interference, even if the pilots overlap in both the time and frequency domains. The proposed algorithm avoids bandwidth waste in conventional channel estimators, in which silent pilots will be required in time and/or frequency to ensure the received MIMO pilots separable. We show that the proposed algorithm is unbiased for the unique OCDM pilots and has better estimate accuracy and system performance. Finally, analysis and numerical results are provided to validate its advantages as a promising algorithm for emerging wireless access technology based on MIMO-OCDM.

Characterization of Orthogonal Chirp Division Multiplexing and Performance Evaluation at THz Frequencies in the Presence of Phase Noise

Characterization of Orthogonal Chirp Division Multiplexing and Performance Evaluation at THz Frequencies in the Presence of Phase Noise

THz-Over-Fiber System With Orthogonal Chirp Division Multiplexing for Integrated Sensing and Communication

THz-Over-Fiber System With Orthogonal Chirp Division Multiplexing for Integrated Sensing and Communication

Orthogonal Circulant Multiplexing for Bandwidth- Limited Direct-Detected Optical Communication Systems

We propose and investigate a novel orthogonal circulant multiplexing (OCM) technology for bandwidth-limited direct detection (DD) optical systems. We analytically derive that any OCM, i.e. using any orthogonal circulant matrix for multiplexing, can redistribute the noise uniformly across the subcarriers. However, the distribution of inter-symbol interference (ISI) and inter-carrier interference (ICI) strongly depends on the design of OCM. The previously proposed orthogonal chirp division multiplexing (OCDM), although showing better ISI/ICI tolerance than discrete-Fourier-transform spread (DFT-S) orthogonal frequency division multiplexing (OFDM), is a kind of OCM with poorer performance. We propose and analytically reveal that OCM based on chirp-like polyphase sequence (CLPS), general chirp sequence (GCS), sparse CLPS (SCLPS), and sparse GCS (SGCS) can achieve flatter ISI/ICI distribution across subcarriers and so better performance than OCDM in bandwidth-limited DD systems. The optimal parameter vector of the E-parameter CLPS is a Zadoff-Chu sequence while the parameter α in GCS should be larger. The optimal performance can be achieved by either CLPS (or GCS) using a larger E (or α) or SCLPS (or SGCS) with optimized sparsity. ∼110Gbit/s experiments using Mach-Zehnder modulator or electro-absorption modulator and receiver of 10-GHz photodiode or 8-GHz avalanche photodiode are conducted. The results agree with the theory and show that the proposed OCM outperforms conventional OFDM, DFT-S OFDM, and OCDM.

OCDM-SDM Optical Communication System Utilizing Four-Dimensional Constellation Mapping

In this paper, an orthogonal chirp division multiplexing (OCDM) Space division multiplexing (SDM) optical communication utilizing four-dimensional constellation mapping is proposed. A new 16-point four-dimensional constellation is designed, and its constellation figure of merit (CFM) can reach 1.17. A direct detection orthogonal chirp division multiplexing (DD-OCDM) transmission scheme based on four-dimensional constellation mapping is designed, and 32.8 Gb/s OCDM signal transmission is performed across 2 km seven core fiber through experiments, which verifies the performance of the proposed constellation. Under the condition of multi-core multiplexing and the bit error rate (BER) of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , the receiver sensitivity of the OCDM signal, which is based on the proposed four-dimensional constellation mapping based on associated constellation mapping (16ACM-4D), has a gain of 0.59 dB, 3.26 dB, and 5.73 dB compared with the OCDM signals based on QPSK, 16QAM, and 16PSK, respectively. The results show that the proposed OCDM short-reach optical communication scheme based on four-dimensional constellation mapping has good bit error performance and anti-interference ability, and has broad application prospects in the future short-reach optical communication.

Low Noise Ultra-Flexible SiP Switching Platform for mmWave OCDM &amp; Multi-Band OFDM ARoF Fronthaul

A highly flexible wavelength and space switched analog radio-over-fiber (ARoF) fronthaul transmission of a millimeter-wave (mmWave) emerging 6G waveform over a centralized/ cloud radio access network (C-RAN) is experimentally demonstrated in this work. A spread spectrum multiplexing technique — orthogonal chirp division multiplexing (OCDM) — which is highly resilient to inter-channel interference and enables enhanced channel estimation is utilized in the fronthaul transmission demonstration. The flexible properties of a low noise silicon photonic (SiP) microring resonator (MRR) based tunable laser and a low cross-talk 4×4 SiP optical wavelength/space switch are combined to form a reconfigurable 10 km fronthaul system enabling 64-QAM OCDM transmission at 24 GHz with consistent performances ~5% EVM across all test wavelengths/ports. A signal constituting Wi-Fi and 5G NR standard compatible 64-QAM orthogonal frequency division multiplexing (OFDM) bands, at 10 GHz and 24 GHz respectively, are also transmitted and evaluated in the proposed system with EVM performances below 64-QAM EVM limit (8%) achieved, thus demonstrating the system’s potential in a future converged multi-service environment.

Peak to average power ratio reduction techniques based on chirp selection for single and multi‐user orthogonal chirp division multiplexing system

AbstractThis article deals with peak to average power (PAPR) reduction in a single and multi‐user orthogonal chirp division multiplexing (OCDM) context. Two methods for PAPR reduction based on the selection of the frequency variation (up or down) of the chirps are first presented in a single user system. The first technique consists in considering two OCDM signals generated with up and down chirps, respectively, and selecting the one offering lowest PAPR. The second PAPR reduction method is based on usual clipping, and in that case the chirp selection aims to reduce the clipping noise. An adapted receiver is presented, based on the maximum likelihood estimation of the frequency variation (up or down) of the chirp. Then, a general procedure for multi‐user OCDM transmission is introduced, where a sub‐band of the available bandwidth is dedicated to each user, whose frequency of the chirps varies within this sub‐band. Next, the PAPR reduction techniques are generalised to this multi‐user OCDM system. Moreover, a performance analysis of the first PAPR reduction method is developed, and it is shown through simulations that theoretical and numerical results match for both Nyquist rate and oversampled signals. It is also shown that the chirp selection reduces the clipping noise, and improves the bit error rate performance compared with clipping only.

Successive Interference Cancellation for Orthogonal Chirp Division Multiplexing

In this paper, we propose a communication receivers’ architecture to simplify the Orthogonal Chirp Division Multiplexing (OCDM) channel equalization and to subtract multi-carrier interference followed by a successive interference cancellation (SIC) scheme in order to cancel the remaining interference. The interference introduced by underwater acoustic channel is estimated using a pre-acknowledged pilot symbol sequence, and then the interference can be optimally estimated and subtracted from the received signal. This process is repeated simultaneously for all OCDM carriers until a stationary point or a threshold is reached. Simulation results from Watermark are applied to illustrate the performance of the OCDM scheme with the presented successive interference cancellation algorithm. Results shows that the Bit Error Rate (BER) enhancement can reaches 102 in BCH1 channel. As expected, the combination of OCDM and presented SIC algorithm is shown to increase the output SNR over OCDM alone in multi-path shall water acoustic channel.

Performance Analysis of Orthogonal Multiplexing Techniques for PLC Systems with Low Cyclic Prefix Length and Symbol Timing Offset.

This paper investigates the degradation caused by interference resulting from cyclic prefix violation and symbol timing offset in narrowband power line communication systems. In this sense, it presents a unified formulation from which Hermitian symmetric orthogonal frequency division multiplexing (HS-OFDM), orthogonal chirp division multiplexing (OCDM), single-carrier cyclic prefix (SCCP), and orthogonal time-frequency division multiplexing (OTFDM) can be easily derived. The paper then provides closed-form expressions for quantifying the aforementioned interference in the presence of a frequency domain equalizer. The numerical analyses exhibit the performances of these schemes under various data communication conditions, such as the availability of channel state information, the presence or absence of interference, modeling of additive noise as a white or colored Gaussian random process, frequency domain equalizer type, and the use of bit and power allocation techniques. The closed-form expressions and performance analyses regarding achievable data rate and bit error probability provide guidance for dealing with distinct constraints in narrowband power line communication (PLC) systems using the HS-OFDM, OCDM, SCCP, or OTFDM scheme. Lastly, the unified formulation and results obtained motivate the design of multi-scheme transceivers.

Comparing the Performance of OFDM and OCDM-based Visible Light Communications: Numerical and Experimental Analysis

Numerical and experimental analysis of visible light communication (VLC) systems based on orthogonal chirp division multiplexing (OCDM) and orthogonal frequency division multiplexing (OFDM) are presented in this paper. Unlike most of the related publications, in this work we numerically compared OCDM and OFDM based VLC systems with the same equalization process, i.e., employing an one tap equalizer (OTE) in both systems. Simulation results in line-of-sight VLC channels show that both systems have the same performance when baseband multicarrier signals are used. The impact of the optical modulation index and the bias current of a previously characterized light-emitting diode were also evaluated. Nevertheless, the experimental demonstrations, in which bandpass signals were used due to the bandpass characteristic of the exploited setup, show that OFDM-based system outperforms the VLC links with OCDM signals, when the OTE equalizer is used in both systems. The performance of the OCDM-based system was improved by using a zero forcing frequency domain equalizer.

A Comprehensive Survey of Candidate Waveforms for 5G, beyond 5G and 6G Wireless Communication Systems

The evolution of global mobile data over the past decades in broadcasting, Internet of Things (IoT), education, healthcare, commerce, and energy has put strong pressure on 3G/4G mobile networks to improve their service offerings. These generations of mobile networks were initially invented to meet the requirements of the above-mentioned applications. However, as the requirements in these applications continue to increase, new mobile technologies such as 5G (fifth generation), 5G and beyond (B5G, beyond fifth generation), and 6G (sixth generation) are still progressing and being experimented. These networks are very heterogeneous generations of mobile networks that will have to offer very high throughput per user, good energy efficiency, better traffic capacity per area, improved spectral efficiency, very low latency, and high mobility. To meet these requirements, the radio interface of future mobile networks will have to be flexible and rationalized the available frequency resources. Therefore, new modulation methods, access techniques and waveforms capable of supporting these technological changes are proposed. This review presents brief descriptions of the types of 5G, B5G, and 6G waveforms. The 5G consists of OFDM including its transmission techniques: generalized frequency division multiplexing (GFDM), filter bank based multi-carrier (FBMC), universal filtered multi-carrier (UFMC), and index modulation (IM). Meanwhile, the 6G covers orthogonal time frequency space (OTFS), orthogonal chirp division multiplexing (OCDM) and orthogonal time sequence multiplexing (OTSM). The networks’ potentialities, advantages, disadvantages, and future directions are outlined.

Power Sparse Code Division Non-Orthogonal Multiple Access Scheme for Next-Generation Flexible Optical Access

In this paper, a power sparse code division non-orthogonal multiple access (PSCD-NOMA) scheme is proposed for next-generation flexible optical access, which is based on the multi-stack network. All the optical network units (ONUs) are allocated with different power levels according to path loss to achieve power multiplexing. Compared with sparse code multiple access (SCMA), the proposed sparse code considers users’ information as a whole, and a larger number of users can be implemented with relatively low complexity and similar or better performance. It can achieve 150% overload by sparse code. Moreover, an irregular-shaped 8 quadrature amplitude modulation (IS-8QAM) constellation diagram is devised that is more suitable for PSCD-NOMA. Orthogonal chirp division multiplexing (OCDM) is employed for its advantages of the stronger anti-dispersion ability. A 10.23 Gb/s PSCD-NOMA transmission over 25 km standard single-mode fiber is experimentally demonstrated. The results show that IS-8QAM can get at least 0.6 dB gain than the conventional 8QAM scheme. The difference in sensitivity between ONUs of different power levels is 2.8 dB, which corresponds to the loss between different paths. The sensitivity difference between different users at the same power level is only 0.3 dB, which indicates the proposed PSCD-NOMA has good fairness. PSCD-NOMA is a potential method for future optical access systems due to its great performance.

High-security and low-complexity OCDM transmission scheme based on GAN enhanced chaotic encryption.

We report a low-complexity and high-security orthogonal chirp division multiplexing (OCDM) transmission scheme based on generative adversarial networks (GAN) enhanced chaotic encryption. Our investigation focuses on the security and efficiency of the communication system. To successfully apply GAN for the encryption scheme, we design our networks with new network architectures and modify the loss functions to improve the adversarial training performance of the networks. In the experiment, a weakly coupled seven cores fiber of 2 km was applied to achieve a 70 Gb/s transmission system. The results reveal that our proposed scheme has a maximum receiver sensitivity gain of about 1.26dB than traditional OFDM transmission system, and our encryption scheme has a large keyspace at about 1 × 10202 against brute force cracking by illegal optical network units with only 0.63% running time compared with the traditional chaotic scheme. The results highlight that the proposed encryption scheme has a remarkable reduction in complexity and improvement in security, which is a promising candidate for next-generation PONs.

Performance-Enhanced Optical Non-Orthogonal Multiple Access Enabled by Orthogonal Chirp Division Multiplexing

In this paper, we propose a novel optical non-orthogonal multiple access (NOMA) scheme based on orthogonal chirp division multiplexing (OCDM) in a low-cost intensity modulation and direct detection system for passive optical networks (PON). The proposed OCDM-NOMA scheme can effectively improve spectral efficiency and serve more users by multiplexing spectrally overlaid OCDM signals in power domain. Under the advantages of the chirp spread spectrum, the proposed OCDM-NOMA scheme can also enhance the bit error rate (BER) performance compared to NOMA scheme based on orthogonal frequency division multiplexing (OFDM). A 17.8 Gb/s OCDM-NOMA PON transmission over 25 km standard single-mode fiber is experimentally demonstrated. The results show that, when compared to OFDM-NOMA and precoding OFDM-NOMA, OCDM-NOMA can achieve receiver sensitivity gains of 1.3 dB and 0.5 dB for the high-power branch signal, and 1.4 dB and 0.6 dB for the low-power branch signal at a BER of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> . Furthermore, we investigate the feasibility of using higher-order modulation in NOMA technology for the first time to further improve data throughput and spectral efficiency. In a 22.2 Gb/s transmission, the optimal power division ratio is determined, and the transmission performance is investigated. According to the experimental results, OCDM-NOMA with higher-order modulation can be a promising candidate for next-generation PONs.

Transmission of OCDM Based on Asymmetric Pair Mapping Over a Seven Core Fiber

In this paper, transmission of orthogonal chirp division multiplexing (OCDM) based on asymmetric pair mapping over a seven core fiber is proposed. High-order 32 quadrature amplitude modulation (QAM) is reduced to quadrature phase-shift keying (QPSK) and 8 QAM signal employing asymmetric pair mapping, which will not affect the rate of the system. Combined with geometric shaping (GS), the average transmission power is successfully lowered, realizing signal damage suppression. In order to verify the performance of the proposed asymmetric pair mapping scheme, a 140 Gb/s asymmetric pair mapping OCDM signal transmission over 2 km seven core fiber is experimentally demonstrated. The experimental results show that the proposed transmission scheme has the best performance when the power distribution ratio (PDR) is 4 dB. Meanwhile, compared with GS 32 QAM with QPSK+rectangle 8 QAM, GS 32 QAM with QPSK+star 8 QAM and GS 32 QAM, the proposed asymmetric pair mapping OCDM signal has improved by 1.55 dB, 1.45 dB, and 0.7 dB, respectively. It has a wide range of applications in the future optical transmission system due to its outstanding performance in the suppression of high-order modulation signal degradation.

Joint Channel Estimation and Schmidl &amp; Cox Synchronization for OCDM-Based Systems

This letter proposes a joint channel estimation and Schmidl & Cox synchronization for the orthogonal chirp-division multiplexing (OCDM) scheme. First, it is proven that a symbol composed of two identical halves in the Fresnel domain has two identical halves in the time domain, which is required by the considered synchronization technique. In sequel, a Fresnel-domain pilot symbol that enables joint channel estimation and synchronization is proposed, allowing overhead reduction and hence higher data rates. Finally, measurement and simulation results validate the obtained findings for both passband and baseband OCDM schemes.