Peak to average power ratio reduction in NC–OFDM systems

Non contiguous orthogonal frequency division multiplexing (NC-OFDM) is an efficient and adaptable multicarrier modulation scheme to be used in cognitive radio communications. However like OFDM, NC-OFDM also suffers from the main drawback of high peak to average power ratio (PAPR). In this paper PAPR has been reduced by employing three different trigonometric transforms. Discrete cosine transform (DCT), discrete sine transform (DST) and fractional fourier transform (FRFT) has been combined with conventional selected level mapping (SLM) technique to reduce the PAPR of both OFDM and NC-OFDM based systems. The method combines all the transforms with SLM in different ways. Transforms DCT, DST and FRFT have been applied before the SLM block or inside the SLM block before IFFT. Simulation results show the comparative analysis of all the transforms using SLM in case of both OFDM and NC-OFDM based systems

OFDM systems design using harmonic wavelets

Orthogonal frequency-division multiplexing (OFDM) is a popular multi-carrier technique used in many digital communication systems such as wireless fidelity (Wi-Fi), long term evolution (LTE) and power line communication systems. It can be designed using fast Fourier transform (FFT) or wavelet transform (WT). The major drawback in using WT is that it is computationally inefficient. In this study, we introduce a simple and computationally efficient WT, harmonic wavelet transform, for OFDM signal processing. The new WT uses the orthogonal basis functions of conventional FFT-OFDM except that it involves translation and dilation of the input signal; the new wavelets is referred to as harmonic wavelets (HW). When compared with pilot-assisted OFDM system in terms of reduction in the peak-to-average power ratio, the results show that HW-OFDM outperforms FFT-OFDM by 3 dB at 10−4 CCDF (complementary cumulative distribution function). Over Rayleigh fading channel with additive white Gaussian noise (AWGN), the bit error ratio of both FFT-OFDM and HW-OFDM perfectly matched, showing that the proposed HW-OFDM is better in terms of peak-to-average power ratio reduction

Optical OFDM based on the fractional Fourier transform for an indoor VLC system

The fractional Fourier transform (FRFT), which is a family of linear transformations generalizing the classical Fourier transform, has been used in the fields of filter design, signal processing, phase retrieval, and pattern recognition due to its unique properties. The FRFT of a signal can be interpreted as a decomposition of the signal in terms of chirps. In this paper, for the first time, to the best of our knowledge, we introduce an optical FRFT (OFRFT)based orthogonal frequency division multiplexing (OFDM) visible light communications (VLC) system and compare numerical results with a direct current-biased optical (DCO)-OFDM system. First, the optimal fractional order is calculated to improve the performance of the proposed system by minimizing the bit error rate (BER). The numerical results show that OFRFT-OFDM with the optimal fractional order offers a significantly improved BER performance compared with DCO-OFDM under the same computational complexity and spectral efficiency. In addition, the peak to average power ratio, which is an issue in light emitting diode-based VLC systems, is reduced by <1 dB using OFRFT-OFDM for the same BER compared with DCO-OFDM

Waveform design for communicating radar systems using fractional Fourier transform

A novel waveform design technique for enabling a communication channel within a pulse radar is presented. The proposed waveform is composed of quasi-orthogonal chirp sub-carriers generated by means of the Fractional Fourier Transform (FrFT), with the aim of preserving the radar performance of a typical Linear Frequency Modulated (LFM) pulse while embedding data to be sent to a cooperative system. Waveform generation and demodulation are described, together with techniques aimed at optimising the design parameters and mitigating the Inter-Carrier Interference (ICI) caused by the quasi-orthogonality of the chirp sub-carriers. The proposed FrFT based communicating-radar (CoRadar) waveform design is compared with Orthogonal Frequency Division Multiplexing (OFDM) based CoRadar with respect to both radar and communication operations. Radar performance is evaluated through examination of the Ambiguity Function (AF) and by assessing the performance of a standard square law detector. Communication performance is shown in terms of Bit Error Ratio (BER) for different channel conditions. Results demonstrate that the proposed FrFT waveform presents performance close to a LFM pulse in terms of probability of detection and probability of false alarm, in exchange for slightly worse range and Doppler resolution. Furthermore, it is shown to maintain comparable communication performance with respect to the OFDM waveform. Finally, a hardware implementation is described that demonstrates the simultaneous radar and communication capabilities of the proposed system

Physical layer authenticated image encryption for Iot network based on biometric chaotic signature for MPFrFT OFDM system

In this paper, a new physical layer authenticated encryption (PLAE) scheme based on the multi-parameter fractional Fourier transform–Orthogonal frequency division multiplexing (MP-FrFT-OFDM) is suggested for secure image transmission over the IoT network. In addition, a new robust multi-cascaded chaotic modular fractional sine map (MCC-MF sine map) is designed and analyzed. Also, a new dynamic chaotic biometric signature (DCBS) generator based on combining the biometric signature and the proposed MCC-MF sine map random chaotic sequence output is also designed. The final output of the proposed DCBS generator is used as a dynamic secret key for the MPFrFT OFDM system in which the encryption process is applied in the frequency domain. The proposed DCBS secret key generator generates a very large key space of (Formula presented.). The proposed DCBS secret keys generator can achieve the confidentiality and authentication properties. Statistical analysis, differential analysis and a key sensitivity test are performed to estimate the security strengths of the proposed DCBS-MP-FrFT-OFDM cryptosystem over the IoT network. The experimental results show that the proposed DCBS-MP-FrFT-OFDM cryptosystem is robust against common signal processing attacks and provides a high security level for image encryption application. © 2023 by the authors

Dual operative radar for vehicle to vehicle and vehicle to infrastructure communication

The research presented in this Thesis deals with the concepts of joint radar and communication system for automotive application. The novel systems developed include a joint radar and communication system based on the fractional Fourier transform (FrFT) and two interference mitigation frameworks. In the joint radar and communication system the FrFT is used to embed the data information into a radar waveform in order to obtain a signal sharing Linear Frequency Modulation (LFM) characteristics while allowing data transmission. Furthermore, in the proposed system multi user operations are allowed by assigning a specific order of the FrFT to each user. In this way, a fractional order division multiplexing can be implemented allowing the allocation of more than one user in the same frequency band with the advantage that the range resolution does not depend on the number of the users that share the same frequency band but only from the assigned of the FrFT. Remarkably, the predicted simulated radar performance of the proposed joint radar and communication system when using Binary Frequency Shift Keying (BFSK) encoding is not significantly affected by the transmitted data. In order to fully describe the proposed waveform design, the signal model when the bits of information are modulated using either BFSK or Binary Phase Shift Keying (BPSK) encoding is derived. This signal model will result also useful in the interference mitigation frameworks. In multi user scenarios to prevent mutual radar interference caused by users that share the same frequency band at the same time, each user has to transmit waveforms that are uncorrelated with those of other users. However, due to spectrum limitations, the uncorrelated property cannot always be satisfied even by using fractional order division multiplexing, thus interference is unavoidable. In order to mitigate the interference, two frameworks are introduced. In a joint radar communication system, the radar also has access to the communication data. With a near-precision reconstruction of the communication signal, this interference can be subtracted. In these two frameworks the interfering signal can be reconstructed using the derived mathematical model of the proposed FrFT waveform. In the first framework the subtraction between the received and reconstructed interference signals is carried out in a coherent manner, where the amplitude and phase of the two signals are taken into account. The performance of this framework is highly depend on the correct estimation of the Doppler frequency of the interfering user. A small error on the Doppler frequency can lead to a lack of synchronization between the received and reconstructed signal. Consequently, the subtraction will not be performed in a correct way and further interference components can be introduced. In order to solve the problem of the lack of the synchronization an alternative framework is developed where the subtraction is carried out in non-coherent manner. In the proposed framework, the subtraction is carried out after that the received radar signal and the reconstructed interference are processed, respectively. The performance is tested on simulated and real signals. The simulated and experimental results show that this framework is capable of mitigating the interference from other users successfully.The research presented in this Thesis deals with the concepts of joint radar and communication system for automotive application. The novel systems developed include a joint radar and communication system based on the fractional Fourier transform (FrFT) and two interference mitigation frameworks. In the joint radar and communication system the FrFT is used to embed the data information into a radar waveform in order to obtain a signal sharing Linear Frequency Modulation (LFM) characteristics while allowing data transmission. Furthermore, in the proposed system multi user operations are allowed by assigning a specific order of the FrFT to each user. In this way, a fractional order division multiplexing can be implemented allowing the allocation of more than one user in the same frequency band with the advantage that the range resolution does not depend on the number of the users that share the same frequency band but only from the assigned of the FrFT. Remarkably, the predicted simulated radar performance of the proposed joint radar and communication system when using Binary Frequency Shift Keying (BFSK) encoding is not significantly affected by the transmitted data. In order to fully describe the proposed waveform design, the signal model when the bits of information are modulated using either BFSK or Binary Phase Shift Keying (BPSK) encoding is derived. This signal model will result also useful in the interference mitigation frameworks. In multi user scenarios to prevent mutual radar interference caused by users that share the same frequency band at the same time, each user has to transmit waveforms that are uncorrelated with those of other users. However, due to spectrum limitations, the uncorrelated property cannot always be satisfied even by using fractional order division multiplexing, thus interference is unavoidable. In order to mitigate the interference, two frameworks are introduced. In a joint radar communication system, the radar also has access to the communication data. With a near-precision reconstruction of the communication signal, this interference can be subtracted. In these two frameworks the interfering signal can be reconstructed using the derived mathematical model of the proposed FrFT waveform. In the first framework the subtraction between the received and reconstructed interference signals is carried out in a coherent manner, where the amplitude and phase of the two signals are taken into account. The performance of this framework is highly depend on the correct estimation of the Doppler frequency of the interfering user. A small error on the Doppler frequency can lead to a lack of synchronization between the received and reconstructed signal. Consequently, the subtraction will not be performed in a correct way and further interference components can be introduced. In order to solve the problem of the lack of the synchronization an alternative framework is developed where the subtraction is carried out in non-coherent manner. In the proposed framework, the subtraction is carried out after that the received radar signal and the reconstructed interference are processed, respectively. The performance is tested on simulated and real signals. The simulated and experimental results show that this framework is capable of mitigating the interference from other users successfully

Characterization and design of coherent optical OFDM transmission systems based on Hartley Transform

Nowadays, due to huge deployment of optical transport networks, a continuous increase towards higher data rates up to 100 Gb/s and beyond is observed. Furthermore, an evolution of the current optical networks is forecasted, acquiring new functionalities, e.g. elastic spectrum assignment for the optical signals. The target for these new challenges in transmission is to find techniques ready to deal with a growth of demand for bandwidth continuously asked by network operators, for whom the standard systems do not meet the new functionalities while higher rates are being set up. A solution for covering all of those needs is to adapt techniques capable to deal with such enormous data rates, and ensuring the same high efficiency for long distances and mitigate the optical impairments accumulated along the transmission path. Additionally, these transmission techniques are expected to provide some degree of flexibility, in order to enhance the network flexibility. A promising technology that can fully cope with those requires is the coherent optical orthogonal frequency division multiplexing (CO-OFDM). CO-OFDM provides several advantages, namely high sensitivity and spectral efficiency, simple integration and possibility to fully recover a signal in phase, amplitude and polarization. These systems are composed by digital signal processing (DSP) blocks that easily process data and can equalize and compensate the main impairments, providing high tolerance for dispersion effects. However, CO-OFDM systems are not free from drawbacks. Their high peak-to-average power ratio (PAPR) reduce their tolerance to nonlinearities. Furthermore, CO-OFDM systems are sensitive to any frequency shift and phase offset. Hence, a constant envelope optical OFDM (CE-OFDM) is proposed for significantly reducing the PAPR and solving high sensitivity to nonlinear impairments. It consists in a phase modulated discrete multi-tone signal, which is coherently detected at the receiver side. An alternative transform, the discrete Hartley transform, is proposed to speed up calculations in the DSP and eliminate the need to have a Hermitian symmetry. The optical CE-OFDM by its unique flexibility and rate scalability turns out as a great technology applicable to different configurations, ranging from access to core networks. In case of access solutions, several cases are investigated. First, the optical CE-OFDM is applied for radio access network signals delivery by means of a wavelength division multiplexing (WDM) overlay in deployed access architecture. A decomposed radio access network is deployed over an existing standard passive optical network (PON), capable to avoid interference and cross talks with access signals between network clients. The system exhibited narrow channel spacing, while reducing losses fed into the access equipment path. Next, a full duplex 10 Gb/s bidirectional PON transmission over a single wavelength with RSOA based ONU is investigated. The key point of that system is the upstream transmission, which is achieved re-modulating the phase of a downstream intensity modulated signal after proper saturation. The reported sensitivity performances show a power budget matching the PON standards and an OSNR easy to reach on non-amplified PON. Next, a flexible metropolitan area network of up to 100km with traffic add/drop using WDM is investigated. There the narrowing effect of the optical filters is studied. Finally, an elastic upgrade of the existing Telefonica model of the Spanish national core network is proposed. For that, the transceiver architecture is proposed to be operated featuring polarization multiplexing. Respect to the existing fixed grid, the flexible approach (enabled by the CE-OFDM transceiver) results into reduced bandwidth occupancy and low OSNR requirement.Hoy en día, debido al gran despliegue de las redes de ópticas de transporte, se espera un aumento continuado hacia mayores velocidades de datos, hasta 100 Gb/s y más allá. Por otra parte, la evolución que se prevé para las redes ópticas actuales, incluye la adquisición de nuevas funcionalidades, por ejemplo, la asignación del espectro de forma elástica para las señales ópticas. Por tanto, el claro desafío en cuanto a las tecnologías de transmisión es encontrar técnicas preparadas para hacer frente a un crecimiento de la demanda de ancho de banda; demanda que continuamente se incrementa por parte de los operadores de red, para quienes los sistemas estándar no se acaban de ajustar a las nuevas funcionalidades que esperan para la red. Una solución para cubrir todas estas necesidades es la adaptación de técnicas capaces de hacer frente a estas velocidades de datos enormes, y garantizar el mismo nivel de eficiencia para las largas distancias y mitigar las deficiencias ópticas acumuladas a lo largo de la ruta de transmisión. Además, se espera que estas técnicas de transmisión puedan proporcionar cierto grado de flexibilidad, a fin de mejorar y hacer más eficiente la gestión de la red. Una tecnología prometedora que puede hacer frente a estos requisitos es lo que se llama multiplexación por división de frecuencias ortogonales, combinado con la detección óptica coherente (CO-OFDM). CO-OFDM ofrece varias ventajas, entre otras: alta sensibilidad y eficiencia espectral y, sobre todo, la posibilidad de recuperar por completo de una señal en fase, la amplitud y la polarización. Estos sistemas están compuestos por bloques de procesado de señales digitales (DSP) que permiten detectar los datos fácilmente así como también compensar las principales degradaciones, proporcionando alta tolerancia a los efectos de dispersión. Sin embargo, los sistemas CO-OFDM no están exentos de inconvenientes. Su alta relación de potencia de pico a potencia media (PAPR) reduce sensiblemente la tolerancia no linealidades. Por otra parte, los sistemas CO-OFDM son sensibles a cualquier cambio de frecuencia y desplazamiento de fase. Por tanto, se propone un sistema OFDM de envolvente constante (CE-OFDM) para reducir significativamente la PAPR y solucionar la alta sensibilidad a las degradaciones no lineales. Consiste en una señal OFDM modulada en fase, que se detecta coherentemente en el receptor. Una transformada alternativa, la transformada discreta de Hartley, se propone para acelerar los cálculos en el DSP. El sistema CE-OFDM por su flexibilidad y escalabilidad única, resulta una tecnología aplicable a diferentes escenarios, que van desde las redes de acceso hasta las redes troncales. En el caso de las soluciones de acceso, se investigan varios casos. En primer lugar, el CE-OFDM aplica para el desarrollo y soporte de datos de una red radio, reutilizando una red óptica de acceso ya desplegada. A continuación, se investiga la transmisión bidireccional dúplex a 10 Gb / s sobre una sola longitud de onda empleando un RSOA a las unidades de usuario. El punto clave de este sistema es la transmisión en sentido ascendente, que se consigue re-modulando la fase de una señal de intensidad modulada después de saturar de forma adecuada. A continuación, se estudia una red de área metropolitana flexible de hasta 100 km. Concretamente el efecto de concatenación de filtros ópticos es el objetivo de este estudio. Finalmente, se propone una actualización elástica del modelo de Telefónica I+D para la red troncal española. Por ello, se propone operar el CE-OFDM en multiplexación de polarización. Los resultados muestran que esta combinación reduce sensiblemente el empleo de ancho de banda esto como los requisitos de los enlaces transmisión, reduciendo también los costes tanto de desarrollo como de operación y mantenimiento de la red.Avui dia, a causa del gran desplegament de les xarxes de òptiques de transport, s'espera un augment continuat cap a majors velocitats de dades, fins a 100 Gb/s i més enllà. D'altra banda, l'evolució que es preveu per a les xarxes òptiques actuals, inclou l'adquisició de noves funcionalitats, per exemple, assignació de l'espectre de forma elàstica per als senyals òptics. Per tant, el clar desafiament pel que fa a les tecnologies de transmissió és trobar tècniques preparades per fer front a un creixement de la demanda d'ample de banda; demanda que contínuament es fa per part dels operadors de xarxa, per als qui els sistemes estàndard no s'acaben d'ajustar a les noves funcionalitats que esperen per a la xarxa. Una solució per a cobrir totes aquestes necessitats és l'adaptació de tècniques capaces de fer front a aquestes velocitats de dades enormes, i garantir el mateix nivell d'eficiència per a les llargues distàncies i mitigar les deficiències òptiques acumulades al llarg de la ruta de transmissió. A més, s'espera que aquestes tècniques de transmissió puguin proporcionar cert grau de flexibilitat, per tal de millorar i tornar més eficient la gestió de la xarxa. Una tecnologia prometedora que pot fer front a aquests requisits és el que s'anomena multiplexació per divisió de freqüències ortogonals, combinat amb la detecció òptica coherent (CO-OFDM). CO-OFDM ofereix diversos avantatges, entre altres: alta sensibilitat i eficiència espectral i, sobretot, la possibilitat de recuperar per complet d'una senyal en fase, l'amplitud i la polarització. Aquests sistemes estan compostos per blocs de processament de senyals digitals (DSP) que permeten detectar les dades fàcilment així com també compensar les principals degradacions, proporcionant alta tolerància pels efectes de dispersió. No obstant això, els sistemes CO-OFDM no estan exempts d'inconvenients. La seva alta relació de potència de pic a potència mitjana (PAPR) redueix sensiblement la tolerància a no linealitats. D'altra banda, els sistemes de CO-OFDM són sensibles a qualsevol canvi de freqüència i desplaçament de fase. Per tant, es proposa un sistema OFDM d'envolvent constant (CE-OFDM) per a reduir significativament la PAPR i solucionar l'alta sensibilitat a les degradacions no lineals. Consisteix en un senyal OFDM modulat en fase, que es detecta coherentment en el receptor. Una transformada alternativa, la transformada discreta d'Hartley, es proposa accelerar els càlculs en el DSP. El sistema CE-OFDM per la seva flexibilitat i escalabilitat única, resulta una tecnologia aplicable a diferents escenaris, que van des de les xarxes d'accés fins a les xarxes troncals. En el cas de les solucions d'accés, s'investiguen diversos casos. En primer lloc, el CE-OFDM s'aplica per al desplegament i suport de dades d'una xarxa radio, reutilitzant una xarxa òptica d'accés ja desplegada. A continuació, s'investiga la transmissió bidireccional dúplex a 10 Gb/s sobre una sola longitud d'ona emprant un RSOA a les unitats d'usuari. El punt clau d'aquest sistema és la transmissió en sentit ascendent, que s'aconsegueix re-modulant la fase d'un senyal d'intensitat modulada després de saturar-la de forma adequada. A continuació, s'estudia una xarxa d'àrea metropolitana flexible de fins a 100 km. Concretament l'efecte de concatenació de filtres òptics és l'objectiu d'aquest estudi. Finalment, es proposa una actualització elàstica del model de Telefónica I+D per a la xarxa troncal espanyola. Per això, es proposa operar el CE-OFDM en multiplexació de polarització. Els resultats mostren que aquesta combinació redueix sensiblement l'ocupació d'ample de banda això com també els requisits dels enllaços transmissió, reduint també els costos tant de desplegament com d'operació i manteniment de la xarxa

Spectrally efficient FDM communication signals and transceivers: design, mathematical modelling and system optimization

This thesis addresses theoretical, mathematical modelling and design issues of Spectrally Efficient FDM (SEFDM) systems. SEFDM systems propose bandwidth savings when compared to Orthogonal FDM (OFDM) systems by multiplexing multiple non-orthogonal overlapping carriers. Nevertheless, the deliberate collapse of orthogonality poses significant challenges on the SEFDM system in terms of performance and complexity, both issues are addressed in this work. This thesis first investigates the mathematical properties of the SEFDM system and reveals the links between the system conditioning and its main parameters through closed form formulas derived for the Intercarrier Interference (ICI) and the system generating matrices. A rigorous and efficient mathematical framework, to represent non-orthogonal signals using Inverse Discrete Fourier Transform (IDFT) blocks, is proposed. This is subsequently used to design simple SEFDM transmitters and to realize a new Matched Filter (MF) based demodulator using the Discrete Fourier Transforms (DFT), thereby substantially simplifying the transmitter and demodulator design and localizing complexity at detection stage with no premium at performance. Operation is confirmed through the derivation and numerical verification of optimal detectors in the form of Maximum Likelihood (ML) and Sphere Decoder (SD). Moreover, two new linear detectors that address the ill conditioning of the system are proposed: the first based on the Truncated Singular Value Decomposition (TSVD) and the second accounts for selected ICI terms and termed Selective Equalization (SelE). Numerical investigations show that both detectors substantially outperform existing linear detection techniques. Furthermore, the use of the Fixed Complexity Sphere Decoder (FSD) is proposed to further improve performance and avoid the variable complexity of the SD. Ultimately, a newly designed combined FSD-TSVD detector is proposed and shown to provide near optimal error performance for bandwidth savings of 20% with reduced and fixed complexity. The thesis also addresses some practical considerations of the SEFDM systems. In particular, mathematical and numerical investigations have shown that the SEFDM signal is prone to high Peak to Average Power Ratio (PAPR) that can lead to significant performance degradations. Investigations of PAPR control lead to the proposal of a new technique, termed SLiding Window (SLW), utilizing the SEFDM signal structure which shows superior efficacy in PAPR control over conventional techniques with lower complexity. The thesis also addresses the performance of the SEFDM system in multipath fading channels confirming favourable performance and practicability of implementation. In particular, a new Partial Channel Estimator (PCE) that provides better estimation accuracy is proposed. Furthermore, several low complexity linear and iterative joint channel equalizers and symbol detectors are investigated in fading channels conditions with the FSD-TSVD joint equalization and detection with PCE obtained channel estimate facilitating near optimum error performance, close to that of OFDM for bandwidth savings of 25%. Finally, investigations of the precoding of the SEFDM signal demonstrate a potential for complexity reduction and performance improvement. Overall, this thesis provides the theoretical basis from which practical designs are derived to pave the way to the first practical realization of SEFDM systems