Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems

Modern radar (military, automotive, weather, etc.) and communication systems seek to leverage the spatio-spectral efficiency of phased arrays. Specifically, there is an increasingly large demand for fully-digital arrays, with each antenna element having its own transmitter and receiver. Further, in order to makes these systems realizable, low-cost, low-complexity solutions are required, often sacrificing the system's linearity. Lower linearity paired with the inherent lack of RF spacial filtering can make these highly digital systems vulnerable to high-power interferering signals-- potentially introducing spectral regrowth and/or gain compression, distorting the signal-of-interest. Digital linearization solutions such as Digital Pre-Distiortion (DPD) and Nonlinear Equalization (NLEQ) have been shown to effectively mitigate nonlinearities for transmitters and receivers, respectively. Further, DPD and NLEQ seek to extend the effective dynamic range of digital arrays, helping the systems reach their designed dynamic range improvement of $10\log_{10}(N)$~dB, where $N$ is the number of transmitters/receivers. However, the performance of these solutions is ultimately determined by training model and waveform. Further, the nonlinear characteristics of a system can change with temperature, frequency, power, time, etc., requiring a robust calibration technique to maintain a high-level of nonlinear mitigation. This dissertation reviews the different types of nonlinear models and the current NLEQ and DPD algorithms for digital array systems. Further, a generalized calibration waveform for both NLEQ and DPD is proposed, allowing a system to maximize its dynamic range over power and frequency. Additionally, an \textit{in-situ} calibration method, leveraging the inherent mutual coupling in an array, is proposed as a solution to maintaining a high level of performance in a fielded digital array system over the system's lifetime. The combination of the proposed training waveform and \textit{in-situ} calibration technique prove to be very effective at adaptively creating a generalized solution to extending the dynamic range of future low-cost digital array systems

Equalização digital para sistemas de transmissão ópticos coerentes

This thesis focus on the digital equalization of fiber impairments for coherent optical transmission systems. New efficient and low-complexity equalization and mitigation techniques that counteract fiber nonlinear impairments are proposed and the tradeoff between performance and complexity is numerically assessed and experimentally demonstrated in metro and long-haul 400G superchannels-based transmission systems. Digital backpropagation (DBP) based on low-complexity split-step Fourier method and Volterra series nonlinear equalizers are experimentally assessed in an uniform superchannel system. In contrast with standard DBP methods, these techniques prove to be able to be implemented with larger step-sizes, consequently requiring a reduced number of multiplications, and still achieve a significant reach extension over linear equalization techniques. Moreover, given its structure, the complexity of the proposed Volterra-based DBP approach can be easily adjusted by changing the nonlinear filter dimension according to the system requirements, thus providing a higher flexibility to the nonlinear equalization block. A frequency-hybrid superchannel envisioning near-future flexible networks is then proposed as a way to increase the system bit-rate granularity. The problematic of the power-ratio between superchannel carriers is addressed and optimized for linear and nonlinear operation regimes using three distinct FEC paradigms. Applying a single FEC to the entire superchannel has a simpler implementation and is found to be a more robust approach, tolerating larger uncertainties on the system parameters optimization. We also investigate the performance gain provided by the application of different DBP techniques in frequency-hybrid superchannel systems, and its implications on the optimum power-ratio. It is shown that the application of DBP can be restricted to the carrier transporting the higher cardinality QAM format, since the DBP benefit on the other carriers is negligible, which might bring a substantially complexity reduction of the DBP technique applied to the superchannel.A presente tese foca-se na equalização digital das distorções da fibra para sistemas óticos de transmissão coerente. São propostas novas técnicas eficientes e de baixa complexidade para a equalização e mitigação das distorções não lineares da fibra, e o compromisso entre desempenho e complexidade é testado numericamente e demonstrado experimental em sistemas de transmissão metro e longa distância baseados em supercanais 400G. A propagação digital inversa baseada no método de split-step Fourier e equalizadores não lineares de séries de Volterra de baixa complexidade são testadas experimentalmente num sistema baseado em supercanais uniformes. Ao contrário dos métodos convencionais utilizados, estas técnicas podem ser implementadas utilizando menos interações e ainda extender o alcance do sistema face às técnicas de equalização linear. Para além disso, a complexidade do método baseado em Volterra pode ser facilmente ajustada alterando a dimensão do filtro não linear de acordo com os requisitos do sistema, concedendo assim maior flexibilidade ao bloco de equalização não linear. Tendo em vista as futuras redes flexı́veis, um supercanal hı́brido na frequência é proposto de modo a aumentar a granularidade da taxa de transmissão do sistema. A problemática da relação de potência entre as portadoras do supercanal é abordada e optimizada em regimes de operação linear e não linear utilizando paradigmas diferentes de códigos correctores de erros. A aplicação de um único código corrector de erros à totalidade do supercanal mostra ser a abordagem mais robusta, tolerando maiores incertezas na optimização dos parâmetros do sistema. O ganho de desempenho dado pela aplicação de diferentes técnicas de propagação digital inversa em sistemas de supercanais hı́bridos na frequência é tamém analizado, assim como as suas implicações na relação óptima de potência. Mostra-se que esta pode ser restringida à portadora que transporta o formato de modulação de ordem mais elevada, uma vez que o benefı́cio trazido pelas restantes portadotas é negligenciável, permitindo reduzir significativamente a complexidade do algoritmo aplicado.Programa Doutoral em Telecomunicaçõe

Nonlinear Distortion in Wideband Radio Receivers and Analog-to-Digital Converters: Modeling and Digital Suppression

Emerging wireless communications systems aim to flexible and efficient usage of radio spectrum in order to increase data rates. The ultimate goal in this field is a cognitive radio. It employs spectrum sensing in order to locate spatially and temporally vacant spectrum chunks that can be used for communications. In order to achieve that, flexible and reconfigurable transceivers are needed. A software-defined radio can provide these features by having a highly-integrated wideband transceiver with minimum analog components and mostly relying on digital signal processing. This is also desired from size, cost, and power consumption point of view. However, several challenges arise, from which dynamic range is one of the most important. This is especially true on receiver side where several signals can be received simultaneously through a single receiver chain. In extreme cases the weakest signal can be almost 100 dB weaker than the strongest one. Due to the limited dynamic range of the receiver, the strongest signals may cause nonlinear distortion which deteriorates spectrum sensing capabilities and also reception of the weakest signals. The nonlinearities are stemming from the analog receiver components and also from analog-to-digital converters (ADCs). This is a performance bottleneck in many wideband communications and also radar receivers. The dynamic range challenges are already encountered in current devices, such as in wideband multi-operator receiver scenarios in mobile networks, and the challenges will have even more essential role in the future.This thesis focuses on aforementioned receiver scenarios and contributes to modeling and digital suppression of nonlinear distortion. A behavioral model for direct-conversion receiver nonlinearities is derived and it jointly takes into account RF, mixer, and baseband nonlinearities together with I/Q imbalance. The model is then exploited in suppression of receiver nonlinearities. The considered method is based on adaptive digital post-processing and does not require any analog hardware modification. It is able to extract all the necessary information directly from the received waveform in order to suppress the nonlinear distortion caused by the strongest blocker signals inside the reception band.In addition, the nonlinearities of ADCs are considered. Even if the dynamic range of the analog receiver components is not limiting the performance, ADCs may cause considerable amount of nonlinear distortion. It can originate, e.g., from undeliberate variations of quantization levels. Furthermore, the received waveform may exceed the nominal voltage range of the ADC due to signal power variations. This causes unintentional signal clipping which creates severe nonlinear distortion. In this thesis, a Fourier series based model is derived for the signal clipping caused by ADCs. Furthermore, four different methods are considered for suppressing ADC nonlinearities, especially unintentional signal clipping. The methods exploit polynomial modeling, interpolation, or symbol decisions for suppressing the distortion. The common factor is that all the methods are based on digital post-processing and are able to continuously adapt to variations in the received waveform and in the receiver itself. This is a very important aspect in wideband receivers, especially in cognitive radios, when the flexibility and state-of-the-art performance is required

Digital Front-End Signal Processing with Widely-Linear Signal Models in Radio Devices

Necessitated by the demand for ever higher data rates, modern communications waveforms have increasingly wider bandwidths and higher signal dynamics. Furthermore, radio devices are expected to transmit and receive a growing number of different waveforms from cellular networks, wireless local area networks, wireless personal area networks, positioning and navigation systems, as well as broadcast systems. On the other hand, commercial wireless devices are expected to be cheap, be relatively small in size, and have a long battery life. The demands for flexibility and higher data rates on one hand, and the constraints on production cost, device size, and energy efficiency on the other, pose difficult challenges on the design and implementation of future radio transceivers. Under these diametric constraints, in order to keep the overall implementation cost and size feasible, the use of simplified radio architectures and relatively low-cost radio electronics are necessary. This notion is even more relevant for multiple antenna systems, where each antenna has a dedicated radio front-end. The combination of simplified radio front-ends and low-cost electronics implies that various nonidealities in the remaining analog radio frequency (RF) modules, stemming from unavoidable physical limitations and material variations of the used electronics, are expected to play a critical role in these devices. Instead of tightening the specifications and tolerances of the analog circuits themselves, a more cost-effective solution in many cases is to compensate for these nonidealities in the digital domain. This line of research has been gaining increasing interest in the last 10-15 years, and is also the main topic area of this work. The direct-conversion radio principle is the current and future choice for building low-cost but flexible, multi-standard radio transmitters and receivers. The direct-conversion radio, while simple in structure and integrable on a single chip, suffers from several performance degrading circuit impairments, which have historically prevented its use in wideband, high-rate, and multi-user systems. In the last 15 years, with advances in integrated circuit technologies and digital signal processing, the direct-conversion principle has started gaining popularity. Still, however, much work is needed to fully realize the potential of the direct-conversion principle. This thesis deals with the analysis and digital mitigation of the implementation nonidealities of direct-conversion transmitters and receivers. The contributions can be divided into three parts. First, techniques are proposed for the joint estimation and predistortion of in-phase/quadrature-phase (I/Q) imbalance, power amplifier (PA) nonlinearity, and local oscillator (LO) leakage in wideband direct-conversion transmitters. Second, methods are developed for estimation and compensation of I/Q imbalance in wideband direct-conversion receivers, based on second-order statistics of the received communication waveforms. Third, these second-order statistics are analyzed for second-order stationary and cyclostationary signals under several other system impairments related to circuit implementation and the radio channel. This analysis brings new insights on I/Q imbalances and their compensation using the proposed algorithms. The proposed algorithms utilize complex-valued signal processing throughout, and naturally assume a widely-linear form, where both the signal and its complex-conjugate are filtered and then summed. The compensation processing is situated in the digital front-end of the transceiver, as the last step before digital-to-analog conversion in transmitters, or in receivers, as the first step after analog-to-digital conversion. The compensation techniques proposed herein have several common, unique, attributes: they are designed for the compensation of frequency-dependent impairments, which is seen critical for future wideband systems; they require no dedicated training data for learning; the estimators are computationally efficient, relying on simple signal models, gradient-like learning rules, and solving sets of linear equations; they can be applied in any transceiver type that utilizes the direct-conversion principle, whether single-user or multi-user, or single-carrier or multi-carrier; they are modulation, waveform, and standard independent; they can also be applied in multi-antenna transceivers to each antenna subsystem separately. Therefore, the proposed techniques provide practical and effective solutions to real-life circuit implementation problems of modern communications transceivers. Altogether, considering the algorithm developments with the extensive experimental results performed to verify their functionality, this thesis builds strong confidence that low-complexity digital compensation of analog circuit impairments is indeed applicable and efficient

Revisiting Efficient Multi-Step Nonlinearity Compensation with Machine Learning: An Experimental Demonstration

Efficient nonlinearity compensation in fiber-optic communication systems is considered a key element to go beyond the "capacity crunch''. One guiding principle for previous work on the design of practical nonlinearity compensation schemes is that fewer steps lead to better systems. In this paper, we challenge this assumption and show how to carefully design multi-step approaches that provide better performance--complexity trade-offs than their few-step counterparts. We consider the recently proposed learned digital backpropagation (LDBP) approach, where the linear steps in the split-step method are re-interpreted as general linear functions, similar to the weight matrices in a deep neural network. Our main contribution lies in an experimental demonstration of this approach for a 25 Gbaud single-channel optical transmission system. It is shown how LDBP can be integrated into a coherent receiver DSP chain and successfully trained in the presence of various hardware impairments. Our results show that LDBP with limited complexity can achieve better performance than standard DBP by using very short, but jointly optimized, finite-impulse response filters in each step. This paper also provides an overview of recently proposed extensions of LDBP and we comment on potentially interesting avenues for future work.Comment: 10 pages, 5 figures. Author version of a paper published in the Journal of Lightwave Technology. OSA/IEEE copyright may appl

Epälineaarinen vääristymä laajakaistaisissa analogia-digitaalimuuntimissa

This thesis discusses nonlinearities of analog-to-digital converters (ADCs) and their mitigation using digital signal processing (DSP). Particularly wideband radio receivers are considered here including, e.g., the emerging cognitive radio applications. In this kind of receivers, a single ADC converts a mixture of signals at different frequency bands to digital domain simultaneously. Different signals may have considerably different power levels and hence the overall dynamic range can be very large (even 50–60 dB). Therefore, even the smallest ADC nonlinearities can produce considerable amount of nonlinear distortion, which may cause a strong signal to block significantly weaker signal bands. One concrete source of nonlinear distortion is waveform clipping due to improper signal conditioning in the input of an ADC. In the thesis, a mathematical model for this phenomenon is derived through Fourier analysis and is then used as a basis for an adaptive interference cancellation (AIC) method. This is a general method for reducing nonlinear distortion and besides clipping it can be used, e.g., to compensate integral nonlinearity (INL) originating from unintentional deviations of the quantization levels. Additionally, an interpolation method is proposed in this thesis to restore clipped waveforms and hence reduce nonlinear distortion. Through several computer simulations and corresponding laboratory radio signal measurements, the performance of the proposed post-processing methods is illustrated. It can be seen from the results that the methods are able to reduce nonlinear distortion from a weak signal band in a considerable manner when there are strong blocking signals in the neighboring channels. According to the results, the AIC method would be a highly recommendable post-processing technique for modern radio receivers due to its general ability to reduce nonlinear distortion regardless of its source. /Kir10Tässä työssä käsitellään analogia-digitaalimuuntimien (AD-muuntimien) epälineaarisuuksia ja niiden lieventämistä digitaalisen signaalinkäsittelyn (DSP) avulla. Tätä on tarkasteltu erityisesti laajakaistaisten radiovastaanottimien näkökulmasta, joka käsittää mm. tulevat kognitiiviseen radioon liittyvät sovellukset. Tällaisissa vastaanottimissa yksittäinen AD-muunnin muuntaa samanaikaisesti useita eri taajuuskaistoilla olevia signaaleita digitaaliseen muotoon, jolloin yhteenlaskettu dynaaminen alue voi olla hyvin suuri (jopa 50–60 dB). Tämän takia AD-muuntimen pienimmätkin epälineaarisuudet voivat aiheuttaa huomattavasti epälineaarista vääristymää, minkä vuoksi voimakas signaali saattaa häiriöllään peittää muilla taajuuskaistoilla olevia selkeästi heikompia signaaleja. Eräs konkreettinen epälineaarisen vääristymän aiheuttaja on aaltomuodon leikkaantuminen AD-muuntimen sisäänmenossa jännitealueen ylittymisen vuoksi. Tässä työssä johdetaan matemaattinen malli kyseiselle ilmiölle Fourier-analyysin avulla ja käytetään sitä lähtökohtana adaptiiviselle häiriönpoistomenetelmälle (AIC-menetelmä). Se on yleisluonteinen menetelmä epälineaarisen vääristymän vähentämiseksi, ja leikkaantumisen lisäksi sitä voidaan käyttää esimerkiksi kompensoimaan integraalista epälineaarisuutta (INL), joka on peräisin kvantisointitasojen tahattomista poikkeamista. Lisäksi tässä työssä esitellään interpolointimenetelmä leikkaantuneen aaltomuodon ehostamiseen siten, että epälineaarinen häiriö vähenee. Esiteltyjen jälkikäsittelymenetelmien suorituskykyä analysoidaan ja havainnollistetaan useilla tietokonesimulaatiolla sekä niitä vastaavilla radiosignaalien laboratoriomittauksilla. Tuloksista voidaan nähdä, että nämä menetelmät kykenevät poistamaan huomattavasti epälineaarista vääristymää heikolta signaalikaistalta silloin, kun naapurikaistoilla on voimakkaita häiriösignaaleja. Tulosten perusteella AIC-menetelmä olisi erittäin suositeltava jälkikäsittelytekniikka moderneihin radiovastaanottimiin, koska se pystyy yleisesti vähentämään epälineaarista vääristymää riippumatta häiriön alkuperästä

Phase-coherent lightwave communications with frequency combs

Fiber-optical networks are a crucial telecommunication infrastructure in society. Wavelength division multiplexing allows for transmitting parallel data streams over the fiber bandwidth, and coherent detection enables the use of sophisticated modulation formats and electronic compensation of signal impairments. In the future, optical frequency combs may replace multiple lasers used for the different wavelength channels. We demonstrate two novel signal processing schemes that take advantage of the broadband phase coherence of optical frequency combs. This approach allows for a more efficient estimation and compensation of optical phase noise in coherent communication systems, which can significantly simplify the signal processing or increase the transmission performance. With further advances in space division multiplexing and chip-scale frequency comb sources, these findings pave the way for compact energy-efficient optical transceivers.Comment: 17 pages, 9 figure

Nonlinear models and algorithms for RF systems digital calibration

Focusing on the receiving side of a communication system, the current trend in pushing the digital domain ever more closer to the antenna sets heavy constraints on the accuracy and linearity of the analog front-end and the conversion devices. Moreover, mixed-signal implementations of Systems-on-Chip using nanoscale CMOS processes result in an overall poorer analog performance and a reduced yield. To cope with the impairments of the low performance analog section in this "dirty RF" scenario, two solutions exist: designing more complex analog processing architectures or to identify the errors and correct them in the digital domain using DSP algorithms. In the latter, constraints in the analog circuits' precision can be offloaded to a digital signal processor. This thesis aims at the development of a methodology for the analysis, the modeling and the compensation of the analog impairments arising in different stages of a receiving chain using digital calibration techniques. Both single and multiple channel architectures are addressed exploiting the capability of the calibration algorithm to homogenize all the channels' responses of a multi-channel system in addition to the compensation of nonlinearities in each response. The systems targeted for the application of digital post compensation are a pipeline ADC, a digital-IF sub-sampling receiver and a 4-channel TI-ADC. The research focuses on post distortion methods using nonlinear dynamic models to approximate the post-inverse of the nonlinear system and to correct the distortions arising from static and dynamic errors. Volterra model is used due to its general approximation capabilities for the compensation of nonlinear systems with memory. Digital calibration is applied to a Sample and Hold and to a pipeline ADC simulated in the 45nm process, demonstrating high linearity improvement even with incomplete settling errors enabling the use of faster clock speeds. An extended model based on the baseband Volterra series is proposed and applied to the compensation of a digital-IF sub-sampling receiver. This architecture envisages frequency selectivity carried out at IF by an active band-pass CMOS filter causing in-band and out-of-band nonlinear distortions. The improved performance of the proposed model is demonstrated with circuital simulations of a 10th-order band pass filter, realized using a five-stage Gm-C Biquad cascade, and validated using out-of-sample sinusoidal and QAM signals. The same technique is extended to an array receiver with mismatched channels' responses showing that digital calibration can compensate the loss of directivity and enhance the overall system SFDR. An iterative backward pruning is applied to the Volterra models showing that complexity can be reduced without impacting linearity, obtaining state-of-the-art accuracy/complexity performance. Calibration of Time-Interleaved ADCs, widely used in RF-to-digital wideband receivers, is carried out developing ad hoc models because the steep discontinuities generated by the imperfect canceling of aliasing would require a huge number of terms in a polynomial approximation. A closed-form solution is derived for a 4-channel TI-ADC affected by gain errors and timing skews solving the perfect reconstruction equations. A background calibration technique is presented based on cyclo-stationary filter banks architecture. Convergence speed and accuracy of the recursive algorithm are discussed and complexity reduction techniques are applied