A Framework for Analyzing Online Cross-correlators using Price's Theorem and Piecewise-Linear Decomposition

Precise estimation of cross-correlation or similarity between two random variables lies at the heart of signal detection, hyperdimensional computing, associative memories, and neural networks. Although a vast literature exists on different methods for estimating cross-correlations, the question what is the best and simplest method to estimate cross-correlations using finite samples ? is still not clear. In this paper, we first argue that the standard empirical approach might not be the optimal method even though the estimator exhibits uniform convergence to the true cross-correlation. Instead, we show that there exists a large class of simple non-linear functions that can be used to construct cross-correlators with a higher signal-to-noise ratio (SNR). To demonstrate this, we first present a general mathematical framework using Price's Theorem that allows us to analyze cross-correlators constructed using a mixture of piece-wise linear functions. Using this framework and high-dimensional embedding, we show that some of the most promising cross-correlators are based on Huber's loss functions, margin-propagation (MP) functions, and the log-sum-exp functions.Comment: 9 figure, 13 page

Hardware Architecture of a QAM Receiver for Short-Range Optical Communications

[EN] Short-reach optical fiber communications systems aim to achieve high throughput, in the order of tens of Gbps. The implementation of these high-speed systems requires parallel processing, which makes low-complexity designs of their subsystems a key to the successful large-scale deployment of this technology. Half-Cycle Nyquist Subcarrier Modulation (HC-SCM) was originally suggested for these systems with the goal of using as much bandwidth as possible and, therefore, achieving high communication rates. Recently, Oversampled Subcarrier Modulation (OVS-SCM) was proposed as an alternative more computational efficient than HC-SCM and also with a better spectral efficiency. This paper proposes a hardware-efficient architecture for an OVS-SCM receiver, which takes into account the inherent parallel processing of these systems. This receiver takes 16 samples in parallel from a 5 GSa/s analog-to-digital converter with a 3.2 GHz 3 dB bandwidth. Design solutions for the frame detection block, the mixer, the resampler, the fractional interpolator, the matched filter and the timing estimator are presented. Our results show that, compared to the HC-SCM receiver, this proposal reduces the computational load of the downconverter stages by 90%. FPGA implementation results are given to demonstrate that our proposal can be implemented in state-of-the-art devices.This work was supported in part by MCIN/AEI/10.13039/501100011033 under Grants RTI2018-101658-B100 and PID2021-126514OB-I00, and in part by the European Union through "ERDF Away of making Europe."Valls Coquillat, J.; Torres Carot, V.; Pérez Pascual, MA.; Almenar Terre, V. (2023). Hardware Architecture of a QAM Receiver for Short-Range Optical Communications. Journal of Lightwave Technology. 41(2):451-461. https://doi.org/10.1109/JLT.2022.321735745146141

Digital image correlation (DIC) analysis of the 3 December 2013 Montescaglioso landslide (Basilicata, Southern Italy). Results from a multi-dataset investigation

Image correlation remote sensing monitoring techniques are becoming key tools for providing effective qualitative and quantitative information suitable for natural hazard assessments, specifically for landslide investigation and monitoring. In recent years, these techniques have been successfully integrated and shown to be complementary and competitive with more standard remote sensing techniques, such as satellite or terrestrial Synthetic Aperture Radar interferometry. The objective of this article is to apply the proposed in-depth calibration and validation analysis, referred to as the Digital Image Correlation technique, to measure landslide displacement. The availability of a multi-dataset for the 3 December 2013 Montescaglioso landslide, characterized by different types of imagery, such as LANDSAT 8 OLI (Operational Land Imager) and TIRS (Thermal Infrared Sensor), high-resolution airborne optical orthophotos, Digital Terrain Models and COSMO-SkyMed Synthetic Aperture Radar, allows for the retrieval of the actual landslide displacement field at values ranging from a few meters (2–3 m in the north-eastern sector of the landslide) to 20–21 m (local peaks on the central body of the landslide). Furthermore, comprehensive sensitivity analyses and statistics-based processing approaches are used to identify the role of the background noise that affects the whole dataset. This noise has a directly proportional relationship to the different geometric and temporal resolutions of the processed imagery. Moreover, the accuracy of the environmental-instrumental background noise evaluation allowed the actual displacement measurements to be correctly calibrated and validated, thereby leading to a better definition of the threshold values of the maximum Digital Image Correlation sub-pixel accuracy and reliability (ranging from 1/10 to 8/10 pixel) for each processed dataset

Chip and Signature Interleaving in DS CDMA Systems

Siirretty Doriast

Validation of the HERA Phase i Epoch of Reionization 21 cm Power Spectrum Software Pipeline

We describe the validation of the HERA Phase I software pipeline by a series of modular tests, building up to an end-to-end simulation. The philosophy of this approach is to validate the software and algorithms used in the Phase I upper-limit analysis on wholly synthetic data satisfying the assumptions of that analysis, not addressing whether the actual data meet these assumptions. We discuss the organization of this validation approach, the specific modular tests performed, and the construction of the end-to-end simulations. We explicitly discuss the limitations in scope of the current simulation effort. With mock visibility data generated from a known analytic power spectrum and a wide range of realistic instrumental effects and foregrounds, we demonstrate that the current pipeline produces power spectrum estimates that are consistent with known analytic inputs to within thermal noise levels (at the 2σ level) for k > 0.2h Mpc-1 for both bands and fields considered. Our input spectrum is intentionally amplified to enable a strong "detection"at k ∼ 0.2 h Mpc-1 - at the level of ∼25σ - with foregrounds dominating on larger scales and thermal noise dominating at smaller scales. Our pipeline is able to detect this amplified input signal after suppressing foregrounds with a dynamic range (foreground to noise ratio) of ⪆107. Our validation test suite uncovered several sources of scale-independent signal loss throughout the pipeline, whose amplitude is well-characterized and accounted for in the final estimates. We conclude with a discussion of the steps required for the next round of data analysis

Generalized discrete Fourier transform with non-linear phase : theory and design

Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in various engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. Among these popular transforms, DFT is a linear phase transform and widely used in multicarrier communications due to its performance and fast algorithms. In this thesis, a theoretical framework for Generalized DFT (GDFT) with nonlinear phase exploiting the phase space is developed. It is shown that GDFT offers sizable correlation improvements over DFT, Walsh, and Gold codes. Brute force search algorithm is employed to obtain orthogonal GDFT code sets with improved correlations. Design examples and simulation results on several channel types presented in the thesis show that the proposed GDFT codes, with better auto and cross-correlation properties than DFT, lead to better bit-error-rate performance in all multi-carrier and multi-user communications scenarios investigated. It is also highlighted how known constant modulus code families such as Walsh, Walsh-like and other codes are special solutions of the GDFT framework. In addition to theoretical framework, practical design methods with computationally efficient implementations of GDFT as enhancements to DFT are presented in the thesis. The main advantage of the proposed method is its ability to design a wide selection of constant modulus orthogonal code sets based on the desired performance metrics mimicking the engineering .specs of interest. Orthogonal Frequency Division Multiplexing (OFDM) is a leading candidate to be adopted for high speed 4G wireless communications standards due to its high spectral efficiency, strong resistance to multipath fading and ease of implementation with Fast Fourier Transform (FFT) algorithms. However, the main disadvantage of an OFDM based communications technique is of its high PAPR at the RF stage of a transmitter. PAPR dominates the power (battery) efficiency of the radio transceiver. Among the PAPR reduction methods proposed in the literature, Selected Mapping (SLM) method has been successfully used in OFDM communications. In this thesis, an SLM method employing GDFT with closed form phase functions rather than fixed DFT for PAPR reduction is introduced. The performance improvements of GDFT based SLM PAPR reduction for various OFDM communications scenarios including the WiMAX standard based system are evaluated by simulations. Moreover, an efficient implementation of GDFT based SLM method reducing computational cost of multiple transform operations is forwarded. Performance simulation results show that power efficiency of non-linear RF amplifier in an OFDM system employing proposed method significantly improved

Wideband Channel Sounding Techniques for Dynamic Spectrum Access Networks

In recent years, cognitive radio has drawn extensive research attention due to its ability to improve the efficiency of spectrum usage by allowing dynamic spectrum resource sharing between primary and secondary users. The concept of cognitive radio was first presented by Joseph Mitola III and Gerald Q. Maguire, Jr., in which either network or wireless node itself changes particular transmission and reception parameters to execute its tasks efficiently without interfering with the primary users [1]. Such a transceiving mechanism and network environment is called the dynamic spectrum access (DSA) network. The Federal Communications Commission (FCC) allows any type of transmission in unlicensed bands at any time as long as their transmit power level obeys specific FCC regulations. Performing channel sounding as a secondary user in such an environment becomes a challenge due to the rapidly changing network environment and also the limited transmission power. Moreover, to obtain the long term behavior of the channel in the DSA network is impractical with conventional channel sounders due to frequent changes in frequency, transmission bandwidth, and power. Conventional channel sounding techniques need to be adapted accordingly to be operated in the DSA networks. In this dissertation, two novel channel sounding system frameworks are proposed. The Multicarrier Direct Sequence Swept Time-Delay Cross Correlation (MC-DS-STDCC) channel sounding technique is designed for the DSA networks aiming to perform channel sounding across a large bandwidth with minimal interference. It is based on the STDCC channel sounder and Multicarrier Direct Sequence Code Division Multiple Access (MC-DS-CDMA) technique. The STDCC technique, defined by Parsons [2], was first employed by Cox in the measurement of 910 MHz band [3{6]. The MC-DS-CDMA technique enables the channel sounder to be operated at different center frequencies with low transmit power. Hence, interference awareness and frequency agility are achieved. The OFDM-based channel sounder is an alternative to the MC-DS-STDCC technique. It utilizes user data as the sounding signal such that the interference is minimized during the course of transmission. Furthermore, the OFDM-based channel sounder requires lower sampling rate than the MC-DS-STDCC system since no spreading is necessary

DSP-based CW lidars for clouds and aerosol

This thesis aims at exploring the limits of low peak-power, low-cost, all-semiconductor, compact lidars (laser radars) for range-resolved remote sensing of atmospheric aerosols and clouds. The systems investigated are based on laser diodes for emitter, avalanche photodiodes for the receiver, and digital signal processors for processing the returns from the atmosphere and the system control. The studied systems are built on the use of M-sequences and other derivated ones, which allows retrieving range-dependent information from the returning echoes, while having almost the same number of ones and zeros to maximize the transmitted average power for a limited peak power. The use of digital processors to generate the modulating sequences and to process the lidar returns allows for systems with agile reconfiguration capabilities and the use of very long sequences while keeping the processing time virtually negligible compared with the time employed to transmit the laser pulse-modulated output and receive the echoes from the atmosphere (the measuring time). The theorical developments are tested and demonstrated by the experimental results obtained with two lidar prototypes designed and build according the theoretical framework. The detection of cloud bases up to 8km with transmission peak powers of 125 mW in the near (almost visible) infrared (785 nm wavelength), with spatial resolution of 70 to 100 m and time resolution from 30 seconds to 4 minutes, has been achieved. Aerosols at lower altitudes are also observed in conditions of high aerosol load. In addition to further developments in low-cost lidar systems for detections of particles suspended in the atmosphere, the technical developments of this work pave also the way to the design of low-power systems por open path, range-resolved detection of gases, for example in industrial environments. After an introductory chapter, chapter 2 reviews the basic principles of lidar systems and focuses on continuous-wave systems with pseudorandom sequence modulation of the transmitted power and the constraints set by the requirement of a low peak-power transmitter. Chapter 3 reviews different types of power-modulating digital sequences that can be used, with the constraint of average 50% duty cycle, selects the best ones to be investigated in the experimental study, and unravels some of the issues associated to possible non-linear behavior of the photoreceiver. Chapter 4 presents the theoretical performance of the system, which is compared to a model that takes into account the technical constraints and non-idealities of the system building blocks. Chapter 5 sets out the complete design of the prototypes that have been built and tested, which are presented in chapter 6. Chapter 7 presents the tests and field results obtained with the prototypes built according to the design discussed in chapter 5. Chapter 8 presents the conclusions and outlines possible lines opened by the thesis work. Two appendices (chapter 9) develop further details on the detrimental effect of non-linear behavior in the receiver chain, and practical aspects of the alignment procedure between the lidar transmitter and the receiving optics.Aquesta tesi té com a objectiu explorar els límits dels lidars compactes (radars làser) de baixa potència de pic, baix cost, tot basat en semiconductors per a la detecció remota de núvols i aerosols atmosfèrics amb resolució en distància. Els sistemes investigats es basen en díodes làser per a l 'emissor, fotodíodes d'allau per al receptor i processadors digitals de senyal per a processar els retorns atmosfèrics i el control del sistema. Els sistemes estudiats es basen en l'ús de seqüències M i altres de derivades, el que permet recuperar la informació de la distancia dependent dels ecos del retorn, al mateix temps que té gairebé el mateix nombre d'uns i zeros per maximitzar la potència mitjana transmesa amb una potència de pic limitada. L'ús de processadors digitals per generar seqüències de modulació i retorns del lidar permet sistemes amb capacitat de canviar de configuració àgil i l'ús de seqüències molt llargues, mantenint el temps de processament pràcticament insignificant en comparació amb el temps dedicat a transmetre la sortida modulada del pols làser i rebre ecos de l'atmosfera (temps de mesurament). Els desenvolupaments teòrics són provats i demostrats amb resultats experimentals obtinguts amb dos prototips lidar dissenyats i construïts segons el marc teòric. La detecció de base de núvols fins a 8 km s'ha aconseguit amb potències de transmissió de 125 mW de potència en infraroig proper (quasi visible, 785 nm de longitud d'ona), amb resolució espacial de 70 a 100 m i resolució de temps de 30 segons a 4 minuts. Els aerosols en altituds més baixes també s'observen sota condicions de càrregues d'aerosols elevades. A més de nous desenvolupaments en sistemes lidar de baix cost per a la detecció de partícules en suspensió a l'atmosfera, els desenvolupaments tècnics d'aquest treball també preparen el camí per al disseny de sistemes de detecció de gasos de baix consum, amb resolució en distància, per exemple , en entorns industrials. Després d'un capítol introductori, el capítol 2 revisa els principis bàsics dels sistemes lidar i es centra en els sistemes d'ona contínua amb modulació amb seqüència pseudoaleatòries de la potència transmesa i les restriccions establertes per l'exigència d'un transmissor de potència de baixa potència de pic. El capítol 3 comentaris els diferents tipus de seqüències digitals per a la modulació de potència que es poden utilitzar, amb la restricció del cicle mitjà de treball del 50%, selecciona les millors per ser investigades en l'estudi experimental i desentranya alguns dels problemes associats amb el possible comportament no lineal del fotoreceptor. El capítol 4 presenta el rendiment teòric del sistema, que es compara amb un model que té en compte les limitacions tècniques i les no idealitats dels components bàsics del sistema. El capítol 5 estableix el disseny complet dels prototips que s'han construït i provat, que es presenten en el capítol 6. El capítol 7 presenta les proves i els resultats de camp obtinguts amb prototips construïts d'acord amb el disseny discutit en el capítol 5. El capítol 8 presenta les conclusions i s'esbossen possibles línies obertes pel treball de la tesi. Dos apèndixs (capítol 9) desenvolupen més detalls sobre l'efecte perjudicial del comportament no lineal en la cadena receptora i aspectes pràctics del procediment d'alineació entre el transmissor LIDAR i l'òptica receptora