From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in Signal Processing, the special issue on Compressed Sensin

Time-Interleaved Analog-to-Digital Converter (TIADC) Compensation Using Multichannel Filters

Published methods that employ a filter bank for compensating the timing and bandwidth mismatches of an M-channel time-interleaved analog-to-digital converter (TIADC) were developed based on the fact that each sub-ADC channel is a downsampled version of the analog input. The output of each sub-ADC is filtered in such a way that, when all the filter outputs are summed, the aliasing components are minimized. If each channel of the filter bank has N coefficients, the optimization of the coefficients requires computing the inverse of an MN times MN matrix if the weighted least squares (WLS) technique is used as the optimization tool. In this paper, we present a multichannel filtering approach for TIADC mismatch compensation. We apply the generalized sampling theorem to directly estimate the ideal output of each sub-ADC using the outputs of all the sub-ADCs. If the WLS technique is used as the optimization tool, the dimension of the matrix to be inversed is N times N. For the same number of coefficients (and also the same spurious component performance given sufficient arithmetic precision), our technique is computationally less complex and more robust than the filter-bank approach. If mixed integer linear programming is used as the optimization tool to produce filters with coefficient values that are integer powers of two, our technique produces a saving in computing resources by a factor of approximately (100.2N(M- 1)/(M-1) in the TIADC filter design.published_or_final_versio

Digitally-Assisted Mixed-Signal Wideband Compressive Sensing

Digitizing wideband signals requires very demanding analog-to-digital conversion (ADC) speed and resolution specifications. In this dissertation, a mixed-signal parallel compressive sensing system is proposed to realize the sensing of wideband sparse signals at sub-Nqyuist rate by exploiting the signal sparsity. The mixed-signal compressive sensing is realized with a parallel segmented compressive sensing (PSCS) front-end, which not only can filter out the harmonic spurs that leak from the local random generator, but also provides a tradeoff between the sampling rate and the system complexity such that a practical hardware implementation is possible. Moreover, the signal randomization in the system is able to spread the spurious energy due to ADC nonlinearity along the signal bandwidth rather than concentrate on a few frequencies as it is the case for a conventional ADC. This important new property relaxes the ADC SFDR requirement when sensing frequency-domain sparse signals. The mixed-signal compressive sensing system performance is greatly impacted by the accuracy of analog circuit components, especially with the scaling of CMOS technology. In this dissertation, the effect of the circuit imperfection in the mixed-signal compressive sensing system based on the PSCS front-end is investigated in detail, such as the finite settling time, the timing uncertainty and so on. An iterative background calibration algorithm based on LMS (Least Mean Square) is proposed, which is shown to be able to effectively calibrate the error due to the circuit nonideal factors. A low-speed prototype built with off-the-shelf components is presented. The prototype is able to sense sparse analog signals with up to 4 percent sparsity at 32 percent of the Nqyuist rate. Many practical constraints that arose during building the prototype such as circuit nonidealities are addressed in detail, which provides good insights for a future high-frequency integrated circuit implementation. Based on that, a high-frequency sub-Nyquist rate receiver exploiting the parallel compressive sensing is designed and fabricated with IBM90nm CMOS technology, and measurement results are presented to show the capability of wideband compressive sensing at sub-Nyquist rate. To the best of our knowledge, this prototype is the first reported integrated chip for wideband mixed-signal compressive sensing. The proposed prototype achieves 7 bits ENOB and 3 GS/s equivalent sampling rate in simulation assuming a 0.5 ps state-of-art jitter variance, whose FOM beats the FOM of the high speed state-of-the-art Nyquist ADCs by 2-3 times. The proposed mixed-signal compressive sensing system can be applied in various fields. In particular, its applications for wideband spectrum sensing for cognitive radios and spectrum analysis in RF tests are discussed in this work

Photonic Technologies for Radar and Telecomunications Systems

The growing interest in flexible architectures radio and the recent progress in the high speed digital signal processor make a software defined radio system an enabling technology for several digital signals processing architecture and for the flexible signal generation. In this direction wireless radar\telecommunications receiver with digital backend as close as possible to the antenna, as well as the software defined signal generation, reaches several benefits in term of reconfigurabilty, reliability and cost with respect to the analogical front-ends. Unfortunately the present scenario ensures direct sampling and digital downconversion only at the intermediate frequency. Therefore these kinds of systems are quite vulnerable to mismatches and hardware non-idealities in particular due to the mixers stages and filtering process. Furthermore, since the limited input bandwidth, speed and precision of the analog to digital converters represent the main digital system‘s bottleneck, today‘s direct radio frequency sampling is only possible at low frequency. On the other hand software defined signals can be generated exploiting direct digital synthesizers followed by an up-conversion to the desired carrier frequency. State-of-the-art synthesizers (limited to few GHz) introduce quantization errors due to digital-to-analog conversion, and phase errors depending on the phase stability of their internal clock. In addition the high phase stability required in modern wireless systems (such as radar systems) is becoming challenging for the electronic RF signal generation, since at high carrier frequency the frequency multiplication processes that are usually exploited reduce the phase stability of the original RF oscillators. Over the past 30 years microwave photonics (MWP) has been defined as the field that study the interactions between microwave and optical waves and their applications in radar and communications system as well as in hybrid sensor‘s instrumentation. As said before software defined radio applications drive the technological development trough high speed\bandwidth and high dynamic range systems operating directly in the radio frequency domain. Nowadays, while digital electronics represent a limit on system performances, photonic technologies perfectly engages the today‘s system needs and offers promising solution thanks to its inherent high frequency and ultrawide bandwidth. Moreover photonic components with very high phase coherence guarantees highly stable microwave carriers; while strong immunity to the electromagnetic interference, low loss and high tunability make a MWP system robust, flexible and reliable. Historical research and development of MWP finds space in a wide range of applications including the generation, distribution and processing of radio frequency signals such as, for example, analog microwave photonic link, antenna remoting, high frequency and low noise photonic microwave signal generation, photonic microwave signal processing (true time delay for phased array systems, tunable high Q microwave photonic filter and high speed analog to digital converters) and broadband wireless access networks. Performances improvement of photonic and hybrid devices represents a key factor to improve the development of microwave photonic systems in many other applications such as Terahertz generation, optical packet switching and so on. Furthermore, advanced in silicon photonics and integration, makes the low cost complete microwave photonic system on chip just around the corner. In the last years the use of photonics has been suggested as an effective way for generating low phase-noise radio frequency carriers even at high frequency. However while a lot of efforts have been spent in the photonic generation of RF carriers, only few works have been presented on reconfigurable phase coding in the photonics-based signal generators. In this direction two innovative schemes for optically generate multifrequency direct RF phase modulated signals have been presented. Then we propose a wideband ADC with high precision and a photonic wireless receiver for sparse sensing. This dissertation focuses on microwave photonics for radar and telecommunications systems. In particular applications in the field of photonic RF signal generation, photonic analog to digital converters and photonic ultrawideband radio will be presented with the main objective to overcome the limitations of pure electrical systems. Schemes and results will be further detailed and discussed. The dissertation is organized as follows. In the first chapter an overview of the MWP technologies is presented, focusing the attention of the limits overcame by using hybrid optoelectronic systems in particular field of applications. Then optoelectronic devices are introduced in the second chapter to better understand their role in a MWP system. Chapters 3,4, and 5 present results on photonic microwave signal generation, photonic wideband analog to digital converters and photonic ultrawideband up\down converter for both radar and telecommunications applications. Finally in the chapter 6 an overview of the photonic radar prototype is given

Time-Interleaved Analog-to-Digital-Converters: Modeling, Blind Identification and Digital Correction of Frequency Response Mismatches

Analog-to-digital-conversion enables utilization of digital signal processing (DSP) in many applications today such as wireless communication, radar and electronic warfare. DSP is the favored choice for processing information over analog signal processing (ASP) because it can typically offer more flexibility, computational power, reproducibility, speed and accuracy when processing and extracting information. Software defined radio (SDR) receiver is one clear example of this, where radio frequency waveforms are converted into digital form as close to the antenna as possible and all the processing of the information contained in the received signal is extracted in a configurable manner using DSP. In order to achieve such goals, the information collected from the real world signals, which are commonly analog in their nature, must be converted into digital form before it can be processed using DSP in the respective systems. The common trend in these systems is to not only process ever larger bandwidths of data but also to process data in digital format at ever higher processing speeds with sufficient conversion accuracy. So the analog-to-digital-converter (ADC), which converts real world analog waveforms into digital form, is one of the most important cornerstones in these systems.The ADC must perform data conversion at higher and higher rates and digitize ever-increasing bandwidths of data. In accordance with the Nyquist-Shannon theorem, the conversion rate of the ADC must be suffcient to accomodate the BW of the signal to be digitized, in order to avoid aliasing. The conversion rate of the ADC can in general be increased by using parallel ADCs with each ADC performing the sampling at mutually different points in time. Interleaving the outputs of each of the individual ADCs provides then a higher digitization output rate. Such ADCs are referred to as TI-ADC. However, the mismatches between the ADCs cause unwanted spurious artifacts in the TI-ADC’s spectrum, ultimately leading to a loss in accuracy in the TI-ADC compared to the individual ADCs. Therefore, the removal or correction of these unwanted spurious artifacts is essential in having a high performance TI-ADC system.In order to remove the unwanted interleaving artifacts, a model that describes the behavior of the spurious distortion products is of the utmost importance as it can then facilitate the development of efficient digital post-processing schemes. One major contribution of this thesis consists of the novel and comprehensive modeling of the spurious interleaving mismatches in different TI-ADC scenarios. This novel and comprehensive modeling is then utilized in developing digital estimation and correction methods to remove the mismatch induced spurious artifacts in the TI-ADC’s spectrum and recovering its lost accuracy. Novel and first of its kind digital estimation and correction methods are developed and tested to suppress the frequency dependent mismatch spurs found in the TI-ADCs. The developed methods, in terms of the estimation of the unknown mismatches, build on statistical I/Q signal processing principles, applicable without specifically tailored calibration signals or waveforms. Techniques to increase the analog BW of the ADC are also analyzed and novel solutions are presented. The interesting combination of utilizing I/Q downconversion in conjunction with TI-ADC is examined, which not only extends the TI-ADC’s analog BW but also provides flexibility in accessing the radio spectrum. Unwanted spurious components created during the ADC’s bandwidth extension process are also analyzed and digital correction methods are developed to remove these spurs from the spectrum. The developed correction techniques for the removal of the undesired interleaving mismatch artifacts are validated and tested using various HW platforms, with up to 1 GHz instantaneous bandwidth. Comprehensive test scenarios are created using measurement data obtained from HW platforms, which are used to test and evaluate the performance of the developed interleaving mismatch estimation and correction schemes, evidencing excellent performance in all studied scenarios. The findings and results presented in this thesis contribute towards increasing the analog BW and conversion rate of ADC systems without losing conversion accuracy. Overall, these developments pave the way towards fulfilling the ever growing demands on the ADCs in terms of higher conversion BW, accuracy and speed

Research of algorithms for the reconstruction of non-uniform sampled discrete-time signals with unknown sampling locations

В монографии изложены результаты исследований алгоритмов восстановления дискретных сигналов (ДС), заданных в узлах временной сетки (ВС) с точно неизвестными значениями координат ее узлов. Проведен анализ состояния предметной области, включая: существующие виды неравномерной дискретизации сигналов по времени и причины ее возникновения. Предложена классификация видов неравномерной дискретизации сигналов во времени. Приведены примеры реальных измерительных систем, на выходе которых получают ДС, заданные в узлах неравномерной временной сетки (НВС), а также методы восстановления ДС данного типа. Приведена постановка задачи восстановления ДС, заданного в узлах НВС, с неизвестными точно значениями координат ее узлов. Изложены результаты исследования особенностей восстановления ДС, заданных в узлах НВС с неизвестными точно значениями координат ее узлов, с помощью интерполяционных методов, а также методов, основанных на уточнении значений координат узлов НВС, и оценки их точности. Предложены новые алгоритмы восстановления ДС, заданных на НВС с точно неизвестными значениями координат ее узлов, продемонстрирована их работоспособность и получены оценки точности восстановления ДС с помощью данных алгоритмов. Проведен анализ точности восстановления периодических ДС, получаемых на выходе реальных цифровых систем (высокоскоростного 8-ми битного АЦП на основе КМОП-технологии 0.18 мкм, системы, состоящей из 8 параллельных 5-ти битных АЦП на основе КМОП-тепхнологии 65 нм), с помощью разработанных алгоритмов восстановления.In this treatise are considered the results of research of algorithms for the reconstruction of non-uniform sampled band-limited discrete-time signal with unknown sampling location. The condition of problem domain is analyzed, including: applying signal sampling schemes and causes of origin of the non-uniform sampling signals. Also is proposed classification of signal sampling schemes. Examples of real measurement systems, on the output of which registers non-uniform sampled signals with unknown sampling location as well as methods to reconstruct this type signals are given. The problem of signal reconstruction from non-uniform samples is considered. Interpolation methods to reconstruct a band-limited discrete-time signal from non-uniform samples with unknown sampling location, and optimization methods by estimating unknown sampling locations values are analyzed. Estimates of accuracy of interpolation methods for recovery of irregularly sampled signals are given. Also are given estimates of accuracy of methods to reconstruct a signal from non-uniform samples with unknown sampling locations by estimating unknown sampling locations values and presenting a solution of certain multiparameter problem of global optimization. Are proposed the new algorithms to reconstruct band-limited discrete-time signal from non-uniform samples with unknown sampling location and is demonstrated their performance. Estimate of accuracy of algorithms is compared and reconstruction errors are given in the numerical examples. The results of the research on the accuracy of the periodic signals reconstruction registered at the high speed 8 parallel 5-bit ADC system output based on the 65 nm CMOS technology and 8-bit high-rate ADC output based on the 0.18µm CMOS technology by means of special algorithms to reconstruct a signal from non-uniform samples with unknown sampling locations are analyzed