Sub-Nyquist Sampling: Bridging Theory and Practice

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin

Detecting and locating electronic devices using their unintended electromagnetic emissions

Electronically-initiated explosives can have unintended electromagnetic emissions which propagate through walls and sealed containers. These emissions, if properly characterized, enable the prompt and accurate detection of explosive threats. The following dissertation develops and evaluates techniques for detecting and locating common electronic initiators. The unintended emissions of radio receivers and microcontrollers are analyzed. These emissions are low-power radio signals that result from the device\u27s normal operation. In the first section, it is demonstrated that arbitrary signals can be injected into a radio receiver\u27s unintended emissions using a relatively weak stimulation signal. This effect is called stimulated emissions. The performance of stimulated emissions is compared to passive detection techniques. The novel technique offers a 5 to 10 dB sensitivity improvement over passive methods for detecting radio receivers. The second section develops a radar-like technique for accurately locating radio receivers. The radar utilizes the stimulated emissions technique with wideband signals. A radar-like system is designed and implemented in hardware. Its accuracy tested in a noisy, multipath-rich, indoor environment. The proposed radar can locate superheterodyne radio receivers with a root mean square position error less than 5 meters when the SNR is 15 dB or above. In the third section, an analytic model is developed for the unintended emissions of microcontrollers. It is demonstrated that these emissions consist of a periodic train of impulses. Measurements of an 8051 microcontroller validate this model. The model is used to evaluate the noise performance of several existing algorithms. Results indicate that the pitch estimation techniques have a 4 dB sensitivity improvement over epoch folding algorithms --Abstract, page iii

Multi-GNSS signals acquisition techniques for software defines receivers

Any commercially viable wireless solution onboard Smartphones should resolve the technical issues as well as preserving the limited resources available such as processing and battery. Therefore, integrating/combining the process of more than one function will free up much needed resources that can be then reused to enhance these functions further. This thesis details my innovative solutions that integrate multi-GNSS signals of specific civilian transmission from GPS, Galileo and GLONASS systems, and process them in a single RF front-end channel (detection and acquisition), ideal for GNSS software receiver onboard Smartphones. During the course of my PhD study, the focus of my work was on improving the reception and processing of localisation techniques based on signals from multi-satellite systems. I have published seven papers on new acquisition solutions for single and multi-GNSS signals based on the bandpass sampling and the compressive sensing techniques. These solutions, when applied onboard Smartphones, shall not only enhance the performance of the GNSS localisation solution but also reduce the implementation complexity (size and processing requirements) and thus save valuable processing time and battery energy. Firstly, my research has exploited the bandpass sampling technique, if being a good candidate for processing multi-signals at the same time. This portion of the work has produced three methods. The first method is designed to detect the GPS, Galileo and GLONASS-CDMA signals’ presence at an early stage before the acquisition process. This is to avoid wasting processing resources that are normally spent on chasing signals not present/non-existent. The second focuses on overcoming the ambiguity when acquiring Galileo-OS signal at a code phase resolution equal to 0.5 Chip or higher and this achieved by multiplying the received signal with the generated sub-carrier frequency. This new conversion saves doing a complete correlation chain processing when compared to conventionally used methods. The third method simplifies the joining implementation of the Galileo-OS data-pilot signal acquisition by constructing an orthogonal signal so as to acquire them in a single correlation chain, yet offering the same performance as using two correlation chains. Secondly, the compressive sensing technique is used to acquire multi-GNSS signals to achieve computation complexity reduction over correlator based methods, like Matched Filter, while still maintaining acquisition integrity. As a result of this research work, four implementation methods were produced to handle single or multi-GNSS signals. The first of these methods is designed to change dynamically the number and the size of the required channels/correlators according to the received GPS signal-power during the acquisition process. This adaptive solution offers better fix capability when the GPS receiver is located in a harsh signal environment, or it will save valuable processing/decoding time when the receiver is outdoors. The second method enhances the sensing process of the compressive sensing framework by using a deterministic orthogonal waveform such as the Hadamard matrix, which enabled us to sample the signal at the information band and reconstruct it without information loss. This experience in compressive sensing led the research to manage more reduction in terms of computational complexity and memory requirements in the third method that decomposes the dictionary matrix (representing a bank of correlators), saving more than 80% in signal acquisition process without loss of the integration between the code and frequency, irrespective of the signal strength. The decomposition is realised by removing the generated Doppler shifts from the dictionary matrix, while keeping the carrier frequency fixed for all these generated shifted satellites codes. This novelty of the decomposed dictionary implementation enabled other GNSS signals to be combined with the GPS signal without large overhead if the two, or more, signals are folded or down-converted to the same intermediate frequency. The fourth method is, therefore, implemented for the first time, a novel compressive sensing software receiver that acquires both GPS and Galileo signals simultaneously. The performance of this method is as good as that of a Matched Filter implementation performance. However, this implementation achieves a saving of 50% in processing time and produces a fine frequency for the Doppler shift at resolution within 10Hz. Our experimental results, based on actual RF captured signals and other simulation environments, have proven that all above seven implementation methods produced by this thesis retain much valuable battery energy and processing resources onboard Smartphones

Cooperative Wideband Spectrum Sensing Based on Joint Sparsity

COOPERATIVE WIDEBAND SPECTRUM SENSING BASED ON JOINT SPARSITY By Ghazaleh Jowkar, Master of Science A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at Virginia Commonwealth University Virginia Commonwealth University 2017 Major Director: Dr. Ruixin Niu, Associate Professor of Department of Electrical and Computer Engineering In this thesis, the problem of wideband spectrum sensing in cognitive radio (CR) networks using sub-Nyquist sampling and sparse signal processing techniques is investigated. To mitigate multi-path fading, it is assumed that a group of spatially dispersed SUs collaborate for wideband spectrum sensing, to determine whether or not a channel is occupied by a primary user (PU). Due to the underutilization of the spectrum by the PUs, the spectrum matrix has only a small number of non-zero rows. In existing state-of-the-art approaches, the spectrum sensing problem was solved using the low-rank matrix completion technique involving matrix nuclear-norm minimization. Motivated by the fact that the spectrum matrix is not only low-rank, but also sparse, a spectrum sensing approach is proposed based on minimizing a mixed-norm of the spectrum matrix instead of low-rank matrix completion to promote the joint sparsity among the column vectors of the spectrum matrix. Simulation results are obtained, which demonstrate that the proposed mixed-norm minimization approach outperforms the low-rank matrix completion based approach, in terms of the PU detection performance. Further we used mixed-norm minimization model in multi time frame detection. Simulation results shows that increasing the number of time frames will increase the detection performance, however, by increasing the number of time frames after a number of times the performance decrease dramatically

Hybrid Beam-Steering OFDM-MIMO Radar: High 3-D Resolution With Reduced Channel Count

We report on the realization of a multichannel imaging radar that achieves uniform 2-D cross-range resolution by means of a linear array of a special form of leaky-wave antennas. The presented aperture concept enables a tradeoff between the available range resolution and a reduction in the number of channels required for a given angular resolution. The antenna front end is integrated within a multichannel radar based on stepped-carrier orthogonal frequency-division modulation, and the advantages and challenges specific to this combination are analyzed with respect to signal processing and a newly developed calibration routine. The system concept is fully implemented and verified in the form of a mobile demonstrator capable of soft real-time 3-D processing. By combining radio frequency (RF) components operating in the W-band (85-105 GHz) with the presented aperture, a 3-D resolution of less than 1.5° x 1.5° x 15 cm is demonstrated using only eight transmitters and eight receivers

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