Analog-to-information Converter Research Articles

Over the Limits of Traditional Sampling: Advantages and Issues of AICs for Measurement Instrumentation

Data acquisition systems have shown the need of wideband spectrum monitoring for many years. This paper describes and discusses a recently proposed architecture aimed at acquiring efficiently wideband signals, named the Analog-to-Information Converter (AIC). AIC framework and working principle implementing the sub-Nyquist sampling are analyzed in general terms. Attention is specifically focused on the idea of exploiting the condition of the signals that, despite their large bandwidth, have a small information content in the frequency domain. However, as clarified in the paper, employing AICs in measurement instrumentation necessarily entails their characterization, through the analysis of their building blocks and the corresponding non-idealities, in order to improve the signal reconstruction.

On the Effects of PRBS Non-Idealities in Signal Reconstruction from AICs

The paper presents a sensitivity analysis of the non-idealities introduced by the Pseudo Random Binary Sequence (PRBS) on two modulation-based architectures of Analog-to-Information Converters (AICs), namely the Random Demodulator and the Modulated Wideband Converter. In particular, the effects of both PRBS pulse shape and jitter are contemplated. The emerging findings from this analysis can guide the design process of AICs, so that the jitter effect can be brought below acceptable levels for a given target application. The analysis is carried out firstly by characterizing the PRBS pulse shape, and then by including the calibration data in the behavioral models of the two architectures. The reconstructed signal is thus evaluated for different values of random and deterministic jitter, in terms of Spurious Free Dynamic Range and Signal to Noise And Distortion Ratio. The results highlight a different behavior of the two architectures due to the different reconstruction models they adopt. Mainly, the identification phase of the measurement matrix proves to be able to compensate the jitter effect when jitter is correlated with the PRBS sequence.

A method for delay estimation between channels of Analog to Information Converters

Analog to Information Converters (AIC) implements signal acquisition in Compressed Sensing. AIC performance is affected by noise and hardware imperfections. In parallel Random Modulator Pre-Integrator (RMPI) architectures, delay among channels reduces the performance; thus, delay estimation and compensation methods are necessary. In previous works, delay estimation compares a reference signal with a reconstructed signal from the AIC output; however, such methods produce different results according to the recovery method. To avoid this problem, we present a method based on a controlled delay signal to estimate channel delay without the necessity of signal recovery. The obtained results show the technique's feasibility and the possibility of its use as a built-in calibration process for AIC.

Characterization of Analog-to-Information Converters [imsawards

The dissertation deals with the characterization of sub-sampling devices, the Analog-to-Information Converters (AICs), recently proposed in research as an alternative to the traditional Analog-to-Digital Converters. By exploiting the Compressive Sampling paradigm, AICs stably recover the input signal, previously acquired with less samples than needed by the Nyquist-Shannon theorem, reducing simultaneously sampling frequency and acquisition memory. The dissertation research was carried out in order to design and develop an AIC prototype to be employed in a measurement instrument: a vector signal analyzer, that acquires and reconstructs sparse wideband signals. The aim of such an instrument is to guarantee proper monitoring, circumventing the trade-off between resolution and sampling frequency, typical of conventional data acquisition systems. With a view to this use, the characterization of AICs is of crucial importance, since their performance conditions the measurement instrument based on them, and, although several efforts have been made in research to propose several architectures, only in a few cases their performance is assessed.

Generalized Analog-to-Information Converter With Analysis Sparse Prior

Conventional analog-to-information converter (AIC) frameworks employ a discrete-time synthesis sparse model to deal with analog signals, which, however, induces a challenging basis mismatch problem. In this paper, we propose a novel AIC framework, called generalized AIC (G-AIC), to tackle this issue. In the new method, an analysis sparse model is taken, for the first time, as the prior information of analog signals being sampled at sub-Nyquist rate. Through the joint optimization for the discretization operator and its analysis sparse operator, the G-AIC removes the model error between an analog signal and its equivalent discrete samples. To validate the G-AIC framework, we design a single channel G-AIC system based on switched-capacitor (SC) circuits. The circuit design is presented at the theoretical-level, the system-level, and the transistor-level. Numerical simulations demonstrate the G-AIC system can well restore an analog signal from its sub-Nyquist measurements, even though its sparse basis is unknown. Compared with two state-of-the-art AIC systems, the new design can achieve at least 2dB reconstruction gain. In brief, the proposed method provides a promising alternative to exploit analog signals in sub-Nyquist sampling systems.

Sub-Nyquist Wideband Spectrum Sensing Based on Analog to Information Converter for Cognitive Radio

With the development of wireless communication technology, higher spectrum efficiency is required for the 5G cellular networks. Cognitive radio (CR) has emerged as one of the most promising candidate solution to improve spectrum utilization and efficency. Wideband spectrum sensing has been the focal challenge point in cognitive radio technology, since existing techniques are reliant on analog to digital converters (ADC) with sampling at the Nyquist rate. However, in order to perform digitization of wideband RF signals at the Nyquist rate, a very high sampling frequency is required with primarily complex and energy inefficient designs. In this paper, a sub-Nyquist wideband spectrum sensing design is proposed. In the proposed design, an analog-to-information converter is presented. It utilizes Compressive Sensing which enables sampling far below the Nyquist rate, thus drastically reducing the power consumption, complexity and cost of the entire Receiver. The main biulding blocks in the proposed design which are: higher speed SAR analog to digital for random demodulator analog to information converter (AIC) were designed and simulated using cadance software for performance evaluation. The design was implemented in targeted technology of 130 nm standard CMOS technology. An optimization method suitable for VLSI implementation, termed Orthogonal Matching Pursuit (OMP), was utilized for spectrum recovery. Following comparative analyses with previously published studies, we demonstrate significant improvements in terms of speed and chip area of the SAR ADC design.

A Pulse Repetition Rate Compressive Sampler for Radar Target Detection

Compressive sampling (CS) is an attractive method to implement analog-to-information conversion (AIC) for a sub-Nyquist radar, where random demodulation (RD) is the most successful AIC. However, RD only considers the sparse characteristic of one single radar pulse, and its mixing circuit still works at the Nyquist sampling rate. To exploit the strong correlation of radar echo pulses, this letter presents a pulse repetition rate compressive sampler for radar target detection. It can acquire these highly correlated pulses by setting a different sampling start time for each pulse and compresses each pulse into one single sample, which means that the low compressive sampling rate is equal to the pulse repetition rate. Compared with RD, this new system reduces the complexity of the hardware circuit and improves the signal compression ratio. Experimental results verify that the proposed radar system outperforms RD by achieving target detection from compressive samples without signal recovery.

Incremental Gaussian Elimination Approach to Implement OMP for Sparse Signal Measurement

An efficient architecture of the orthogonal matching pursuit (OMP) algorithm is proposed to recover signals compressively measured at the sub-Nyquist rate. The proposed architecture is implemented on the field-programmable gate array (FPGA) for performance validation. In the place of matrix factorization-based pseudoinverse computation, Gaussian elimination (GE) is used to compute the signal estimate. A novel incremental Gaussian elimination (IGE) algorithm is proposed and used in the OMP algorithm. The proposed design is targeted to the Virtex6 FPGA device to compare with other reported works for $K=256$ , $N=1024$ , and $m=36$ , where $N$ is the number of samples, $K$ is the measurement vector length, and $m$ is the signal sparsity level. The recovery signal-to-noise ratio (RSNR) of 23.98 dB is achieved. The proposed work is validated by implementing it on the Artix7 FPGA device by taking compressed measurements from an analog to information converter (AIC). The input signal is synthesized as a random combination of sine waves with different frequencies. The proposed architecture is hardware-efficient and faster, and consumes low dynamic power than other existing designs. The proposed design is hardware-efficient even for the higher value of $m/K$ .

Novel IEEE-STD-1241-Based Test Methods for Analog-to-Information Converter

The compressive sensing theory is implemented by means of analog-to-information converter (AIC) that provides a digitized and compressed output $y$ directly from its analog input signal $x$ . A reconstruction algorithm, in turn, is needed to obtain a reconstructed signal $\hat {x}$ that estimates $x$ from $y$ . This algorithm can be far away from the AIC, linked through a communication channel, and embedded in a remote machine, for instance. In general, $\hat {x}$ is evaluated in order to test the AIC itself and, in consequence, the performance of the reconstruction algorithm affects the test result of the AIC-under-test and, as a result, can invalidate the AIC test at all. Few state-of-the-art works have proposed the test methods that take into account only the AIC output $y$ . However, they take into consideration a single-sine test signal to follow the IEEE Standard 1241 for analog-to-digital converter testing. In this paper, two new AIC test methods are introduced in which only the AIC outputs, that is, only the compressed outputs $y$ , are taken in account. In the first one, multisine signals can be applied and, in the second one, four-parameters sine-wave fit methods, as recommended by the IEEE Standard 1241, can be applied. Experimental results were obtained for two different AIC implementations (namely, random demodulator and random modulation preintegrator) and the signal-to-noise and distortion ratio (SINAD) of both was measured directly from the AIC output proving that the proposed AIC test methods are effective.

Analog-to-information conversion by encoded multi-cosets

ABSTRACT This paper presents an Analog-to-Information Conversion (AIC) model to acquire and simultaneously compress, with Time-Interleaved Analog-to-Digital Converters (TI-ADC), wide-band analog signals that can be sparse in a variety of domains. Compared with current AIC acquisition methods also based on TI-ADC, the proposed scheme represents a useful generalisation because it embodies a recently theoretically proved Restricted Isometry Property (RIP)-compliant sampling operator structure in the Compressed Sensing (CS) framework and, hence, favours the universal acquisition requirement for stable information recovery. The proposed model achieves its enhanced measurement characteristics by means of a Digital Signal Processing (DSP)-based encoding multi-coset core that operates completely in the low-rate section.

A High-Resolution Joint Angle-Doppler Estimation Sub-Nyquist Radar Approach Based on Matrix Completion

In order to reduce power consumption and save storage capacity, we propose a high-resolution sub-Nyquist radar approach based on matrix completion (MC), termed as single-channel sub-Nyquist-MC radars. While providing the high-resolution joint angle-Doppler estimation, this proposed radar approach minimizes the number of samples in all three dimensions, that is, the range dimension, the pulse dimension (also named temporal dimension), and the spatial dimension. In range dimension, we use a single-channel analog-to-information converter (AIC) to reduce the number of range samples to one; in both spatial and temporal dimensions, we employ a bank of random switch units to regulate the AICs, which greatly reduce the number of spatial-temporal samples. According to the proposed sampling scheme, the samples in digital processing center forwarded by M receive nodes and N pulses are only a subset of the full matrix of size M times N. Under certain conditions and with the knowledge of the sampling scheme, the full matrix can be perfectly recovered by using MC techniques. Based on the recovered full matrix, this paper addresses the problem of the high-resolution joint angle-Doppler estimation by employing compressed sensing (CS) techniques. The properties and performance of the proposed approach are demonstrated via simulations.

Optimization Paradigm in the Signal Recovery after Compressive Sensing

Abstract Compressive sensing is a processing approach aiming to reduce the data stream from the observed object with the inherent sparsity using the optimal signal models. The compression of the sparse input signal in time or in the transform domain is performed in the transmitter by the Analog to Information Converter (AIC). The recovery of the compressed signal using optimization based on the differential evolution algorithm is presented in the article as an alternative to the faster pseudoinverse algorithm. Pseudoinverse algorithm results in an unambiguous solution associated with lower compression efficiency. The selection of the mathematically appropriate signal model affects significantly the compression efficiency. On the other hand, the signal model influences the complexity of the algorithm in the receiving block. The suitability of both recovery methods is studied on examples of the signal compression from the passive infrared (PIR) motion sensors or the ECG bioelectric signals.

Wideband Power Spectrum Estimation Based on Sub-Nyquist Sampling in Cognitive Radio Networks

The wideband spectrum estimation is an essential step in the wireless network. In order to avoid employing power-hungry high-rate analog-to-digital converters (ADCs), the CS-based sub-Nyquist sampling approaches are used to estimate the wideband spectrum. In this paper, we propose a sub-Nyquist sampling system based on the analog to information converter (AIC), and the proposed system is constructed by multiple parallel channels with a banks of low pass filters. The system model is constructed in the time domain. To estimate the power spectrum, we define a new power spectrum of samples with a finite length, called the circular power spectrum (CPS), served as the aim we strive to estimate. The defined CPS can clearly reflect the power of the signal varying with frequency and is also with the same length as the equivalent digital samples. The experimental results indicate that the defined CPS can be successfully estimated from samples captured by the proposed sub-Nyquist sampling system whose overall sampling rate is much lower than the Nyquist rate.

Non-Uniform Wavelet Bandpass Sampling Analog-to-Information Converter: A hardware implementation and its experimental assessment

The paper presents the experimental assessment of an architecture of Analog-to-Information Converter (AIC), based on Non-Uniform Wavelet Bandpass Sampling (NUWBS), for use in wideband signal acquisition. To this aim, a preliminary simulation analysis was carried out, with the aim of verifying the capability of the architecture of correctly reconstructing the compressively acquired signal and evaluating the Spurious Free Dynamic Range (SFDR) of the reconstructed signals, in presence of additive noise, quantization noise, and timing jitter of the sampling clock. Then, a modified hardware implementation for the NUWBS AIC architecture was realized, by using commercial off-the-shelf components, that uses a low-pass filter in the analog correlator block. The realized prototype was experimentally characterized by evaluating the SFDR of the reconstructed signals. The paper describes the realized prototype and discusses the results obtained in both the simulation and the experimental phase.

From Compressed Sensing to Compressed Bit-Streams: Practical Encoders, Tractable Decoders

Compressed sensing is now established as an effective method for dimension reduction when the underlying signals are sparse or compressible with respect to some suitable basis or frame. One important, yet under-addressed problem regarding the compressive acquisition of analog signals is how to perform quantization. This is directly related to the important issues of how “compressed” compressed sensing is (in terms of the total number of bits one ends up using after acquiring the signal) and ultimately whether compressed sensing can be used to obtain compressed representations of suitable signals. In this paper, we propose a concrete and practicable method for performing “analog-to-information conversion”. Following a compressive signal acquisition stage, the proposed method consists of a quantization stage, based on $ \Sigma \Delta $ (sigma-delta) quantization, and a subsequent encoding (compression) stage that fits within the framework of compressed sensing seamlessly. We prove that, using this method, we can convert analog compressive samples to compressed digital bitstreams and decode using tractable algorithms based on convex optimization. We prove that the proposed analog-to-information converter (AIC) provides a nearly optimal encoding of sparse and compressible signals. Finally, we present numerical experiments illustrating the effectiveness of the proposed AIC.

How to Make Analog-to-Information Converters Work in Dynamic Spectrum Environments With Changing Sparsity Conditions

Compressed sensing (CS) analog to information converters (AICs) offer key benefits for signal reception or detection when the input signal is sparse. So far AICs have been demonstrated in environments with controlled input signal conditions and with fixed sparsity levels. This paper investigates how to make AICs effectively operate in dynamic environments with changing signal conditions and thus changing sparsity levels. We focus on RF spectrum scanning, where signals or interferers need to be detected across a wide dynamic RF spectrum, but the presented concepts are widely applicable for low-pass and band-pass CS AICs. The number of measurements and hence the number of branches required in a CS RF front end scales with the sparsity level, i.e. the number of signals that need to be detected. In practice this leads to excessively large silicon area for more than a few signals (e.g., six). We introduce the time-segmented quadrature analog-to-information converter (TS-QAIC), a scalable architecture for signal detection in dynamically changing spectrum environments. While our TS-QAIC prototype implements a fixed number of hardware branches, we experimentally demonstrate adaptive thresholding and adaptive time segmentation to adjust its signal detection capability to the sparsity level of the input signal.

Analog to information conversion for sparse signals band-limited in fractional Fourier transform domain

The classical Shannon sampling theorem has a profound influence on signal processing and communication. With the increasing contradiction between high rate sampling and conversion accuracy, the traditional analog to digital conversion technology, which is based on the Shannon sampling theorem, is facing a great challenge, especially for the bottleneck effect on reducing the sampling rate. In recent years, the analog-to-information conversion (AIC) technology, which is based on the theory of compressive sensing, provides an effective method to solve this problem. However, the signal model of the existing AIC is only suitable for sparse signals band-limited in the Fourier transform (FT) domain. It cannot be applied to non-bandlimited chirp signals which is widely used in electronic information systems, including radar and communications. Towards this end, we propose a new AIC based on the fractional Fourier transform (FRFT), which is not only the extension of the traditional AIC in the FRFT domain, but also can solve the problem as mentioned above. The theoretical derivation is presented, and the corresponding simulation analysis is also given. The simulation results are consistent with the theoretical analysis.

Cramer-Rao bounds for the joint delay-Doppler estimation of compressive sampling pulse-Doppler radar

Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling (CS) pulse-Doppler (CSPD) radar are developed with different analog-to-information conversion (AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound (CRB) for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio (SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.

Orthogonal circulant structure and chaotic phase modulation based analog to information conversion

Modulated wideband converter (MWC) is used to implement analog to information conversion (AIC) to realize sub-Nyquist sampling of sparse multiband analog signal. In this paper, we combine orthogonal circulant matrix with chaos to develop an orthogonal circulant structure and chaotic phase modulation based modulated wideband converter (OCSCPM-MWC). Firstly, random waveforms of different channels in the system correspond to the row vectors of measurement matrix. We use the frequency-domain approach to construct orthogonal circulant matrix. The waveforms of different channels can be generated by various cyclic shifts of the same original waveform and orthogonal to each other. This can greatly reduce the degrees of freedom of the random waveforms, and a superior recovery performance can be obtained. Secondly, we construct chaotic phases of generating elements of orthogonal circulant matrix. The input signal is modulated according to the power spectrum of chaos. We derive the theoretical condition for the orthogonal circulant measurement matrix to satisfy expected restricted isometry property (ExRIP). In addition, we analyze the impact of measurement noise and signal noise on the OCSCPM-MWC system, respectively. Computer simulations are carried out under different situations and they confirm the effectiveness of the proposed approach.

A general and yet efficient scheme for sub-Nyquist radar processing

We study the target parameter estimation for sub-Nyquist pulse-Doppler radar. Several past works have addressed this problem but either have low estimation accuracy for off-grid targets, take large computation load, or lack versatility for analog-to-information conversion (AIC) systems. To overcome these difficulties, we present a general and efficient estimation scheme. The scheme first formulates a general model in the sense that it is applicable to all AICs regardless of whether the targets are on or off the grids. The estimation of Doppler shifts and delays is performed sequentially, in which the Doppler estimation is formulated into a spatial spectrum estimation problem and the delay estimation is decomposed into a series of compressive parameter estimation problems with each corresponding to an estimated Doppler shift. By the sequential and decomposed processing, the computational complexity is substantially reduced, and by the parametric estimation techniques, the high accurate estimation is obtained. Theoretical analyses and numerical experiments show the effectiveness and the correctness of the proposed scheme.