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

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

A Novel Iterative Structure for Online Calibration of M-Channel Time-Interleaved ADCs

published_or_final_versio

An RF BIST Architecture for Output Stages of Multistandard Radios

Article accepté pour publicationInternational audienceSoftware defined radios (SDR) platforms are in-creasingly complex systems which combine great flexibility and high performance. These two characteristics, together with highly integrated architectures make production test a challenging task. In this paper, we introduce an Radio Frequency (RF) Built-in Self-Test (BIST) strategy based on Periodically Nonuniform Sampling of the signal at the output stages of multistandard radios. We leverage the I/Q ADC channels and the DSP resources to extract the bandpass waveform at the output of the power amplifier (PA). Analytical expressions and simulations show that our time-interleaved conversion scheme is sensitive to time-skew. We show a time-skew estimation technique that allows us to surmount this obstacle. Simulation results show that we can effectively reconstruct the bandpass signal of the output stage using this architecture, opening the way for a complete RF BIST strategy for multistandard radios. Future developments will be focused on an efficient mapping to hardware of our new time-skew estimation for TIADC bandpass conversion

Iterative correction of frequency response mismatches in time-interleaved ADCs: A novel framework and case study in OFDM systems

In this paper, we study a versatile iterative framework for the correction of frequency response mismatch in time-interleaved ADCs. Based on a general time varying linear system model, we establish a flexible iterative framework, which enables the development of various efficient iterative correction algorithms. In particular, we study the Gauss-Seidel iteration in detail to illustrate how the correction problem can be solved iteratively, and show that the iterative structure can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. Simulation results show that the proposed iterative structure performs better than conventional compensation structures. Moreover, a preliminary study on the BER performance of OFDM systems due to TI ADC mismatch is conducted. © 2010 IEEE.published_or_final_versionThe 1st International Conference on Green Circuits and Systems (ICGCS 2010), Shanghai, China, 21-23 June 2010. In Proceedings of the 1st ICGCS, 2010, p. 253-25

LMS-Based RF BIST Architecture for Multistandard Transmitters

Article accepté pour publicationInternational audienceSoftware defined radios (SDR) platforms are increasingly complex systems which combine great flexibility and high performance. These two characteristics, together with highly integrated architectures make production test a challenging task. In this paper, we introduce an Radio Frequency (RF) Built-in Self-Test (BIST) strategy based on Periodically Nonuniform Sampling of the signal at the output stages of multistandard radios. We leverage the I/Q ADC channels and the DSP resources to extract the bandpass waveform at the output of the power amplifier (PA). Analytic expressions and simulations show that our time-interleaved conversion scheme is sensitive to time-skew. We propose a time-skew estimation technique based on a Least Mean Squares (LMS) algorithm to solve this problem. Simulation results show that we can effectively reconstruct the bandpass signal of the output stage using this architecture, opening the way for a complete RF BIST strategy for multistandard radios

A flexible BIST strategy for SDR transmitters

International audienceSoftware-defined radio (SDR) development aims for increased speed and flexibility. The advent of these system level requirements on the physical layer (PHY) access hardware is leading to more complex architectures, which together with higher levels of integration pose a challenging problem for product testing. For radio units that must be field-upgradeable without specialized equipment, Built-in Self-Test (BIST) schemes are arguably the only way to ensure continued compliance to specifications. In this paper we introduce a loopback RF BIST technique that uses Periodically Nonuniform Sampling (PNS2) of the transmitter (TX) output to evaluate compliance to spectral mask specifications. No significant hardware costs are incurred due to the re-use of available RX resources (I/Q ADCs, DSP, GPP, etc.). Simulation results of an homodyne TX demonstrate that Adjacent Channel Power Ratio (ACPR) can be accurately estimated. Future work will consist in validating our loopback RF BIST architecture on an in-house SDR testbed

Analog‐to‐Digital Conversion for Cognitive Radio: Subsampling, Interleaving, and Compressive Sensing

This chapter explores different analog-to-digital conversion techniques that are suitable to be implemented in cognitive radio receivers. This chapter details the fundamentals, advantages, and drawbacks of three promising techniques: subsampling, interleaving, and compressive sensing. Due to their major maturity, subsampling- and interleaving-based systems are described in further detail, whereas compressive sensing-based systems are described as a complement of the previous techniques for underutilized spectrum applications. The feasibility of these techniques as part of software-defined radio, multistandard, and spectrum sensing receivers is demonstrated by proposing different architectures with reduced complexity at circuit level, depending on the application requirements. Additionally, the chapter proposes different solutions to integrate the advantages of these techniques in a unique analog-to-digital conversion process