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

Multichannel Sampling of Pulse Streams at the Rate of Innovation

We consider minimal-rate sampling schemes for infinite streams of delayed and weighted versions of a known pulse shape. The minimal sampling rate for these parametric signals is referred to as the rate of innovation and is equal to the number of degrees of freedom per unit time. Although sampling of infinite pulse streams was treated in previous works, either the rate of innovation was not achieved, or the pulse shape was limited to Diracs. In this paper we propose a multichannel architecture for sampling pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. This architecture is motivated by recent work on sub-Nyquist sampling of multiband signals. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches

Designing Power-Efficient Modulation Formats for Noncoherent Optical Systems

We optimize modulation formats for the additive white Gaussian noise channel with a nonnegative input constraint, also known as the intensity-modulated direct detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical and optical power. The nonnegativity input signal constraint is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some remarkably dense packings are found, which yield more power-efficient modulation formats than previously known. For example, at a spectral efficiency of 1 bit/s/Hz, the obtained modulation format offers a 0.86 dB average electrical power gain and 0.43 dB average optical power gain over the previously best known modulation formats to achieve a symbol error rate of 10^-6. This modulation turns out to have a lattice-based structure. At a spectral efficiency of 3/2 bits/s/Hz and to achieve a symbol error rate of 10^-6, the modulation format obtained for optimizing the average electrical power offers a 0.58 dB average electrical power gain over the best lattice-based modulation and 2.55 dB gain over the best previously known format. However, the modulation format optimized for average optical power offers a 0.46 dB average optical power gain over the best lattice-based modulation and 1.35 dB gain over the best previously known format.Comment: Submitted to Globecom 201

Contribution to Efficient Use of Narrowband Radio Channel

Předkládaná práce se soustředí na problematiku využívání úzkopásmového rádiového kanálu rádiovými modemy, které jsou určené pro průmyslové aplikace pozemní pohyblivé rádiové služby, specifikované v dominantní míře Evropským standardem ETSI EN 300 113. Tato rádiová zařízení se používají v kmitočtových pásmech od 30 MHz do 1 GHz s nejčastěji přidělovanou šířkou pásma 25 kHz a ve většině svých instalací jsou využívána ve fixních nebo mobilních bezdrátových sítích. Mezi typické oblasti použití patří zejména datová telemetrie, aplikace typu SCADA, nebo monitorování transportu strategických surovin. Za hlavní znaky popisovaného systému lze označit komunikační pokrytí značných vzdáleností, dané především vysokou výkonovou účinnosti datového přenosu a využívaní efektivních přístupových technik na rádiový kanál se semiduplexním komunikačním režimem. Striktní požadavky na elektromagnetickou kompatibilitu umožňují těmto zařízením využívat spektrum i v oblastech kmitočtově blízkým jiným komunikačním systémům bez nutnosti vkládání dodatečných ochranných frekvenčních pásem. Úzkopásmové rádiové komunikační systémy, v současnosti používají převážně exponenciální digitální modulace s konstantní modulační obálkou zejména z důvodů velice striktních omezení pro velikost výkonu vyzářeného do sousedního kanálu. Dosahují tak pouze kompromisních hodnot komunikační účinnosti. Úpravy limitů příslušných rádiových parametrů a rychlý rozvoj prostředků číslicového zpracování signálu v nedávné době, dnes umožňují ekonomicky přijatelné využití spektrálně efektivnějších modulačních technik i v těch oblastech, kde je prioritní využívání úzkých rádiových kanálů. Cílem předkládané disertační práce je proto výzkum postupů směřující ke sjednocení výhodných vlastností lineárních a nelineárních modulací v moderní konstrukci úzkopásmového rádiového modemu. Účelem tohoto výzkumu je efektivní a „ekologické“ využívání přidělené části frekvenčního spektra. Mezi hlavní dílčí problémy, jimiž se předkládaná práce zabývá, lze zařadit zejména tyto: Nyquistova modulační filtrace, navrhovaná s ohledem na minimalizaci nežádoucích elektromagnetických interferencí, efektivní číslicové algoritmy frekvenční demodulace a rychlé rámcové a symbolové synchronizace. Součástí práce je dále analýza navrhovaného řešení z pohledu celkové konstrukce programově definovaného rádiového modemu v rovině simulací při vyšetřování robustnosti datového přenosu rádiovým kanálem s bílým Gaussovským šumem nebo kanálem s únikem v důsledku mnohacestného šíření signálu. Závěr práce je pak zaměřen na prezentování výsledků praktické části projektu, v níž byly testovány, měřeny a analyzovány dvě prototypové konstrukce rádiového zařízení. Tato finální část práce obsahuje i praktická doporučení, vedoucí k vyššímu stupni využitelnosti spektrálně efektivnějších komunikačních režimů v oblasti budoucí generace úzkopásmových zařízení pozemní pohyblivé rádiové služby.he industrial narrowband land mobile radio (LMR) devices, as considered in this dissertation project, has been subject to European standard ETSI EN 300 113. The system operates on frequencies between 30 MHz and 1 GHz, with channel separations of up to 25 kHz, and is intended for private, fixed, or mobile, radio packet switching networks. Data telemetry, SCADA, maritime and police radio services; traffic monitoring; gas, water, and electricity producing factories are the typical system applications. Long distance coverage, high power efficiency, and efficient channel access techniques in half duplex operation are the primary advantages the system relays on. Very low level of adjacent channel power emissions and robust radio receiver architectures, with high dynamic range, enable for a system’s coexistence with various communication standards, without the additional guard band frequency intervals. On the other hand, the strict limitations of the referenced standard as well as the state of the technology, has hindered the increase in communication efficiency, with which the system has used its occupied bandwidth. New modifications and improvements are needed to the standard itself and to the up-to-date architectures of narrowband LMR devices, to make the utilization of more efficient modes of system operation practically realizable. The main objective of this dissertation thesis is therefore to find a practical way how to combine the favorable properties of the advanced nonlinear and linear digital modulation techniques in a single digital modem solution, in order to increase the efficiency of the narrowband radio channel usage allocated to the new generation of the industrial LMR devices. The main attention is given to the particular areas of digital modem design such as proposal of the new family of the Nyquist filters minimizing the adjacent channel interference, design and analysis of the efficient algorithms for frequency discrimination, fast frame and symbol

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

Ultrawide Bandwidth Signals as Shot-Noise: a Unifying Approach

We present a shot noise based model for a large family of ultrawide bandwidth (UWB) signals. These include time-hopping and direct-sequence signaling with pulse position, interval, and amplitude modulations. Each specific signal is constructed by adding features to a basic model in a modular, simple, and tractable way. Our work unifies the contributions scattered in the literature and provides a general approach that allows various extensions of previous works as well as new results. The exact power spectrum is then evaluated using shot noise spectral theory, which provides a simpler, systematic, and rigorous approach to the spectra evaluation of complicated UWB signals. The strength of our methodology is that different features of the signal model contribute clearly and separately to the resulting spectral expressions

Threshold Study of Phase Lock Loop Systems Interim Technical Report

Threshold studies of phase lock loop systems - effect of phase comparator on overall performance and threshold phenomen