Photonic Analog-to-Digital Conversion

Transcription

1 Photonic Analo-to-Diital Conversion Patrick T. Callahan, Michael L. Dennis, and Thomas R. Clark Jr. he analo-to-diital converter () performs the crucial transformation of physical electromanetic sinals into ones and zeros that can be processed by computers. As such, it is of reat importance to a vast number of electronic systems and is often a limitin component for the performance of such systems. Photonic technoloy is capable of overcomin many of the limitations in traditional electronic s and is therefore the subject of much experimental investiation. In this article we provide a brief overview of s within the context of receiver systems and of the advantaes that photonic technoloy has to offer, as well as a discussion of recent developments in research performed at APL that promise to extend the functionality of photonic s. Finally, we present the results of experiments implementin nonuniform photonic samplin techniques to unambiuously identify sinals separated by many traditional Nyquist zones. INTRODUCTION Accurate collection and processin of electromanetic information is critical to a wide variety of applications. Present day RF and microwave sensor systems must cover many frequency bands, detect and identify a lare rane of sinal powers, and analyze the sinal information on an ever-decreasin time scale. Simultaneously achievin these attributes typically requires multiple hardware systems, stressin even the most accommodatin platforms and requirin the elimination of functionality on some. The power of diital sinal processin to deliver increased functionality and improved system performance has lon been reconized. The resultin preference for diital representation of sinals as the format for receiver system outputs has elevated the importance of the analo-to-diital converter (), which serves as the interface between the received analo sinals and the diital domain. ith this move to the diital domain, the is and will continue to be a major bottleneck for many systems. 1 The aim of the authors current research is to leverae the unique benefits of photonic technoloy to build systems capable of far reater speed, bandwidth, and accuracy. In this article we describe novel samplin techniques developed and implemented at APL that 280

2 enable the accurate capture and processin of incomin sinals without requirin hih-speed electronics. ELECTRONIC s Fundamentals An performs two basic functions: samplin and quantization of an incomin continuous-time sinal. These consist of the discretization of a sinal in time and amplitude, respectively, as illustrated in Fi. 1. The number of discrete amplitude levels for the is most often written in terms of the number of bits required to express the levels in binary form. For example, an with a resolution of 8 bits would have 2 8 = 256 different amplitude levels to approximate the continuous sinal. The quantization function is therefore completely specified by two system parameters, the number of bits and the full-scale voltae of the. Since most s take a measurement of the sinal amplitude once every m seconds, the timin resolution is described in terms of this uniform sample rate 1/m. The samplin function is specified by the frequency of samplin instants (1/m), the temporal precision of samplin instants, and the duration of the samplin window. Timin jitter of the uniform clock that defines the samplin instants will lead to errors in the diital representation of the sampled sinal. In eneral, this effect can be inored if the timin jitter dt is small compared with the error that is introduced by quantization. This condi- (c) (d) Fiure 1. Illustration of samplin and quantization functions. The quantization function is performed by roundin down to the nearest discrete level. A continuous-time, continuous-amplitude sinal (analo). A discrete-time, continuous-amplitude sinal (sampled). (c) A continuous-time, discrete-amplitude sinal (quantized). (d) A discrete-time, discrete-amplitude sinal (diital). The oriinal analo sinal is shown in blue for comparison. tion can be expressed mathematically as dt < 1/(2 q pf 0 ), where f 0 is the hihest frequency of the input sinal and q is the number of bits of the. If this condition is not met, the timin jitter of the samplin clock will derade the effective resolution of the, hence the need for hih-precision clock sources. For the case of excessive jitter, the equation can be inverted to find the effective number of bits. Another error that can be caused by the samplin process is sinal aliasin, which is a fundamental limitation on the ability of uniform samplin to accurately represent the oriinal continuous-time sinal. The samplin theorem states that a sinal of finite bandwidth can be completely reconstructed by an interpolation formula from its uniformly sampled values, so lon as the sample rate is at least twice the hihest frequency component of the oriinal sinal. 2 Another way of statin this theorem is to say that for a iven sample rate f s = 1/m, unambiuous identification of the input sinal frequency is only possible for frequencies at less than half the sample rate f s /2, known as the Nyquist frequency. After interpolation, sampled sinals of hiher frequency will erroneously appear to have a frequency between 0 and f s /2, known as the first Nyquist zone. For example, a sinal with frequency f 0 = f s /2 + a (where 0 < a < f s /2) will appear to have the frequency f r = f s /2 a after reconstruction. In eneral, this alias will have the frequency f r = f s min[mod[f 0, f s ],1 mod[f 0, f s ]], where mod[x, y] is the remainder function. There is therefore a tradeoff between Nyquist frequency and resolution that must be balanced for uniformly clocked s: samplin hiher-frequency sinals makes the timin jitter requirements increasinly difficult to satisfy, resultin in a reduced effective number of bits. Traditional Electronic Receiver Architectures As an alternative to buildin an with hih-rate diitization hardware, one approach that is often used is to interleave several lower-sample-rate diitizers, which will achieve a hih sample rate in areate. The channels are staered in time, as shown in Fi. 2a, collectin samples at a low rate which are then interleaved usin diital sinal processin. This allows for the use of hihresolution, low-sample-rate diitizers, but it does not entirely avoid the need for hih-precision timin: any timin or ain errors between channels will lead to spurious sinals in the processed spectrum, known as interleavin spurs, which will distort the reconstructed sinal. Another approach, shown in Fi. 2b, is to interleave in the frequency domain, usin filters and mixers to downconvert a reion of the spectrum to within the rane of low-rate s. In this architecture, each channel downconverts a different reion of frequency space, usin filters to eliminate aliasin. This approach is especially well suited to applications in which the sinals of interest consist of narrow-bandwidth information encoded on hih-frequency carriers. However, althouh this system 281

3 P. T. CALLAHAN, M. L. DENNIS, AND T. R. CLARK JR. Input Incomin spectrum... Frequency RF successfully reduces the timin jitter requirements on the s and avoids the sinal aliasin problem, downconversion introduces added noise, harmonic distortion, and loss via the mixin process, not to mention the fact that such a system is very hardware intensive. The size, weiht, and power requirements of a downconversion system can be prohibitive for many applications in which a wide operational bandwidth is needed. T 2 T PHOTONIC SOLUTIONS As has been investiated at lenth in Ref. 3, the use of photonic technoloy in analoto-diital conversion can be oranized into four broad cateories: photonics-assisted s, in which photonic components aument the capabilities of an electronic that is responsible for both the samplin and quantization functions; photonic samplin with electronic quantization; electronic samplin with photonic quantization; and photonic samplin and quantization. This article will focus on photonic samplin with electronic quantization. It has lon been reconized that the ultrashort pulses enerated by mode-locked lasers can be of reat utility to the samplin function within the analo-.. n T RF Diital interleavin LO LO LO. Output. Fiure 2. Electronic receiver architectures for a time-interleaved system and a channelized downconversion system. ΔT, time delay; LO, local oscillator. Stable modelocked laser Optical clock Optical clock to-diital conversion process. 4 Mode-locked lasers capable of eneratin subpicosecond pulse widths with extraordinary pulseto-pulse timin stability have developed to the point that they are now commercially available from several vendors. Coupled with hih-speed electro-optic modulators, these pulse sources can provide direct samplin capability over 50 GHz of bandwidth or wider, with jitter levels that enable reater than 10-bit resolution systems. The basic desin for a photonically sampled is shown in Fi. 3a. A stable mode-locked laser provides a stream of ultrashort optical pulses, which define the samplin instants for the sinal to be diitized. The sinal of interest is sampled by an electro- optic modulator, which encodes the RF input onto the pulse train as an amplitude variation. The encoded optical sinal is then converted to the electrical domain usin a hih-speed photodiode, the output of which is quantized by an electronic. The main benefit of this system is that all of the timin characteristics are controlled by the low-noise optical clock. The samplin time is set by the pulse width and the bandwidth of the electro-optic modulator, the samplin rate is set by the pulse repetition rate, and the timin jitter is set by the jitter of the laser. Althouh the photonic samplin RF input Electro-optic amplitude modulator RF input Optical switch Hih-speed photodiode (PD) PD 8 Fiure 3. Traditional photonic-sampled architectures. Basic photonic link. demultiplexed system. Interleavin/processin 282

4 improves the timin noise of the system, the architecture of Fi. 3a does not reduce the rate at which the quantization function must take place. Because this simple architecture relies on a sinle electronic to quantize the photodiode output, the must be clocked at the samplin rate. For continuous broadband sinals, such as hih-data-rate communications, the aliasin problem once aain necessitates a hih sample rate and thus hih-speed electronics. If the information bandwidth is small compared with the carrier frequency, a technique known as photonic downsamplin can be used. This is most useful for systems in which the carrier frequency is known to be in some fixed band and the information on the carrier occupies a bandwidth less than half the sample rate. In this case the mode-locked laser and the modulator accurately sample the incomin sinal below its Nyquist rate, allowin the operational bandwidth of the photodiode and electronic to be sinificantly reduced. An RF filter before the electro-optic modulator can be used to prevent sinals outside the frequency band of interest from aliasin into the bandwidth of the. This technique allows for information encoded on hih-frequency carriers to be captured with hih precision without the use of hih-speed electronics or RF downconversion hardware, but it is inherently limited to applications that require only a relatively narrow operational bandwidth. As with the all-electronic, time demultiplexin into several interleaved channels can reduce the rate requirement for individual s, as well as the operational bandwidth needed for the photodiode. An example of such a system is shown in Fi. 3b, where the demultiplexin is accomplished usin an optical switch. 5, 6 Another method that has been used for an interleaved photonic relies instead on a sequence of pulses at different wavelenths such that the optical switch is replaced by a wavelenth demultiplexer. 7 Both of these architectures suffer from the limitations common to all interleaved systems, in particular path-mismatch of time and amplitude between channels, which can lead to unwanted spurs in the reconstructed spectrum. hat is needed is a method for samplin below the Nyquist rate that has a wide operational bandwidth with- PHOTONIC ANALOG-TO-DIGITAL CONVERSION out aliasin. Uniform samplin is simply not capable of achievin this oal with a sinle channel. THEORY: NONUNIFORM SAMPLING Randomized Samplin Techniques Nonuniform samplin techniques can defeat aliasin of hih-frequency carriers while samplin well below their Nyquist rate, allowin the sample rate requirement of the system to be dictated by the bandwidth of the encoded data on the incomin sinal rather than by its carrier frequency. The basic concept behind nonuniform samplin is illustrated in Fi. 4. Fiure 4a shows an example of uniform samplin in which several sinals of different frequencies could all equally have produced the same set of samples; there is no way to determine the frequency of the oriinal sinal from these samples alone. This is another formulation of the sinal aliasin problem described in Electronic s. However, if we allow the samplin instances to deviate from the uniform times (denoted by {t i } in the fiure), it is clear that only one of the candidate frequencies could have produced this new set of samples. This result is shown in Fi. 4b, where the nonuniform sample times are denoted in red by $ tl i.. Nonuniform samplin, coupled with the t 0 t 1 t 2 t 3 t 4 t 0 ' t 1 ' t 2 ' t 3 ' t 4 ' t 0 t 1 t 2 t 3 t 4 Fiure 4. Illustration of nonuniform samplin. Shown as ray dots in panel a are the samples obtained for a uniform samplin process at the rate 1/µ, whose samplin instants are shown on the time axis as {t i }. Red dots in panel b denote the samples obtained for a nonuniform samplin process, whose samplin instants are shown in red as {t i }. t t 283

5 P. T. CALLAHAN, M. L. DENNIS, AND T. R. CLARK JR. appropriate reconstruction alorithms, can therefore determine the oriinal carrier frequency of a sampled sinal without samplin at twice the frequency of interest. Althouh there are several possible ways to sample nonuniformly, optimal reconstruction of a sinal with an arbitrary carrier frequency will only be achieved for samplin processes that meet certain statistical requirements. A more complete theoretical investiation of the statistical merits of various nonuniform samplin techniques can be found in Ref. 8 and in much more mathematical detail in numerous papers on compressive samplin. 9, 10 Sinal Reconstruction An intuitive method for sinal reconstruction involves the Fourier decomposition of the nonuniformly sampled sinal by projectin onto a function space and performin a least-squares analysis. This is simply a best fit of the data to a set of frequencies. The basis functions are constructed by usin the vector of nonuniform samplin instants and a set of frequencies {f i } chosen to be analyzed. Choosin sines and cosines as the basis functions, a matrix of these transforms can be formed as follows: Rcos( 2 ft) S 1 1 S sin( 2 ft 1 1) = S h S cos( 2 fmt1) Ssin( 2 fmt1) T cos( 2 ft 1 2) sin( 2 ft 1 2) h cos( 2 fmt2) sin( 2 f t ) M 2 j cos( 2 ft ) V 1 N sin( 2 ft 1 N) h, cos( 2 fmtn) sin( 2 fmtn) X where {t k } are the known samplin instants. Note that the number of frequencies M in the analyzed set is directly related to the bandwidth and frequency resolution considered in the reconstruction alorithm. In order for reconstruction to be possible, M must be less than half the number of samples N, 2M < N. Lettin c denote the vector of Fourier coefficients and y the vector of sampled data, the optimal estimate of the unknown coefficients can be obtained usin the pseudoinverse of the matrix, 1 T c = `^ h jy, which can then be used to approximate the frequency spectrum of the oriinal sinal. It is important to note that sinal reconstruction requires knowlede of the samplin times, which has consequences for the hardware implementation of a nonuniform samplin system. Aliasin will manifest itself as deeneracy in the rows of, that is to say that basis functions of aliased frequen- Samplin pulse eneration 10-GHz repetition rate CLK MLL PPG 10-MHz reference cies will yield identical values when evaluated at the samplin times {t k }, renderin the matrix sinular and makin reconstruction impossible. Therefore there still exist restrictions on {f i } in order to ensure successful reconstruction, but with careful choice of the samplin times, the alias-free bandwidth can be extended to a bandwidth that is many times reater than half the mean sample rate. The key advantae for nonuniform samplin is that information about the carrier frequency can be obtained without havin to sample at twice the carrier frequency. To accurately capture the encoded data, all that is required is a mean sample rate scalin with the information bandwidth, a much less strinent requirement than scalin with the carrier frequency. NONUNIFORM PHOTONIC SAMPLING SYSTEM Experimental System Desin Fiure 5 diarams the eneral experimental setup of our nonuniformly sampled photonic e used an actively mode-locked laser with a pulse repetition rate of 10 GHz to act as a rid of samplin times from which to choose. Individual pulses were then selected pseudorandomly usin an amplitude modulator confiured to act as an on off switch. A prorammable pulse-pattern enerator (PPG) controlled the transmission of pulses, with the pattern desined such that the mean time interval between two successive pulses was m = 10 ns. The PPG was clocked with the same 10-GHz reference oscillator drivin the laser, thereby ensurin that the PPG output would be synchronous with the optical pulses enterin the modulator. The lenth of the pattern and therefore the total measurement time was set to be 20 ms. After eneratin the nonuniformly spaced train of samplin pulses, the incomin RF sinal was captured usin a second amplitude modulator with a 3-dB bandwidth of 20 GHz. The encoded pulse train was then converted to the electrical domain by a photodiode and passed to an electrical track-and-hold (T/H) circuit. This created EDFA Sinal encodin Nonuniform CLK O-E conversion and quantization PD T/H Uniform CLK Fiure 5. Diaram of the nonuniform photonic samplin system. CLK, clock; EDFA, erbiumdoped fiber amplifier;, electro-optic modulator; MLL, mode-locked laser; O-E, optical to electrical. PD 284

6 a series of held voltaes for the diitizer to analyze. Note that the input bandwidth of the system is still determined by the photonic samplin operation and can be reater than 50 GHz with commercially available technoloy. The purpose of the T/H circuit was to allow the to be uniformly clocked, thus convertin the nonuniformly sampled sinal to a uniformly sampled sinal. Quantization is easier to implement with an electronic when the clock is periodic, and the nonuniform-to-uniform conversion facilitates the use of commercially available hih-resolution s to perform this function. Crucial to these experiments was the synchronous nonuniform clockin of the T/H circuit with an electronic replica of the samplin pulse train, which ensured that none of the encoded pulses (and thus sinal samples) were missed by the electronic diitizer. Finally, the T/H output was diitized by a 14-bit, which was clocked uniformly at the rate of 100 MHz. The timin of the uniform clock, which was synchronous with the master laser oscillator, was adjusted with respect to the T/H output such that the uniform sample times always fell approximately in the middle of the held voltaes and not on an ede. Experimental Results and Discussion To demonstrate the alias-defeatin capability of this technique, two-tone X-band sinals from a frequency synthesizer were sampled by the system and reconstructed usin the alorithm described in Sinal Reconstruction. The results are shown in Fi. 6 for several different frequency separations of the two-tone sinal. The nonuniform samplin techniques implemented by the system yielded an alias-free bandwidth of 5 GHz, even thouh the mean sample rate was 100 MHz. As can be seen from the spectra, the system is able to unambiuously identify sinals that are separated by many traditional Nyquist zones (a Nyquist zone for this case would span 50 MHz). In Fi. 6c, the two tones are separated by the equivalent of 74 traditional Nyquist zones. The sinal-to-noise-floor ratio for this system is limited primarily by the poor amplitude noise performance of the actively mode-locked laser used as the master optical clock. Sinificant improvement in noise can be achieved by usin a passively mode-locked laser, althouh these sources typically have lower pulse repetition rates. A nonuniform samplin system usin this type of laser as the optical clock (c) Power (dbc) PHOTONIC ANALOG-TO-DIGITAL CONVERSION would therefore require some method of pulse multiplication in order to be practical. This is an area of research that will be investiated in the future. e are also currently developin a hih-repetition-rate, low-noise laser that promises to provide a dramatic increase in the achievable sinal-to-noise performance. e have developed an architecture that capitalizes on the very wide bandwidth of photonic samplin and the data-manaement efficiency of diital alias-free sinal processin, enablin a sinle hardware system to simultaneously observe many sinals across multiple frequency bands without scannin and without parallel filtered receivers. There will be no instantaneous blindness to sinals at any frequency, as would occur when scannin one frequency reion while a sinal resides in another, nor will there be static frequency blind spots, as would occur in parallel filtered receivers. This work represents the first and only demonstration, to our knowlede, of a nonuniformly sampled photonic and is presently bein evaluated as a very wide input bandwidth (coverin from 1 GHz up to 100 GHz) electronic receiver to support applications with a very wide processin bandwidth (up to 50 GHz in a sinle output). This approach will improve the receiver probability of detection by eliminatin frequency blindness and sinificantly improve the size, weiht, and power requirements as compared with parallel receiver systems, for which a 50-GHz processin bandwidth would be inconceivable for all but the larest of platforms. f 1 = 9.17 GHz, f 2 = 9.30 GHz f 1 = 7.08 GHz, f 2 = 9.30 GHz f 1 = 5.60 GHz, f 2 = 9.30 GHz Frequency (GHz) Fiure 6. Reconstructed RF spectra for two-tone input sinals. Input sinal frequencies are indicated as f 1 and f 2. Mean sample rate was 100 MHz, and the equivalent Nyquist-limited bandwidth is therefore 50 MHz. The input frequencies are accurately identified over an operatin bandwidth of up to 80 Nyquist zones. dbc, decibels relative to the carrier. 285

7 P. T. CALLAHAN, M. L. DENNIS, AND T. R. CLARK JR. FUTURE ORK Photonic analo-to-diital conversion architectures have lon been reconized as havin the potential to provide sinificant advantaes in bandwidth, timin precision, and timin stability. In our work we have focused on desinin a system architecture that will maximally realize the advantaes of photonics while retainin the ability to utilize the hih performance and maturity of electronic diitization and processin. Experimental demonstration of a photonic samplin system based on nonuniform samplin techniques has shown the capability of such methods to defeat traditional sinal aliasin. This suests that optimization of the sinal reconstruction alorithms could further extend the alias-free bandwidth of nonuniform samplin systems. The vast literature available in the related field of compressed sensin presents a fertile round for further inquiry. Future work will also include optimization of the hardware implementation to better alin the functionalities offered by photonic technoloy with the sinal-processin techniques. ACKNOLEDGMENTS: The work presented here was performed throuh internal research and development prorams with support from APL's Precision Enaement Business Area and the Air and Missile Defense Department. This material was also based on work supported by the Defense Advanced Research Projects Aency (DARPA) under DoD Award 911NF Any opinions, findins, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of DARPA or the DoD. REFERENCES 1 alden, R. H., Analo-to-Diital Converter Survey and Analysis, IEEE J. Sel. Areas Commun. 17(4), (1999). 2 Shannon, C. E., Communication in the Presence of Noise, Proc. Inst. Radio En. 37(1), (1949). 3 Valley, G. C., Photonic Analo-to-Diital Converters, Opt. Express 15(5), (2007). 4 Taylor, H. F., An Electrooptic Analo-to-Diital Converter, Proc. IEEE 63(10), (1975). 5 Juodawlkis, P.., Twichell, J. C., Betts, G. E., Harreaves, J. J., Youner, R. D., et al., Optically Sampled Analo-to-Diital Converters, IEEE Trans. Microw. Theory Tech. 49(10), (2001). 6 Clark, T. R., and Dennis, M. L., Toward a 100 Gsample/s Photonic Analo-Diital Converter, IEEE Photonics Technol. Lett. 13(3), (2001). 7 Clark, T. R., Kan, J. U., and Esman, R. D., Performance of a and avelenth-interleaved Photonic Sampler for Analo Diital Conversion, IEEE Photonics Technol. Lett. 11(9), (1999). 8 Callahan, P. T., Dennis, M. L., and Clark, T. R., Nonuniform Photonic Samplin Techniques for Broadband Frequency Identification, in Proc. IEEE International Topical Meetin on Microwave Photonics 2009, Valencia, Spain, pp. 1 4 (2009). 9 Candès, E., Romber, J., and Tao, T., Robust Uncertainty Principles: Exact Sinal Reconstruction from Hihly Incomplete Fourier Information, IEEE Trans. Inf. Theory 52(2), (2006). 10 Mishali, M., and Eldar, Y. C., From Theory to Practice: Sub-Nyquist Samplin of Sparse ideband Analo Sinals, IEEE J. Sel. Top. Sinal Process. 4(2), (2010). 11 Airola, M., Dennis, M. L., Novak, D., and Clark, T. R., A Pseudorandom Sampled Hih Speed Photonic Analo-to-Diital Converter Architecture, in Proc. IEEE Lasers and Electro-Optics Society Annual Meetin, 2007, Lake Buena Vista, FL, pp (2007). 12 O Connor, S. R., Airola, M. B., Dennis, M. L., and Clark, T. R., Proress Toward a Hih-Speed Pseudorandom Photonic Sampled Analo to Diital Converter, in Proc. IEEE Lasers and Electro-Optics Society Annual Meetin, 2008, Newport Beach, CA, pp (2008). 13 Airola, M. B., O Connor, S. R., Dennis, M. L., and Clark, T. R., Experimental Demonstration of a Photonic Analo-to-Diital Converter Architecture with Pseudorandom Samplin, IEEE Photonics Technol. Lett. 20(24), (2008). The Authors Patrick T. Callahan Michael L. Dennis Thomas R. Clark Jr. Patrick T. Callahan was previously a member of the Associate Professional Staff in the Electro- Optical and Infrared Systems and Technoloy Group in APL s Air and Missile Defense Department and is now with the Department of Electrical Enineerin and Computer Science at the Massachusetts Institute of Technoloy. For this project, he was responsible for assemblin and characterizin the prototype system, as well as conductin simulations on nonuniform samplin. Michael L. Dennis and Thomas R. Clark Jr. are Principal Professional Staff members in the Electro-Optical and Infrared Systems and Technoloies Group and were co-principal Investiators for the APL internal research and development and DARPA prorams that funded the concept and laboratory demonstrations reported in this article. For further information on the work reported here, contact Thomas R. Clark Jr. His address is thomas.clark@jhuapl.edu. The Johns Hopkins APL Technical Diest can be accessed electronically at 286