CHIRPED and other spread spectrum waveforms are widely

Transcription

1 3580 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 20, OCTOBER 15, 2014 Photonc Synthess of Spread Spectrum Rado Frequency Waveforms Wth Arbtrarly Long Tme Apertures Yhan L, Student Member, IEEE, Amr Dezfoolyan, Student Member, IEEE, and Andrew M. Wener, Fellow, IEEE Abstract A photonc technque s proposed to generate spread spectrum rado frequency waveforms wth both hgh RF bandwdth and arbtrarly long temporal perod. By swtchng the polarty of full duty cycle chrped waveforms accordng to a pseudorandom sequence, we can ncrease the waveform repetton perod under electronc control whle preservng RF bandwdth and average power. Proof-of-prncple rangng experments are presented to demonstrate the mprovement our technque provdes wth respect to range ambguty. Index Terms Mcrowave photoncs, optcal pulse shapng, rado frequency. I. INTRODUCTION CHIRPED and other spread spectrum waveforms are wdely utlzed n rado-frequency (RF) applcatons, ncludng ultra-wdeband (UWB) channel soundng [1], [2], RADAR and magng [3], [4], and others. In contrast to drect electrcal approaches for generatng spread spectrum waveforms, photonc technques offer hgher bandwdth, better mmunty to electromagnetc nterference, and compatblty wth rado-over-fber technology. Varous photonc approaches have been proposed n recent years [5] [13]. Generally, these methods employ ether drect optcal pulse shapng [7] or spectral shapng n conjuncton wth frequency-to-tme mappng (FTM) va dspersve propagaton [8], [9], [12], followed n all cases by photodetecton. However, technques such as [7] [9], [12] delver nonrepeatng waveforms only over lmted tme aperture (nanoseconds and below) and wth lmted tme-bandwdth product (TBP). Ultmately n such schemes the TBP s lmted by the complexty of the pulse shapng element to at most a few hundred; when the maxmum TBP s reached, the tme-aperture Manuscrpt receved January 9, 2014; revsed March 26, 2014; accepted Aprl 26, Date of publcaton Aprl 28, 2014; date of current verson September 1, Ths work was supported n part by the Natonal Scence Foundaton under Grant ECCS and by the Offce of the Assstant Secretary of Defense for Research and Engneerng under Grant N from the Naval Postgraduate School. Any opnon, fndngs, and conclusons or recommendatons expressed n ths publcaton are those of the authors and do not necessarly reflect the vews of the sponsors. Y. L and A. M. Wener are wth the Ultrafast Optcal and Optcal Communcatons Laboratory, Purdue Unversty, West Lafayette, IN USA (e-mal: l592@purdue.edu; amw@ecn.purdue.edu). A. Dezfoolyan was wth the Ultrafast Optcal and Optcal Communcatons Laboratory, Purdue Unversty, West Lafayette, IN USA. He s now wth the Newfeld Wreless, Berkeley, CA USA (e-mal: amr@pudue.edu). Color versons of one or more of the fgures n ths paper are avalable onlne at Dgtal Object Identfer /JLT of the waveform cannot be ncreased wthout sacrfcng RF bandwdth [14]. These restrctons are ncompatble wth establshed applcatons such as chrped radar [15], whch typcally employs waveforms wth tme apertures n the mcrosecond to mllsecond range and much larger TBPs. Waveforms wth fast chrp rates and tme apertures n the mcrosecond range have been generated by heterodyne mxng of a fxed frequency and a rapdly frequency swept laser, e.g., [13], but the repeatablty of the generated waveforms s a challenge. Another approach [10], [11], [16], whch does provde a hgh degree of repeatablty, s based on swtchng between multple bass waveforms obtaned va lne-by-lne pulse shapng of optoelectroncally generated frequency combs [17]. Here waveform swtchng under electronc control allows for arbtrarly large tme apertures wthout waveform repetton. However, constrants n pulse shaper resoluton have lmted such experments to swtchng between low complexty bass waveforms, each of whch has tme apertures lmted to a few hundred pcoseconds and RF spectral features programmable only at the 5 GHz level. In ths paper, we ntroduce a novel photonc spread spectrum rado-frequency waveform generaton technque that for the frst tme combnes FTM and waveform swtchng approaches. In ths work we generate bass waveforms wth substantally ncreased complexty, wth tme apertures spannng several nanoseconds and RF spectral features programmable at the several hundred MHz level. By swtchng between postve and negatve polarty versons of a bass waveform under electronc control, we are able to ncrease the repeat-free tme aperture arbtrarly by ncreasng the length of the swtchng sequence. Such expanson could be realzed by gatng out pulses to drectly ncrease the repetton perod of the waveform, but at the cost of substantally reduced average power. Snce our swtchng nvolves polarty-flppng only, average power s mantaned. The waveforms generated are hghly repeatable and, analogous to nose radar technology [18], are characterzed both by hgh RF bandwdth and energy spread substantally n tme. Moreover, as RF bandwdth and repeat-free tme aperture may be controlled ndependently, arbtrarly large tme-bandwdth products are possble. The waveforms generated smultaneously offer several attractve features. The ablty to generate large RF bandwdth supports the potental for hgh resoluton rangng [19]. In vew of the peak-voltage-lmted nature of most RF photonc transmtters, ncreasng the tme aperture provdes hgher average power [15], [20], boostng maxmum operatng dstances n RF wreless applcatons wth hgh path loss. Furthermore, n IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See standards/publcatons/rghts/ndex.html for more nformaton.

2 LI et al.: PHOTONIC SYNTHESIS OF SPREAD SPECTRUM R F WAVEFORMS WITH ARBITRARILY LONG TIME APERTURES 3581 applcatons such as rangng and soundng of propagaton channels wth strong multpath, the ablty to ncrease the repeat perod of the transmt waveform to a value larger than the roundtrp delay tme or the maxmum delay spread of the channel, respectvely, avods ambgutes. The hgh degree of repeatablty supports sgnal averagng for addtve nose suppresson. Fnally, the relatvely large tme aperture of ndvdual bass waveforms offers potental compatblty wth precompensaton schemes applcable to mult-path RF wreless propagaton, as n [21]. The remander of ths paper s organzed as follows: The theory of our pseudorandom modulaton scheme s dscussed n Secton II, followed by Secton III n whch the expermental setup s descrbed n detal. Waveform generaton results are presented n Secton IV. Then n Secton V, proof-of-prncple rangng experments are presented to demonstrate the mprovement our technque provdes wth respect to range ambguty. In the end, Secton VI presents our concluson. II. THEORY In conventonal photonc approaches for generatng arbtrary RF waveforms, a repettve optcal pulse tran from a modelocked laser s fed nto the generaton apparatus. The shape of the output RF waveform can be talored but s constraned to repeat perodcally at the laser repetton rate. Thus, the temporal perod of the generated waveform s always clamped to the repetton perod of the source laser. Mathematcally, f the RF waveform tran, s (t), s expressed as Fg. 1. Schematc dagram of ampltude-msmatched PN sequence modulaton. (a) Repettve lnear up-chrp waveform tran wth perod T. (b) Autocorrelaton functon of (a), T between peaks. (c) Chrp tran n (a) modulated by a length L regular PN sequence. Polarty of chrps s ether mantaned (black ones) or flpped (red ones). (d) Autocorrelaton functon of (c), T L between man peaks. T between suppressed peaks. (e) Chrp tran n (a) modulated by a length-l ampltude-msmatched PN sequence. Peak-to-peak ampltude of the polarty-mantaned chrps n (c) s adjusted to 1+p, where p s a PN length dependent value. p =0.5for a length-15 PN sequence and 0.06 for length (f) Autocorrelaton functon of (e), T L between peaks. s (t) = w (t) δ (t T ) (1) where w (t) denotes an arbtrary waveform havng a autocorrelaton functon R w (τ),t s the repetton perod, denotes convoluton, then the autocorrelaton functon R s (τ) equals R s (τ) = R w (τ) δ (τ T ) (2) where R w (τ) = w (t) w (t + τ) dt Fg. 1(a) depcts a repettve lnear up-chrp waveform tran wth repetton perod T, and Fg. 1(b) shows the correspondng autocorrelaton functon wth the same perod T. When a length- L bnary pseudorandom sequence, also known as a PN sequence [22], s modulated onto such repettve waveform, t can be expressed as s (t) = PN [] w (t) δ (t T ) = w (t) [PN [] δ (t T )] (3) as llustrated by Fg. 1(c). PN [] s the -th element n the PN sequence and PN [] =PN [ + L]. Due to the propertes of PN sequences, the autocorrelaton of such a modulated waveform wll have man peaks repeatng wth perod T L, whle all other peaks are reduced and nverted [22], as shown n Fg. 1(d). We have found that by approprately adjustng the ampltude of the postve polarty chps n the pseudorandom sequence modulaton, t s possble n prncple to completely null the unwanted peaks, as mathematcally derved n Appendx I and llustrated n Fg. 1(e). The autocorrelaton functon of the new waveform, R s (τ), can now be expressed as R s (τ) = R w (τ) δ (τ LT ) (4) ndcatng that the modulaton ncreases the temporal perod of the new waveform by a factor of L, as llustrated n Fg. 1(f). By alterng the length of the PN sequence, the temporal perod can be set to an arbtrarly large value. The temporal profle of the bass waveform,.e., the temporal profle wthn a sngle perod T, s not dsturbed, leavng the RF bandwdth preserved. Thus, the spread spectrum waveform generaton whch controls the temporal shape and thus the RF bandwdth, and the PN modulaton whch determnes the temporal perod as well as the tme-aperture, are kept ndependent to realze arbtrarly large tme-bandwdth product. III. EXPERIMENTAL CONFIGURATION Our expermental apparatus for RF arbtrary waveform generaton s sketched n Fg. 2(a). Overall our setup resembles the popular approach based on pulse shapng plus frequency-totme mappng, but modfed for dfferental detecton [23] and

3 3582 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 20, OCTOBER 15, 2014 Fg. 2. (a) Schematc of expermental setup. ML Laser: Mode-locked laser. IM: Intensty modulator. PD: Photodetector. (b) Detal setup of the dsperson block ndcated by the red dash rectangle n (a). polarty swtchng. A mode-locked fber laser (Menlo Systems FC WG) wth 250 MHz repetton rate and 80 nm optcal bandwdth ( 1520 nm 1600 nm) outputs an optcal pulse tran nto a commercal pulse shaper through an ntermedate fber amplfer (not shown n the fgure). The pulse shaper (FINISAR 1000S) has a resoluton of 10 GHz and 5000 addressable pxels across an 5 THz or 40 nm wavelength range (1527 nm 1567 nm). It s programmed usng the near-feld frequency-to-tme mappng (NFFTM) technque [14], whch predstorts both the ampltude and phase of the optcal spectrum to acheve target RF waveforms wth hgh fdelty, whle overcomng the far-feld constrant whch otherwse may lmt the maxmum attanable RF bandwdth of the generated waveform [24]. After the shaper the sgnal s splt equally nto two arms through a optcal coupler. Synchronzed to the laser repetton rate, a pattern generator provdes complementary drve sgnals to a par of ntensty modulators (IM). As a result the pulse s transmtted n one arm and blocked n the other, wth the transmttng arm selected accordng to a preprogrammed PN sequence. The length of the dspersve fber ( 6.6 km of SMF-28 at 17 ps/nm/km) s carefully chosen so that each 40-nm bandwdth, spectrally shaped pulse s stretched to a temporal duraton of 4 ns, matched to the laser perod. Wth our dfferental detecton geometry, t s mportant to ensure stable matchng of both the length and the dsperson experenced n each arm. Accordngly we desgned a dsperson block, llustrated n Fg. 2(b), n whch both arms use the same pece of dspersve fber, but n a counter-propagatng geometry mplemented usng a par of crculators. Both arms are provsoned wth varable optcal attenuators (not shown n the fgure) to adjust the relatve sgnal power rato. Then the optcal sgnals n the two arms are converted nto electrcal sgnals by two photodetectors (PD) of the same model (DSC 30S, DC-22GHz). The outputs of the PDs are dfferenced by a 180 degree electrcal hybrd (NARDA 4346, 2 18 GHz). In the end, the pedestal of the generated waveform s removed when a hgh-pass flter (K&L, 2 18 GHz) s added to elmnate baseband frequences. Background-free waveforms are then acheved. Upon dfferental detecton our swtchng scheme results n sgnals wth smlar shape but complementary polarty, wth the polarty determned by the photodetector onto whch lght s ncdent durng that swtchng cycle. Generated waveforms are measured n the temporal doman by a real-tme osclloscope (Tektronx 72004B, 20 GHz, 50 GS/s) wth a samplng perod of 20 ps and n the frequency doman by an RF spectrum analyzer (Aglent 8565EC). Fg. 3. Demonstraton of Frequency-to-tme Mappng. (a) Shaped Optcal Power Spectrum; (b) correspondng temporal profle. IV. WAVEFORM GENERATION RESULTS As a frst example, we program the pulse shaper to generate a lnear down-chrp bass waveform coverng the frequency range from 2 to 10 GHz and spannng the 4 ns laser repetton perod. In ths way, the generated waveform has a full duty cycle. Fg. 3 llustrates the great resemblance between the optcal power spectrum, as shown n Fg. 3(a), and the mapped waveform n the tme doman, as shown n Fg. 3(b). For ths parameter range, the far-feld condton s well satsfed, and FTM apples. (For hgher bandwdth waveform generaton, the far-feld condton breaks down, and the mportance of waveform predstorton va the NFFTM technque becomes more evdent [14].) To demonstrate waveform swtchng acton, we program the pattern generator wth a sequence of [11 1 1] and adjust both arms of the apparatus for equal ampltude. The resultng waveform s shown n Fg. 4(a) over a 16 ns tme span, correspondng to four down-chrped bass waveforms. The polarty of each waveform s labeled on top; the frst and second tme slots have postve polarty, whle the thrd and fourth tme slot has opposte polarty. To better llustrate, the second and thrd waveform from Fg. 4(a) are overlapped and plotted on an expanded scale n Fg. 4(b). As clearly seen, waveforms wth opposte polartes are antpodal. To exemplfy the temporal perod expanson due to waveform swtchng under PN modulaton, we set the length of the modulaton sequence to be 15 and adjust the relatve sgnal ampltude of the two arms such that a p value of 0.5 s obtaned, as defned n Fg. 1(e). A temporal measurement s recorded

4 LI et al.: PHOTONIC SYNTHESIS OF SPREAD SPECTRUM R F WAVEFORMS WITH ARBITRARILY LONG TIME APERTURES 3583 Fg. 4. Expermental measurements. (a) A temporal frame of 16 ns consstng of 4 down-chrped waveforms wth polartes labeled on top; (b) 2nd and 3rd chrp n (a) plotted n a same frame of 4 ns. Fg. 6. RF spectra correspondng to Fg. 5. (a) No PN modulaton, bandwdth 2 to 10 GHz. (b) Length-15 PN modulaton, bandwdth 2to10GHz. (c) Length-1023 PN modulaton, bandwdth 2to20GHz. Fg. 5. Autocorrelaton functons. (a) No PN modulaton, 4 ns between peaks. (b) Length-15 PN modulaton, 60 ns between peaks. Inset: magnfcaton from 22 to 30 ns horzontally and 0.1 to 0.1 vertcally. Extncton rato 19.1 db. (c) Length-1023 PN modulaton, 4092 ns between peaks. Extncton rato 21 db. over a span of 180 ns. For comparson, a waveform s recorded over the same tme span wthout waveform swtchng, as n conventonal FTM. Crcular autocorrelatons are computed offlne for both cases. Such correlaton measurements are relevant for pulse compresson n spread-spectrum rangng and related applcatons. As shown n Fg. 5(a), the autocorrelaton of the unmodulated waveform has a perod of 4 ns, the same as the laser repetton perod. In contrast, as shown n Fg. 5(b), the waveform swtched accordng to a length-15 PN sequence has an autocorrelaton wth strong peaks separated by 60 ns, correspondng to an ncrease n perod by a factor of 15. Weak peaks reman at the orgnal 4 ns perod. A magnfed vew of these sdelobes s shown n the nset to Fg. 5(b). The extncton rato, defned as the rato between the ampltude of the remanng strong peaks to the ampltude of the strongest of the resdual peaks, s mproved from 11 db, as n the case wthout ampltude msmatchng, to 19.1 db, ndcatng strong resdual peak suppresson and low sdelobe level. The spectra of both waveforms, measured by the RF spectrum analyzer wth a frequency resoluton of 100 khz, are plotted n Fg. 6(a) and (b). Two prncpal effects are evdent. Frst, Fg. 6(a) shows a clear comb structure, whch reflects the 250 MHz waveform repetton frequency. The spectrum flls n n Fg. 6(b), consstent wth the 15-fold decrease n waveform repetton frequency. Second, we observe that the envelope of the RF spectrum s largely unaffected by the ncrease of the temporal perod. As stated prevously, bass waveform generaton and PN-modulated waveform swtchng are separated n our technque. Ths enables us to ncrease the tme-aperture and the RF bandwdth smultaneously. By settng the length of the PN sequence to 1023 and programng a hgher rate chrp modulaton on the optcal power spectrum, we are able to generate a waveform wth more than 4 mcroseconds tme aperture (see autocorrelaton n Fg. 5(c)) and a RF bandwdth of 20 GHz (see RF spectrum n Fg. 6(c)). The resultng TBP exceeds The autocorrelaton peaks have a wdth of 50 ps, makng the rato of peak spacng to peak-wdth The suppressed autocorrelaton peaks, wth an extncton rato of 21 db, are too small to dscern gven the lnear scale of Fg. 5(c). Our technque also exhbts excellent stablty and repeatablty. Because our hybrd optcal-electrcal desgn combnes sgnals n the electrcal doman rather than the optcal doman, the system s nsenstve to the relatve optcal phases of the two generaton arms n Fg. 2. Moreover, the dsperson block descrbed n Fg. 2(b) provdes sgnals from ether arm wth the same fber propagaton envronment, elmnatng an mportant source of potental nstablty. To quantfy the stablty and repeatablty performance, we conduct a long-term measurement n whch 336 real-tme osclloscope measurements of the sgnal descrbed n Fg. 5(b) are recorded over one hour. The frst measurement s chosen as the reference, and cross-correlaton

5 3584 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 20, OCTOBER 15, 2014 Fg. 9. Sketches of waveforms transmtted n rangng experment. (a) Unmodulated repettve chrps; (b) repetton perod ncreased chrps; (c) PN-modulated chrps, red ones are polarty-flpped. Fg. 7. (a) Autocorrelaton of the reference measurement; (b) Crosscorrelaton functons between reference and all other measurements. 335 traces overlapped n a same temporal frame of 4 ns. Fg. 8. Block dagram of the rangng experment. Measurements are carred out n the hallway n the subbasement of the MSEE buldng at Purdue Unversty. P1 s m away from P0 and P2 s 2.43 m away from P0. Assumng a propagaton speed of lght, relatve temporal delay between P1 and P2 s 4 ns. functons between the reference and all other measurements are computed off-lne. All 335 cross-correlaton functons are overlapped n the same 4 ns temporal frame n Fg. 7(b). Clearly, all the cross-correlatons are very smlar. Compared wth the autocorrelaton of the reference measurement, as shown n Fg. 7(a), the curve n Fg. 7(b) s slghtly thcker because of the ampltude dfferences between each cross-correlaton. Mnor dstortons may also be seen at both man negatve sdelobes. These results provde compellng evdence of stable waveform generaton. Thus, data averagng can be mplemented to reduce the addtve nose n channel soundng and other applcatons. Furthermore, the reference waveform may be stored and used n later experments as a template for pulse compresson va offlne correlaton processng. V. PROOF-OF-PRINCIPLE RANGING EXPERIMENT A smple 1-D rangng experment s conducted to llustrate one of the applcatons of our technque. The expermental schematc nvolvng a par of horn antennas (DORADO, 1 12 GHz) s descrbed n Fg. 8. The transmt antenna s located at poston P0. The receve antenna s located ether at poston P1 ( 1.22 m away from P0) or poston P2 ( 2.43 m away from P0). The ca. 4 ns propagaton delay between postons P1 and P2 s ntentonally chosen to match the laser repetton perod n order to hghlght the range ambguty ssue. The transmt sgnal (descrbed below) s launched nto the channel through a cascaded par of RF amplfers (Pcosecond 5828A, GHz, 10 db gan; Mncrcuts ZVA-183, GHz, 26 db gan), and the receved sgnal s amplfed by a low nose amplfer (B&Z 110UC1, GHz, 34 db gan). The nput sgnal and the receved sgnal at poston P1 and P2 are recorded usng the real-tme osclloscope. All measurements are trggered by the same clock sgnal from the pattern generator. Cross-correlaton functons between the nput sgnal and both receved sgnals are computed off-lne and plotted n the same temporal frame. As dscussed n [25], the sgnal receved n such a system can be severely dstorted due to the frequency dependent delay of the antennas. To cancel such dstorton, we mplement post-compensaton. The system mpulse response (ncludng RF amplfers, antennas and free-space propagaton) s obtaned from the nput sgnal and the receved sgnal at poston P1 by applyng deconvoluton, an algorthm n whch the frequency response of the channel s determned by dvdng the frequency profle of output sgnal by that of the nput one [2], [26]. Both frequency profles are obtaned by Fourer transformng the correspondng temporal measurements. The mpulse response s employed to modfy both receved sgnals usng a phase compensaton algorthm through whch frequency dependent spectral phase dstorton ntroduced by the system s subtracted. Ths compresses the cross-correlaton peak to the bandwdth lmt [27], [28]. By evaluatng the relatve temporal delay between the cross-correlaton peaks for both receved antenna locatons, the dfference n range between P1 and P2 can be determned. We compare rangng wth three dfferent RF transmt waveforms. In the frst scenaro, the nput sgnal s a chrped waveform tran as sketched n Fg. 9(a), generated by conventonal FTM wthout waveform swtchng. Each chrped waveform spans from 2 to 12 GHz, wth a 4 ns perodcty and 100% duty cycle. The peak-to-peak voltage level rght after the PD s 8 mv. The cross-correlaton functons obtaned for receve antenna postons P1 and P2 are overlad n the same 60 ns temporal frame n Fg. 10(a). The ampltude of the sgnal from P2 s less than that from P1 because of a longer propagaton dstance.

6 LI et al.: PHOTONIC SYNTHESIS OF SPREAD SPECTRUM R F WAVEFORMS WITH ARBITRARILY LONG TIME APERTURES 3585 whle mantanng the hghest possble average power consstent wth a gven peak ampltude level. Such waveforms are well matched to the requrements of applcatons such as RF rangng and channel soundng. Fg. 10. Cross-correlatons obtaned by transmttng three dfferent waveforms sketched n Fg. 9. Normalzed to 3.2 V 2 ps. (a) Unmodulated chrps as n Fg. 9(a) are transmtted, 4 ns between peaks of P1, 4 ns between peaks of P2. Horzontal magnfcaton from 2 to 10 ns s shown on rght. (b) Repetton perod ncreased chrps as n Fg. 9 (b) are transmtted ns between peaks of P1 and P2. Peaks are attenuated by a factor of 15 compared wth those n (a). Magnfcaton from 2 to 10 ns horzontally and 0.1 to 0.1 vertcally s shown on rght. (c) Length-15 PN modulated chrps as n Fg. 9(c) are transmtted ns between peaks of P1 and P2, correspondng to 1.2 m assumng a propagaton speed of lght. Horzontal magnfcaton from 2 to 10 ns s shown on rght. Because the propagaton delay between P1 and P2 postons matches the laser repetton perod, the P1 and P2 correlaton peaks overlap. Ths clearly llustrates the ambguty n range poston that results when tme delays greater than or equal to the 4 ns repetton perod are consdered. In the second scenaro an ntensty modulator s added mmedately after the laser. The ntensty modulator blocks 14 pulses out of every 15, ncreasng the waveform repetton perod to 60 ns whle keepng the same energy per bass waveform. Each pulse s shaped the same as n the frst scenaro, resultng n a 4 ns long chrped waveform repeatng every 60 ns, as sketched n Fg. 9(b). Although the temporal perod s ncreased to 60 ns, extendng the range over whch unambguous measurements can be made, the average power s reduced 15-fold. Although the cross-correlaton peaks correspondng to postons P1 and P2 are now dstnct (see Fg. 10(b)), the ampltudes of the peaks are attenuated by approxmately ths same factor of 15 compared wth those n Fg. 10(a). Thus, as a result of the low transmtted power n ths waveform gatng scheme, sgnal-to-nose suffers. In the thrd scenaro the chrped waveform tran undergoes waveform swtchng accordng to a length-15 PN sequence, as sketched n Fg. 9(c). As the temporal perod s agan ncreased by a factor of 15 to 60 ns, the relatve temporal delay correspondng to P1 and P2 ( 4.04 ns) can be determned easly, as shown n Fg. 10(c). Moreover, approxmately the same average power s transmtted n the frst and thrd scenaros. Consequently, comparng Fg. 10(a) and (c), we see that the correspondng cross-correlaton peaks are now of comparable ampltude. Comparng the results for these three scenaros hghlghts the ablty of our waveform swtchng technque to generate RF waveforms wth extended ambguty-free tme range VI. CONCLUSION To sum up, we propose and demonstrate a novel photonc rado-frequency waveform generaton technque whch s able to create spread spectrum waveforms wth arbtrarly long temporal perod. In addton, ndependent control of tme-aperture and RF bandwdth s realzed and thus arbtrarly large tmebandwdth product can be obtaned. The RF bandwdth reaches as hgh as 20 GHz and s just lmted by avalable RF bandwdth of O/E converson. Our generated RF waveforms, wth arbtrarly long temporal perod, hgh RF bandwdth and average power, can be mplemented n a wde range of applcatons such as UWB channel soundng, wreless communcatons and RADAR. APPENDIX I Pseudorandom (PN) sequences are certan bnary sequences of length 2 m 1 where m s an nteger [22]. Such sequences have two key propertes: There are 2 m 1 1 s and 2 m s n any PN sequence (A.1) Ther crcular (perodc) autocorrelaton, defned for any dscrete length-l sequence f [], 1 L as (f f)[n] = L f [] f [( + n) mod L] =1 (A.2) where denotes correlaton operator, s gven by { L n =0, ±L, ±2L... (PN PN)[n] = 1 elsewhere (A.3) To get rd of the non-zero floor n Equaton (A.3), we found that the ampltude of all 2m 2 1 s can be adjusted to 1+p, where p s a postve number. Ths new pseudorandom sequence PN wth ampltude msmatchng can be expressed as ( PN = 1+ p ) PN + p 2 2 U (A.4) where U s an unt sequence of length L defned as U [] = 1for1 L. Computng the crcular autocorrelaton functon of such a sequence reveals that ( (PN PN )= 1+ p ) 2 ( p ) 2 PN PN + U U 2 2 ( p )( p PN U (A.5) 2 2) The frst correlaton on the rght hand sde of Equ. (A.5) s defned n Equ. (A.3). The second correlaton s the summaton of the unt sequence and thus equals to L for all delays. The last correlaton s the summaton of the PN sequence, whch

7 3586 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 20, OCTOBER 15, 2014 accordng to (A.1), equals 1 for all delays. Then Equ. (A.5) can be further smplfed to (PN PN )[n] = L +1 p 2 +(L +1)p + L, 2 L +1 p n =0, ±L, ±2L... elsewhere (A.6) Then floor of the autocorrelaton becomes zero when 2 p = (A.7) L +1. When the conventonal pseudorandom sequence n Equ. (3) s replaced by an ampltude-msmatched pseudorandom sequence PN of length L, the autocorrelaton of such sgnal can be expressed as R s (τ) = s (t) s (t + τ) dt = PN [j] PN [k] w (t jt) w (t kt+τ) dt j k = PN [j] PN [k] R w ((j k) T+τ) j k Replacng j k wth = R w (τ + T ) PN [j] PN [j ] (A.8) j Notce that the second summaton on the rght hand sde of Eq. (A.8) s a tme-reversed verson of the autocorrelaton of the ampltude-msmatched pseudorandom sequence and thus only has non-zero value at = ml, where m s an nteger and L s the sequence length. Therefore Eq. (A.8) can be rewrtten as R s (τ) R w (τ + mlt )= R w (τ) δ (τ + mlt ) m (A.9) Equaton (A.9) clearly demonstrates that when a pseudorandom sequence wth ampltude msmatchng s modulated onto a repeatng waveform at the same rate, the separaton of the autocorrelaton peaks, and thus the non-repeatng tme-aperture, wll be expanded by a factor of the length of the sequence. REFERENCES [1] J. Mar, Y. R. Ln, and Y. C. Yeh, Ultra-wde bandwdth n-vehcle channel measurements usng chrp pulse soundng sgnal, IET Sc. Meas. Technol., vol. 3, pp , [2] A. Dezfoolyan and A. M. Wener, Evaluaton of tme doman propagaton measurements of UWB systems usng spread spectrum channel soundng, IEEE Trans. Antennas Propag., vol. 60, no. 10, pp , Oct [3] K. Do, T. Matsumura, K. Mzutan, and R. Kohno, Ultra wdeband rangng system usng mproved chrp waveform, n Proc. Boston Rado Wreless Rawcon Conf., pp , [4] K. B. Cooper, R. J. Dengler, N. Llombart, T. Bryllert, G. Chattopadhyay, E. Schlecht et al., Penetratng 3-D magng at 4-and 25-m range usng a submllmeter-wave radar, IEEE Trans. Mcrow. Theory Tech., vol. 56, no. 12, pp , Dec [5] J. D. McKnney and A. M. Wener, Photonc synthess of ultrabroadband arbtrary electromagnetc waveforms, n Mcrowave photoncs, C. H. Lee, Ed. Boca Raton, FL, USA: CRC Press, [6] J. P. Yao, Photoncs for ultrawdeband communcatons, IEEE Mcrow. Mag., vol. 10, no. 4, pp , Jun [7] J. D. McKnney, D. E. Leard, and A. M. Wener, Mllmeter-wave arbtrary waveform generaton wth a drect space-to-tme pulse shaper, Opt. Lett., vol. 27, pp , Aug [8] J. Chou, Y. Han, and B. Jalal, Adaptve RF-photonc arbtrary waveform generator, IEICE Trans. Electron., vol. E86c, pp , Jul [9] I. S. Ln, J. D. McKnney, and A. M. Wener, Photonc synthess of broadband mcrowave arbtrary waveforms applcable to ultra-wdeband communcaton, IEEE Mcrow. Wreless Compon. Lett., vol. 15, no. 4, pp , Apr [10] C. B. Huang, D. E. Leard, and A. M. Wener, Tme-multplexed photoncally enabled rado-frequency arbtrary waveform generaton wth 100 ps transtons, Opt. Lett., vol. 32, pp , Nov [11] C. M. Long, D. E. Leard, and A. M. Wener, Photoncally enabled agle rf waveform generaton by optcal comb shftng, Opt. Lett., vol. 35, pp , Dec [12] C. Wang and J. P. Yao, Large tme-bandwdth product mcrowave arbtrary waveform generaton usng a spatally dscrete chrped fber Bragg gratng, J. Lghtw. Technol., vol. 28, no. 11, pp , Jun [13] J. M. Wun, C. C. We, J. H. Chen, C. S. Goh, S. Y. Set, and J. W. Sh, Photonc chrped rado-frequency generator wth ultra-fast sweepng rate and ultra-wde sweepng range, Opt. Exp., vol. 21, pp , May [14] A. Dezfoolyan and A. M. Wener, Photonc synthess of hgh fdelty mcrowave arbtrary waveforms usng near feld frequency to tme mappng, Opt. Exp., vol. 21, pp , Sep [15] J. R. Klauder, A. C. Prce, S. Darlngton, and W. J. Albershem, The theory and desgn of chrp radars, Bell Syst. Tech. J., vol. 39, pp , [16] V. Torres-Company, A. J. Metcalf, D. E. Leard, and A. M. Wener, Multchannel rado-frequency arbtrary waveform generaton based on multwavelength comb swtchng and 2-D lne-by-lne pulse shapng, IEEE Photon. Technol. Lett., vol. 24, no. 11, pp , Jun [17] V. Torres-Company and A. M. Wener, Optcal frequency comb technology for ultra-broadband rado-frequency photoncs, Laser Photon. Rev., [18] S. R. J. Axelsson, Nose radar usng random phase and frequency modulaton, IEEE Trans. Geosc. Remote Sens.,vol.42,no.11,pp , Nov [19] A. W. Rhaczek, Prncples of Hgh-Resoluton Radar. New York, NY, USA: McGraw-Hll, [20] R. Zetk, J. Sachs, and R. S. Thoma, UWB short-range radar sensng, IEEE Instrum. Meas. Mag., vol. 10, pp , Apr [21] A. Dezfoolyan and A. M. Wener, Mcrowave photoncs for space-tme compresson of ultrabroadband sgnals through multpath wreless channels, Opt. Lett., vol. 38, pp , Dec [22] F. J. Macwllams and N. J. A. Sloane, Pseudo-random sequences and arrays, Proc. IEEE, vol. 64, no. 12, pp , Dec [23] J. D. McKnney, Background-free arbtrary waveform generaton va polarzaton pulse shapng, IEEE Photon. Technol. Lett., vol. 22, no. 16, pp , Aug., 15, [24] V. Torres-Company, D. E. Leard, and A. M. Wener, Dsperson requrements n coherent frequency-to-tme mappng, Opt. Exp., vol. 19, pp , Nov [25] J. D. McKnney, D. Perouls, and A. M. Wener, Dsperson lmtatons of ultra-wdeband wreless lnks and ther compensaton va photoncally enabled arbtrary waveform generaton, IEEE Trans. Mcrow. Theory Tech., vol. 56, no. 3, pp , Mar [26] M. K. Tsatsans and G. B. Gannaks, Blnd estmaton of drect sequence spread spectrum sgnals n multpath, IEEE Trans. Sgnal Process., vol. 45, no. 5, pp , May [27] J. D. McKnney and A. M. Wener, Compensaton of the effects of antenna dsperson on UWB waveforms va optcal pulse-shapng technques, IEEE Trans. Mcrow. Theory Tech.,vol.54,no.4,pp , Apr

8 LI et al.: PHOTONIC SYNTHESIS OF SPREAD SPECTRUM R F WAVEFORMS WITH ARBITRARILY LONG TIME APERTURES 3587 [28] A. Dezfoolyan and A. M. Wener, Phase compensaton communcaton technque aganst tme reversal for ultra-wdeband channels, IET Commun., vol. 7, pp , Aug Yhan L was born n Xuzhou, Chna, n He receved the B.S. degree n optcal nformaton scence and technology from the Unversty of Scence and Technology of Chna, Hefe, Chna, n From 2006 to 2010, he was a Research Assstant wth the Key Laboratory of Optoelectronc Scence and Technology, USTC, Hefe, Chna. He joned Insttute of Physcs, Chnese Academy of Scence, Bejng, Chna, as a Research Assstant brefly n Snce 2010, he has been a Research Assstant wth the Ultrafast Optcs and Optcal Communcatons Laboratory, Purdue Unversty, West Lafayette, IN, USA. Hs research nterests nclude fber lasers, RF photoncs, optcal pulse shapng, optcal communcatons, and ultra wdeband RADAR. Amr Dezfoolyan receved the Ph.D. degree n electrcal and computer engneerng from Purdue Unversty, West Lafayette, IN, USA, n He s currently an RF Systems Engneer n Newfeld Wreless, a Tektronx Communcatons Company. From September 2009 to September 2013, he was a Graduate Research Assstant wth the Ultrafast Optcs and Optcal Fber Communcatons Laboratory, Purdue Unversty. Hs current research nterests nclude ultrafast optcs, optcal pulse shapng, mcrowave photoncs, RF measurements, and wreless communcatons. Andrew M. Wener receved the Sc.D. degree n electrcal engneerng from the Massachusetts Insttute of Technology, Cambrdge, MA, USA, n He s currently the Scfres Famly Dstngushed Professor of electrcal and computer engneerng. In 2008, he was elected to membershp n the Natonal Academy of Engneerng and n 2009 was named a Department of Defense Natonal Securty Scence and Engneerng Faculty Fellow. He recently served a three year term as the Char of the Natonal Academy s U.S. Fronters of Engneerng Meetng. He s currently servng as an Edtor-n-chef of Optcs Express, an all-electronc, open access journal publshng more than 3000 papers a year emphaszng nnovatons n all aspects of optcs and photoncs. He joned Bellcore, a premer telecommuncatons ndustry research organzaton, frst as Member of Techncal Staff and later as the Manager of Ultrafast Optcs and Optcal Sgnal Processng Research. He joned Purdue as a Professor n 1992, and has snce graduated more than 30 Ph.D. students. He has also spent sabbatcals at the Max Born Insttute for Nonlnear Optcs and Ultrashort Pulse Spectroscopy, Berln, Germany, and at JILA, Unversty of Colorado and Natonal Insttute of Standards and Technology, Boulder, Colorado. Hs research focuses on ultrafast optcs, wth a focus on processng of extremely hgh speed lghtwave sgnals. He s especally well known for hs poneerng work on programmable generaton of arbtrary ultrashort pulse waveforms, whch has found applcaton both n fber optc networks and n ultrafast optcal scence laboratores around the world. He s the author of a textbook enttled Ultrafast Optcs, has publshed eght book chapters and more than 270 journal artcles, and s nventor of 15 U.S. patents. Hs numerous awards nclude the Hertz Foundaton Doctoral Thess Prze n 1984, the Optcal Socety of Amerca s Adolph Lomb Medal n 1990 and R.W. Wood Prze n 2008, the Internatonal Commsson on Optcs Prze n 1997, and the IEEE Photoncs Socety s Wllam Strefer Scentfc Achevement Award n 1999, and Quantum Electroncs Prze n At Purdue, he has been recognzed wth the naugural Research Excellence Award from the Schools of Engneerng n 2003, the Provost s Outstandng Graduate Student Mentor Award n 2008, and the Herbert Newby McCoy Award for outstandng contrbutons to the natural scences n 2013.