1. Introduction

Arbitrary waveform generation (AWG) has become an interesting research area due to the wide number of applications in which is involved such as: radar systems, wireless communications, software defined radio and modern instrumentation. Photonically assisted microwave AWG is one of the major topics covered by Microwave Photonics due to the capability to generate high frequency and large bandwidth signals. Moreover, Microwave Photonics involves the inherent advantages of operating in optical domain such as: low loss, small size, tunability, reconfigurability and immunity to electromagnetic interferences (EMI). In fact, it achieves a great potential in Radio-over-Fiber (RoF) systems since they profit from the different components which are involved in the transport and distribution of the signals by optical fiber [1].

In the literature, a great number of approaches related to microwave AWG in the optical domain have been proposed. Direct space-to-time pulse shaping is used to achieve the desired waveform by means of the combination of lens and spatial masks [2]. Although the capacity of these systems allows to obtain high frequency signals up to 50 GHz, their practical implementation involves fiber-to-space coupling in RoF environments making these systems bulky, complicated and with additional losses. All-fiber methods are also proposed by temporal pulse shaping (TPS) [3,4], optical spectral shaping and frequency-to-time mapping [5,6] or more recently line-by-line intensity and phase modulation of each individual spectral line across the entire bandwidth of a coherent optical frequency comb [7,8]. In this context, many AWG applications (wireless communications, vehicular radar, imaging, sensing …) are developed by means of UWB technology since brings advantages compared to traditional narrowband systems such as: lower power consumption, immunity to multipath fading, interference mitigation or high bit-rate [9]. Therefore, different AWG schemes have been adapted to the generation of UWB signaling formats as Impulse Radio UWB (IR-UWB) [10–13] and Multiband UWB (MB-UWB) [14,15].

Most of these techniques present fixed experimental conditions, the reconfigurability and tuning of the generated signal is not easy to achieve. In this sense, we propose a novel optical architecture for microwave arbitrary waveform generation (AWG) which overcomes the main limitations of previous reports. Our proposal combines the use of a broadband optical signal which is optically chirped with a dispersive element and an interferometric structure with balanced photodetection. A theoretical analysis in terms of equivalent transfer function is presented in section 2 in order to show the perfomance of the structure and corroborate the experimental results. A fully reconfiguration of generated signal waveform is achieved with the control of the optical source spectrum and the interferometric structure. The potentiality of the proposed system in terms of reconfigurability and tunability is experimentally demonstrated in section 3 with the adaptation of the architecture to the generation of MB-UWB signaling format since few attempts have been reported experimentally due to the complexity to satisfy the FCC requirements [9]. Finally, the main conclusions achieved in our work are summarized in section 4.

2. Theoretical description of the system

In general terms, an arbitrary waveform generator (AWG) can be considered as a discrete time microwave photonic filter where impulse response is adjusted allowing the desirable waveform [13]. The recent advances produced in the optically implementation of flexible RF filters which have achieved a full reconfiguration of the corresponding electrical transfer function, increase the interest of using them as waveform synthesizers [16]. We analyze our approach for arbitrary waveform generation in terms of microwave photonic filtering. In the following, we carried out a description of the proposed system whose layout can be observed in Fig. 1 .

 

Fig. 1 Experimental layout of AWG based on a single bandpass photonic filter with balanced photodetection. Insets (a) and (b) represent the optical power in points A and B which are plotted as a function of the central optical frequency ω₀ and normalized to the optical periodicity Δω which is related to Δτ by Δω = 2π/ Δτ.

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Firstly, we consider an optical signal S(ω) whose power spectra distribution comes from an optical broadband source (BBS) and can be modified by using a dynamic optical filter (DOF). As example, inset (a) of Fig. 1 plots the optical spectra distribution at the point A of the structure as a uniform profile centred around the optical frequency ω_o = 2π x 193.8 THz with an optical bandwidth δω = 2π x 1 THz.

The optical signal S(ω) is amplitude modulated by using an electrooptical modulator (EOM). The resulting signal is launched into a dispersive element characterized by the optical transfer function H_DISP(ω):

The phase dependence $\phi (\omega )$ can be developed by means of a Taylor expansion centered at the frequency ω₀. The parameters ${\dot{\phi }}_0$ and ${\ddot{\phi }}_0$ corresponds to the group delay time at the optical frequency ω₀ and the dispersion induced in the system, respectively [17].

At the end of the dispersive element, a Mach-Zehnder Interferometer (MZI) is located which is based on two 50/50 couplers and a Variable Delay Line (VDL). The optical transfer function at each output of the MZI (P1 and P2 respectively) is given by:

Finally, a balanced photodetector (BPD) is placed to detect the optical signal. The use of this type of photodetection produces an electrical transfer function of the system, H^RF(Ω), given by:

The term ${\text{H}}_{\text{0}}^{\text{RF}}(\Omega )$ corresponds to the transfer function which is given by the following expression:

The frequency of design Ω_o = 2π x f_o which appears in Eq. (5) takes into account the passband component of the electrical transfer function and depends on the slicing realized by the MZI and the total dispersion induced in the system as:

As we have commented, our approach uses an amplitude modulator previously to the dispersive element. Therefore, Carrier Suppression Effect (CSE) would be present around the frequency of design Ω_o since Double-Side-Band (DSB) modulation is used in photonic systems as known [17]. Nevertheless, we can observe from Eq. (5) that the first term is a modified version of the CSE which is negligible around the frequency Ω_o. In this way, our structure avoids the restriction of the frequency operation range in terms of Carrier Suppression Effect over full radiofrequency range.

In order to show the structure performance through the theoretical analysis, we have included in this section the numerical simulation for an input optical signal according to insets (a) and (b) of Fig. 1. As example, we set a dispersive element characterized by a dispersion ${\ddot{\phi }}_0=115{\text{ps}}^{\text{2}}$ and a Δτ = 4.98 ps for a design frequency of 7 GHz, In this way, the numerical simulation allows to obtain the frequency and temporal responses of the system. Figures 2(a) and 2(b) show the electrical transfer function of the system as a function of the RF frequency normalized to the design frequency Ω₀ when only port 1 (P1) or port 2 (P2) of balanced photodetector are used. Figure 2(a) corresponds with the electrical transfer function ${\text{H}}_{\text{OUT1}}^{\text{RF}}(\Omega )$ and Fig. 2(b) corresponds with term ${\text{H}}_{\text{OUT2}}^{\text{RF}}(\Omega )$of Eq. (4). As we can observe, both amplitude responses have a similar behaviour with two main components which are related to the terms ${\text{H}}_{\text{0}}^{\text{RF}}(\Omega )$ and ${\text{H}}_{\text{0}}^{\text{RF}}(\Omega \pm {\Omega }_0)$of Eq. (5) which depends on the optical source power distribution S(ω) according to Eq. (6). As has been demonstrated in previous proposals [18,19], when the system is used in balanced operation, the baseband component is removed so only bandpass component is present as shown in Fig. 2(c).

 

Fig. 2 Theoretical results of frequency response of the system for 1 THz uniform optical source power profile, 115 ps² of dispersion and Δτ = 4.98 ps when photodetection is considered in port 1 (a), port 2 (b) and balanced operation (c). The corresponding temporal responses are plotted in (d), (e) and (f), respectively.

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On the other hand, the temporal responses of the system are also plotted in Fig. 2. The waveform obtained in Fig. 2(d) and 2(e) is similar but polarity is inverted depending of the input port P1 and P2, respectively. Under balanced regimen, the corresponding waveform is shown in Fig. 2(f) which is similar to the previous but DC component is removed. As we can observe from temporal responses, the shape of the signal obtained is according to the optical source power distribution set.

The operation principle of the proposed AWG has been analyzed in terms of microwave photonic filtering as previously mentioned. Nevertheless, AWGs are also performed by a frequency-to-time process [3–8]. Therefore, our structure can be understood by a frequency-to-time mapping of a reshaped incoherent light source [20].

3. Experimental capabilities of the system

In this section, the main capabilities of the system for arbitrary waveform generation (AWG) proposed such as the reconfigurability of the generated signal waveform and frequency tuning are demonstrated. The experimental implementation of the AWG follows the setup presented in Fig. 1. The input optical signal distribution S(ω) is obtained by means of a 80 nm ASE source as broadband source (BBS) and an optical channel selector (OCS) centred at 1546.9 nm with 48 channels. Each channel has a width of 0.8 nm and its attenuation can be controlled independently allowing to set different profiles of S(ω). The optical signal is amplitude modulated using an EOM by an electrical signal coming from a RF pulse generator with a fixed pattern of one “1” and sixty-three “0” (total 64 bits) with 12.5 Gb/s bit rate. Then, modulated signal is launched into a 5 km standard SMF-28 fiber link which is used as dispersive element characterized by β₂ = −23 ps²/km. At the end of the fiber link a MZI is placed based on two 50/50 couplers and a Variable Delay Line (VDL) in one of the interferometer arms to control the optical delay (Δτ) between them with a delay range of 330 ps. Finally, the detection is carried out by a Balanced Photodetector (BPD) which presents 50 GHz of bandwidth. In this case, each output of the MZI is driven to one of the input ports (P1 and P2) of the BPD which provides an RF output given by the subtraction of the two detected optical signals coming from the MZI as has been mentioned in the description of the system.

Figure 3 shows in solid line the waveform and the electrical power of the generated signals when the experimental layout is set in the same conditions used for numerical simulations in the previous section. In Fig. 3(a) the signals are plotted when only port 1 or port 2 of BPD are used. As can be observed, both present a similar shape but opposite polarity. The electrical power corresponding to the waveform with positive polarity is shown in Fig. 3(b). We note as only one of the two electrical powers has been plotted since both are similar. On the other hand, the signal generated in balanced regime is presented in Fig. 3(c) where the waveform is similar to Fig. 3(a) but DC component has been removed. This fact can be also observed in terms of electrical power of the signal which is plotted in Fig. 3(d) where only the passband is present in the frequency components. In this way, we have demonstrated that the behaviour of the arbitrary waveform generator is according to the numerical simulations of Fig. 2 which has been enclosed both in terms of temporal and frequency responses in dashed line. Therefore, the feasibility and performance of the system have been demonstrated since the excellent agreement existing between experimental and theoretical results.

 

Fig. 3 Experimental results in solid line of waveforms obtained for 1 THz uniform optical source power profile, 115 ps² of dispersion and Δτ = 4.98 ps when photodetection is considered in port 1 and port 2 (a), and balanced operation (c). The corresponding electrical powers are plotted in (b) and (d) respectively. Theoretical results enclosed by dashed line.

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In order to show the potentialities of the system, the arbitrary waveform generator proposed is adapted to UWB systems. For wireless communications, the US Federal Communications Commission (FCC) approved the use without license of the UWB spectrum from 3.1 to 10.6 GHz with a restriction in the power spectral density of −41.3dBm/MHz. Specifically, the proposed structure has been adapted to Multiband Ultra-Wideband signalling format which divides the UWB spectrum different channels with a specific bandwidth. In this way, gaussian pulses have been experimentally generated by means of the proper adjustment of the optical source. As known, the main restriction is produced from 0.96 to 1.6 GHz which corresponds to the GPS band (0.96-1.61 GHz) [9]. Therefore, the use of a balanced photodetection removes the baseband component of the generated signal avoiding the problems related to the strong restriction around GPS band

A gaussian profile with a 3-dB optical bandwidth of 16 nm is set for the optical source by properly adjusting the OCS giving a S(ω) as shown in dashed line of Fig. 4(a) . The optical delay of the MZI is set to 4.98 ps. The electrical power of the generated signal can be observed in Fig. 3(b) centred at 7 GHz. Moreover, the optical delay of the MZI has been also adjusted to 2.89, 3.90, 6.06 and 7.20 ps giving the electrical powers showed in Fig. 4(b) around 4, 5.4, 8.4 and 10 GHz, respectively. As we can observe, the optical apodisation profile determines the shape of the generated signal spectrum. Therefore, it can be set a proper optical source power distribution in order to fulfil the FCC spectral requirements. Moreover, the proposed structure removes the baseband component of the signal generated which allows to increase the flexibility on the election of the source profile. On the other hand, one of the main limitations of UWB systems is related to the reduced area of service due to the power restriction in terms of the power spectral density of the signal which finally will be radiated [9]. In this case, since the baseband component is removed, it can be achieved a better adjustment to the FCC maximum power emitted which allows an increase on the coverage area of the signal. In Fig. 4(b), theoretical simulations of the spectrum of the different generated signals have been included. An excellent agreement is found between theoretical and experimental results.

 

Fig. 4 (a) Experimental optical signal spectra at points A (dashed line) and B (solid line) for a gaussian profile of a 16 nm 3-dB optical bandwidth. (b) Experimental electrical powers for passband tuned at different frequencies, theoretical simulations are in dashed line, respectively (FCC mask included in bold line).

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The waveforms of the Multiband UWB generated signals are tuned around 4, 7 and 10 GHz as shown in Figs. 5(a) , 5(b) and 5(c), respectively. As we expect, the shape of the signals present also a gaussian behavior since a gaussian optical source power distribution is selected. As it is known, the limitation of the AWGs which involve the processing of incoherent-light is related to the high signal-to-noise ratio [21]. Nevertheless, this restriction can be overcome through a proper average of the output waveforms obtaining an excellent agreement between experimental and theoretical results as can be observed in Fig. 5.

 

Fig. 5 The corresponding signal waveforms of the electrical powers in Fig, 3b (a) 4 GHz, (b) 7 GHz and (c) 10 GHz. Theoretical results added in dashed line.

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The tuning capability of the system has been also demonstrated. The optical delay introduced by a Variable Delay Line in the MZI allows the possibility of controlling the frequency of the generated signal as was expected from Eq. (7). Figure 6(a) shows the relationship between the frequency of the generated signal which is measured (■) as a function of the optical delay (Δτ), the theoretical prediction according to Eq. (7) has been added in dashed line. As can be observed, a linear dependence is obtained when the Δτ is increased with a slope of 1.37 GHz/ps which is related to the total dispersion (β₂L) introduced. Therefore, in an UWB environment, the tuning capability allows to change the position of the Multiband UWB generated signal and fulfilling the FCC spectral requirements. Figure 6(a) also shows the optical delay that must be introduced for remaining inside UWB region from 2.1 ps to 7.55 ps which corresponds to 3.1 and 10.6 GHz respectively. Nevertheless, a frequency operation range larger than UWB region has been measured, achieving frequencies up to 15 GHz. We emphasize since CSE is avoided as shown in Eq. (5), the generated signals can be extended to higher frequencies depending on the frequency content of the RF pulse generator.

 

Fig. 6 (a) Generated signal frequency experimentally measured (■) and theoretical prediction (dashed line). (b) Relationship between 10-dB channel bandwidth (●) and optical source width. Theoretical prediction obtained by numerical simulation (dashed line).

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Finally, as has been previously shown, the shape of the electrical power of the generated signal can be controlled by means of the optical source. Therefore, the proposed system introduces the possibility of obtaining different channels width, as shown in Fig. 6(b), where 10-dB bandwidth of a channel has been measured (●) related to the optical source width. In this case, it has been used a gaussian profile where the 3-dB optical bandwidth has been increased by means of the OCS maintaining the total dispersion in 115 ps² and setting the optical delay (Δτ) in 4.98 ps to tune the channel around 7 GHz. We observe that the wider the optical source is selected, the narrower bandwidth is produced. Therefore, the system allows controlling the bandwidth of each channel by means the optical source and so the number of channels which can be achieved in UWB region. We have added the theoretical prediction of the channel bandwidth to the experimental results observing an excellent agreement between both of them.

4. Conclusion

In this paper we have proposed a novel photonic structure for arbitrary waveform generation (AWG) based on a microwave photonic filter fed by an optical source whose power spectra distribution can be modified, a dispersive element and the combination of an interferometric structure with balanced photodetection. The performance of the system proposed has been analyzed by means of a description of the equivalent microwave photonic filter using a numerical proof. The capacity of controlling the generated signal waveform provides to our system a large degree of flexibility in contrast with previous optical techniques which present fixed experimental conditions.

The flexibility in terms of reconfigurability has been analyzed through the adaption of the structure to Multiband Ultra-Wideband signalling format. In this sense, gaussian pulses have been experimentally generated by means of the proper adjustment of the optical source. This fact has allowed to generate UWB pulses whose spectral characteristics are according to the FCC requirements. In this sense, the use of a balanced photodetection permits to eliminate the baseband component of the generated signal avoiding the problems related to the strong restriction around GPS band (0.96-1.61 GHz). Therefore, the power efficiency of the signal is improved respect to the FCC mask increasing the coverage area of the UWB system. On the other hand, the control over the central frequency of the different channels by means of the optical delay introduced in the interferometric structure with the Variable Delay Line has been also experimentally demonstrated by generating different UWB signals. Nevertheless, in order to show the potentiality of the system, we have also generated signals with a frequency operation range up to 15 GHz. In this sense, since the bandwidth of the system is not restricted optically due to Carrier Suppression Effect (CSE) is avoided, the generated signal could be extended to higher frequencies depending on the frequency content of the initial RF pulse. Finally, we have demonstrated the control of the bandwidth for each electrical channel by means of the optical source showing experimental values from 1 to 8.75 GHz.