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Pulse amplitude modulation wireless communication in the 300 GHz-band employing an integrated-optic interferometer-based signal emulator

Koichi Takiguchi and Nozomu Nishio

Open Access Open Access

Abstract

Wireless communication using a pulse amplitude modulation signal was carried out in the 300 GHz-band. In this investigation, the used THz-wave signal was generated with a silica waveguide-type optical signal emulator and high-speed photo-mixing. The optical signal emulator consisting of a tunable asymmetric Mach-Zehnder interferometer produces an optical pulse amplitude modulation signal from an optical on-off keying signal by partly adopting lightwave interference. 25 Gsymbol/s three and four-level pulse amplitude modulation signals in the 300 GHz-band were generated and used for the wireless communication. Bit error rates of received signals were evaluated with off-line processing, and the bit error rates were estimated to be 1.9 × 10−4 and 8.0 × 10−3 in the communications using the three and four-level signals, respectively.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Terahertz (THz)-wave communication is attractive since it has potential for providing us with high-speed wireless communication of more than 10 Gbit/s by employing its wide bandwidth [1–3]. In addition to research and development on single-carrier communication using an on-off keying (OOK) signal, multi-level communication, which employs phase information including quadrature phase shift keying (QPSK) and quadrature amplitude modulation (QAM) [4–6], and spectrally efficient multi-carrier communication including orthogonal frequency division multiplexing (OFDM) and Nyquist wavelength division multiplexing (WDM) [4–8] are being arduously carried out. Also, the investigation into communication using a multi-level pulse amplitude modulation (PAM) signal is significant in the THz-band because the multi-level PAM can increment the signal speed with a relatively simple configuration [9,10].

In this paper, we report on wireless communication in the 300 GHz-band, which adopts PAM3/4 signals. The THz-wave PAM signals are produced with an integrated-optic PAM signal emulator and a high-speed photo-mixer [11]. The optical PAM signal emulator is composed of a silica waveguide-based tunable asymmetric Mach-Zehnder interferometer (MZI) and generates an optical PAM signal from an optical OOK signal. The emulator has the advantage that it can produce a high symbol rate PAM signal without being affected by the speed limit of electrical-domain processing. The produced optical PAM signal with the emulator is converted into a PAM signal in the 300 GHz-band by utilizing a unitraveling-carrier photodiode (UTC-PD)-type photo-mixer [11]. Bit error rates (BERs) of received PAM signals are evaluated with off-line processing. We attained 25 Gsymbol/s multi-level PAM communication in the THz-band without adopting special signal processing and/or coherent detection. Although we could produce 40 Gsymbol/s PAM3/4 signals, we could not achieve 40 Gsymbol/s PAM3/4 communications due to bandwidth and linearity limits of used components. In this investigation, one of objects is to increase the symbol rate of the THz-wave PAM signal by partially adopting lightwave interference. The optical PAM signal is typically generated with the combination of an electrical digital-to-analogue converter (DAC) and an optical modulator, but the DAC bandwidth is limited. As the time required for the interference is disregardable, the use of interference between two optical binary signals can enhance the PAM signal symbol rate. As a first step toward implementation of a high-speed optical PAM signal modulator with the use of interference, we verify the optical interference-based PAM signal emulator.

We start by explaining an experimental set-up of the wireless PAM3/4 communications in the 300 GHz-band. After describing the configuration and operating principle of the optical PAM signal emulator in detail, we report on some experimental results on the PAM communication. The BERs of 1.9 × 10−4 (below the first KP4 forward error correction (FEC) threshold 2.2 × 10−4 [12]) and 8.0 × 10−3 (below the 20% overhead soft-decision FEC threshold 2.0 × 10−2 [9]) were obtained for 25 Gsymbol/s PAM3/4 communications, respectively. Partial results of the PAM3 communication were presented at [13].

2. Experimental set-up of wireless PAM communication in the 300 GHz-band and the integrated-optic PAM signal emulator

2.1 Experimental set-up

Figure 1 shows an experimental set-up of the wireless multi-level PAM communication in the 300 GHz-band and the schematic configuration of the integrated-optic PAM signal emulator. Some specifications of used components and measurement equipment are described in this figure. The intensity of the light, which was poured from a laser diode (LD) 1 (wavelength: 1552.40 nm), was modulated with a non-return to zero maximum-length (M)-sequence code from a pulse pattern generator (PPG). A bit rate and pseudo-random bit sequence (PRBS) relating to the used M-sequence code were 25 or 40 Gbit/s and 27-1, respectively. The generated optical OOK signal at an optical intensity modulator was input into the optical PAM signal emulator to generate a 25 or 40 Gsymbol/s optical PAM signal. An amplified optical PAM signal with an erbium-doped fiber amplifier (EDFA) was mixed with a continuous wave local LD2 (wavelength: 1550.00 nm) by utilizing a UTC-PD-type photo-mixer [11]. Figure 2 indicates a measured frequency response of the UTC-PD we used. We used the same UTC-PD as [8]. The intensity of the total lights, which were input into the photo-mixer, was adjusted with a variable optical attenuator (VOA). The intensity of both the signal and local lights, which entered the VOA, was 12.0 dBm, and the VOA loss was 0.4 dB. The photo-mixer produced a wireless PAM signal whose carrier frequency was equal to the frequency difference 300 GHz between the LDs 1 and 2. The linewidth, frequency accuracy, and side mode suppression ratio of the used LDs were less than 100 kHz, less than 0.3 GHz, and more than 60 dB, respectively. The wireless PAM communication employs a single carrier and envelope detection, and 3 dB down bandwidth of the UTC-PD around a 300 GHz frequency was 102 GHz as shown in Fig. 2. As this bandwidth was wide enough compared to the frequency accuracy of the used free running lasers, we did not employ mode-locked lasers for the THz-wave generation.

 figure: Fig. 1.

Fig. 1. Experimental set-up of wireless multi-level PAM communication in 300 GHz-band and schematic configuration of integrated-optic PAM signal emulator.

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 figure: Fig. 2.

Fig. 2. Measured response of UTC-PD versus frequency.

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The generated THz-wave PAM signal was radiated to a 0.5 m free-space link through a horn antenna 1 and was received at an antenna 2. The operational frequency range, gain, and full 3 dB beamwidth of both antennas were 220 to 325 GHz, 27 dBi, and 10 degrees, respectively. The envelope of the PAM signal was detected with a Schottky barrier diode (SBD), and the BERs of the detected signals were estimated with off-line processing.

2.2 Integrated-optic PAM signal emulator

Figure 3 shows the detailed configuration of the integrated-optic PAM signal emulator. The emulator is composed of two arms, which differ in length and are sandwiched between two symmetric MZIs. The MZIs function as coupling ratio tunable couplers. This tunable asymmetric MZI-type emulator was fabricated with silica waveguide technology [14] with the relative index difference Δ of 1.2%. We made two kinds of emulators for generating 25 and 40 Gsymbol/s PAM signals, whose delay time differences between the two arms (correspondent length differences ΔL) between the two arms were set at 80 ps (about 8.0 mm) and 50 ps (about 5.0 mm), respectively. Each time difference corresponds to two time slots of the signal. Although we understand that the delay time difference, which corresponds to half the cycle time of the used M-sequence, is suitable for minimizing the correlation between two sequences input into the second symmetric MZI, requisite ΔL values for generating 25 and 40 Gsymbol/s PAM signals are about 0.51 and 0.32 m, respectively, when the PRBS is 27-1. These long length differences were difficult to substantialize with the waveguide fabrication process we utilized. Therefore, we selected two time slot delay difference for early-stage investigation. Thermo-optic (TO) effect was used to adjust a phase shift of the silica waveguide precisely. The fiber-to-fiber losses of the emulators for generating 25 and 40 Gsymbol/s PAM signals were 1.4 and 1.3 dB, respectively.

 figure: Fig. 3.

Fig. 3. Detailed configuration of integrated-optic PAM signal emulator.

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The transfer matrix TSMi of the i-th tunable coupler (i = 1, 2) is expressed as

$${T_{SMi}} = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{cc} 1&{ - j}\\ { - j}&1 \end{array}} \right)\left( {\begin{array}{cc} {\exp ( - j\frac{{{\phi_i}}}{2})}&0\\ 0&{\exp (j\frac{{{\phi_i}}}{2})} \end{array}} \right)\frac{1}{{\sqrt 2 }}\left( {\begin{array}{cc} 1&{ - j}\\ { - j}&1 \end{array}} \right) ={-} j\left( {\begin{array}{cc} {\sin \frac{{{\phi_i}}}{2}}&{\cos \frac{{{\phi_i}}}{2}}\\ {\cos \frac{{{\phi_i}}}{2}}&{ - \sin \frac{{{\phi_i}}}{2}} \end{array}} \right),$$
where j and ϕi are an imaginary unit and a phase shift provided at the i-th tunable coupler, respectively. Then, when signals at back-ends of the two arms, namely at two input ports of the second tunable coupler in the emulator are both marked, the total emulator transfer matrix T11 between input ports I1, I2 and output ports O1, O2 is calculated as
$${T_{11}} = {T_{SM2}}\left( {\begin{array}{cc} {\exp ( - j\frac{{\beta \Delta L + \phi }}{2})}&0\\ 0&{\exp (j\frac{{\beta \Delta L + \phi }}{2})} \end{array}} \right){T_{SM1}} ={-} \left( {\begin{array}{cc} {{t_{11}}}&{{t_{12}}}\\ {{t_{21}}}&{{t_{22}}} \end{array}} \right),$$
$$\begin{aligned} {t_{11}} &= [\sin \frac{{{\phi _2}}}{2}\sin \frac{{{\phi _1}}}{2} + \cos \frac{{{\phi _2}}}{2}\cos \frac{{{\phi _1}}}{2}\exp \{ j(\beta \Delta L + \phi )\} ]\exp ( - j\frac{{\beta \Delta L + \phi }}{2}),\\ {t_{12}} &= [\sin \frac{{{\phi _2}}}{2}\cos \frac{{{\phi _1}}}{2} - \cos \frac{{{\phi _2}}}{2}\sin \frac{{{\phi _1}}}{2}\exp \{ j(\beta \Delta L + \phi )\} ]\exp ( - j\frac{{\beta \Delta L + \phi }}{2}),\\ {t_{21}} &= [\cos \frac{{{\phi _2}}}{2}\sin \frac{{{\phi _1}}}{2} - \sin \frac{{{\phi _2}}}{2}\cos \frac{{{\phi _1}}}{2}\exp \{ j(\beta \Delta L + \phi )\} ]\exp ( - j\frac{{\beta \Delta L + \phi }}{2}),\\ {t_{22}} &= [\cos \frac{{{\phi _2}}}{2}\cos \frac{{{\phi _1}}}{2} + \sin \frac{{{\phi _2}}}{2}\sin \frac{{{\phi _1}}}{2}\exp \{ j(\beta \Delta L + \phi )\} ]\exp ( - j\frac{{\beta \Delta L + \phi }}{2}), \end{aligned}$$
where β and ϕ denote a propagation constant of the waveguide and a phase shift provided at the longer arm, respectively. When the input port I1 is used, the vector TF11, whose elements represent transfer functions between the two output ports and the input port, is derived as
$$T{F_{11}} = {T_{11}}\left( {\begin{array}{c} 1\\ 0 \end{array}} \right) ={-} \left( {\begin{array}{c} {{t_{11}}}\\ {{t_{21}}} \end{array}} \right).$$
Next, when the input port I1 is used, and the signals at the back-ends of the longer and shorter arms are marked and spaced, respectively, the vector TF10 composed of the two transfer functions is derived, just like (4), as
$$\begin{aligned} T{F_{10}} &= {T_{SM2}}\left( {\begin{array}{cc} 1&0\\ 0&0 \end{array}} \right)\left( {\begin{array}{cc} {\exp ( - j\frac{{\beta \Delta L + \phi }}{2})}&0\\ 0&{\exp (j\frac{{\beta \Delta L + \phi }}{2})} \end{array}} \right){T_{SM1}}\left( {\begin{array}{c} 1\\ 0 \end{array}} \right)\\ & ={-} \left( {\begin{array}{c} {\sin \frac{{{\phi_2}}}{2}\sin \frac{{{\phi_1}}}{2}\exp ( - j\frac{{\beta \Delta L + \phi }}{2})}\\ {\cos \frac{{{\phi_2}}}{2}\sin \frac{{{\phi_1}}}{2}\exp ( - j\frac{{\beta \Delta L + \phi }}{2})} \end{array}} \right). \end{aligned}$$
Finally, when the input port I1 is used, and signals at back-ends of the longer and shorter arms are spaced and marked, respectively, the vector TF01 composed of the two transfer functions is calculated as
$$\begin{aligned} T{F_{01}} &= {T_{SM2}}\left( {\begin{array}{cc} 0&0\\ 0&1 \end{array}} \right)\left( {\begin{array}{cc} {\exp ( - j\frac{{\beta \Delta L + \phi }}{2})}&0\\ 0&{\exp (j\frac{{\beta \Delta L + \phi }}{2})} \end{array}} \right){T_{SM1}}\left( {\begin{array}{c} 1\\ 0 \end{array}} \right)\\ &={-} \left( {\begin{array}{c} {\cos \frac{{{\phi_2}}}{2}\cos \frac{{{\phi_1}}}{2}\exp (j\frac{{\beta \Delta L + \phi }}{2})}\\ { - \sin \frac{{{\phi_2}}}{2}\cos \frac{{{\phi_1}}}{2}\exp (j\frac{{\beta \Delta L + \phi }}{2})} \end{array}} \right). \end{aligned}$$
The optical OOK signal input into the port I1 of the emulator is divided into the two arms after the first tunable coupler. Signal branching ratio after the tunable coupler is determined depending on a phase shift ϕ1 of the first tunable coupler. Table 1 summarizes the ϕ1 values and resultant signal branching ratio in amplitude between the longer and shorter arms for generating PAM3/4 signals. The branching ratio is obtained from (1). We then set the remaining phase shifts ϕ and ϕ2 at π/2 to transform the OOK signal into the PAM signal.

Tables Icon

Table 1. Phase Shift ϕ1 and Resultant Signal Branching Ratio in Amplitude between Longer and Shorter Arms of Emulator for Generating PAM3/4 Signals

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We assume that βΔL is set at 2π times an integer at a center frequency of the signal. When we generate the PAM3 signal, the vectors (4) to (6) are transformed into the following vectors.

$$T{F_{11}} ={-} \frac{1}{2}\exp ( - j\frac{{\beta \Delta L + \phi }}{2})\left( {\begin{array}{c} {1 + j}\\ {1 - j} \end{array}} \right),$$
$$T{F_{10}} ={-} \frac{1}{2}\exp ( - j\frac{{\beta \Delta L + \phi }}{2})\left( {\begin{array}{c} 1\\ 1 \end{array}} \right),$$
$$T{F_{01}} ={-} \frac{1}{2}\exp (j\frac{{\beta \Delta L + \phi }}{2})\left( {\begin{array}{c} 1\\ { - 1} \end{array}} \right).$$
Table 2 indicates the intensity of the two emulator output ports O1 and O2 depending on the signals at the back-ends of the two arms in the emulator. The output port intensity is derived from (7) to (9). Then, the vectors (4) to (6) are deformed in the following vectors when generating the PAM4 signal.
$$T{F_{11}} ={-} \frac{1}{{\sqrt 6 }}\exp ( - j\frac{{\beta \Delta L + \phi }}{2})\left( {\begin{array}{c} {\sqrt 2 + j}\\ {\sqrt 2 - j} \end{array}} \right),$$
$$T{F_{10}} ={-} \frac{1}{{\sqrt 3 }}\exp ( - j\frac{{\beta \Delta L + \phi }}{2})\left( {\begin{array}{c} 1\\ 1 \end{array}} \right),$$
$$T{F_{01}} ={-} \frac{1}{{\sqrt 6 }}\exp (j\frac{{\beta \Delta L + \phi }}{2})\left( {\begin{array}{c} 1\\ { - 1} \end{array}} \right).$$
From (10) to (12), the intensity of the two emulator output ports is tabulated in Table 3. From Tables 2 and 3, we confirm that the PAM signals can be produced from the OOK signal by utilizing the emulator in Fig. 3. The number of produced PAM symbol levels is determined by the combination of marked and spaced OOK signals, which simultaneously enter the two input ports of the second tunable coupler. The maximum signal level is obtained by the interference of the two marked OOK signals at the second tunable coupler. The PAM signal is obtainable from each output port. When the mark ratio of the input OOK signal is 1/2 as the M-sequence code we used, the ratios of the produced PAM3 maximum, medium, and minimum signal levels are 1/4, 1/2, and 1/4, respectively. The ratios of the PAM4 four signal levels become equal (1/4) under the same condition. The emulator does not suffer from the speed limit of electrical-domain processing. The PAM signal generated with the emulator differs from a real PAM signal in the following respects. The generated symbols will have different phases depending on the PAM symbol levels. The symbols were partially generated with interference of the two signals, which were divided from an original signal and had only two time slot difference. Therefore, the symbols were not completely random and could not be generated with widely used Gray labeling, which provides us with the best BER performance in the usual case [15]. In addition, the asymmetric MZI functions as an optical frequency filter, which induces some temporal waveform distortion. While there exist these differences, the investigation of the PAM signal emulator is meaningful toward the implementation of the interference-based high-speed optical PAM signal modulator.

Tables Icon

Table 2. Intensity of Two Emulator Output Ports O1 and O2 Depending on Signals at Back-ends of Two Arms in Emulator When Generating PAM3 Signal

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Tables Icon

Table 3. Intensity of Two Emulator Output Ports O1 and O2 Depending on Signals at Back-ends of Two Arms in Emulator When Generating PAM4 Signal

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3. Experimental results

3.1 Results of optical PAM signal generation using optical PAM signal emulator

Figures 4(a), 4(b), and 4(c) show measured optical eye diagrams of the original 25 Gbit/s OOK signal and produced 25 Gsymbol/s PAM3/4 signals with the emulator, respectively. As shown in Figs. 4(b) and 4(c), the eyes of produced optical PAM signals were clearly open, which confirmed proper function and operation of our emulator. We could similarly generate optical 40 Gsymbol/s PAM3/4 signals from an optical 40 Gbit/s OOK signal as shown in Fig. 5. Figure 5 indicates that the optical 40 Gsymbol/s PAM signals were also properly produced with the emulator. As compared to the eye diagrams of 25 Gsymbol/s optical PAM signals, the eyes of 40 Gsymbol/s optical PAM signals both vertically and horizontally deteriorated due to inter-symbol interference of the PAM signals. The inter-symbol interference stemmed from signal distortion caused by bandwidth limits of the used components and sampling oscilloscope.

 figure: Fig. 4.

Fig. 4. Measured eye diagrams of optical 25 Gsymbol/s signals. Eye diagrams of (a) original 25 Gbit/s OOK signal, (b) generated 25 Gsymbol/s PAM3 signal, and (c) generated 25 Gsymbol/s PAM4 signal.

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 figure: Fig. 5.

Fig. 5. Measured eye diagrams of optical 40 Gsymbol/s signals. Eye diagrams of (a) original 40 Gbit/s OOK signal, (b) generated 40 Gsymbol/s PAM3 signal, and (c) generated 40 Gsymbol/s PAM4 signal.

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Figure 6 indicates an example of optical spectra for producing the THz-wave PAM signals. This figure shows measured optical spectra of the 25 Gsymbol/s PAM3 signal and local LD2, which were used to produce the 25 Gsymbol/s PAM3 signal in the 300 GHz-band with the high-speed photo-mixing. A slightly derived light from the VOA input was used for the measurement.

 figure: Fig. 6.

Fig. 6. Measured optical spectra of 25 Gsymbol/s PAM3 signal and local LD2 for producing 25 Gsymbol/s PAM3 signal in 300 GHz-band with high-speed photo-mixing.

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3.2 Evaluated results of the received THz-wave PAM signals

Figures 7(a) and 7(b) show examples of eye diagrams relating to received 25 Gsymbol/s PAM3/4 signals, respectively. The eyes were measured at some output intensity P of the UTC-PD. Figure 8 denotes a measured eye diagram of a received 40 Gsymbol/s PAM3 signal. In Fig. 7, the eye diagrams of received PAM signals, both vertically and horizontally, degraded as compared to the eyes of the initially generated optical PAM signals shown in Figs. 4(b) and 4(c). As shown in Fig. 8, an eye diagram of the received 40 Gsymbol/s PAM3 signal was completely closed. The eye degradation became conspicuous with the increase of the signal symbol rate.

 figure: Fig. 7.

Fig. 7. Measured eye diagrams of received (a) 25 Gsymbol/s PAM3 signals and (b) 25 Gsymbol/s PAM4 signals.

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 figure: Fig. 8.

Fig. 8. Measured eye diagram of received 40 Gsymbol/s PAM3 signal.

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Figures 9(a) and 9(b) show BERs versus UTC-PD output intensity relating to received 25 Gsymbol/s PAM3/4 signals, respectively. We estimated the BERs with off-line processing of the measured eye diagrams, some of which were included in Fig. 7. We calculated the BERs using numerical data acquired with the sampling oscilloscope and the following equation [15,16].

$$BER = \sum\limits_{q = 0,\,q \ne k}^{N - 1} {\sum\limits_{k = 0}^{N - 1} {{p_k}} } {P_{qk}},$$
where N, pk, and Pqk denote the number of PAM symbol levels (3 or 4), the probability of transmitting PAM symbol with a level k, and the probability of deciding the received symbol level as q when the level k symbol was transmitted, respectively. We assumed that each sampled level value had a Gaussian probability density function [15,16]. Each threshold value was optimized to minimize the BER. The BERs showed the minimum values of 1.9 × 10−4 (below the first KP4 FEC threshold 2.2 × 10−4 [12]) and 8.0 × 10−3 (below the 20% overhead soft-decision FEC threshold 2.0 × 10−2 [9]) for the PAM3/4 signals, respectively. We were not able to evaluate the BER of the received 40 Gsymbol/s PAM3 signal shown in Fig. 8. In Fig. 7(b), the vertical eye opening between the lowest and the second lowest levels notably degraded. The degradation was brought about by the inter-symbol interference relating to the PAM signal [9], which was caused by the signal distortion due to the bandwidth limits of the used components. In addition, the degradation was attributable to the non-linear characteristics of the used components, which mainly originated from the SBD. We need to resolve these degradation factors to realize better characteristics and larger capacity relating to the THz-wave wireless PAM communication.

 figure: Fig. 9.

Fig. 9. Estimated BERs versus UTC-PD output intensity relating to received (a) 25 Gsymbol/s PAM3 and (b) 25 Gsymbol/s PAM4 signals.

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4. Conclusion

We demonstrated wireless PAM3/4 communications in the 300 GHz-band. We first produced an optical 25 or 40 Gsymbol/s PAM signal from an optical 25 or 40 Gbit/s OOK signal, respectively, by utilizing an integrated-optic PAM signal emulator and then converted the produced optical PAM signal into a THz-wave PAM signal with high-speed photo-mixing using a UTC-PD. The optical PAM signal emulator was composed of a silica waveguide-type tunable asymmetric MZI. The optical emulator could produce high symbol rate optical PAM signals without being affected by the speed limit of electrical-domain processing. We achieved 25 Gsymbol/s multi-level PAM communication in the THz-band without employing special signal processing and/or coherent detection. Estimated bit error rates of received 25 Gsymbol/s PAM3/4 signals with off-line processing were 1.9 × 10−4 (below the first KP4 FEC threshold 2.2 × 10−4) and 8.0 × 10−3 (below the 20% overhead soft-decision FEC threshold 2.0 × 10−2), respectively. However, we could not carry out 40 Gsymbol/s PAM communication due to bandwidth and linearity limits of used components.

Funding

Takahashi Industrial and Economic Research Foundation; Japan Society for the Promotion of Science (22H00219); Support Center for Advanced Telecommunications Technology Research Foundation; Ministry of Internal Affairs and Communications (JP215007002).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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13. K. Takiguchi and N. Nishio, “Pulse amplitude modulation communication in terahertz-band using asymmetric Mach-Zehnder interferometer-type optical signal emulator,” in Proc. Photonics West (SPIE, 2022), paper 12000-22, San Francisco.

14. K. Takiguchi and Y. Ikeyama, “Tunable optical OFDM demultiplexer utilizing slab star coupler-based optical DFT circuit,” IEEE Photonics Technol. Lett. 31(16), 1327–1330 (2019). [CrossRef]  

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (9)
Fig. 1.
Fig. 1. Experimental set-up of wireless multi-level PAM communication in 300 GHz-band and schematic configuration of integrated-optic PAM signal emulator.

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Fig. 2.
Fig. 2. Measured response of UTC-PD versus frequency.

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Fig. 3.
Fig. 3. Detailed configuration of integrated-optic PAM signal emulator.

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Fig. 4.
Fig. 4. Measured eye diagrams of optical 25 Gsymbol/s signals. Eye diagrams of (a) original 25 Gbit/s OOK signal, (b) generated 25 Gsymbol/s PAM3 signal, and (c) generated 25 Gsymbol/s PAM4 signal.

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Fig. 5.
Fig. 5. Measured eye diagrams of optical 40 Gsymbol/s signals. Eye diagrams of (a) original 40 Gbit/s OOK signal, (b) generated 40 Gsymbol/s PAM3 signal, and (c) generated 40 Gsymbol/s PAM4 signal.

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Fig. 6.
Fig. 6. Measured optical spectra of 25 Gsymbol/s PAM3 signal and local LD2 for producing 25 Gsymbol/s PAM3 signal in 300 GHz-band with high-speed photo-mixing.

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Fig. 7.
Fig. 7. Measured eye diagrams of received (a) 25 Gsymbol/s PAM3 signals and (b) 25 Gsymbol/s PAM4 signals.

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Fig. 8.
Fig. 8. Measured eye diagram of received 40 Gsymbol/s PAM3 signal.

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Fig. 9.
Fig. 9. Estimated BERs versus UTC-PD output intensity relating to received (a) 25 Gsymbol/s PAM3 and (b) 25 Gsymbol/s PAM4 signals.

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Tables (3)

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Table 1. Phase Shift ϕ1 and Resultant Signal Branching Ratio in Amplitude between Longer and Shorter Arms of Emulator for Generating PAM3/4 Signals

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Table 2. Intensity of Two Emulator Output Ports O1 and O2 Depending on Signals at Back-ends of Two Arms in Emulator When Generating PAM3 Signal

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Table 3. Intensity of Two Emulator Output Ports O1 and O2 Depending on Signals at Back-ends of Two Arms in Emulator When Generating PAM4 Signal

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Equations (13)

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T S M i = 1 2 ( 1 − j − j 1 ) ( exp ⁡ ( − j ϕ i 2 ) 0 0 exp ⁡ ( j ϕ i 2 ) ) 1 2 ( 1 − j − j 1 ) = − j ( sin ⁡ ϕ i 2 cos ⁡ ϕ i 2 cos ⁡ ϕ i 2 − sin ⁡ ϕ i 2 ) ,
T 11 = T S M 2 ( exp ⁡ ( − j β Δ L + ϕ 2 ) 0 0 exp ⁡ ( j β Δ L + ϕ 2 ) ) T S M 1 = − ( t 11 t 12 t 21 t 22 ) ,
t 11 = [ sin ⁡ ϕ 2 2 sin ⁡ ϕ 1 2 + cos ⁡ ϕ 2 2 cos ⁡ ϕ 1 2 exp ⁡ { j ( β Δ L + ϕ ) } ] exp ⁡ ( − j β Δ L + ϕ 2 ) , t 12 = [ sin ⁡ ϕ 2 2 cos ⁡ ϕ 1 2 − cos ⁡ ϕ 2 2 sin ⁡ ϕ 1 2 exp ⁡ { j ( β Δ L + ϕ ) } ] exp ⁡ ( − j β Δ L + ϕ 2 ) , t 21 = [ cos ⁡ ϕ 2 2 sin ⁡ ϕ 1 2 − sin ⁡ ϕ 2 2 cos ⁡ ϕ 1 2 exp ⁡ { j ( β Δ L + ϕ ) } ] exp ⁡ ( − j β Δ L + ϕ 2 ) , t 22 = [ cos ⁡ ϕ 2 2 cos ⁡ ϕ 1 2 + sin ⁡ ϕ 2 2 sin ⁡ ϕ 1 2 exp ⁡ { j ( β Δ L + ϕ ) } ] exp ⁡ ( − j β Δ L + ϕ 2 ) ,
T F 11 = T 11 ( 1 0 ) = − ( t 11 t 21 ) .
T F 10 = T S M 2 ( 1 0 0 0 ) ( exp ⁡ ( − j β Δ L + ϕ 2 ) 0 0 exp ⁡ ( j β Δ L + ϕ 2 ) ) T S M 1 ( 1 0 ) = − ( sin ⁡ ϕ 2 2 sin ⁡ ϕ 1 2 exp ⁡ ( − j β Δ L + ϕ 2 ) cos ⁡ ϕ 2 2 sin ⁡ ϕ 1 2 exp ⁡ ( − j β Δ L + ϕ 2 ) ) .
T F 01 = T S M 2 ( 0 0 0 1 ) ( exp ⁡ ( − j β Δ L + ϕ 2 ) 0 0 exp ⁡ ( j β Δ L + ϕ 2 ) ) T S M 1 ( 1 0 ) = − ( cos ⁡ ϕ 2 2 cos ⁡ ϕ 1 2 exp ⁡ ( j β Δ L + ϕ 2 ) − sin ⁡ ϕ 2 2 cos ⁡ ϕ 1 2 exp ⁡ ( j β Δ L + ϕ 2 ) ) .
T F 11 = − 1 2 exp ⁡ ( − j β Δ L + ϕ 2 ) ( 1 + j 1 − j ) ,
T F 10 = − 1 2 exp ⁡ ( − j β Δ L + ϕ 2 ) ( 1 1 ) ,
T F 01 = − 1 2 exp ⁡ ( j β Δ L + ϕ 2 ) ( 1 − 1 ) .
T F 11 = − 1 6 exp ⁡ ( − j β Δ L + ϕ 2 ) ( 2 + j 2 − j ) ,
T F 10 = − 1 3 exp ⁡ ( − j β Δ L + ϕ 2 ) ( 1 1 ) ,
T F 01 = − 1 6 exp ⁡ ( j β Δ L + ϕ 2 ) ( 1 − 1 ) .
B E R = ∑ q = 0 , q ≠ k N − 1 ∑ k = 0 N − 1 p k P q k ,
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