Probabilistic shaping for ROF system with heterodyne coherent detection

To catch up with the rapidly growing requirement of the Internet and communication networks, emerging technologies are required to provide a higher data rate, higher spectral efficiency (SE), and greater transmission distance.¹ Probabilistic shaping (PS) is a particularly promising technology that can reach these needs and meet surging data traffic demands. Recently PS is attracting considerable attention for higher SE, higher capacity, and longer transmission distance in an optical fiber communication system.^2–9 What is more, the advent of PS offers unparalleled flexibility to optical systems without increasing the complexity of the optical network.⁷ Because of the nonlinearities, the fiber communication system is actually power-constrained. Therefore, it is necessary to increase the SE with no increase in the transmitted power which can be realized by PS. The idea of PS is to send signal points using nonuniform probabilities. That is, signal points with lower energy are sent more often than those with higher energy, which therefore saves the average transmitted energy.³ The aim is to optimize the signal quality at the receiver or to keep the same quality with less transmitting energy. Therefore, PS is a promising candidate to improve performances in future optical fiber communication systems. However, to the best of our knowledge, PS is an underexplored field until now. There are only few theoretical analysis and simulation results employing PS in optical communication systems, and experimental demonstration is rarely implemented in the existing publications so far. PS is attracting more interest of researchers since September 2016 when Nokia Bell Labs et al. demonstrated 1 Tbit/s data transmission over 4-carrier super-channel in the backbone network of Germany leveraging probabilistically shaped constellations, which has achieved unprecedented transmission capacity and SE as a breakthrough in optical communications.¹⁰ In October 2016, researchers of Alcatel-Lucent and Nokia Bell Labs declared that they have realized a staggering breakthrough, namely, the implementation of 65 Tbit/s data transmission over a 6600 km single mode fiber in laboratory trials utilizing the PS technology.¹¹ As a groundbreaking technology, PS will surely become an epoch-making technique in the future optical communication field to transmit data faster, further, and with wonderful flexibility.

In recent years, a heterodyne coherent system has been widely investigated as a hot topic with the development of the digital signal processing (DSP) technology as well as the improvement of the bandwidth and speed for photodiodes (PDs) and analog-to-digital converters (ADCs). Coherent detection can be basically divided into two major categories: homodyne coherent detection^12–15 and heterodyne coherent detection.^12,16–22 The heterodyne coherent detection has an advantage over the homodyne coherent detection. That is, only half of the balanced photodiodes (BPDs) and ADCs are needed, which thus simplifies the coherent receiver.^16,21–23 Fortunately, the development of the PDs and ADCs helps us to realize the required wider bandwidth for intermediate frequency (IF) signals.^16,19

In this paper, we not only investigate and compare the performance of normal- and PS-16-ary quadrature amplitude modulation (16QAM) in a photonic vector millimeter-wave (mm-wave) signal generation system based on heterodyne coherent detection but also experimentally demonstrate the feasibility of PS-polarization-division-multiplexing (PDM)-16QAM in a heterodyne photonic vector mm-wave signal generation system and get excellent results. Here, we apply PS to the photonic vector mm-wave signal generation system employing heterodyne coherent detection. To the best of our knowledge, this is the first time heterodyne coherent detection at the receiver side is adopted in the PS scheme. What is more, we experimentally investigate the performance of PS in a 16QAM-modulated radio over fiber (ROF) system with 40 m wireless delivery for the first time.

Coherent detection is a detection method to obtain useful information at the receiver side utilizing the interference beating of an optical signal and optical local oscillator (LO), which has an advantage over direct detection on the improvement of receiver sensitivity. According to whether the frequency of the LO is equal to that of the received signal, coherent detection falls into two basic types: homodyne coherent detection and heterodyne coherent detection. Figure 1 shows the principle of heterodyne coherent detection. We employ one external cavity laser (ECL) with a narrow linewidth as a LO with a frequency interval f_IF = f_S − f_LO, namely, IF from the signal frequency, where f_S and f_LO are the frequencies of the optical signal and LO, respectively. f_IF is zero for homodyne coherent detection. The optical signal and LO are both split into two branches with a 90° phase shift added upon one branch of the LO. The two parallel branch groups are coupled and then detected by a BPD, respectively. In this way, we get the in-phase and quadrature (I/Q) parts of the signal at the output of the BPDs. The I and Q parts can be expressed as

where R is the responsivity of the BPD, P_S is the signal power, P_LO is the LO power, θ_sig(t) is the phase of the output signal, and θ_LO(t) is the LO phase. The phase of the output signal is θ_sig = θ_S + θ_sn, where θ_S and θ_sn are the phase of the signal and phase noise, respectively. The demodulated phase noise is defined as θ_n = θ_sn − θ_LO. Therefore, the output signal determined together by the I and Q parts can be expressed as

The principle of the PS technology is to cleverly transmit lower-energy signals more frequently than higher-energy signals, in order to reduce the average transmitted power as shown in Fig. 2. In other words, the signal points near the origin appear more often than the signal points far from the origin. Traditionally, the signal points at the input are always distributed uniformly on a constellation in most actual systems as shown in Fig. 2(a). However in a PS scheme, the input signals are distributed with nonuniform probabilities, called Maxwell–Boltzmann distribution, in each dimension on a constellation for the additive white Gaussian noise (AWGN) channel as illustrated in Fig. 2(b). It is well known that the transmitted power has influence on the introduced nonlinear distortion, and therefore the PS scheme is more robust to noise or other impairments, which thus leads to a better system performance. The distribution of signal points is a two-dimensional (2D) problem. Because of the symmetry of the constellation, we consider one-dimensional (1D) 4-pulse amplitude modulation (PAM) probability distribution for the sake of convenience.²⁴ We employ the input alphabet X = {−3, −1, 1, 3}, and the probability of the signal points x $∈$ X is $PX(x)=k𝑣e−𝑣|x|2$⁠, also called the probability mass function (PMF) of the input.^24,25 Here $k𝑣=1/∑x′∈Xe−𝑣|x′|2$⁠. The scalar k_v helps keeping the summation of the probabilities as 1. In our following simulation and experiment, we calculate the bit rate according to the principle of conservation of energy, considering that the energy that every bit carries is equal. If the baud rate is fixed, we get different bit rates when we choose different values of v. In other words, in order to get the same bit rate, different baud rates are needed when we choose different values of v. Fig. 2(c) shows the generation of PS drive signals including pseudo-random binary sequence (PRBS) generation, 16QAM mapping, PS distributing, and lowpass filtering.

The structure of the proposed heterodyne system simulation setup is shown in Fig. 3. ECL1, generating a continuous-wave (CW) lightwave, offers the optical input of the I/Q modulator. The normal/PS-16QAM modulated signal generated by DSP is used to drive the I/Q modulator. After added by a Gaussian-distributed optical white noise source, the generated optical normal/PS-16QAM modulated signal is sent to the 90° optical hybrid. The other input of the 90° optical hybrid is a CW lightwave generated from ECL2, as an optical LO with a 15 GHz frequency interval from the central frequency of the generated 16QAM optical baseband signal. The linewidth of the two ECLs is ideally set to be zero and no phase noise is considered. Then a BPD is employed at the I output of the 90° optical hybrid for up-conversion, to get a 15 GHz 16QAM vector mm-wave signal. The noise in the channel comes from the thermal noise and shot noise of the BPD. The Q output of the 90° optical hybrid is grounded because we do not need to use it. The 15 GHz 16QAM vector mm-wave signal is processed by a DSP at the receiver side. The operation in the optical domain is implemented by the VPI platform and the operation in the electrical domain is implemented by MATLAB programing. The data can be recovered by MATLAB programing including IF down conversion, symbol decision, 16QAM de-mapping, and bit-error ratio (BER) calculation based on the comparison of the recovered data and the original transmitted data.

The calculated BER performance is shown in Fig. 4. The curves of the BER versus the optical signal-to-noise ratio (OSNR) input to optical hybrid are given in four different situations: (1) 20 Gb/s (5 Gbaud) normal-16QAM modulated, (2) 20 Gb/s (20/3.4 Gbaud) PS-16QAM modulated, (3) 20 Gb/s (20/3 Gbaud) PS-16QAM modulated, and (4) 20 Gb/s (20/2.6 Gbaud) PS-16QAM modulated. Here, the denominator of each baud rate in the brackets represents the number of bits per symbol. If the bit rate is the same, the baud rate should be different for the PS scheme with different v. In the second to fourth situations, we set v as 0.079 199 513 812 927, 0.137 326 536 083 514, and 0.209 994 892 771 603, respectively. From the simulation results shown in Fig. 4, we conclude that, in the case of the same bit rate, PS-16QAM has a better BER performance than normal-16QAM. What is more, the fewer the bits per symbol carries, the better the BER performance obtained. Figure 5 shows the recovered constellations of the 20 Gb/s normal-16QAM and PS-16QAM mm-wave signals at 15 GHz corresponding to a certain point of different cases in Fig. 4, respectively. Figure 5(a) is calculated at 17.26 dB OSNR input to optical hybrid in situation (1) and gets a BER of 3.3 × 10⁻³. Figure 5(b) is calculated at 16.07 dB OSNR input to optical hybrid in situation (2) and gets a BER of 2.8 × 10⁻³. Figure 5(c) is calculated at 15.1 dB OSNR input to optical hybrid in situation (3) and gets a BER of 2.9 × 10⁻³. Figure 5(d) is calculated at 13.9 dB OSNR input to optical hybrid in situation (4) and gets a BER of 2.8 × 10⁻³. Figure 6 shows the captured 15 GHz spectra at different locations for the situation in Fig. 5(c). The optical spectrum in Fig. 6(a) is calculated before the BPD and the electrical spectrum in Fig. 6(b) is calculated after the BPD when the signal OSNR is 15.1 dB. In conclusion, the PS-16QAM scheme has superiority over the normal-16QAM scheme in BER performance. In the ideal case, different SNRs need different PMFs, namely, different values of v. However in a realistic system, we can use the same v over a SNR range because of the tolerance for the mismatch between the channel SNR and the SNR corresponding to our PMF,²⁴ which makes the implementation of PS easier.

In order to verify the performance improvement of PS, we carry out two experiments. We first investigate the performance of PS in a PDM-16QAM modulated heterodyne coherent system without a wireless link and then carry out the performance investigation of PS in a 16QAM-modulated ROF system with 40 m wireless delivery. In the ROF system, the baud rate is lower because of the limited operating frequency range of the employed antennas.

The experimental setup for the generation of the normal/PS-PDM-16QAM modulated mm-wave signal employing heterodyne coherent detection is shown in Fig. 7. At the transmitter side, ECL1 is employed to offer the optical input of the I/Q modulator, the optical bandwidth of which is 32 GHz, by generating a CW lightwave at 1552.460 nm with 16 dBm output power and <100 kHz linewidth. One DAC gets I and Q inputs from the I and Q outputs of the DSP to generate a normal/PS-16QAM electrical baseband signal, with sampling rates of 80 GSa/s and 88 GSa/s for normal- and PS-16QAM, respectively. The modulated electrical signal is generated by MATLAB programing in the DSP. The pseudo-random binary sequence (PRBS) length of the 16QAM electrical baseband signal is 2.¹³ After amplified by an electrical amplifier (EA), the I and Q outputs of the DAC are used to drive the I/Q modulator. We get a normal/PS-16QAM optical signal at the output of the I/Q modulator and the optical power is −10 dBm. After boosted by a polarization-maintaining erbium-doped fiber amplifier (PM-EDFA), the generated optical 16QAM signal is sent to a polarization multiplexer to accomplish polarization multiplexing, to obtain a PDM-16QAM optical baseband signal. Next, we use a variable optical attenuator 1 (VOA1), EDFA1, and VOA2 to change the OSNR. VOA1 is employed to change the input power into EDFA1 for BER measurement. Then the generated PDM-16QAM optical baseband signal is sent to an integrated polarization-diversity phase-diversity 90° optical hybrid to complete the polarization-diversity process. To accomplish the heterodyne coherent detection, a CW lightwave, generated from ECL2 and amplified by EDFA2, offers the other input of the optical hybrid and acts as an optical LO with a 15 GHz frequency interval from the central frequency of the generated PDM-16QAM optical baseband signal. Two polarization beam splitters (PBSs) and two 90° optical hybrids make up the integrated optical hybrid. Then two BPDs, each with 50 GHz optical bandwidth, are employed at the XI and YI outputs of the integrated optical hybrid for up-conversion, to get a 15 GHz PDM-16QAM vector mm-wave signal. The optical bandwidth of the BPD is 50 GHz. After passing through two parallel EAs, the 15 GHz PDM-16QAM vector mm-wave signal is sent into a digital storage oscilloscope (DSO) with 80 GSa/s sampling rate and 30 GHz 3 dB electrical bandwidth. Finally, we use the offline DSP to recover the transmitted signal. DSP includes the following procedures: down conversion, resample, clock recovery, 13-tap cascaded multi-modulus algorithm (CMMA) equalization, carrier recovery, differential decoding, and BER calculation.

Figure 8 shows the experimental results for the generation of the normal/PS-PDM-16QAM modulated mm-wave signal employing heterodyne coherent detection. The BER performance is measured as shown in Fig. 8. The curves of the BER versus the input power into a pre-EDFA are measured in six different situations: (1) 10 Gbaud (80 Gb/s) normal-PDM-16QAM modulated, (2) 10 Gbaud (72 Gb/s) PS-PDM-16QAM modulated, (3) 11 Gbaud (88 Gb/s) normal-PDM-16QAM modulated, (4) 11 Gbaud (79.2 Gb/s) PS-PDM-16QAM modulated, (5) 11 Gbaud (80.08 Gb/s) PS-PDM-16QAM modulated, and (6) 11 Gbaud (80.96 Gb/s) PS-PDM-16QAM modulated. As shown in Fig. 8, under the circumstance of the same baud rate, the PS-PDM-16QAM modulated scheme has a lower BER, and meanwhile a lower bit rate can be obtained because of PS. On the other hand, in the first, fourth, fifth, and sixth cases, a quite similar BER can be obtained. The 11 Gbaud (80.96 Gb/s) PS-PDM-16QAM modulated scheme can provide a 0.96 Gb/s higher bit rate, and thus transmit more information compared with the 10 Gbaud (80 Gb/s) normal-PDM-16QAM modulated scheme. Therefore the PS-PDM-16QAM scheme has superiority over the normal-PDM-16QAM scheme. The recovered constellations and captured 15 GHz signal spectrum of the 11 Gbaud (79.2 Gb/s) PS-PDM-16QAM at a −26.2 dBm input power into the pre-EDFA are shown in Fig. 9. Here, we get a BER of 1.64 × 10⁻³. Figures 9(a) and 9(b) give the recovered X- and Y-polarization constellations, respectively. Fig. 9(c) shows the captured 15 GHz signal spectrum.

We experimentally carry out the performance investigation of PS in a 16QAM-modulated ROF system. The experimental setup is shown in Fig. 10. At the transmitter side, ECL1 is employed to offer the optical input of the I/Q modulator by generating a CW lightwave at 1552.508 nm with 16 dBm output power and <100 kHz linewidth. One Tektronix arbitrary waveform generator (AWG 7122B) gives a 0.5V_pp normal/PS-16QAM electrical baseband signal, amplified by two parallel EAs, to drive the I/Q modulator. A −14 dBm normal/PS-16QAM optical signal is obtained at the output of the I/Q modulator and then it is boosted by EDFA1. Then a VOA is used to change the input power into the integrated optical hybrid for BER measurement. Next, the 16QAM optical baseband signal is sent to an integrated optical hybrid after a polarization controller (PC). The integrated optical hybrid used in Fig. 10 is identical to that used in Fig. 7. On the other hand, a CW lightwave generated from another ECL is employed as an optical LO with a 23 GHz frequency interval from the central frequency of the 16QAM optical baseband signal, to offer the other input of the integrated optical hybrid after passing through EDFA2 and PC2. Figure 11 gives the captured optical spectrum (0.02 nm resolution) of the 2 Gbaud normal-16QAM signal at the output of the integrated optical hybrid. As can be seen, there is a 23 GHz frequency interval between the signal and the LO. After passing through a broadband EA with the operating frequency range from direct current (DC) to 60 GHz, the generated 23 GHz 16QAM wireless vector mm-wave signal by a BPD is transmitted by a 40 m wireless link, which comprises a pair of horn antennas (HAs) with 34 dBi gain, diameter no more than 1 ft, and 21.2–23.6 GHz operating frequency range. After wireless transmission, the 23 GHz 16QAM wireless vector mm-wave signal is detected by a DSO with 80 GSa/s sampling rate and 30 GHz 3 dB electrical bandwidth.

Figure 12 shows the experimental results for the normal/PS-16QAM-modulated ROF system employing heterodyne coherent detection. The BER performance is measured as shown in Fig. 12. The curves of the BER versus the input power into hybrid are measured in six different situations in all. In Fig. 12(a), the BER curves are measured in four cases: (1) 2 Gbaud (8 Gb/s) normal-16QAM modulated, (2) 2.2 Gbaud (8.096 Gb/s) PS-16QAM modulated, (3) 2.3 Gbaud (8.464 Gb/s) PS-16QAM modulated, and (4) 2.4 Gbaud (8.832 Gb/s) PS-16QAM modulated. As shown in Fig. 12(a), in the second and third cases, the PS-16QAM scheme can transmit more data with a lower BER compared with the normal-16QAM scheme. The fourth case shows a very close BER to the normal-16QAM scheme with a higher bit rate. When the transmission baud rate is relatively low (around 2 Gbaud), the filtering effect can be neglected and the PS-16QAM scheme can have a better BER performance than the normal-16QAM scheme. Therefore the PS-16QAM scheme has superiority over the normal-16QAM scheme. In Fig. 12(b), the BER curves are measured in two cases: (1) 3 Gbaud (12 Gb/s) normal-16QAM modulated and (2) 3.3 Gbaud (12.144 Gb/s) PS-16QAM modulated. As we can see, when the transmission baud rate is relatively high (around 3 Gbaud), the degradation caused by the filtering effect is much severe than the improvement by PS, and therefore we cannot get a better performance when PS is employed. The filtering effect is mainly because of the limited operating frequency range of the employed antennas. The recovered constellation and captured 23 GHz RF signal spectrum of the 2.3 Gbaud (8.464 Gb/s) PS-16QAM at a −16 dBm input power into hybrid are shown in Fig. 13. Here, we get a BER of 5.7 × 10⁻⁴.

We have compared the performance of normal- and PS-16QAM in a heterodyne system and got a better BER performance in the PS-16QAM scheme compared to the normal-16QAM scheme in the simulation. We also proposed and experimentally demonstrated the feasibility of PS-PDM-16QAM in a photonic vector mm-wave signal generation system employing heterodyne coherent detection. We obtain a quite similar BER in the PS and normal scheme with the PS scheme providing a higher bit rate. Then in the PS-16QAM ROF system with over 40 m wireless delivery, we can transmit more data with a lower BER compared with the normal-16QAM scheme when the system bandwidth is wide enough. However, when the baud rate is increased to one certain value, the filtering effect of the antennas will degrade the system performance, and the PS scheme with a higher baud rate cannot get a good performance.

The financial support from the National NSFC (Nos. 61425022, 61522501, 61675004, 61475024, 61675033, 61605013, and 61372109), National High Technology 863 Program of China (Nos. 2015AA015501, 2015AA015502, 2015AA015504, 2015AA016904, and 2015AA016901), Beijing Nova Program (No. Z141101001814048), Beijing Excellent Ph.D. Thesis Guidance Foundation (No. 20121001302), Visiting Scholar Foundation of Key Laboratory of OT&S (Chongqing University), Ministry of Education is gratefully acknowledged.