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Abstract
The time-interleaved analog-to-digital converter (TI-ADC) is a good option to realize high-speed data conversion for both single-carrier and multi-carrier optical communication systems. Offset mismatch is one of its drawbacks, which causes distortion in the sampled data and degrades the bit error rate (BER) performance of communication systems. In this article, a low-complexity online digital offset mismatch compensation (OMC) scheme based on time-domain averaging is proposed and implemented with a commercial off-the-shelf field programmable gate array (FPGA) chip for high-speed optical OFDM communications. The proposed OMC scheme is experimentally demonstrated in real-time direct-detection optical OFDM receiver with a 5 GS/s TI-ADC. The experimental results show that the BER performance can be improved by more than an order of magnitude, by using the proposed OMC scheme, for both 16- and 64-QAM modulation formats. The receiver sensitivity can be improved by more than 5-dB in terms of the received optical power at the BER of 1e-3. What’s more, the real-time measured BER performance is similar to that of by using offline DSP approaches and has good stability during the measurement period. Numerical simulations are performed under additive white Gaussian noise (AWGN) channel to fully verify the performance of the OMC scheme. It exhibits that the error floor in BER performance can be eliminated by using the OMC scheme and a negligible signal-to-noise ratio (SNR) penalty can be achieved compared with that of offset mismatch-free case.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical orthogonal frequency-division multiplexing (OFDM) has been widely considered as one of the most promising technologies for future high-speed optical communications, due to its high spectral efficiency (SE), robustness to optical fiber dispersions and effective mitigation of transmission impairments with powerful digital signal processing (DSP) [1,2]. Prior to the digital baseband OFDM receiver, the analog-to-digital converters (ADC) with a high sampling rate are required to perform the analog-to-digital conversion. The time-interleaving (TI) technique is widely used to significantly increase the sampling rate of ADC for high-speed optical communications [3]. The TI-ADC consists of M sub-ADCs with a low sampling rate operating in parallel and uses different clock phases to achieve M times the sampling rate of the individual sub-ADCs. Ideally, characteristics of sub-ADCs should be identical and clock phases for each sub-ADC should be stable. However, the sub-ADCs are not exactly identical due to errors in the manufacturing process. Thus there are mismatches such as offset, gain, timing and frequency response mismatches among sub-ADCs [4]. Furthermore, the mismatches may change slowly with temperature and aging. As a result, these mismatches will distort the sampled data leading to a degraded bit error rate (BER) performance. Therefore, an online mismatch estimation and compensation scheme may be more suitable for practical applications. Offset mismatch as one of the major mismatches in a TI-ADC and its calibration has received significant attention. In this article, we only focus on offset mismatch estimation and compensation of TI-ADC for high-speed optical OFDM communications.
In a TI-ADC, a periodic offset sequence will generate due to offset mismatch, which can be seen as discrete tones in the frequency domain. It has been proved in [5] that, if the fast Fourier transform (FFT) size N is multiple of M in the OFDM receiver, the discrete tones caused by offset mismatch could only affect the subcarriers with the index multiple of N/M; otherwise, most or all of the discrete tones could spread out over the entire subcarriers. It showed that offset mismatch may cause error floor in the BER performance of OFDM systems [6]. To deal with this issue, the subcarriers affected by discrete tones caused by offset mismatch can be simply filled with zeros [7] or low-order modulation symbols [8] for the former case mentioned above; however, it reduces SE. In [9], two preamble-based offset mismatch estimation schemes, i.e., least-squares (LS) estimation and linear minimum mean-square-error (LMMSE) estimation, are proposed for high-speed OFDM system and studied by numerical simulations. However, it is difficult to estimate the offset mismatch described in the latter case. Recently, discrete Fourier transform (DFT)-spread technique has been employed in optical OFDM systems to reduce peak-to-average power ratio (PAPR) as well as improve BER performance [10,11]. The BER performance on the subcarriers, which are affected by ADC offset mismatch, may be improved by using DFT-spread technique with the advantage of SNR averaging. However, at the same time, it may degrade BER performance on the other subcarriers with high SNR before the use of DFT-spread technique. In [5], a comb-type pilot aided offset mismatch estimation scheme has been proposed for ultra-wideband OFDM receiver, where M is constrained to be prime with N. The estimation scheme proposed in [5] has also been extended to estimate two TI-ADCs in in-phase and quadrature branches simultaneously, based on decorrelation least-mean-square (LMS) and recursive-least-square (RLS) algorithms [12]. Although such a pilot-aided scheme can effectively estimate offset mismatch of TI-ADCs, it reduces SE and has relatively high hardware implementation complexity, especially for high-speed optical communication systems. Another interesting online blind offset mismatch estimation method by using random chopper sampling in the analog domain and time-domain averaging in the digital domain has been presented in [13]. It has a very low-complexity hardware implementation in the digital domain, but additional circuits in front of TI-ADC are required for the chopping operation. The random chopper employed in [13] transforms any input signal to noise with a mean value of zero in the analog domain. In this way, the batch size for the averaging operation can be determined and the limitation described in [14] can be overcome. Fortunately, the OFDM signal has an approximately zero-mean Gaussian amplitude distribution [15]. Thus, the offset mismatch caused by TI-ADC in OFDM systems can be estimated and compensated by only using time-domain averaging in the digital domain.
In this article, a low-complexity online digital offset mismatch compensation scheme, which is similar to the method proposed in [13], is employed to high-speed TI-ADC in real-time optical OFDM systems. Its performance is experimentally investigated in a direct-detection optical OFDM transmission system by both offline and real-time DSP approaches. Moreover, the stability of the BER performance is also investigated in real-time. This article is organized as follows. Section 2 describes the principle of the OMC scheme for high-speed real-time optical OFDM systems in detail. Section 3 presents the experimental setup and offline/real-time DSP algorithms. Offline and real-time results are provided and discussed in Section 4. Numerical simulations are performed to fully verify the performance of the OMC scheme in Section 5. Conclusions are drawn in Section 6.
2. The principle of the online digital OMC scheme for optical OFDM system
Taking offset mismatch of TI-ADC into consideration, the n-th output of TI-ADC with M sub-ADCs can be written as
where denotes DC offset induced by -th sub-ADC, where mod presents the modulo operation. ,and are the transmitted signal, the impulse response of the channel and zero-mean AWGN, respectively. is the received signal without offset mismatch and AWGN.As we know that OFDM signal s(n) obeys zero-mean Gaussian distribution. Therefore, the signal s'(n) described in Eq. (1) can also be regarded as a zero-mean Gaussian random variable. In this way, DC offset induced by the m-th sub-ADC can be estimated with time-domain averaging and given by
where Nb is the batch size for averaging operation. The range of m is from 0 to M-1. The optimal batch size may vary with the received optical power. We will discuss this point in Section 4 in detail. Thereafter, the offset induced by each sub-ADC can be reduced or removed by subtracting the corresponding offset estimate from the TI-ADC output r(n).Here, we propose a low-complexity digital OMC scheme according to Eq. (2) for high-speed real-time optical OFDM systems, and its block diagram of hardware implementation is presented in Fig. 1. The input OFDM signal is sampled by a TI-ADC with a sampling rate of Fclk, which contains M sub-ADCs in parallel operating at a low speed Fclk/M, but in M different clock phases. The outputs from M sub-ADCs are then sent to field programmable gate array (FPGA) chips through high-speed interfaces such as parallel low-voltage differential signaling (LVDS) and JESD204A/B. The high-speed serial samples received by FPGA should be first converted into P samples in parallel at low FPGA clock of Fclk/(M*P), since the state-of-the-art FPGA can only operate at about a few hundred megahertz. There are M tree adders (TA) followed by M serial-to-parallel converters (S/P) are used to realize the addition operation of M samples in parallel from the corresponding sub-ADC. The result from each TA is fed into an accumulator which calculates the sum of Nb samples from the same sub-ADC. Once the sum value is calculated, the offset can be estimated by dividing by batch size Nb. This division operation can be easily implemented in hardware by using the right shift in binary logic if both P and Nb are chosen to be a power of two. The offset estimated from Nb OFDM samples for m-th sub-ADC is stored in m-th buffer (BUF) for correcting the next batch of OFDM samples. In addition, there is a counter for counting from 0 to Nb/P −1 is realized in FPGA and used to clear accumulator, enable division operation and buffer output. Subsequently, the offset compensated samples are realigned for timing synchronization.
3. Experimental setup
To fully evaluate the performance of the proposed OMC scheme for optical OFDM systems, a simple intensity-modulated and direct-detection optical OFDM transmission system has been established, as shown in Fig. 2, where a real-time OFDM receiver with OMC based on FPGA is realized and its register-transfer level (RTL) schematic is inserted.
Fig. 2 Experimental setup. Inset is the RTL schematic of the proposed real-time OFDM receiver with OMC.
In the OFDM transmitter, the OFDM signal is generated offline by running Matlab code on a personal computer (PC), and then uploaded to a commercial Tektronix arbitrary waveform generator (AWG), with a model number of AWG7122C, operating at 10-GSa/s and 10-bit vertical resolution. In the offline DSP algorithms, a pseudo-random binary sequence (PRBS15) with a length of 215-1 is mapped into 81,600 complex-valued symbols with 16/64-QAM modulation formats to generate 800 data-carrying OFDM symbols. These QAM symbols are equally divided into 800 groups each containing 102 QAM symbols which are used to modulate 102 low-frequency subcarriers. DC subcarrier and eighteen high-frequency subcarriers are filled with zeros. Since the frequency response of the employed Mach-Zehnder modulator (MZM) is imperfect, seven low-frequency subcarriers around DC with a low signal-to-noise ratio (SNR) are not used for data transmission and zero padded. In this article, both inverse FFT (IFFT) and FFT size are 256. The input vector of IFFT is constrained to having a Hermitian symmetry (HS) so as to obtain a real-valued OFDM symbol for intensity modulation. A cyclic prefix (CP) of 32 samples is appended in front of each OFDM symbol to combat inter-symbol interference (ISI). Digital clipping is performed at a clipping ratio of 13-dB for PAPR reduction. A single training symbol (TS) with a length of 288 samples is added and used to realize both timing synchronization and channel estimation in the receiver. Thereafter, an OFDM frame consists of one TS and followed by 800 data-carrying OFDM symbols. To improve SNR of the output signal from DAC, the OFDM signal is upsampled by a factor of 2 before being uploaded to AWG.
The 2-GHz converted OFDM signal with a peak-to-peak voltage of 700 mVpp is amplified with a 14-GHz electrical amplifier (EA, Mini-Circuit ZX60-14012L-S + ) and directly drives a 12-GHz Olcaro MZM biased at quadrature point to reduce nonlinear distortion of MZM. The half-wave voltage of the MZM is about 5 V. A laser diode (LD) with an output power of 14-dBm and wavelength of 1550 nm is used as the optical source for the MZM. The output optical signal with a power of 5 dBm from MZM is coupled into a 20 km single-mode fiber (SMF, ITU-T G.652). The loss and dispersion of the SMF are 0.18 dB/km and less than 18-ps/nm/km, respectively. At the receiver end, a variable optical attenuator (ATT) placed in front of a 2 × 1 optical coupler (OC) with a spilt ratio of 10/90 is used to change the received optical power (ROP), which can be measured with 10% power from OC by using a power meter (PM). At the same time, the output signal with 90% power from OC is directly detected via a 10 GHz PIN photodiode integrated with transimpedence amplifier (PIN-TIA). The recovered signal is amplified by the second EA, and then sampled by a 5 GS/s TI-ADC (e2v EV10AQ190) consists of four sub-ADCs each has 10-bit vertical resolution. The captured samples are sent to a Xilinx Virtex-7 FPGA (XC7VX485T) via parallel LVDS interface operating at the double data rate (DDR).
In the FPGA-based real-time baseband OFDM receiver, the serial samples at a data rate of 1.25 GS/s sent by each sub-ADC are converted to 8 samples in parallel operating at 156.25 MHz by using on-chip serializer/deserializer (SERDES) blocks in ADC interface module. The 32 unsigned samples per parallel clock cycle from the ADC interface module are converted to 32 signed integers and then fed into the OMC module. Once OMC is complete, TS-aided low-complexity timing synchronization is realized [16], and then data are reorganized for CP removal. After 256-point FFT operation [17], a simple TS-aided and intra-symbol frequency averaging (ISFA) enhanced channel estimation and equalization is performed [18]. The optimal ISFA taps are 3 in our experiments. The equalized data are demapped with hard-decision. Subsequently, errors are counted and sent to PC via using Xilinx ChipScope Pro tool for real-time BER measurement. Besides, the signed integers, after unsigned to signed conversion, are also sent to PC and stored for offline DSP processing.
4. Experimental results and discussion
4.1 Hardware implementation complexity and convergence
The on-chip resource usage of the proposed FPGA-based real-time OFDM receiver with OMC is summarized as shown in Table 1. The resource usage of ChipScope tool is excluded. Parallel DSP algorithms in the receiver, described in Fig. 2, are implemented with 32 parallel data paths for reducing FPGA operating clock frequency to 156.25-MHz. Such a low FPGA clock can provide more powerful data processing capability by increasing data paths in parallel, and relax timing requirements in the process of FPGA implementation.
Table 1. FPGA Chip Resource Usage
As mentioned in Section 2, the parameters for the proposed OMC are included as follows: Fclk = 5 GS/s, M = 4 and P = 8. It shows that there are only 795 Registers and 1,266 LUTs located in 376 Slices, 0.5% on-chip Slices, used for OMC hardware implementation. Fifty-six on-chip dedicated memory elements RAMB32E1 are used to store the transmitted bits for error count. On-chip 492 DSP48E1 elements are mainly utilized to implement multiplication operation in FFT and channel equalization modules. Division operations, presented in Eq. (2), are realized with right shift operations in binary logic. Thus no DSP48E1s are needed. Compared with the pilot-aided LMS and RLS algorithms proposed in [12], which require lots of iteration and multiplication operations, the proposed OMC has a very low-complexity hardware implementation and may be more suitable for high-speed optical OFDM systems.
The convergence of the proposed OMC is experimentally investigated with offline DSP approaches. At the ROP of −4 dBm, the estimated offset in the least significant bits (LSB) induced by each sub-ADC of 5 GS/s TI-ADC as a function of batch size Nb is given in Fig. 3(a). It shows that the proposed OMC achieves the convergence when batch size is larger than 10,000, which is equivalent to about 139 data-carrying OFDM symbols. The corresponding convergence time for all of sub-ADCs is 8 µs (10,000*4/32/156.25 µs) in our experiments. The estimated offsets for four sub-ADCs are −6, 4.36, −1.28 and 1.24. The BER performances of 64-QAM-encoded OFDM signal versus batch size, at ROPs of −1, −4, −7 and −10 dBm, are also measured and shown in Fig. 3(b). It indicates that offset and BER performance have the same convergence at the ROP of −4 dBm, and the BER value converges to 5e-4 when the batch size is more than 10,000. It is also exhibited that there is faster BER convergence at low ROPs than that of at high ROPs. This fact is the reduced power of received OFDM signal at low ROPs and its effect on offset estimation is reduced, results in fast offset and BER performance convergences. In our experiments, a batch size of more than 16,384 for the real-time OFDM receiver with the proposed OMC is enough to obtain an accurate offset estimation and achieve an optimal BER performance.
4.2 Performance of the proposed OMC with offline DSP approaches
In our experiments, the values of N and M are 256 and 4. Thus the discrete tones induced by offset mismatch will be located on the 64-th and 128-th subcarriers and the corresponding frequencies are 1.25 and 2.5 GHz, respectively. As shown in Fig. 4(a), at the ROP of −4 dBm, there are two additional tones at the specified frequencies of the received electrical power spectrum after TI-ADC. The imperfect frequency response around DC is caused by MZM. The estimated SNR without OMC as a function of subcarrier (SC) index is shown in Fig. 4(c). It shows that the SNR performance on the 64-th SC is seriously deteriorated due to the offset mismatch. ISFA-enhanced channel estimation can be used to improve SNR; however, estimated SNR on the 64-th SC is almost the same as the case of without using ISFA. The main reason is that we cannot obtain an accurate estimate on the 64-th SC, which is interfered by offset mismatch induced discrete tone. Moreover, there two SCs around the 64-th SC have lower SNR also due to the interference of the induced discrete tone in the averaging process of ISFA with taps of 3. By using the proposed OMC, the offset mismatch can be well compensated as shown in Figs. 4(b) and 4(d). We can see clearly from Fig. 4(b) that the discrete tones at 1.25 and 2.5 GHz are disappeared after OMC. The SNR performance on the 64-th SC is also significantly improved by using OMC with or without ISFA. In addition, the poor SNR performance on the 87-th subcarrier, as shown in Figs. 4(c) and 4(d), is caused by using inaccurate channel estimation rather than offset mismatch. It can be obviously improved by using ISFA-enhanced channel estimation.
According to Eq. (1), we can obtain a simple frequency-domain form when N/M is an integer and the recovered data on the k-th SC of l-th OFDM symbol can be expressed as, whereand is the length of an OFDM symbol with CP. Therefore, the estimated channel response on the k-th SC will suffer from offset mismatch as well as AWGN by using TS-based channel estimation. After one-tap channel equalization, the amplitude and phase of the equalized QAM symbols on the k-th SC may be are distorted by using the inaccurate channel estimation, as shown in Figs. 5(a) and 5(e). We observe from the expression of, the recovered QAM symbols may deviate from their nominal positions caused by offset mismatch even though ISFA-enhanced channel estimation is used, as shown in Figs. 5(b) and 5(f). Especially, equals towhen is an integer, which means the effects of offset mismatch on the k-th of each OFDM symbol are the same. In this article, is an integer number of 72 for k = 64. Here, is related to the sampling instants of four sub-ADCs in the TI-ADC, and its phase may vary over different experiments even though the offset mismatch is stable for all of the experimental measurements. Therefore, there is a different phase rotation between 16- and 64-QAM constellations, as shown in Figs. 5(a), 5(b), 5(e) and 5(f). By using the proposed OMC, the constellations diagrams of the equalized QAM symbols are presented in Figs. 5(c), 5(d), 5(g) and 5(h). It exhibits that both the inaccurate channel estimation and the deviation in the nominal position of constellations caused by offset mismatch can be well compensated.
Fig. 5 Constellation diagrams for 64/16-QAM on the 64-th SC: (a), (e) w/o OMC and w/o ISFA, (b), (f) w/o OMC and w/ ISFA, (c), (g) w/ OMC and w/o ISFA, and (d), (h) w/ OMC and w/ ISFA
4.3 Real-time BER measurements for the FPGA-based receiver with OMC
The real-time BER performance is measured by counting errors over continuous 65,536 OFDM frames each containing 800 OFDM symbols, with a total of 32,086,425,600 and 21,390,950,400 bits for 16 and 64-QAM modulation, respectively. To obtain more accurate offset estimate, the batch size in our real-time experiments is 65,536 and the corresponding convergence time is 54.2 µs. After 20-km SMF transmission, at the ROP of −1 dBm, the real-time measured errors for 64-QAM encoded OFDM receiver with the proposed OMC and ISFA is shown in Fig. 6. Here, both frame number and symbol number start counting zero. It shows that there are 2,300,959 errors, and the corresponding BER value is 7.2e-5.
The real-time and offline measured BER curves as functions of ROP for both 16 and 64-QAM modulation formats are presented in Fig. 7(a) and 7(b), respectively. The results show that the BER performance is seriously degraded by offset mismatch, and can only be slightly improved by using ISFA-enhanced channel estimation. We can also observe that significant BER performance improvements can be achieved by using the proposed OMC, especially with high ROPs. Meanwhile, the ISFA-enhanced channel estimation can be used to further improve BER performance. The BER value can be improved by more than an order of magnitude at high ROPs for both 16 and 64-QAM modulation formats. Moreover, error-free transmission enabled by OMC and ISFA is observed for 16-QAM modulation with a ROP of higher than −3 dBm. The receiver sensitivities of both 16- and 64-QAM encoded OFDM receivers in terms of ROP can be improved by more than 5 dB at the BER of 1e-3. In addition, it also indicates that there is a negligible power penalty between the offline and real-time DSP approaches. It should be pointed out that only one OFDM frame is used for offline BER measurements.
Fig. 7 Real-time (RT) and offline (OL) measured BER performance versus ROP: (a) 16-QAM and (b) 64-QAM.
To further verify the feasibility of the proposed OMC, the stability of BER performance of 64-QAM encoded OFDM real-time OFDM receiver with OMC and ISFA over 60 minutes are investigated, and the real-time recorded BER values are shown in Fig. 8. The BER values are around 1e-4 over the measurement period. However, there are slow and slight BER fluctuations over time, which is mainly attributed to the bias voltage drift of the MZM without a bias control circuit.
5. Simulation and discussion
The proposed OMC scheme has been experimentally demonstrated in a real-time optical OFDM system mentioned above, where N/M is an integer number. To fully verify the performance of the OMC scheme, the other case, as mentioned in Introduction, i.e., N isn’t the multiple of M, will also be investigated via numerical simulation in this section.
The OFDM signal is offline generated with the same DSP algorithms as experiment except for upsampling. Here, for the sake of simplicity, an OFDM frame consists of 2,000 64-QAM-encoded OFDM symbols without upsampling. We simulate the BER performance of the OFDM frame as a function of SNR in an AWGN channel followed by a 10-bit TI-ADC with 15 sub-ADCs. The TI-ADC is modeled with only taking offset mismatch into account among the three major mismatches. Moreover, the effects of both ADC clipping and quantization noise [19] are also applied to the TI-ADC model. The output OFDM signal from the TI-ADC model is demodulated with the same DSP algorithms as offline experiments. In our simulation, we set the offset mismatch in the level of 1%. It means the offset errors in LSB for each-ADC are chosen uniformly in the interval [-2Nbit/100, 2Nbit/100], where Nbit and 2Nbit are vertical resolution bits and the total number of ADC codes, respectively. The offset errors of 15 sub-ADCs are set to −3.65, −3.76, 2.74, −9.65, −3.10, −7.83, −2.05, −1.06, −0.52, −8.12, −2.72, −0.95, −2.53, −3.85 and 4.81. The corresponding variance is 15. It should be noted that the effect of offset errors with different variances on the BER performance will be different. In addition, we set ADC clipping level to 4.5 to reduce clipping noise as well as maintain a low quantization noise in our simulations.
When the SNR of the AWGN channel is set to 30 dB, the estimated SNR without and with the OMC scheme as a function of SC index is provided and shown in Fig. 9. It indicates that the SCs with index close to the multiple of N/M are interfered due to offset mismatch between 15 parallel sub-ADCs. And more than six data-carrying SCs are deteriorated. By using the OMC scheme and ISFA-enhanced channel estimation, the offset mismatch is well compensated and the estimated SNR on the interfered SCs is significantly improved.
The simulated BER performance without/with using the OMC scheme and ISFA as a function of SNR is shown in Fig. 10. Besides, for comparison purpose, the BER performance of two offset mismatch (OM)-free cases is also plotted in Fig. 10. We can see clearly that the error floor in BER performance is introduced at high SNRs. This fact is due to the uncompensated offset mismatch. After using the proposed OMC scheme, there is no error floor in BER performance. A negligible SNR penalty is also observed in comparison with that of OM-free case. Moreover, the ISFA can be utilized to further improve BER performance for both without and with OMC cases.
6. Conclusion
We have proposed a low-complex online digital OMC scheme for TI-ADC in high-speed optical communication systems. The hardware implementation and convergence of the proposed OMC are analyzed, and its BER performance is investigated by offline and real-time DSP approaches in a simple direct-detection optical OFDM transmission system. The experimental results indicated that, by using the proposed OMC and ISFA-enhanced channel estimation, the BER performance can be significantly improved for both 16 and 64-QAM modulation formats. Meanwhile, there is a negligible power penalty in terms of BER performance between offline and real-time DSP approaches. Moreover, the BER performance over 1 hour was continuously recorded and showed it has good stability. Numerical simulation was also performed under AWGN channel to further verify the performance of the proposed OMC scheme. The results showed that the error floor in BER performance can be eliminated by using the OMC scheme and a negligible SNR penalty can be achieved compared with that of OM-free case. It is expected that the proposed OMC scheme can be used to relax the design of high-speed TI-ADC and improve BER performance of optical communication systems with offset mismatch problem.
Funding
National Natural Science Foundation of China (61805079, 61701180); Hunan Provincial Natural Science Foundation of China (2017JJ3212, 2016JJ6097); Scientific Research Fund of Hunan Provincial Education Department (18B026, 17C0957).
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