## Abstract

A bandpass sampling based digital coherent receiver is presented for phase modulated radio-over-fiber links with coherent detection. In the scheme, the bandpass sampling technique is introduced in RoF systems to overcome the high sampling rate requirement and front-end hardware dependency of conventional digtal coherent receivers. In particular, the selection rule of bandpass sampling rate was defined by taking into account the frequency offset induced by free-running optical local oscillator. Analytical assessment and simulations are used to determine the ultimate performance in terms of tolerances to ADC bit resolution and laser linewidth. Thereafter, a 40Mbps QPSK modulated data signal at 2.4GHz RF carrier frequency is experimentally demonstrated over the proposed 50.6-km radio-over-fiber link employing bandpass sampling.

© 2014 Optical Society of America

## 1. Introduction

As one of the most promising technologies, radio-over-fiber (RoF) has been long studied as a way of simplifying the architecture of the remote front end and realizing high-performance backhaul links [1–8]. Most approaches utilized in RoF links employ simple intensity modulation with direct detection (IM-DD), which suffers from inherent nonlinearity and poor dynamic range. In order to achieve transmission of a microwave photonic signal with more spectral-efficiency, optical phase modulation and coherent detection (PM-CD) is introduced to realize high-performance RoF uplinks [9, 10]. One immediate advantage of optical phase modulation over intensity modulation is the inherent linearity when imposing a wireless radio-frequency (RF) signal on an optical carrier. Another advantage is that the optical phase modulator at a RAU does not require bias control. In addition, coherent detection offers improved receiver sensitivity with respect to direct detection, which permits higher optical loss in the link.

One of the challenges in a PM-CD optical coherent receiver with free-running optical local oscillator (LO) laser is nonzero and varying frequency offset. In addition, both the LO laser and transmitter laser possess phase noise, which further necessitates carrier recovery [11, 12]. It is well known that optical coherent detection with digital signal processing (DSP) has been applied in 100G fiber-optic communication systems [13]. The concept of an optical coherent receiver involving high-speed DSP has also been introduced in PM-CD RoF systems [14, 15]. Thus, more accurate compensation of various signal distortions in PM-CD has become possible. Therefore, we take advantage of DSP technique to pursuit better link performance.

The typical setup of a DSP-aided coherent receiver of interest is shown in Fig. 1. The phase-modulated optical signal is first mixed with the LO through a 90° optical hybrid. Afterwards, two pairs of balanced photodiode (BPD) measure the real and imaginary part of the complex electrical field of the incoming optical signal, respectively. Thereafter, an ADC converts the analog electrical signal into the digital domain for subsequent DSP. Finally, transmission impairments, including the frequency offset, would be compensated by DSP.

Another challenge in the PM-CD optical coherent receiver is the analog-to-digital converter (ADC) and DSP hardware dependency. In practice, when using an RF carrier (*f _{c}*) working in the GHz frequency band, the required sampling rate (

*f*) for the ADC can be too high to be achieved if the Nyquist sampling theorem is to be satisfied. Moreover, it would be a waste to process at this rate, for information that only appears within a relatively narrow band. Therefore, we take advantage of bandpass sampling [16] which is a technique that directly samples high-frequency RF signals with smaller sampling rate to relax the demand for ADCs and DSPs. When using the bandpass sampling technique, the sampling rate requirement is no longer based on the RF carrier frequency, but rather on the information bandwidth of the signal. Thus, the resulting processing rate can be signiðcantly reduced [17]. As a result, the amount of memory needed to capture a given time interval of a continuous signal can be reduced, thus decreasing overall computational complexity. Moreover, bandpass sampling can realize the direct frequency down-conversion function which can simplify the architecture of the central unit (CU) by eliminating additional analog devices required in analog transmission links, such as electrical mixers and local oscillators. These features are attractive when implementing a low power and flexible receiver [18].

_{s}The use of bandpass sampling and DSP on an optical link has been demonstrated to offer advantages in dynamic range and minimizing hardware complexity. A. Nirmalathas and Y. Yang evaluated the digitized RF-over-fiber (DRoF) transmission based on bandpass sampling in [19, 20]. The RF signals were bandpass sampled and digitized at the remote front end and then transmitted back to the CU. P. Bakopoulos presented a heterodyne demodulator in WDM coherent optical access network in [21], which employ bandpass sampling to overcome the high sampling rate requirement. This scheme demonstrated the feasibility of using bandpass sampling in intensity modulated optical link. As an alternative to the proposed intensity modulation schemes, phase modulation offers improved sensitivity. And unlike the DRoF system, we concern on integration of all the processing units at the CU and transmit analog signal over the fiber.

Concerning these issues, a DSP-aided PM-CD RoF link employing bandpass sampling is proposed and experimentally demonstrated in this paper. An algorithm for determining the proper ADC sampling rate is presented to ensure no overlapping of frequency bands within each Nyquist zone due to the potential aliasing created by frequency offset. Moreover, the impact of ADC bit resolution, laser linewidth and dynamic range of RF input power and received optical power is evaluated. This work is expected to help practical implementation of PM-CD RoF links in software defined radio, radar and resources limited systems.

## 2. Practical bandpass sampling design in the presence of frequency offset

According to the first-order bandpass sampling theory [16], the sampling rate is dependent on both the bandwidth of the RF signals and the RF carrier frequency. When sampled by an ADC, spectral replicas of the original signal appear in the digital frequency domain at regular intervals determined by the sampling rate, as shown in Fig. 2(a) and 2(b).

To ensure exact reconstruction of the original signal and prevent spectral aliasing, the acceptable sampling rate${f}_{\text{s}}$must satisfy the following condition [16]

Equation (1) can be illustrated by Fig. 3, where the carrier frequency and the sampling rate are normalized to the signal bandwidth *B*. The resulting ‘white wedges’ define the acceptable operating regions where no aliasing occurs. When increasing *m*, the wedges become much narrower, which places more stringent limits on the sampling frequency variation.

However, Eq. (1) does not take into account the presence of frequency offset and ADC jitter, which would pull the operating point out of the wedge regions and lead to aliasing, as shown in Fig. 2(c) and 2(d). For example, when signal bandwidth *B* = 200MHz, carrier frequency ${f}_{\text{c}}$ = 2.4GHz, Table 1 lists the acceptable ranges of ${f}_{\text{s}}$ for aliasing-free operation according to Eq. (1). Here, we take a bandpass sampling rate of ${f}_{\text{s}}$ = 750MHz which is located in the 7th (*m* = 7) wedge region to sample the signal. It is obvious that there is no aliasing in the first Nyquist zone in the absence of frequency offset, as shown in Fig. 4(a). However, in the presence of 200MHz frequency offset, aliasing takes place, as shown in Fig. 4(b). Therefore, the theoretical sampling rate given by in Eq. (1) needs to be practically considered in the presence of frequency offset in an optical coherent receiver with free-running LO laser.

Before modifying Eq. (1), let’s first observe the wedge regions shown in Fig. 3. The wedge regions are confined by two intersecting lines defined by Eq. (1). In the presence of time-varying frequency offset and sampling jitter, the operating region is defined by a rectangle with a central point (*f _{c}*,

*f*). As shown in Fig. 5, the minimum

_{s}*f*and

_{c}*f*can be determined by letting the lower right corner of the rectangle on the lower edge of the wedge and the upper left corner below the upper edge. Otherwise, aliasing will occur. Consequently, Eq. (1) can be modified to Eq. (2), where we define ∆c as the carrier frequency offset and ∆s as the deviation of ADC sampling rate.

_{s}Equation (2) is more practical for engineering use by considering the ADC sampling frequency instability and carrier frequency offset uncertainty, which leads to more accurate and relaxed estimates for actual applications. However, note that jitter of modern ADCs usually represents a tiny fraction of the baud rate of a typical RoF communication system, so this uncertainty sometimes can be negligible in practice [21]. Therefore, the frequency mismatch between transmitter laser and free-running optical LO laser becomes the primary issue to consider.

## 3. DSP aided optical coherent receiver

A typical PM-CD RoF system with DSP is shown in Fig. 6. Due to the absence of bias control for phase modulation, the remote access unit (RAU) only consists of a laser source and a phase modulator driven by the RF signal from antenna. At the receiver end, a 90° optical hybrid is used to mix the received signals with an optical LO laser. The inphase and quadrature components are detected using two pairs of BPD and then sampled by ADCs. Note that a special ADC with enough analog bandwidth to cover the RF carrier frequency is required for bandpass sampling despite its low sampling rate. As mentioned earlier, direct bandpass sampling takes advantage of eliminating use of RF mixers. Afterwards, the digitized signals can form a discrete complex signal as *Y*(*k*) = *I _{i}*(

*k*) +

*jI*(

_{q}*k*), where

*k*is an integer.

*Y*(

*k*) contains all the necessary information to recover the incoming RF signals.

Thereafter, DSP is employed to compensate for the channel impairments and recover the information data. The DSP flow consists of carrier recovery digital phase-locked loop (DPLL), linear signal demodulation, digital down-conversion, residual carrier frequency compensation, carrier phase estimation and decoding unit. In particular, a 2nd-order DPLL, as described in Fig. 7, is used to remove the optical frequency offset between the LO and transmitter lasers.

The DPLL consists of phase detector (PD), numerical loop filter (NLF), numerical controlled oscillator (NCO), *exp*(∙) processor and phase rotator. The input signal to the DPLL unit can be expressed as

*Y*(

*k*) is the complex value of the symbol transmitted in the

*k*-th symbol period, ∆

*w*(

*k*) is the frequency offset between the LO and transmitter laser in angular coordinate,

*S*(

_{RF}*k*) is the RF signal which is modulated on the optical carrier phase,

*K*is the modulation index and

_{p}*n*(

*k*) is phase noise.

The phase detector takes the imaginary part *Im*(∙) of the phase rotator output, which is proportional to the phase error. Thereafter, the output from the PD is passed through a 2nd-order NLF to wipe out its high frequency components. In the NFL, the PD output is multiplied by the integral gain constant *C*_{1} and *C*_{2} in the two arms. The result is then fed to an integrator consisting of an adder and a unit delay register in the upper arm. The final output is then the sum of both branches, which is fed to the NCO to update the phase value. The *exp*(∙) processor accepts the NCO phase samples as input and delivers sine and cosine samples to produce a complex signal which can be expressed as *exp*(-*j*∆*w'*(*k*)), where ∆*w'*(*k*) is the estimation of frequency offset between transmitter and LO laser. Finally, the phase rotator performs a complex multiplication between the input data signals from ADCs and the signals generated by the DPLL to remove the frequency offset. When the DPLL is locked, the final output is proportional to *exp*(*jK _{p}S_{RF}*(

*k*)).

After the DPLL the phase modulated RF signal is linearly demodulated through Im[ln(exp(*jK _{p}S_{RF}*(

*k*))] [7]. The linear demodulated signal is then sent to digital down converter (DDC), where the signal is down-converted from the intermediate frequency (IF) in the first bandpass sampled Nyquist zone to baseband. At this stage, the baseband signal needs to be resampled for further demodulation, since the sampling rate of ADCs is still much higher than the RF signal bandwidth despite bandpass sampling. Constant modulus algorithm (CMA) is used for adaptive equalization [22]. Thereafter, carrier recovery was done including the residual frequency offset estimation based on the fast Fourier transform (FFT) method and carrier phase estimation based on fourth-power Viterbi–Viterbi algorithm [22]. Finally, the signal is sent to the decoding unit to complete demodulation.

## 4. Numerical investigation

Numerical simulations were carried out by MATLAB based on the setup shown in Fig. 6. The RF signal was assumed to be a QPSK signal with 100 MHz bandwidth at 2.4 GHz carrier frequency. Note that according to the Nyquist sampling theorem at least 4.9 GSa/s is needed for sampling the RF signal.

As the signal recovery relies on DSP, we first studied the impact of the quantization resolution of ADCs. Assuming the E_{b}/N_{0} of incoming RF signal was 50 dB (i.e. high enough to identify the impact of quantization) and frequency offset is absent, Fig. 8 shows the error vector magnitude (EVM) as a function of ADC bit resolution varying from 2 to 10 bits for different sampling rates.

It is evident from the plot that the incremental improvement in EVM performance at each sampling rate beyond 7 bit resolution is small for QPSK-modulated RF signals. More importantly, it also indicates that the use of bandpass sampling puts little burden on ADCs.

Next, we investigate the tolerance of the PM-CD system to laser linewidth when absence of frequency offset. Figure 9 shows the system performance as a function of laser linewidth of either Tx or Rx for different modulation indices (MI) varying from 1/32 to 3/4. The linewidth of Tx and Rx lasers were assumed to be identical in the simulations. It can be observed that an MI of 1/16 is needed to achieve an EVM below 4% when given a 1 MHz laser linewidth. Linewidth of this level can easily be achieved with standard distributed feedback lasers (DFB).

The laser linewidth tolerance at different sampling rates varying from 1 GSa/s to 20 GSa/s is shown in Fig. 10, where the MI was set as 1/4. It can be seen that bandpass sampling reduces the laser linewidth tolerance of a PM-CD system. Given a 3% EVM threshold, the laser linewidth is suggested to be ~100 kHz, which is typical for lasers used in optical coherent transmission systems.

At last, we take an example to prove the effectiveness of the proposed DPLL. We assume a RF signal at 2.4 GHz with 100 MHz signal bandwidth and a fixed frequency offset Δc = 200MHz. Figure 11 illustrates the signal spectrum before and after the 2nd-order DPLL at two sampling rates of 12 GSa/s and 2 GSa/s, respectively. It clearly shows that the DPLL removes the frequency offset produced during coherent detection with a free-running LO laser.

Table 2 shows the simulated receiver sensitivity after the DPLL compensation in different ADC sampling rate and frequency offset, where the laser linewidth set as 0 and the E_{b}N_{0} of the incoming RF signal set as 50 dB.

## 5. Experimental investigations

The experimental setup is shown in Fig. 12. A vector signal generator (VSG, Agilent E8267D) was used to generate a 20 MSymbol/s QPSK RF signal at 2.4 GHz. A Nyquist square root raised cosine pulse-shaping filter with 0.25 roll-off factor was used to shape the pulses to achieve suitable modulation characteristics. The generated QPSK RF signal then drove an optical phase modulator supplied with a 100 kHz linewidth continuous wave (CW) laser working at 1550 nm.

After 50.6-km single mode fiber (SMF) transmission, signals arrived at the receiver where a 90° optical hybrid with 7.5 dB insertion loss (KyLia COH24-X) was used to mix the received optical data signal with a tunable local oscillator laser with 15 dBm optical power and less than 100 kHz laser linewidth (ID Photonics CoBrite DX_{4}). The optical signal was then detected with a couple of balanced photodiodes (BPD, Discovery 20 GHz 3 dB bandwidth). The two resultant photocurrents (in-phase (I) and quadrature (Q)) were sampled using a digital sampling oscilloscope (DSO, LeCroy 7300A 3GHz analog bandwidth), as shown in Fig. 13. The nominal quantization resolution of the DSO is 8 bits and its sampling rate is adjustable in steps up to 20 GSa/s. At last, offline DSP was implemented to demodulate the detected signal, as mentioned in Section 3.

Figure 13 shows the DSO sampled in-phase and quadrature signal component in the time domain. The low frequency component (‘the big sinusoid’) is the free-running LO caused frequency offset, and the high-frequency component (‘the small sinusoid’) denotes the modulated RF signal. Figure 14 shows the spectra of the bandpass sampled RF signal at 1 GSa/s. It is evident from the plots that the signal at 2.4 GHz carrier frequency is down-converted to the first Nyquist zone and the frequency offset due to the free-running LO can be successfully removed by the 2nd-order DPLL.

Figure 15 illustrates the measured EVM as a function of ADC sampling rate for different incoming RF signal powers. It shows that the power of incoming RF signals have a great influence on the EVM performance when using bandpass sampling. Therefore, the use of low noise amplifiers in front of a PM-CD link is essential for performance optimization.

Figure 16 shows the back-to-back EVM performance as a function of RF input power for different ADC sampling rates when the received optical power is fixed at 10 dBm, 0 dBm and −10 dBm, respectively. As bandpass sampling deteriorates the SNR, it can be seen that for all three received optical power levels the minmum tolerable RF input power at 1 GSa/s is increased by ~10 dB with respect to that at 10 GSa/s, given an EVM threshold of 17.5% for QPSK. This means the received optical power impacts little on the bandpass sampled signal. However, there is still a large amount of margin in optical power budget for potential optical link loss, such as >15 dB power budget for −10 dBm RF received optical power.

Figure 17 illustrates EVM versus received optical power at different ADC sampling rates when the incoming RF power is fixed at 10 dBm, 0 dBm and −10 dBm, respectively. It is evident that when sampling rate decreases from 10 GSa/s to 1 GSa/s, the optical sensitivity of the PM-CD link decreases respectively by 8 dB, 10 dB and 16 dB, when given a QPSK EVM limit of 17.5%. It once again proves that the power of incoming RF signals have a great influence on the link performance when using bandpass sampling. Therefore, low noise amplifiers is essential in the link performance improvement.

Figure 18 shows BER as a function of received optical power at different sampling rates for back-to-back and 50.6-km fiber transmission, respectively. The link loss of 50.6-km fiber transmission is roughly 10dB. It can be seen that the performance maintains even after 50.6-km transmission. Again, it is also proved that the sensitivity penalty is ~10dB when the sampling rate decreases from 10 GSa/s to 1 GSa/s. Note that in the experiment, if an electrical bandpass filter centered on 2.4 GHz with enough bandwidth to accommodate only the data signal by reducing out-of-band noise prior to the ADC, this could further improve the link performance we have achieved by employing a 3GHz low pass filter.

## 6. Conclusion

We have proposed and experimentally demonstrated a bandpass sampling based PM-CD RoF system. This architecture presents benefits for the deployment due to the centralization of the optical coherent receiver with free-running LO lasers at the CU and a simple RAU at the remote antenna. The frequency offset between the incoming signal and LO wavelengths can be compensated with DSP assistance. Experimental results were presented to evaluate its performance for transmitting a 40 Mbps QPSK modulated signal at a 2.4GHz RF carrier and then phase modulated on an optical carrier at 1550nm. Results showed that the proposed system can be achieved with low linewidth lasers and 8 bits ADC resolution is sufficient to achieve successful transportation. We can conclude that for the PM-CD links with bandpass sampling, it is possible to achieve satisfactory EVM performance with commercially available optical components. However, with the progress of ADCs and DSPs, the proposed simple scheme could be implemented in a more efficient way and close to real-time.

## Acknowledgments

This work was in part supported by National 973 Program (2012CB315705), National 863 Program (2013AA014203), NSFC Program (61302086, 61271042, 61107058, 61302016, 61335002, 61265003, 61362034 and 61465007), Specialized Research Fund for the Doctoral Program of Higher Education (20130005120007), Program for New Century Excellent Talents in University (NCET-13-0682), Fund from Key Laboratory of Broadband Optical Fiber Transmission & Communication Networks, Ministry of Education of China, Fundamental Research Funds for the Central Universities, the Fundamental Research Funds for the Gansu Universities (No.1114ZTC142) and Natural Science Foundation for Young Scientists of Gansu Province (1310RJYA010).

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