There has long existed a debate over whether analog or digital optical link is more suitable for wireless convergence applications. Digital link achieves the highest fidelity, with the sacrifice of huge bandwidth due to the high resolution of digitization, and large power consumption due to the exhaustive digital data recovery. Analog link avoids these drawbacks, but it inevitably suffers from the SNR degradation. In this paper, we propose the angle modulation for analog optical link, which successfully breaks the SNR ceiling of amplitude modulation, and achieves ultrahigh link fidelity. Using the digital link (CPRI) equivalent bandwidth, angle modulation exhibits around 30-dB SNR advantage over the conventional amplitude modulation. Combined with its high tolerance on link nonlinearity, angle modulation has great potential in the future SNR-hungry analog optical applications.
© 2016 Optical Society of America
The wireless communication has reshaped human’s life. The end users nowadays not only fully enjoy the primary benefit of wireless networks – mobility, but also continue demanding even larger bandwidth [1,2]. Higher wireless capacity requires the reduction of cellular size , resulting in more base stations to be deployed. To aggregate multiple wireless channels and connect them to the core networks economically, centralized radio access network (C-RAN) has been proposed as an attractive architecture [3,4]. In C-RAN, the base station (BS) is separated into 2 elements : the baseband unit (BBU) is responsible for signal control and processing, while the remote radio unit (RRU) for interface with antennas. The optical fiber between the BBU and RRUs delivers the signal to each antenna via downlink, and collects multiple wireless channels via uplink. This optical connection, normally referred as radio-over-fiber (RoF), can be realized either by analog  or digital  transmission.
There long exists a debate on whether analog or digital link is more suitable for RoF. The digital link achieves the highest signal fidelity, because digital transmission suffers from no degradation when the bit stream is error free. The digital interface has been defined as common public radio interface (CPRI) , or open base station architecture initiative (OBSAI)  specifications. However, the digitization brings 2 drawbacks. (1) It requires a huge bandwidth when the digitization resolution is high to maintain the signal fidelity. Taking CPRI as an example, a 20-MHz LTE channel requires 1.228-Gb/s bit rate when each sampling point entails 15 bits for digitization and 1 bit for control . This leads to a huge RF and optical bandwidth consumption. (2) It requires the full digital signal regeneration that involves channel estimation, frequency/timing synchronization, and symbol decision, which is complicated on both devices and digital signal processing (DSP) levels, resulting in energy-inefficiency. In contrast, the analog link successfully avoids the above 2 drawbacks, but it inevitably suffers from the signal-to-noise ratio (SNR) degradation. Although the amplitude modulation (AMP-M) based analog link can satisfy the SNR requirement of current wireless applications, one can envisage that the future technologies would demand much higher SNR to provide larger link power budget, serve more end users, or support higher order modulation. The analog optical link have to overcome its intrinsic SNR ceiling.
In this paper, we propose the angle modulation (ANG-M), i.e., phase or frequency modulation (PM or FM) for analog optical link, and demonstrate the concept via the channel aggreagation based mobile fronthaul links. ANG-M can be realized by various methods, such as the optical PM combined with optical coherent detection proposed for RoF link [9,10]. However, they rely on the complicated and expensive optical coherent detection; more vitally, the optical local oscillator phase noise would degrade the low baud-rate RF signals. Here we choose the optical direct detection (DD) for ANG-M, and for the first time demonstate the remarkable increase of the SNR of analog optical link using ANG-M. Using CPRI equivalent bandwidth, ANG-M can achieve around 30 dB SNR advantage over AMP-M. Moreover, AMP-M analog link suffers from the inter-modulation distortion arising from the analog link nonlinearity . We reveals the superior nonlinearity tolerance of ANG-M, which could achieve additional SNR gains over the AMP-M.
2. Angle modulation based analog optical link
To introduce the architecture of a typical analog optical link, we take the BS structure in C-RAN as an example, illustrated in Fig. 1. For uplink, RRUs receive multiple RF signals from end users. These wireless channels are aggregated at different intermediate frequency (IF) in RF domain and are modulated onto a single-wavelength optical channel. The multi-IF channel aggregation can be realized by either analog signal processing (ASP)  or DSP . Conventionally, the output of the channel aggregation (CH-A) directly drives an intensity modulator, leading to an AMP-M analog link [12,13]. After the fiber transmission, the optical receiver recovers the CH-A signal at BBU, followed by the channel de-aggregation (CH-DA) to retrieve each baseband signal. For downlink, the reverse procedures are performed. The fundamental challenge for analog optical link is the requirement of extremely high fidelity, as the optical link shall only contribute a small fraction of the overall noise margin. It is well known that the spectrum expansion in analog communication via ANG-M can significantly enhance the SNR . Assuming a baseband signal a(t), an ANG-M signal can be expressed asFig. 1 to replace the conventional amplitude modulator / demodulator.
ANG-M can be realized either in RF domain or optical domain, shown in Fig. 2. By modulating the baseband signal to the phase of an IF in Fig. 2(a), ANG-M output maintains a real-value stream, which can drive an optical intensity transmitter, such as a directly modulated laser (DML). The optical receiver can be simply a photodiode, followed by the RF coherent detection to downconvert the IF signal to baseband, as shown in Fig. 2(b). Alternetively, the baseband signal can directly drive an optical phase (or frequency) modulator  in Fig. 2(c). ANG-M to AMP-M conversion  can be performed before the optical receiver, so that the optical direct detection can be applied to recover the ANG-M signal in Fig. 2(d). More strarightforwardly, the optical phase or frequency variation can be charactierized by optical coherent detection  in Fig. 2(e). It is noted that by performing the conversion between AMP-M and ANG-M completely in optical domain (like Fig. 2 (c) and (d)), the signal spectrum only expands in optical region, while the RF spectrum keeps a tight bandwidth. This would be more cost-efficient in the future considering the optical domain has much wider bandwidth resources than RF domain.
The SNR of a PM signal can be calculated from :14]:Eqs. (3) and (4), one can discover that the SNR of ANG-M increases with the square of the modulation index, namely, the signal bandwidth; that is, the SNR increases by 6 dB for each doubling of the signal bandwidth. Moreover, it is shown that  the system SNR are the same between PM and FM under the same modulation index, when the baseband signal spectrum has rectangular shape . In fact, the analog signal after CH-A is an OFDM-like signal, whose spectrum is exactly rectangular. This guarantees similar overall SNR performance between PM and FM. However, while PM offers a flat SNR to all the aggregated channels, FM has a drawback: SNR varies with frequency. When the white noise is added to the FM signal, the baseband signal after frequency demodulation has the following PSD due to the differential operation:15].
3. Bandwidth of angle modulation
The signal bandwidth of ANG-M is determined by the modulation index (MI). In the classic analog communication theory, there is a well-known formula estimating the ANG-M bandwidth, namely, the Carson’s rule :1]). This corresponds to a CPRI equivalent bandwidth of 6.2 GHz.
For narrow-band modulation (NBM), MI is small, resulting in mpp<<4πB. In this case, the signal bandwidth can be approximated as 2B, which is double of the baseband bandwidth because the PM upconverts the baseband signal to IF carrier. Figure 3(a) shows bandwidth as the function of RMS(φ(t)). We fix the receiver noise when the AMP-M system has the SNR of 30 dB (small noise) and 21 dB (large noise), respectively. For both cases, the PM signal can be no longer regarded as NBM when the RMS exceeds 0.3. Figure 3(b) provides the SNR for various RMS. Using 2B (namely, 200 MHz) bandwidth, PM achieves 18 dB SNR when AMP-M has 21 dB SNR; 27 dB SNR when AMP-M is 30 dB. Even for NBM ANG-M, there exists the spectrum leakage out of the baseband. Filtering out the leakage spectrum brings SNR penalty. AMP-M (with bandwidth of B) normally outperforms ANG-M (with bandwidth of 2B). To get an SNR the same as AMP-M, 100-MHz channel requires 280-MHz bandwidth for PM, as shown in Fig. 3(b).
For wide-band modulation (WBM), MI is large, resulting in kmpp>>4πB. In this case, the mpp dominates the ANG-M signal bandwidth. The distributions of d[φ(t)]/dt would determine the shape of signal spectrum. The signal after CH-A (namely, a(t)) is in essence an OFDM-like signal, which obeys Gaussian distribution. After differential operation, d[φ(t)]/dt in Fig. 4(a) maintains Gaussian distribution as shown by Fig. 4(b), leading to an Gaussian-shape-like signal spectrum. We can use the Carson rule of Eq. (6) to estimate the signal bandwidth. For example, in Fig. 4(a), when the RMS(φ(t)) is 1, the mpp is 3.3178 GHz. Substituting it to Eq. (6), the PM bandwidth is 0.7280 GHz. Varying the RMS, Fig. 4(c) presents the bandwidth for different RMS from the Carson rule. The signal bandwidth defined from the filter bandwidth is slightly smaller than that from the Carson rule in Fig. 4(c). This is because the OFDM-like signal normally has an extremely high PAPR, which results in very low power density of PM spectrum within high frequency range. In practice, the PAPR of d[φ(t)]/dt may be controlled by the OFDM PAPR reduction algorithms  before driving the angle modulator, to shrink the bandwidth of ANG-M.
We experimentally demonstrate the DD-PM based analog optical link, shown by Fig. 5. The RF domain operations are emulated by offline DSP. In practice, all these operations can be fulfilled by low-cost analog devices or DSP chips. The maximum achievable RF bandwidth expansion is set as as 6 GHz in offline DSP, corresponding to the DAC sampling rate of 12 GSa/s in the experiment. Each 20-MHz LTE channel occupies 30.72-MHz bandwidth, according to the LTE standard. The baseband signals are aggregated with the Hermitian-symmetric spectrum to guarantee a real-value CH-A output, which drives an RF phase modulator. The PM carrier frequency ωc is set as 3 GHz. The offline stream is loaded on a DAC to drive a DFB directly modulated laser (DML) working around 1550 nm. At receiver, a PIN photo-diode (PD) performs DD, whose output is sampled by a real-time ADC. The offline DSP then performs the phase demodulation, CH-DA and SNR (or EVM) evaluation for each baseband signal. Because the PIN PD has much lower responsivity than the avalanche PD mostly used in analog optical link, we compare the SNR difference between the AMP-M and PM, instead of the absolute receiver sensitivity. The SNR (or EVM) is calculated from the signal constellation.
4.1 Performance of single wireless channel
We first try the 100-MHz channel (6.2 GHz CPRI equivalent bandwidth), which contains 5 gapless 20-MHz bands (5-carrier-agreegation in LTE-A standard ). Figure 6(a) shows the SNR as the function of ANG-M bandwidth. When the modulation index keeps increasing and the bandwidth expands to 4.5 GHz, both PM and FM shows a dramatic SNR improvement of 27 dB, which coincides well with the theory: . In Fig. 6(d), the PM constellations nearly converge to 64 points, indicating the superb fidelity of this analog link. Figure 6(b) illustrates the SNR as the function of baseband frequency. As predicted in Section 2, while PM has a flat SNR curve, FM offers various SNR across the frequency band. From this perspective, PM may be more suitable in wireless convergence applications, because it offers similar SNR performance to the aggregated wireless channels. Below PM is adopted as the example.
4.2 Performance of multiple aggregated wireless channels
We then consider a more practical mobile fronthaul application: an LTE cell site with 3 RRUs, 4 aggregated carriers, and 2 × 2 MIMO, leading to 24 20-MHz LTE bands. Each band occupies 30.72-MHz bandwidth. 256-QAM is used to simulate an SNR-hungry channel. According to 3GPP standard, the maximum EVM for 256-QAM is 4% . The inset of Fig. 5(iii) illustrates the optical spectra for AMP-M and PM (when the expanded bandwidth is 5.28 GHz). PM bandwidth obviously expands, together with the impact of DML chirp. Figure 7 illustrates the RF spectra after optical direct detection. AMP-M clearly shows 24 aggregated bands in Fig. 7(a) from 0 to about 750 MHz. In contrast, Fig. 7(b) varifies the PM spectrum expansion effect. When AMP-M has similar bandwidth with PM, AMP-M outperforms PM in Fig. 8(a), as we analyzed in Section 3. The constellation of AMP-M is shown in Fig. 8(b), with the EVM around 4%. To obtain more system margin, we use PM to expand the bandwidth to 5.28 GHz. The SNR increases by 10 dB, which decreases the EVM to only 1.4%, as shown by Fig. 8(c). We transmit the signal by 6 km SSMF. The SNR penalty is less than 0.5 dB in Fig. 8(a). Externally modulated lasers (EML) can be used to avoid chirp-induced penalty if much longer reach is so desired.
Without the sophisticated full digitization in digital optical link, ANG-M successfully breaks the SNR ceiling of analog link. ANG-M occupies 5.28-GHz bandwidth for a 737-MHz CH-A signal to achieve 10 dB SNR improvement. Although this requires a 5.2-GHz optical transponder, it is still much smaller than the CPRI equivalent bandwith of about 30 GHz. In practice, the bandwidth expansion can be adjusted to fit for various SNR requirements. Thus, in most cases the ANG-M bandwidth can be much smaller than that of the CPRI. ANG-M bridges between the analog AMP-M and full digital link, offering a novel approach to flexibly adjust the analog link SNR with varying bandwidth.
4.3 Nonlinearity tolerance advantage of PM
The AMP-M based analog optical link suffers from the channel nonlinearity such as nonlinear E-O and O-E conversion . AMP-M CH-A results in an OFDM-like signal, which has a high PAPR, thus is more sensitive to nonlinear distortion. Moreover, regardless of the low PAPR, even if the PM signal is clipped, the SNR penalty is still much smaller than the AMP-M, because PM carries the information via phase, relatively immune to amplitude distortion. In the experiment, we induce nonlinear asymmetric clipping of DML by increasing the peak-to-peak voltage (Vpp) of the drive signal. 24 20-MHz CH-A signal is used. When Vpp = 2.7V, both AMP-M and PM CH-A signal are free from clipping effects. When Vpp increases, the maximal DML output amplitude becomes saturated, which leads to an asymmetric clipping, clearly shown in Fig. 9(a-b) when Vpp = 4V. The SNR of AMP-M signal decreases by 5 dB in Fig. 9(c), while PM nearly suffers from no SNR penalty. This advantage may be even larger if we keep increasing the Vpp.
The amplitude modulation based analog optical link is limited by the SNR ceiling. Realized in RF or optical domain, angle modulation can significantly enhance the analog link SNR by spectrum expansion, meanwhile achieve a high link nonlinearity tolerance. In the experiment, phase modulation achieves 27-dB SNR improvement when the bandwidth expands from 200 MHz to 4.5 GHz; when nonlinear O-E and E-O conversions exist in channel, phase modulation shows additional 5-dB SNR advantage over amplitude modulation. Angle modulation bridges the analog amplitude modulation and full digital link, offering a flexible approach to enhance the link SNR with varying bandwidth. Therefore, it has great potential in the future analog optical applications that requires high link fidelity.
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