Experimental investigation on multi-dimensional digital predistortion for multi-band radio-over-fiber systems

Hao Chen; Jianqiang Li; Kun Xu; Yinqing Pei; Yitang Dai; Feifei Yin; Jintong Lin

doi:10.1364/OE.22.004649

1. Introduction

Diverse wireless communication standards allocated in different frequency bands such as wireless local-area networks (WLAN), Universal Mobile Telecommunications System (UMTS), and Long Term Evolution (LTE), are all playing their own roles in our daily life [1, 2], and are anticipated to co-exist for a long time. Therefore, multi-standard multi-band integrated technologies are under intensive research for potential cost and energy saving. Meanwhile, in the context of distributed antenna systems, multi-band analog radio-over-fiber (RoF) systems based on subcarrier multiplexing (SCM) also attract much attention due to their well-known benefits such as low-loss transmission, radio-technology transparency, shared front-haul fiber infrastructure, good scalability [3, 4], and potential compatibility to several microwave photonic processing techniques [5, 6]. Like digital optical communication systems, there are also two categories of analog RoF systems in terms of modulation technique: directly-modulated and externally-modulated RoF systems. The former one is suited to low-cost applications, while the latter one offers high performance due to reduced relative intensity noise, low chirp, and large bandwidth. Basically, both RoF systems suffer from the inherent nonlinearities from either directly-modulated lasers or external optical modulators. Several linearization techniques have been proposed for single-band ROF systems [7, 8]. For multi-band RoF systems, the modulation nonlinearities can result in both in-band and cross-band nonlinear distortions, which ultimately limits the link performance and radio-frequency (RF) power transmitting efficiency [9, 10]. Recently, we developed a multi-dimensional digital predistortion (DPD) technique based on memory polynomial model for linearizing multi-band RoF systems [11], inspired by the two-dimensional DPD that was originally proposed for concurrent dual-band RF front-ends [12,13]. However, detailed investigations on the behavioral models of RoF links and the hardware requirements of the multi-dimensional digital predistortion technique are not reported.

In this paper, the multi-dimensional digital predistortion method developed in [11] is experimentally investigated in both directly-modulated and externally-modulated multi-band RoF systems in terms of nonlinearity order, memory length, oversampling rate, digital-to-analog conversion (DAC) resolution, carrier frequency dependence and RF input power tolerance, as not provided in the prior arts. This work is expected to help practical implementation of DPD in multi-band RoF systems.

2. Review of the developed multi-dimensional DPD

The indirect learning architecture of the multi-dimensional (multi-D) DPD algorithm is shown in Fig. 1. $x_{i} (n)$ ( $i$ = 1, 2… L) denotes the original baseband complex signal of the $i^{t h}$ band. $z_{i} (n)$ and $y_{i} (n)$ are the output baseband complex signals of the predistorter and the RoF link, respectively. Ideally, we hope $y_{i} (n) = G_{i} x_{i} (n)$ , where $G_{i}$ is the intended RoF link gain for the $i^{t h}$ band. However, the nonlinearity of the directly-modulated or externally-modulated RoF link results in distorted $y_{i} (n)$ . In order to compensate for the nonlinear distortions, the digital predistorter has an inverse transfer function with respect to the RoF link. The memory polynomial model of the derived multi-dimensional DPD can be described by [11]:

z_{i} (n) = \sum_{k = 1}^{K} \sum_{q = 0}^{Q} \sum_{m {}_{k}= 1}^{M_{k}} a_{i, k, q}^{(m_{k})} \frac{x_{i} (n - q)}{| x_{i} (n - q) |} \prod_{\begin{matrix} j = 1 \\ f_{i} = \sum_{j = 1}^{k} \pm f_{j} \end{matrix}}^{k} | x_{j} (n - q) | .

where

k

is nonlinearity order,

q

is memory length,

a_{i, k, q}^{(m_{k})}

is memory polynomial coefficient,

f_{i}

(

f_{i} \in {f_{1}, f_{2} ... f_{L}}

) is the carrier frequency of the i^th band.

f_{i} = \sum_{j = 1}^{k} \pm f_{j}

denotes the condition for selecting j that the linear combination of all possible k carrier frequencies equals to f_i. The superscript m_k (

m_{k} \in {1, 2, .., M_{k}}

) denotes the m_k ^th linear combination of k carrier frequencies satisfying.

Fig. 1 The indirect learning architecture of the multi-dimensional DPD.

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Given y_i(n) and z_i(n), the memory polynomial coefficient $a_{i, k, q}^{(m_{k})}$ can be extracted from the block labeled “Multi-Dimensional Predistorter training” (Block A) that has $y_{i} (n) / G_{i}$ as its input and ${\hat{z}}_{i} (n)$ as its output. The actual predistorter that has x_i(n) as its input and z_i(n) as its output is an exact copy of Block A when ${| e_{i} (n) |}^{2} = {| {\hat{z}}_{i} (n) - z_{i} (n) |}^{2}$ is minimized through least-squares (LS) algorithm. In theory, $a_{i, k, q}^{(m_{k})}$ can be extracted by finding the solution of

z_{i} = U_{i} a_{i} .

where

z_{i} = {[z_{i} (0), z_{i} (1), .., z_{i} (N - 1)]}^{T},

\begin{array}{l} a_{i} = [^{a_{i, 1, 0}^{(1)}, .., a_{i, 1, Q}^{(1)}, .., a_{i, k, 0}^{(1)}, .., a_{i, k, Q}^{(1)}, .., a_{i, k, 0}^{(M_{k})}, .., a_{i, k, Q}^{(M_{k})}, .., a_{i, K, Q}^{(M_{K})}] T}, \\ U_{i} = [u_{i, 1, 0}^{(1)}, .., u_{i, 1, Q}^{(1)}, .., u_{i, k, 0}^{(1)}, .., u_{i, k, Q}^{(1)}, .., u_{i, k, 0}^{(M_{k})}, .., u_{i, k, Q}^{(M_{k})}, .., u_{i, K, Q}^{(M_{K})}], \\ u_{i, k, q}^{(m_{k})} = [^{u_{i, k, q}^{(m_{k})} (0), .., u_{i, k, q}^{(m_{k})} (N - 1)] T}, and u_{i, k, q}^{(m_{k})} (n) = \frac{y_{i} (n - q)}{| y_{i} (n - q) |} \prod_{\begin{matrix} j = 1 \\ f_{i} = \sum_{j = 1}^{k} \pm f_{j} \end{matrix}}^{k} | \frac{1}{G_{j}} y_{j} (n - q) | . \end{array}

The LS-algorithm-based solution of Eq. (2) is

{\hat{a}}_{i} = {(U_{i}^{H} U_{i})}^{- 1} U_{i}^{H} z_{i}

, where (▪)^H denotes complex conjugate transpose.

3. Experiments for directly-modulated RoF systems

3.1 Experimental setup

As shown in Fig. 2, we took a two-band directly-modulated RoF system as an example in the experiments to study the multi-dimensional DPD technique. Two vector signal generators (VSG Agilent E8267D and Anritsu MS2690A) were used to generate two 64-ary quadrature amplitude modulation orthogonal frequency division multiplexing (64 QAM-OFDM) RF signals both with 20 MHz bandwidth at 2.3 GHz and 2.462 GHz. The RF carrier frequencies at 2.3 GHz and 2.462 GHz are compliant to the projected indoor bands for time-division LTE (TD-LTE) and WLAN in China, respectively. The two RF signals were combined and then applied to a commercial directly-modulated multi-quantum-well (MQW) distributed-feedback (DFB) 3-GHz laser diode at a wavelength of around 1550 nm. The threshold current of the used MQW-DFB laser was ~10 mA and the operating bias current was 30 mA. The load impedance of the laser chip was ~5 ohm, but the laser module was matched to 50 ohm. Hence, the rough applied current on the laser chip can be calculated according to the RF input power. After transmission over standard single-mode fiber (SMF) and a variable optical attenuator, a photodetector (PD) with a responsivity of 0.85A/W was used. The optical input power to the PD kept 0dBm. A vector signal analyzer (VSA Agilent N9030A) was used to capture y_i(n) and z_i(n) (i = 1, 2) from which we can extract the predistorter model coefficients by Matlab. Two separate RF power amplifiers (PAs) with high saturation powers were used instead of a dual-band RF amplifier to boost the input RF power into the RoF link. In addition, note that z_i(n) in fact involves the distortions from the RF components (i.e. VSGs and PAs), as shown in Fig. 2. The way allowed us to exclude the impact of RF components and separately focus on the nonlinear distortions from the RoF link when extracting the predistorter coefficients.

Fig. 2 Experimental setup for a two-band directly-modulated RoF system.

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3.2 Experimental results

First, the multi-dimensional DPD technique was experimentally investigated in terms of different nonlinearity order (K = 3, 5, 7, 9), memory length (Q = 0, 1, 2, 3), and sampling rate (40 MSa/s, 60 MSa/s, 80 MSa/s). The RF power applied on the LD was 8.5 dBm per band. The results are illustrated in Fig. 3. It can be observed that higher sampling rate only gives slight performance improvement. The nonlinearity orders up to 5 are required to be involved during DPD for better performance. Taking into account higher nonlinearity orders only provides limited performance improvement, whereas the computational complexity increases. No distinct performance improvement occurs as the memory length increase, which differs from the situations for RF PAs [12, 13]. Note that we tried multiple DFB-LDs from different vendors and similar results were obtained. Intuitively, the higher nonlinearity orders are supposed to be considered for higher RF input power. However, the same conclusion was made even when the RF input power further increased to the level on which the performance was too bad to identify the impact of predistortion. Therefore, balancing the performance and the implementation complexity, we suggest a memory-free (i.e. Q = 0) multi-dimensional DPD involving nonlinearity orders up to 5 (i.e. K = 5) at 2 × oversampling rate (i.e. sampling rate = 40 MSa/s for a RF bandwidth of 20 MHz) for a practical multi-band directly-modulated RoF system. The following investigations were all based on the suggested parameters for directly-modulated RoF systems.

Fig. 3 EVM performance of output of directly-modulated RoF link for different sample rates, nonlinearity orders and memory lengths. (a) Band 1, sampling rate = 40 MSa/s; (b) Band 1, sampling rate = 60 MSa/s; (c) Band 1, sampling rate = 80 MSa/s; (d) Band 2, sampling rate = 40 MSa/s; (e) Band 2, sampling rate = 60 MSa/s; (f) Band 2, sampling rate = 80 MSa/s.

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Second, three scenarios were evaluated: the scenario without DPD, the scenario with independent DPD [14] (i.e. only in-band DPD is performed), and the scenario with multi-dimensional DPD (i.e. both in-band and cross-band DPD are performed). The RF power applied on the LD was 7.5 dBm per band. Figure 4 shows the measured RF power spectra and constellation diagrams of the output signal from the RoF link. The quantitative results are summarized in Table 1. It is obvious that the independent DPD only provides limited performance improvement, whereas about 5 dB adjacent channel power ratio (ACPR) improvement is observed at both upper sideband (USB) and lower sideband (LSB) for the multi-dimensional DPD. The use of the multi-dimensional DPD reduces the error vector magnitude (EVM) from 3.78% and 4.16% to 1.22% and 1.15% for the two bands, respectively.

Fig. 4 Power spectra and constellation diagrams after directly-modulated RoF link. (a) power spectra of Band 1 at 2.3 GHz; (b) constellation diagram of Band 1 without DPD; (c) constellation diagram of Band 1 with independent DPD; (d) constellation diagram of Band 1 with multi-dimensional DPD; (e) power spectra of Band 2 at 2.462 GHz; (f) constellation diagram of Band 2 without DPD; (g) constellation diagram of Band 2 with independent DPD; (h) constellation diagram of Band 2 with multi-dimensional DPD.

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Table 1. Comparison in ACPR and EVM for directly-modulated RoF systems

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Third, the tolerance of the multi-dimensional DPD to the RF power difference between the two bands (P₁ and P₂) was evaluated. In the experiments, the total RF input power of two bands was kept to be 10.5 dBm while the RF input power difference of the two bands varied from 3 dB to 6 dB with a step of 1 dB. Table 2 summarizes the experimental results. Given a fixed total RF input power to the RoF link, the band with lower RF power suffers from more nonlinear distortions in terms of EVM, which indicates that the cross-band nonlinearity dominates. However, the multi-dimensional DPD is capable of compensating for the nonlinear distortions in both bands even in the presence of up to 6 dB RF power difference.

Table 2. Tolerance to the RF power difference for directly-modulated RoF systems

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Fourth, the performance of the multi-dimensional DPD was analyzed in terms of DAC resolution. The used VSGs in the experiments have a nominal DAC resolution of 14 bits. Therefore, we implemented quantization to I/Q samples of two bands in Matlab before the data was fed to VSGs, through which we simulated different DAC resolutions. The RF power applied on the LD was 7.5 dBm per band.The EVMs of both scenarios with and without multi-dimensional DPD are depicted in Fig. 5 as a function of DAC resolution bits. For comparison, the EVM of back-to-back (B2B) scenario (i.e. VSG directly connected to VSA without RoF links) is also illustrated in Fig. 5. For all three scenarios, a threshold of 8 bits in DAC resolution can be observed, which is mainly determined by the employed 64 QAM-OFDM format. It can also be concluded that the multi-dimensional DPD puts no more burdens on the DAC in terms of resolution, as compared with the B2B case. In practice the effective number of bits (ENOB) is more important. If taking the ENOB into account, DACs with larger nominal resolution bits are needed.

Fig. 5 EVM as a function of DAC resolution for directly-modulated RoF systems. (a) Band 1 at 2.3 GHz; (b) Band 2 at 2.462 GHz.

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Fifth, given a fixed carrier frequency of Band 1 at 2.3 GHz, the dependency to the carrier frequency was studied by changing the carrier frequency of Band 2 to 2.412 GHz (IEEE 802.11g Channel 1), 2.427 GHz (IEEE 802.11g Channel 4) and 2.442 GHz (IEEE 802.11g Channel 7). The RF power applied on the LD was 7.5 dBm per band. As shown in Table 3, the EVM performance maintains as the carrier frequency of Band 2 varies for both cases with and without multi-dimensional DPD.

Table 3. The dependency on carrier frequency for directly-modulated RoF systems

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Finally, the tolerance to the input RF power per band of the RoF links was investigated. Note that the input RF power of both bands kept identical. The EVM against the RF input power is illustrated in Fig. 6. For IEEE 802.11n standard, the EVM requirement of a transmitter is limited to around 3% [15]. Given an EVM threshold of 3%, the proposed multi-dimensional DPD approach is able to improve the RF input power tolerance by greater than 3dB for both bands.

Fig. 6 EVM performance against RF input power after directly-modulated RoF link. (a) Band 1 at 2.3 GHz; (b) Band 2 at 2.462 GHz.

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4. Experiments for externally-modulated RoF systems

4.1 Experimental setup

Similar investigations on the multi-dimensional DPD were done for externally-modulated RoF systems. In the externally-modulated RoF link shown in Fig. 7, a 10 dBm CW light at 1550 nm was sent to a broadband LiNbO₃ Mach-Zehnder modulator (MZM) with a half-wave voltage of about 1.5 V. The RF signals at two bands were combined and then applied to the MZM. After transmission over standard SMF and a variable optical attenuator, a PD with a responsivity of 0.9 A/W was used. The optical input power to the PD kept 0 dBm. Like in the experiments for directly-modulated RoF systems, z_i(n) in fact involves the distortions from the RF components (i.e. VSGs and embedded RF amplifiers), as shown in Fig. 7. This way allowed us to exclude the impact of RF components and separately focus on the nonlinear distortions from the RoF link when extracting the predistorter coefficients.

Fig. 7 Experimental setup for a two-band externally-modulated RoF system.

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4.2 Experimental results

First, the multi-dimensional DPD technique was experimentally investigated in terms of different nonlinearity order (K = 3, 5, 7, 9), memory length (Q = 0, 1, 2, 3), and sampling rate (40 MSa/s, 80 MSa/s). The RF power applied on the MZM was 1.5 dBm per band. The results are illustrated in Fig. 8. It can be observed that higher sampling rate only gives slight performance improvement. The nonlinearity terms with orders up to 5 are required to be involved during DPD for optimum performance since more terms with higher orders might result in more coefficient-extraction errors. No distinct performance improvement occurs as the memory length increase. Similar to the cases for directly-modulated ROF systems, the same conclusion was made when the RF input power varied. Therefore, balancing the performance and the implementation complexity, we suggest a memory-free (i.e. Q = 0) multi-dimensional DPD involving nonlinearity orders up to 5 (i.e. K = 5) at 2 × oversampling rate (i.e. sampling rate = 40 MSa/s for a RF bandwidth of 20 MHz) for a practical multi-band externally-modulated RoF system. The following investigations were all based on the suggested parameters for externally-modulated RoF systems.

Fig. 8 EVM performance of output of externally-modulated RoF link for different sample rates, nonlinearity orders and memory lengths. (a) Band 1, sampling rate = 40 MSa/s; (b) Band 1, sampling rate = 80 MSa/s; (c) Band 2, sampling rate = 40 MSa/s; (d) Band 2, sampling rate = 80 MSa/s.

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Second, three scenarios were evaluated: the scenario without DPD, the scenario with independent DPD (i.e. only in-band DPD is performed), and the scenario with multi-dimensional DPD (i.e. both in-band and cross-band DPD are performed). The RF power applied on the MZM was 1.5 dBm per band. Figure 9 shows the measured RF power spectra and constellation diagrams of the output signal from the RoF link. The quantitative results are summarized in Table 4. It is obvious that the independent DPD only provides limited performance improvement, whereas about 5 dB ACPR improvement is observed at both upper sideband (USB) and lower sideband (LSB) for the multi-dimensional DPD. The use of the multi-dimensional DPD reduces the EVM from 4.51% and 4.46% to 1.52% and 1.53% for the two bands, respectively.

Fig. 9 Power spectra and constellation diagrams after externally-modulated RoF link. (a) power spectra of Band 1 at 2.3 GHz; (b) constellation diagram of Band 1 without DPD; (c) constellation diagram of Band 1 with independent DPD; (d) constellation diagram of Band 1 with multi-dimensional DPD; (e) power spectra of Band 2 at 2.462 GHz; (f) constellation diagram of Band 2 without DPD; (g) constellation diagram of Band 2 with independent DPD; (h) constellation diagram of Band 2 with multi-dimensional DPD.

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Table 4. Comparison in ACPR and EVM for externaltly-modulated RoF systems

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Third, the tolerance of the multi-dimensional DPD to the RF power difference between the two bands (P₁ and P₂) was evaluated. In the experiments, the total RF input power of two bands was kept to be 4.5 dBm while the RF input power difference of the two bands varied from 3 dB to 6 dB with a step of 1 dB. Table 5 summarizes the experimental results. Given a fixed total RF input power to the RoF link, the band with lower RF power suffers from more nonlinear distortions in terms of EVM, which indicates that the cross-band nonlinearity dominates. However, the multi-dimensional DPD is capable of compensating for the nonlinear distortions in both bands even in the presence of up to 6 dB RF power difference.

Table 5. Tolerance to the RF power difference for externally-modulated RoF systems

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Fourth, the performance of the multi-dimensional DPD was analyzed in terms of DAC resolution. The RF power applied on the MZM was 1.5 dBm per band. The EVMs of both scenarios with and without multi-dimensional DPD are depicted in Fig. 10 as a function of DAC resolution bits. For comparison, the EVM of back-to-back (B2B) scenario (i.e. VSG directly connected to VSA without RoF links) is also illustrated in Fig. 10. For all three scenarios, a threshold of 8 bits in DAC resolution can be observed, which is mainly determined by the employed 64 QAM-OFDM format. It can also be concluded that the multi-dimensional DPD puts no more burdens on the DAC in terms of resolution, as compared with the B2B case.

Fig. 10 EVM as a function of DAC resolution for externally-modulated RoF systems. (a) Band 1 at 2.3 GHz; (b) Band 2 at 2.462 GHz.

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Fifth, given a fixed carrier frequency of Band 1 at 2.3GHz, the dependency to the carrier frequency was studied by changing the carrier frequency of Band 2 to 2.412 GHz (IEEE 802.11g Channel 1), 2.427 GHz (IEEE 802.11g Channel 4) and 2.442 GHz (IEEE 802.11g Channel 7). The RF power applied on the MZM was 1.5 dBm per band. As shown in Table 6, the EVM performance maintains as the carrier frequency of Band 2 varies for both cases with and without multi-dimensional DPD.

Table 6. The dependency on carrier frequency for externally-modulated RoF systems

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Finally, the tolerance to the input RF power per band of the RoF links was investigated. Note that the input RF power of both bands kept identical. The EVM against the RF input power is illustrated in Fig. 11. For IEEE 802.11n standard, the EVM requirement of a transmitter is limited to around 3%. Given an EVM threshold of 3%, the proposed multi-dimensional DPD approach is able to improve the RF input power tolerance by greater than 3dB for both bands.

Fig. 11 EVM performance against RF input power after externally-modulated RoF link. (a) Band 1 at 2.3 GHz; (b) Band 2 at 2.462 GHz.

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5. Discussion on practical implementation of adaptive training by feedback

In the RoF link which may be a few kilometers long, it’s difficult to feedback the output of RoF link for training. We suggest two methods to address this issue. One is transmitting feedback RF signals in a RoF uplink, as shown in Fig. 12. However, the additional RoF uplink not only increases the overall cost, but also brings a further problem that the nonlinearity of the feedback RoF uplink is also required to be carefully handled. Another alternative method is illustrated in Fig. 13. An additional PD is used to detect the output of directly-modulated laser or MZM modulator at the central unit. The method is based on the assumption that the nonlinearity of the RoF link is mainly induced by the directly-modulated lasers or MZM modulators, the PD usually operates at its linear region. This assumption is often satisfied in practice. We repeated the experiments using the second method. The results showed no distinct performance degradation, which demonstrated the feasibility of the second feedback method. This conclusion gives us an instruction for future practical implementation.

Fig. 12 DPD system model for practical RoF link using uplink feedback.

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Fig. 13 DPD system model for practical RoF link using additional PD at central unit.

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6. Conclusion

We have experimentally investigated the developed multi-dimensional DPD technique for linearizing multi-band RoF systems. For both directly-modulated and externally-modulated RoF systems, the experimental results show that the cross-band nonlinear distortion is much more distinct than the in-band nonlinear distortion, which necessitates multi-dimensional DPD technique. According to the investigations, memory-free multi-dimensional digital predistorters involving nonlinearity orders up to 5 at 2 × oversampling rate are suggested for practical directly-modulated and externally-modulated multi-band RoF systems. Using the suggested parameters, the multi-dimensional DPD is able to improve the RF input power tolerance by greater than 3dB for each band in a two-band RoF system, indicating an enhancement of RF power transmitting efficiency.

Acknowledgments

This work was supported in part by National 973 Program (2012CB315705), NSFC Program (61271042, 61107058, 61302086, and 61302016), Specialized Research Fund for the Doctoral Program of Higher Education (20130005120007), Program for New Century Excellent Talents in University (NCET-13-0682), and Fundamental Research Funds for the Central Universities.

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Case	ACPR (in dBc)		EVM
Case	Band 1 (LSB/USB)	Band 2 (LSB/USB)	Band 1	Band 2
w/o DPD	−35.8/-35.6	−34.6/-34.8	3.78%	4.16%
w/ independent DPD	−36.0/-36.4	−35.6/-35.8	3.07%	3.03%
w/ multi-D DPD	−40.8/-40.7	−39.4/-40.9	1.22%	1.15%

RF Power Difference between P₁ and P₂	EVM (Band 1/ Band 2)
RF Power Difference between P₁ and P₂	w/o DPD	with multi-D DPD
0 dB (P₁ = P₂ = 7.5 dBm)	3.78% / 4.16%	1.22% / 1.15%
3 dB (P₁ = 5.74 dBm, P₂ = 8.74 dBm)	4.55% / 4.00%	1.27% / 1.09%
4 dB (P₁ = 5.04 dBm, P₂ = 9.04 dBm)	4.82% / 4.05%	1.25% / 1.14%
5 dB (P₁ = 4.31 dBm, P₂ = 9.31 dBm)	5.09% / 4.18%	1.35% / 1.19%
6 dB (P₁ = 3.53 dBm, P₂ = 9.53 dBm)	5.35% / 4.31%	1.41% / 1.24%

Carrier Frequency of Band 2	EVM w/o DPD		EVM w/ multi-D DPD
Carrier Frequency of Band 2	Band 1	Band 2	Band 1	Band 2
2.412 GHz	4.19%	3.98%	1.23%	1.19%
2.427 GHz	4.11%	4.07%	1.20%	1.16%
2.442 GHz	3.88%	4.27%	1.18%	1.15%
2.462 GHz	3.78%	4.16%	1.22%	1.15%

Case	ACPR (in dBc)		EVM
Case	Band 1 (LSB/USB)	Band 2 (LSB/USB)	Band 1	Band 2
w/o DPD	−35.0/-35.0	−35.4/-35.5	4.51%	4.46%
w/ independent DPD	−35.9/-35.9	−36.6/-36.7	4.06%	3.60%
w/ multi-D DPD	−39.7/-39.5	−40.2/-40.0	1.52%	1.53%

RF Power Difference between P₁ and P₂	EVM (Band 1/ Band 2)
RF Power Difference between P₁ and P₂	w/o DPD	with multi-D DPD
0 dB (P₁ = P₂ = 1.5 dBm)	4.51% / 4.46%	1.52% / 1.53%
3 dB (P₁ = −0.26 dBm, P₂ = 2.74 dBm)	5.20% / 4.68%	1.19% / 1.96%
4 dB (P₁ = −0.96 dBm, P₂ = 3.04 dBm)	5.40% / 4.75%	1.17% / 2.13%
5 dB (P₁ = −1.69 dBm, P₂ = 3.31 dBm)	5.70% / 4.91%	1.07% / 2.26%
6 dB (P₁ = −2.47 dBm, P₂ = 3.53 dBm)	5.95% / 5.06%	1.10% / 2.41%

Experimental investigation on multi-dimensional digital predistortion for multi-band radio-over-fiber systems

Abstract

1. Introduction

2. Review of the developed multi-dimensional DPD

3. Experiments for directly-modulated RoF systems

3.1 Experimental setup

3.2 Experimental results

4. Experiments for externally-modulated RoF systems

4.1 Experimental setup

4.2 Experimental results

5. Discussion on practical implementation of adaptive training by feedback

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (13)

Tables (6)

Equations (3)

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