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Abstract
Implementing preprocessing in a delay-division multiplexing (DDM) orthogonal frequency-division multiplexing (OFDM) passive optical network (PON) requires a priori knowledge of channel responses, which need to be estimated under the constraint of sub-Nyquist analog-to-digital sampling. The localized approach allocates subcarriers in different frequency zones to training symbols in different time slots for channel estimation without spectral overlap. Unfortunately, the localized scheme is susceptible to inaccurate estimation when using an avalanche photodiode (APD), due to variations in APD saturation associated with different training symbols. Instead of localizing all subcarriers of a training symbol in a single frequency zone, we propose distributing training subcarriers through various frequency zones. This distributed scheme would prevent spectral overlap and also reduce the degree of variation in APD saturation, thereby improving the accuracy of channel estimation. Alternatively, we propose an orthogonal scheme in which each training symbol uses all of the subcarriers simultaneously. The orthogonality specified among consecutive training symbols should make it possible to estimate the channel response with low computational complexity. We conducted experiments to compare various schemes used for channel estimation in a 25-Gbps APD-based OFDM-PON. Our results revealed that the orthogonal scheme achieved the best results, and the localized scheme provided the worst channel estimates. We demonstrate the application of the orthogonal scheme in a penalty-free DDM system at 1/32 of the Nyquist rate, which provided a loss budget of 28 dB after fiber transmission over a distance of 25 km.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Growth in the number of mobile devices and internet services is driving demand for broadband access, which can only be met through further advances in optical access networks. Passive optical networks (PONs) use a passive point-to-multipoint (PtMP) architecture to provide cost-effective broadband access to end-users. Moreover, significant advancements in digital signal processing (DSP) technologies have made orthogonal frequency-division multiplexing (OFDM) a viable scheme for future high-speed PONs [1–3]. This technology provides high spectral efficiency and sufficient flexibility for a wide range of services. The passive PtMP architecture requires that OFDM-PONs with time-division multiple access (TDMA) or orthogonal frequency-division multiple access (OFDMA) provide a high-speed aggregated downstream to satisfy the bandwidth requirements imposed by multiple optical network users (ONUs). Despite the fact that only a small portion of downstream data is dedicated to an ONU, the receivers of ONUs must be able to detect the entire aggregated downstream. Demodulating aggregated OFDM signals without aliasing or signal distortion requires that each ONU employ an analog-to-digital converter (ADC) operating at a sampling rate equal to or higher than the Nyquist rate (i.e., double the signal bandwidth). The delay-division multiplexing (DDM) scheme has been proposed as a solution to reduce the required sampling rate of ADCs and the necessary computational capability of DSPs at receivers without the need for additional hardware [4,5]. In addition, an ADC with a reduced sampling rate can also be applied to detect multi-band signals [6,7]. By implementing preprocessing in a central office (CO), the DDM scheme allows an ONU to receive a set proportion of OFDM subcarriers with a preallocated sampling delay at a sub-Nyquist sampling rate. This means that receivers in a DDM system can be equipped with analog-to-digital converter (ADC) at a sub-Nyquist sampling rate. Preprocessing requires channel responses across the entire signal bandwidth, thereby necessitating estimates of channel response in DDM-OFDM systems operating within the constraints of sub-Nyquist sampling. We introduced a straightforward scheme for channel estimation (referred as the localized scheme) in our earlier works [4,5]. This scheme involves the sequential transmission of training symbols comprising subcarriers localized in a single frequency zone to achieve channel estimation without the spectral overlap associated with sub-Nyquist sampling.
In [4, 5], an insufficient power budget necessitated the use of an optical preamplifier prior to a p-i-n photodiode (PIN), which would greatly increase the cost of receivers at ONUs. In this work, we incorporated an avalanche photodiode (APD) in a DDM-OFDM-PON to avoid the need for an optical preamplifier [8, 9]. Unfortunately, the localized scheme suffers from severe fluctuations in channel estimation in APD-based DDM-OFDM systems, due to variations in APD saturation [10,11] associated with training symbols located within different frequency zones. These fluctuations can cause preprocessing failures in DDM systems. Maintaining careful control over estimation conditions in the localized scheme can help to overcome inaccuracies in estimation; however, we demonstrate in this paper that the resulting penalty in system sensitivity cannot be disregarded.
In this work, we sought to enhance the accuracy of channel response estimation to facilitate signal preprocessing in APD-based DDM-OFDM-PONs. We developed two novel schemes for channel estimation. The first is a distributed scheme aimed at reducing the degree of variation in APD saturation by distributing the subcarriers of each training symbol over various frequency zones, while avoiding spectral overlap. The second is an orthogonal scheme in which all subcarriers are employed simultaneously to ensure that the power distribution of training symbols is similar to that of downstream signals. More importantly, we specified orthogonality among consecutive training symbols to enable estimates of the whole channel response with low computational complexity. Experiment results demonstrate that the proposed orthogonal scheme provides the most reliable channel estimates, followed in order by the distributed scheme and the localized scheme. The distributed and localized schemes both require careful control over estimation conditions in order to optimize channel estimation. In comparison to conventional detection using Nyquist sampling in a 25-Gbps APD-based OFDM-PON, we demonstrate a penalty-free DDM scheme operating at 1/32 of the Nyquist rate in conjunction with the proposed orthogonal scheme for channel estimation, achieving a loss budget of 28 dB after 25-km fiber transmission. In contrast, the distributed and localized schemes reduced the loss budget by at least 1 and 2 dB, respectively.
2. Channel estimation schemes: concepts
In a DDM system, the ONUs are divided into M virtual groups, and the sampling rate of the ADC at each ONU can be only 1/M of the Nyquist rate. However, when a receiver is unable to provide Nyquist sampling, channel estimation based on traditional training symbols (i.e., using all subcarriers simultaneously) can be hindered by spectral aliasing, as schematically shown in Fig. 1(a). This issue has been resolved using the localized scheme, in which only subcarriers localized in a Nyquist zone are used in the training time slot, and subcarriers in different frequency zones are transmitted sequentially in order to estimate the whole channel response without the effects of aliasing, as shown in Fig. 1(b). However, most systems are limited in terms of bandwidth; therefore, subcarriers localized in lower frequency zones may show higher power, as shown in the inset (i) of Fig. 1. For a receiver operating in a saturation region, the localized scheme can lead to different degrees of saturation in different time slots. Compared to a PIN receiver, an APD receiver presents pronounced saturation characteristics, and the APD-based DDM system in this work indeed suffers from severe estimation error when using the localized scheme. We propose using the distributed scheme in Fig. 1(c) to equalize the power of different training symbols without prior knowledge of channel characteristics, wherein each training symbol is composed of subcarriers distributed in different frequency zones. The subcarriers must be distributed in a manner that allows for similar power levels in different time slots (inset (ii) of Fig. 1) without subcarrier superposition under sub-Nyquist sampling. Without prior knowledge of channel responses, the rules used in designating subcarriers in the distributed scheme are as follows. We assume that the frequency response decreases monotonically with frequency (i.e., a subcarrier at a lower frequency should have higher power). Thus, our objective is to give every training symbol the chance to consist of a subcarrier of the lowest frequency in a frequency zone. In the example in Fig. 1(c), the subcarriers in the 1st frequency zone are sequentially assigned (from lowest to highest frequency) to the training symbols in the following order: 1st, 2nd, 3rd and 4th. The subcarriers in the 2nd frequency zone are sequentially assigned in the same manner; however, the order of the training symbols is shifted as follows: 4th, 1st, 2nd and 3rd. The assignment of subcarriers in the 3rd frequency zone is the same as above; however, the order of the training symbols is shifted as follows: 3rd, 4th, 1st and 2nd. We refer to this shift in the order of training symbols as a “cycling shift”.
Fig. 1 Frequency-domain concepts with 1/4 of the Nyquist sampling rate: (a) spectral superposition due to aliasing, (b) localized training symbols, (c) distributed training symbols, and (d) orthogonal training symbols. Waveforms exemplify time-domain characteristics of (i) localized training symbols and (ii) distributed training symbols.
Eliminating the concern for variations in power among different training symbols opened the door to development of another scheme in which all subcarriers are used simultaneously. The modulation symbols assigned to training subcarriers in different frequency zones and time slots are related in a manner that makes channel estimation feasible and reduces computational complexity. In the example in Fig. 1(d), the modulation symbols for the ith subcarriers in the 1st–4th frequency zones are , , and , respectively, in the 1st time slot of the orthogonal scheme, where θks refer to different phases to avoid high peak-to-average power ratio caused by using identical modulation symbols. The modulation symbols in the 2nd time slot become , , and , and the signs of modulation change over time in accordance with the rows of a Hadamard matrix. Thus, the relation between the transmitted and received ith subcarriers can be summarized in matrix form as ri = DΘhi ti, or
where rl,i denotes the received symbol for the ith subcarrier in the lth time slot using sub-Nyquist sampling; hk,i is the required channel response of the ith subcarrier in the kth frequency zone, and D is a Hadamard matrix [12]. It should be noted that the special case in Eq. (1) is easily extended to a general case with 1/M of the Nyquist rate, but M must be 1, 2, or a positive multiple of 4, such that a Hadamard matrix exists. In general, there are M frequency zones, which means that ri and hi are M × 1 vectors, and D and Θ are M × M Hadamard and diagonal matrices, respectively. In accordance with Eq. (1), channel estimation can be realized by . The orthogonality among the rows (and columns) of the matrices D and Θ avoids the necessity of calculating the required matrix inversion for channel estimation; i.e., D−1 = M−1DT and Θ−1 = Θ*, where T denotes the transpose, and ∗ denotes the operation which takes the complex conjugate of each entry. Thus, means the estimation of relative responses in the orthogonal scheme. Specifically, a relative response Mhk,i can be obtained via dividing (DTri)k by , where (DTri)k represents the kth component of the vector DTri; therefore, the required number of division operations is N, which denotes the total number of sent subcarriers. Note that the same number of division operations is also required in the other schemes, in which a received symbol without aliasing is divided by the corresponding sent symbol to acquire the channel response. This implies that the extra computational complexity in the orthogonal scheme comes from only the multiplication between DT and ri, which in fact involves only the addition and subtraction among the components of ri because the entries of DT are either +1 or −1. When M is a power of 2, the number of additions and subtractions in calculating DTri is M log2 M. In the example of M = 4 in Eq. (1), the required 4 log2 4 = 8 operations are r1,i + r2,i = α1, r3,i + r4,i = α2, r1,i − r2,i = β1, r3,i − r4,i = β2, α1 + α2 = (DTri)1, β1 + β2 = (DTri)3 and α1 − α2 = (DTri)4. Since the number of subcarriers in each zone is N/M the orthogonal scheme requires a total of extra N log2 M additions and subtractions, compared to the traditional, localized, and distributed schemes.3. Experiment setup
The experiment setup of DDM-OFDM-PON is plotted in Fig. 2. The optical transmitter was an electro-absorption modulated DFB laser (EML) operating at a center wavelength of 1556 nm. We first measured the channel response using various schemes, and then preprocessed the downstream signals based on the measured channel responses. The electrical driving signals for channel estimation and DDM data transmission were generated using offline signal processing and an arbitrary waveform generator (AWG, Keysight M8195A) with a sampling rate of 28 GSa/s. Using a fast-Fourier transform size of 2048, the OFDM signals occupied a bandwidth of 7 GHz, corresponding to the Nyquist rate of 14 GSa/s. In this experiment, M was set to 32, which resulted in a sub-Nyquist rate of 437.5 MSa/s. The measured spectra of the preprocessed signal are also shown in Fig. 2; the spectrum before sub-Nyquist sampling clearly reveals the signal bandwidth of 7 GHz, but the sub-Nyquist sampling makes the visible bandwidth to only 218.75 MHz (i.e., 7/32 GHz). Different values of M could be examined [5]; however, assigning a value of M = 32 does not lose generality. The number of used subcarriers, cyclic prefix and the modulation format were set to 480 (excluding those cannot be used in DDM [5]), 3/64 and 16 quadrature amplitude modulation (QAM), respectively, resulting in a total capacity of 25 Gbps. An Erbium-doped fiber amplifier (EDFA) was inserted to enable launch power of 9 dBm, and an optical bandpass filter (OBPF) was used to reduce out-of-band amplified spontaneous emission (ASE) noise. Following single-mode fiber (SMF) transmission over 25 km, an APD (AT10EC-J57) was used to detect the optical signals. Instead of using ADCs with sub-Nyquist sampling, the received electrical signal was captured using a real-time oscilloscope (Keysight DSA-X 93204A) at a sampling rate of 80 GSa/s. An offline DSP was then used to emulate the results based on sub-Nyquist sampling, to realize the required sampling delays in the DDM system in a simple yet consistent manner. Besides, the oscilloscope also ensures sufficient analog bandwidth to prevent the significant loss of subcarriers at high frequencies before spectral aliasing [5]. The proposed DSP program performs resampling to 437.5 MSa/s and standard OFDM demodulation without the need for additional signal processing at the receiver. Note that channel estimation was performed using the same sub-Nyquist sampling before the preprocessing of downstream data. In addition, each training set could be used estimate a complete response, which means that the average result from multiple training sets could reduce inaccuracies caused by random noise. The number of training sets in this work ranged from 30 to 120, and dependency on different numbers can be used to evaluate the channel estimation scheme in terms of noise tolerance. Since the laboratory environment is stable, the channel characteristics would remain unchanged. However, the channel estimation would need to be repeated occasionally to update channel characteristics, considering the fact that a practical channel would change slowly with the surrounding environment.
Fig. 2 Experiment setup of APD-based DDM-OFDM-PON. The received spectra (i) before and (ii) after sub-Nyquist sampling.
APD features gain saturation under high input power. Thus, we investigated the channel response using various electrical driving powers and received optical powers (E/O powers), which were respectively controlled using an electrical attenuator (Att) and a variable optical attenuator (VOA), as shown in Fig. 2. Disregarding the DC part, the amplitude of the AC photo-current is proportional to received optical power, which is proportional to the electrical driving voltage of an EML. This means that the power of a detected electrical signal is proportional to the square of the received optical power and to the electrical driving power. Thus, if ΔPe,dB and ΔPo,dB respectively indicate the differences in electrical driving power and received optical power (in dB), compared to a unsaturated reference, then the ideal difference in the detected signal power (without saturation) can be derived as follows:
We originally avoided specially designed training symbols for sub-Nyquist sampling. Instead, we opted for traditional training symbols (as used in Fig. 1(a)) and sampling at the Nyquist rate in our examination of the saturation characteristics of the APD. Figure 3(a) presents the measured responses obtained using 120 training sets with electrical driving power of −1, −5, or −9 dBm, and received optical power of −18 or −22 dBm. The responses presented a drop of approximately 17 dB at 7 GHz, which can be attributed to the AWG. As shown in Fig. 3(a), we set the unsaturated reference as the case with the lowest E/O powers of −9/−22 dBm, the response of which at the lowest frequency was set to 0 dB. Increasing the electrical driving power by 4 dB from that of the unsaturated reference (i.e., E/O powers of −5/−22 dBm) indeed increased the response by approximately 4 dB, as shown in Fig. 3(a). In accordance with Eq. (2), we expected an 8-dB increase in the power of the detected signal in the cases with the E/O powers of −1/−22 and −9/−18 dBm. This increase is slightly greater than that observed in Fig. 3(a), which is indicative of slight saturation. When the E/O powers were increased to −5/−18 and −1/−18 dBm, the increases in the responses should ideally be 12 and 16 dB, respectively. However, the effects of saturation resulted in increases of only ∼11 dB, as shown in Fig. 3(a). We sought to characterize saturation in a simple manner by calculating the ratio of a measured response to the unsaturated reference response (i.e., the case with E/O powers of −9/−22 dBm in Fig. 3(a)) for all subcarriers. We then calculated the arithmetic mean of the ratios, as denoted by (in dB). Finally, represents the degree of saturation. Figure 3(b) illustrates the degree of saturation (under various E/O powers), which clearly depends on ΔPd,dB. When ΔPd,dB is smaller than ∼11 dB, the degree of saturation is limited to < 1 dB. In contrast, when ΔPd,dB exceeds ∼11 dB, the degree of saturation increases dramatically.Fig. 3 (a) Measured responses using traditional training symbols and Nyquist sampling rate, and corresponding (b) degree of saturation
It should be noted that the absolute values of the responses are inconsequential in preprocessing; however, the relative responses at different frequencies (i.e., shape of a frequency response) do matter. Thus, despite the fact that saturation can cause the power of detected signals to deviate from the ideal case, the relative frequency responses in Fig. 3(a) are similar. This implies that saturation has an insignificant impact on preprocessing and DDM performance, when channel responses are estimated using traditional training symbols at the Nyquist rate. In other words, there is no need to adjust the responses in preprocessing when the electrical driving power or received optical power changes.
4. Results and discussion
We plotted the channel responses estimated by the localized, distributed and orthogonal training symbols in Figs. 4(a)–4(c), to investigate the impact of saturation on channel estimation with sub-Nyquist sampling. Each of the schemes in Fig. 4 used 120 training sets with electrical driving power of −1, −5 or −9 dBm and received optical power of −18 or − 22 dBm. As in Fig. 3(a), the response at the lowest frequency with the E/O powers of −9/−22 dBm was set to 0 dB in each case in Fig. 4. The frequency components of training symbols can vary with time (e.g., when using the localized scheme); therefore, we defined the powers as the average power of 32 different training symbols. When applying the localized scheme, the maximum difference in electrical driving power between the training symbols in the lowest and highest frequency zones was ∼11 dB. Under this wide margin, estimations in different frequency zones must deal with different degrees of saturation, resulting in distortion in the relative frequency responses, particularly when the E/O powers are high, such as the E/O powers of −1/−18 or −5/−18 dBm in Fig. 4(a). When applying the distributed scheme, the maximum difference in electrical driving power among the training symbols was only 2 dB. This provides evidence that the cycling shifts applied in the assignment of low-frequency subcarriers to different training symbols equalized the power of the training symbols. It is possible to reduce the difference in power by inspecting relative subcarrier powers and then rearranging the assignment of subcarriers to training symbols accordingly; however, this would require complete knowledge of the relative responses, which would make such a scheme impractical. The difference in power between training symbols when using the proposed distributed scheme was smaller than that of the localized scheme, thereby limiting the amount of distortion in the channel responses due to variations in APD saturation. As shown in Fig. 4(b), the distributed scheme did not produce significant distortion except in the cases involving the highest E/O powers of −1/−18 dBm. Finally, under the orthogonal scheme, the relative power distribution among training symbols was similar to that observed under the traditional scheme, such that the measured responses in Fig. 4(c) are similar to those in Fig. 3(a). In other words, similarity in APD saturation associated with individual orthogonal training symbols rendered the relative frequency responses insensitive to variations in electrical driving power and received optical power.
Fig. 4 Measured responses with sub-Nyquist sampling using various schemes: (a) localized, (b) distributed, and (c) orthogonal
Comparing the effectiveness of channel estimation schemes simply requires a single-value indicator to reveal the degree of dissimilarity between a measured response and a reference response. As mentioned above, relative responses can make a significant difference; therefore, two different responses with the same ratio for all subcarriers would indicate that they are equivalent from the aspect of preprocessing. Thus, if γn denotes the ratio of a measured response to a reference response for the nth subcarrier, we can define the dissimilarity according to variance in the normalized response ratio, as follows:
where N is the number of subcarriers, and is the mean value of γn. In Eq. (3), normalization using makes the dissimilarity irrelevant to a common scaling of response. In the discussion of dissimilarity, the reference response was measured using 120 training sets with E/O powers of −1/−18 dBm using traditional training symbols at the Nyquist rate. These E/O power levels were selected because the received power of −18 dBm is close to the sensitivity at a bit-error rate (BER) of 10−3 and driving power of −1 dBm is the optimal value for data modulation.Figure 5 plots the measured dissimilarities as functions of electrical driving and received optical powers, where the different columns indicate different estimation schemes, and the 1st and 2nd rows represent cases respectively using 120 and 60 training sets. The reference case is marked by a star ([img]) in Fig. 5(a). As shown in Figs. 3(a) and 4, lowering the electrical power and/or optical power led to an increase in noise-related fluctuations in the responses at higher frequencies, due to a reduction in the received power and signal-to-noise ratio (SNR). As a consequence, we see an increase in the degree of dissimilarity associated with traditional training symbols following a decrease in either optical or electrical power, as shown in Fig. 5(a). Figure 5(b) shows that lowering the electrical power and/or optical power in the localized scheme decreases the degree of dissimilarity by reducing saturation. Moreover, the distributed scheme reduces the degree of dissimilarity in Fig. 5(c), compared to the localized scheme. Nonetheless, the distributed scheme fails to fully eliminate differences in saturation due to the remaining variations in power among training symbols, as shown in Fig. 4(b). A moderate reduction in electrical power and/or optical power in the distributed scheme may still be helpful in reducing the degree of dissimilarity by suppressing the residual difference in saturation. This trade-off between the effects of noise and saturation resulted in the lowest dissimilarity in Fig. 5(c). Finally, the orthogonal scheme in Fig. 5(d) resulted in less dissimilarity than did the other two schemes with sub-Nyquist sampling, with values similar to those in Fig. 5(a). This demonstrates the efficacy of the orthogonal scheme in overcoming issues caused by APD saturation. In addition, the similarity between Figs. 5(a) and 5(d) suggests the efficacy of the orthogonal scheme even in a different transmission configuration (e.g., different fiber length and/or a different APD). Furthermore, reducing the number of training sets lowers tolerance of noise, which increased the degree of dissimilarity under all of the schemes. The pronounced effect of saturation in the localized schemes reduced the influence of the number of training sets on the degree of dissimilarity, particularly when the driving and/or received powers were relatively high (i.e., in the regions with ΔPd,dB >∼ 10 dB) in Fig. 5(b). Dissimilarities imposed by the distributed scheme were insensitive to the number of training sets in smaller regions, in cases where ΔPd,dB exceeded roughly 15 dB, due to smaller differences in saturation. In Figs. 5(b) and 5(c), the inference that the influence of saturation dominates dissimilarity in these regions is also consistent with the fact that the curves of constant dissimilarities are nearly straight lines with a slope of −1/2, in accordance with Eq. (2). On the other hand, when these dissimilarities were dominated by noise, the curves of constant values in Fig. 5 tended to be steeper (i.e., with slopes of < −1/2), which indicates that the dissimilarity was less sensitive to the received optical power. This may be explained by the fact that a portion of the noise is contributed in the optical domain, such that an increase in optical power has less of an effect in enhancing the SNR. Moreover, if the powers are extremely low (e.g., ΔPd,dB < 1 dB), then the degree of dissimilarity associated with all of the schemes are comparable because the low SNR is the only determining factor, as shown in Fig. 5.
Fig. 5 Dissimilarities in channel responses as functions of driving power and received power with Nyquist sampling using (a) traditional scheme, and with sub-Nyquist sampling using (b) localized, (c) distributed and (d) orthogonal schemes
We evaluated the corresponding preprocessed DDM signals following 25-km SMF transmission with sub-Nyquist sampling based on channel responses estimated using the various schemes. Note that the electrical driving power of the preprocessed signals was fixed at −1 dBm. The measured BER curves of the DDM signals are presented in Figs. 6(a)–6(c), respectively using E/O powers of −1/−18, −1/−21 and −9/−21 dBm for channel estimation with 120 training sets. Furthermore, sub-Nyquist sampling does not impose a performance penalty (in theory) [4,5]; therefore, we also show the BER curve of a normal OFDM signal without the DDM scheme (i.e., M = 1) in Fig. 6 for comparison. When the E/O powers were relatively high (i.e., ΔPd,dB = 16 dB), we can see in Fig. 6(a) that the signals preprocessed according to responses estimated using the traditional scheme (i.e, based on the reference response) performed as well as the case without the DDM scheme. This confirms that the reference response is sufficient for preprocessing in the DDM system. However, the response estimated using the localized scheme did not allow the DDM signal to achieve a BER of 10−3, due to severe distortion in channel estimation, as shown in Fig. 6(a). This severe distortion can be alleviated by the distributed scheme, thereby allowing the DDM signal to reach a BER of 10−3. However, this scheme still suffers from a ∼3.5-dB penalty in sensitivity. As shown in Fig. 5(d), the orthogonal scheme did not cause any issues due to APD saturation, thereby allowing the DDM signal to perform as well as the normal OFDM signal in Fig. 6(a). As shown in Fig. 6(b), lowering the received optical power to −21 dBm (i.e., ΔPd,dB = 10 dB) did not impose a significant penalty for the traditional or orthogonal schemes. Due to the fact that the difference in the degree of saturation was suppressed in Fig. 6(b), the penalty in sensitivity was reduced to ∼1 for the distributed scheme and 2 dB for the localized scheme. As shown in Fig. 6(c), when the E/O powers was reduced to −9/−21 dBm (i.e., ΔPd,dB = 2 dB), all of the schemes suffered a ∼2-dB penalty in sensitivity, thereby confirming that the estimated results are determined solely by SNR.
Fig. 6 Measured BER curves based on channel responses estimated using E/O powers of (a) −1/−18, (b) −1/−21 and (c) −9/−21 dBm (M = 1 indicates normal OFDM without DDM scheme)
Figure 6 indicates the sensitivity of normal OFDM (about −19.1 dBm), whereas Fig. 7 summarizes the penalty in the sensitivity of the DDM signals as a function of dissimilarity in estimated channel responses. The channel responses in Fig. 7 were estimated using high, moderate, and low E/O powers of −1/−18, −1/−21 and −9/−21 dBm respectively under various numbers of training sets. The penalty was reduced to less than 1 dB, when the dissimilarity value was less than 10−2.5. The traditional and orthogonal schemes achieved a penalty of < 1 dB in only 30 sets when using the condition of high E/O powers. Using the distributed scheme, the condition of high E/O powers resulted in a penalty of > 3 dB. The condition of moderate E/O powers reduced the penalty to less than ∼1 dB; however, this required ≥90 training sets. When the estimation condition was set to low E/O powers, the penalty under the distributed scheme exceeded 2 dB. When using the localized scheme, the severe effects of saturation under condition of high E/O powers prevented the achievement of a BER of 10−3; and despite using lower powers in estimation, the penalty could not be reduced to less than 2 dB. Finally, when using the distributed and localized scheme, superior channel estimation and less sensitivity penalty required a reduction in E/O powers. As a result, the number of training sets was critical. In contrast, inaccuracies in channel estimation using the orthogonal scheme could be reduced by employing higher E/O powers, thereby reducing the required number of training sets.
5. Conclusions
In this paper, we propose distributed and orthogonal channel estimation schemes for an APD-based DDM system under the constraint of sub-Nyquist sampling. The severe deviations of channel estimation imposed by the localized scheme were largely overcome by the proposed scheme. The orthogonal scheme proved to be largely unaffected by the saturation of APD, which indicates that it is not necessary to change the estimation conditions from those used in DDM data transmission. Using APD and sub-Nyquist sampling at 437.5 MSa/s, the distributed and orthogonal schemes respectively reduced the penalty in the sensitivity of the 25-Gbps DDM-OFDM signal to 1 and 0 dB. The accurate channel estimation achieved using the proposed scheme makes it possible to increase the loss budget of a 25-Gbps APD-based DDM-OFDM-PON to 28 dB.
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