Adaptively loaded SP-offset-QAM OFDM for IM / DD communication systems

In this paper, we propose adaptively loaded set-partitioned offset quadrature amplitude modulation (SP-offset-QAM) orthogonal frequency division multiplexing (OFDM) for low-cost intensity-modulation direct-detection (IM/DD) communication systems. We compare this scheme with multi-band carrier-less amplitude phase modulation (CAP) and conventional OFDM, and demonstrate >40 Gbit/s transmission over 50-km single-mode fiber. It is shown that the use of SP-QAM formats, together with the adaptive loading algorithm specifically designed to this group of formats, results in significant performance improvement for all these three schemes. SP-offset-QAM OFDM exhibits greatly reduced complexity compared to SP-QAM based multi-band CAP, via parallelized implementation and minimized memory length for spectral shaping. On the other hand, this scheme shows better performance than SP-QAM based conventional OFDM at both back-to-back and after transmission. We also characterize the proposed scheme in terms of enhanced tolerance to fiber intra-channel nonlinearity and the potential to increase the communication security. The studies show that adaptive SP-offset-QAM OFDM is a promising IM/DD solution for mediumand long-reach optical access networks and data center connections. © 2017 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.4080) Modulation. References and links 1. Z. Li, L. Yi, X. Wang, and W. Hu, “28 Gb/s duobinary signal transmission over 40 km based on 10 GHz DML and PIN for 100 Gb/s PON,” Opt. Express 23(16), 20249–20256 (2015). 2. X. Ouyang, W. Jia, P. Gunning, P. D. Townsend, and J. Zhao, “Experimental demonstration and field-trial of an improved optical fast OFDM scheme using intensity modulation and full-field detection,” J. Lightwave Technol. 33(20), 4353–4359 (2015). 3. K. Zhong, X. Zhou, T. Gui, L. Tao, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. 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Vol. 25, No. 18 | 4 Sep 2017 | OPTICS EXPRESS 21603 #302539 https://doi.org/10.1364/OE.25.021603 Journal © 2017 Received 17 Jul 2017; revised 18 Aug 2017; accepted 24 Aug 2017; published 28 Aug 2017 13. H. Tang, S. Fu, H. Liu, M. Tang, P. Shum, and D. Liu, “Low-complexity carrier phase recovery based on constellation classification for M-ary offset-QAM signal,” J. Lightwave Technol. 34(4), 1133–1140 (2016). 14. T. H. Nguyen and C. Peucheret, “Kalman filtering for carrier phase recovery in optical offset-QAM Nyquist WDM systems,” IEEE Photonics Technol. Lett. 29(12), 1019–1022 (2017). 15. A. Saljoghei, F. A. Gutierrez, P. Perry, D. Venkitesh, R. D. Koipillai, and L. P. Barry, “Experimental comparison of FBMC and OFDM for multiple access uplink PON,” J. Lightwave Technol. 35(9), 1595–1604 (2017). 16. J. Zhao and A. D. Ellis, “Transmission of 4-ASK optical fast OFDM with chromatic dispersion compensation,” IEEE Photonics Technol. Lett. 24(1), 34–36 (2012). 17. E. Giacoumidis, A. 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Introduction
The ever-growing Internet content is driving the rapid development of optical access networks.Intensity modulation and direct detection (IM/DD) systems are preferred in these applications due to their simplicity and low cost, although some other technologies have also been proposed to push the performance beyond the limit of IM/DD systems at the expense of additional components/complexity at the transmitter and/or the receiver [1,2].Traditional IM/DD systems are based on on-off keying signal format.With the increasing bandwidth/reach demands, advanced signal formats including 4-level pulse amplitude modulation (PAM4), carrier-less amplitude phase modulation (CAP), and orthogonal frequency division multiplexing (OFDM) have been investigated [3][4][5][6].In general, singlecarrier formats, such as PAM4 and CAP, have a lower peak-to-average power ratio (PAPR) and thus have relaxed requirement on quantization resolution, device linearity, etc.Therefore, they may be suitable for high-capacity short-reach connections.However, dispersion-induced channel fading exists for medium and long distances (>40 km), and multi-carrier formats are preferred due to their higher dispersion tolerance.In addition, by using adaptive loading, multi-carrier signals can maximize the capacity of IM/DD systems in the presence of dispersion-induced spectral nulls.In the literature, IM/DD based OFDM and multi-band CAP have been extensively investigated.
In this paper, we propose adaptively loaded set-partitioned offset quadrature amplitude modulation (SP-offset-QAM) OFDM for IM/DD systems.This scheme simultaneously explores the advantages of SP-QAM formats and offset-QAM (de-)multiplexing.By properly selecting the constellation points, SP-QAM formats can achieve better power efficiency than conventional QAM formats at the same data rate.Although this type of formats has been studied in coherent systems [7,8], few works in IM/DD systems have been done until recently.In [9], 4-dimensional coded PAM4 was proposed in point-to-point short-reach links, enabling high receiver sensitivity and low latency.In [10], we proposed, for the first time, an adaptive loading algorithm specific to this group of formats.On the other hand, offset-QAM OFDM can greatly relax the requirement of signal spectrum for subcarrier orthogonality and has been proposed in coherent transmission systems [11][12][13][14].In [15], it has been shown that offset-QAM OFDM is more favorable than conventional OFDM as upstream signals in optical access networks, because it can greatly relax the requirement of time and frequency synchronization between optical network units.
In this paper, we compare the proposed scheme with multi-band CAP and conventional OFDM, modulated with either conventional QAM or SP-QAM formats.It is shown that the use of SP-QAM formats, together with the adaptive loading algorithm specifically designed to this group of formats, results in significant performance improvement for all multi-carrier systems.SP-offset-QAM OFDM exhibits greatly reduced complexity compared to SP-QAM based multi-band CAP, and better performance than SP-QAM based conventional OFDM.Although not specifically investigated, the proposed scheme is also better than SP-QAM based Nyquist FDM, which can be viewed as a special case of multi-band CAP or offset-QAM OFDM.The proposed scheme can also have better performance than optical fast OFDM, because fast OFDM, although based on simple real-valued operations, has the same spectral profile for orthognality and the same requirement of cyclic prefix as conventional OFDM [16,17].The studies give clear implications that the proposed scheme is a very promising solution for medium-and long-reach access networks and data center connections.We firstly give an overview of the principle of adaptively loaded SP-offset-QAM OFDM, as depicted in Fig. 1.Different format levels are allocated to different subcarriers according to the signal-to-noise ratio (SNR).For each subcarrier, every two OFDM symbols are jointly encoded to generate the SP-QAM format; the quadrature tributary of the SP-QAM signal is then delayed by T/2 with respect to the in-phase tributary to generate the SP-offset-QAM signal, where T is the period of one OFDM symbol.SP-offset-QAM OFDM multiplexes multiple SP-offset-QAM signals in the frequency domain, with π/2 phase difference between adjacent subcarriers.This scheme can greatly relax the required signal spectrum for subcarrier orthogonality and avoid the infinite spectral tails of the sinc function employed in the conventional OFDM.On the other hand, it avoids the guard band in the multi-band CAP (as will be studied in this paper) and/or the increasing complexity of pulse shaping as the spectral shape approaches to the rectangular function.In the following, we will describe detailed implementations of SP-offset-QAM OFDM, as depicted in Fig. 2.

Encoding of the SP-QAM formats
We firstly describe the principle of the SP-QAM formats.In this paper, every two OFDM symbols of the same subcarrier are jointly encoded to generate the SP-QAM formats, but the principle can be extended to jointly encode two subcarriers in each OFDM symbol.Figure 3 depicts the constellation of SP-128QAM, as an example.The two consecutive symbols of a subcarrier construct a 4-dimensional constellation: the in-phase and quadrature tributaries of Symbol #1 and the in-phase and quadrature tributaries of Symbol #2.In conventional 16QAM, for an arbitrary point in Symbol #1, any point in Symbol #2 can be selected.The number of constellation points per two symbols is 16 × 16 = 256.In contrast, SP-QAM only uses a subset of points in order to increase the Euclidean distance: when the point in Symbol #1 is a solid (or empty) point, only the solid (or empty) points in Symbol #2 can be selected.The number of possible constellation points per two symbols is 16 × 8 = 128.The Euclidean distance is increased by 2 1/2 while the spectral efficiency (SE) is reduced from 4 to 3.5 per symbol.Other SP-QAM formats (SP-2QAM, SP-8QAM, SP-32QAM, SP-512QAM, and SP-2048QAM) can also be designed accordingly [10], with the SEs of 0.5, 1.5, 2.5, 4.5, and 5.5, respectively.These SP-QAM formats may not be optimal in terms of power efficiency in the 4-dimensional space, but their data mapping is simple: for SP-QAM with 2 2m−1 constellation points (per two symbols), m bits can be used to encode the constellation points in Symbol #1 in the same way as in the conventional 2 m QAM, while another m-1 bits are used to encode the points in Symbol #2 given the mapping information in Symbol #1.

Adaptive loading algorithm for the SP-QAM formats
In IM/DD systems, the channel frequency response is not even, especially when there are dispersion-induced spectral nulls, as will be discussed later.Therefore, adaptive loading is used to allocate format levels and power, according to the SNR of the subcarriers, to maximize the capacity.Conventional Chow's algorithm [18] is a well-known technique to approach the optimal water-filling solution with discrete distributed format levels.However, this algorithm is based on the conventional QAM.It cannot be applied to the SP-QAM formats and should be modified according to the symbol error rates (SERs) of these new formats.The key differences between the SERs of the SP-QAM formats and those of the conventional QAM are: 1) the increased Euclidean distance by 2 1/2 ; 2) the loss of the SE by 0.5 bit; 3) the coefficient to evaluate the average number of constellation points that give the minimal Euclidean distance.Therefore, we can derive the SER of SP-QAM (SE = 2 m-1/2 ) based on the SER of conventional QAM (SE = 2 m ) as: where K represents the average number of points that achieve the minimal distance, and is bounded by 12 [10].Assume that the SNR of the n th subcarrier in OFDM (or sub-band in multi-band CAP) is SNR n , the number of bits on that subcarrier can be obtained by re-writing Eq. (1) as: where SER pre-set is the pre-set SER.γ is a parameter, determined similarly as in the conventional Chow's algorithm.After the bit allocation, the power of each subcarrier is adjusted by using the precise SERs of the SP-QAM formats [10].In practice, SNR n can be estimated using a training sequence before the payload is sent.This bit and power loading algorithm was originally proposed for SP-QAM based conventional OFDM [10], but it can be applied to any multi-carrier systems using the SP-QAM formats, including offset-QAM OFDM and multi-band CAP studied in this paper.

Multiplexing of SP-offset-QAM OFDM
After the generation of the SP-QAM signals, their in-phase and quadrature tributaries are processed separately, as shown in Fig. 2. The subcarrier spacing of offset-QAM OFDM is equal to the symbol rate per subcarrier, and so the multiplexing can be realized using parallelized processing.We assume ai,n is the SP-QAM data at the n th subcarrier in the i th OFDM symbol, n = 1, 2…M, where M is the number of data subcarriers.The phases of tributaries are firstly adjusted: for the in-phase tributary, the phases of even subcarriers are set to be 0 (or π) while those of odd subcarriers are set to be π/2 (or 3π/2).Conversely, for the quadrature tributary, the phases of odd subcarriers are set to be 0 (or π) while those of even subcarriers are set to be π/2 (or 3π/2).Frequency-domain Hermitian extension is then applied to generate a real time-domain signal.To facilitate the illustration, we assume the point size of the fast Fourier transform (FFT), N, is equal to 2M + 2 (as used in this paper).The data after the Hermitian extension, bi,n, are represented by: , The k th time-domain sample in the i th OFDM symbol, s(i⋅N + k), can be written as: Therefore, in Fig. 2, the implementation of the FIR filter can be parallelized.The complexity of an N-point FFT is O{N/2•log 2 (N)} while that of N parallelized FIR filters is ~(J/2 + 1)⋅N, considering the symmetric property of the pulse shape, where J is the memory length of the filter.As will be shown later, J = 2 is sufficient for pulse shaping in the proposed scheme.We should note that multi-band CAP is also investigated for comparison in this paper.This scheme, however, cannot be realized using parallelized processing in Fig. 2, unless there is no spectral guard band between sub-bands (i.e.Nyquist FDM).In order to clearly see this, we assume that the number of sub-bands is still N but the period per symbol in the time domain (in the discrete form) is N + G.The k th time-domain sample in the i th CAP symbol, s(i⋅(N + G) + k), k = 0,1,…,(N + G-1), can be derived as: Equation ( 6) cannot be simplified via an FFT and parallelized FIRs if G is not equal to zero.
The complexity to generate a multi-band CAP signal is thus O{(J/2 + 1)⋅N 2 }, higher than that of SP-offset-QAM OFDM.Similarly, the de-multiplexing at the receiver also has the complexity of O{(J/2 + 1)⋅N 2 }.The comparison above is based on the assumption that the number of sub-bands in multi-band CAP is the same as that of the subcarriers in OFDM.In practice, the number of sub-bands in multi-band CAP is not large, i.e. 8 or 16, due to the increasing complexity as discussed above.Under a small number of sub-bands, multi-band CAP may have a lower PAPR than OFDM, and possibly better performance at back-to-back.However, a small number of sub-bands reduces the resolution of adaptive loading, especially when there are dispersion-induced spectral nulls.Therefore, as will be studied in Section 3, the performance after transmission is significantly degraded.

Dispersion-induced spectral nulls
The generated signal after digital-to-analogue conversion, s(t), modulates a CW light and transmits over fibers.At the receiver, the received optical signal is represented by (D + r(t)), where D is the DC bias and r(t) is the signal with dispersion.Note that this model is applied to intensity modulation using Mach-Zehnder modulator (MZM) in the linear region, as in our experiment, and should be modified for other transmitters, e.g.electro-absorption modulator.
After the square-law detection, the received electronic signal can be written as: where Re[⋅] extracts the real part of the signal.The term of interest in Eq. ( 7) is the DC-signal beating, whose spectrum can be written: )) where F{⋅} (F −1 {⋅}) is the operator of (inverse) Fourier transform.S p (ω) is the spectrum of s(t) at the positive frequency (ω ≥ 0) and is zero for ω < 0. β 2 is the dispersion parameter and L is the fiber length.It is clear that there are spectral nulls arising from the term of cos(β 2 L/2 × ω 2 ).As an example, when β 2 = 20 ps 2 /km and L = 50 km, the positions of the spectral nulls are calculated at 8.9 GHz, 26.7 GHz, and so on.

De-multiplexing of SP-offset-QAM OFDM
After the photodiode and analogue-to-digital conversion, the start-of-frame symbol of the received signal is identified and the OFDM symbols are precisely synchronized.The signal is then serial-to-parallel (S/P) converted in the digital domain with an access time of N/2, that is, the in-phase tributary accesses the sampled points from times i⋅N, while the quadrature tributary accesses the sampled points from times (i + 1/2)⋅N.The outputs pass through FIR filters, which are matched to those at the transmitter.An FFT is then applied to transform the signals to the frequency domain.Without the loss of generality, we only derive the in-phase tributary of the m th subcarrier in the i th OFDM symbol at the output of the FFT as: where E(q⋅N + k) is the discrete version of E(t) in Eq. ( 7), and is approximated by the DCsignal beating term with the spectrum shown in Eq. ( 8).h receiver_filter ((i-q)⋅N-k) is the impulse response of the k th matched filter and is equal to h filter (q⋅N + k-i•N).From Eqs. ( 4), ( 8) and ( 9), we can derive , where C i,m is real and includes the contribution of all crosstalk (from the in-phase tributary of the (m + 1) th and the (m-1) th subcarriers, and the quadrature tributary of the m th , the (m + 1) th , and the (m-1) th subcarriers).H b (m) represents the back-to-back response, including the lowpass filtering effect of optical/electronic components.H d (⋅) is the dispersion-induced channel response: From Eq. ( 10), we can see that the crosstalk term, C i,m , is orthogonal to the desirable signal where m = 1, 2…M.In practice, the estimation of H b (m) and H d (m) is different from that in conventional OFDM, and requires particular design due to the nonlinear operator Re[⋅].In this paper, we use the methods in [12] to estimate the responses.

Decoding of the SP-QAM formats
The decoding of the SP-QAM formats requires joint consideration of two consecutive OFDM symbols of the same subcarrier, namely Symbol #1 and Symbol #2.The recovered signal in these two symbols constructs a 4-dimensional vector.We calculate the Euclidean distances between this vector and the means of all possible constellation points (in the 4-dimensional space), and find the point that gives the minimal distance.For example, in SP-128QAM (derived from two 16QAM symbols), 128 distances are calculated and compared per two symbols.This decoding is more complicated than the conventional QAM.In conventional 16QAM, Symbol #1 and Symbol #2 are decoded individually, and the number of calculated distances is 2 × 16 = 32.However, there are methods to reduce the complexity.For example, in SP-128QAM, Symbol #1 and Symbol #2 can also be decoded individually to find 4 minimal distances for each symbol.These two symbols are then jointly considered to get the minimal distance in the 4-dimensional space.In this design, the complexity is greatly reduced to 16 × 3 = 48.Considering that other modules (FFT, equalization etc.) are the same for conventional QAM and SP-QAM formats, their overall system complexities are still comparable.

Experimental setup
Figure 4 shows the experimental setup.In this paper, we implemented three schemes, namely offset-QAM OFDM, conventional OFDM, and multi-band CAP, all modulated with either conventional QAM or SP-QAM formats.The number of data subcarriers (M in Section 2) was 63 and that after the frequency-domain Hermitian extension (N in Section 2) was 128.
The subcarriers at the DC and the highest frequency were zero padded.Conventional OFDM and offset-QAM OFDM were multiplexed via an FFT with a point size of 128, while multiband CAP was realized by convolving signals with filters and summing up.For adaptive loading, 8QAM format was firstly used to estimate the SNR.The number of allocated bits was calculated using Eqs.( 2) and ( 3) for the SP-QAM formats, or Chow's algorithm for conventional QAM.Cyclic prefix (CP) with varied lengths was added to conventional OFDM, while offset-QAM OFDM and multi-band CAP did not require the CP.On the other hand, multi-band CAP employed 6.25% spectral guard band between sub-bands, which was not needed in conventional OFDM and offset-QAM OFDM.The spectra of subcarriers in offset-QAM OFDM and multi-band CAP had a profile of square-root-raised-cosine (SRRC) function, and unless otherwise stated, had roll-off factors of 0.5 and 0.05, respectively.The PAPR was optimized by clipping.The signal was uploaded into a 24-GS/s arbitrary waveform generator (AWG) with ~6.5-GHz analogue bandwidth (without the sinc roll-off).
Pre-equalization was included to compensate the limited bandwidth of the AWG and the sinc roll-off in the D/A conversion.A laser with ~5-MHz laser linewidth was used to generate the CW light.A MZM was used for modulation and the input electrical peak-to-peak voltage was ~Vπ /2.The optical signal was amplified by an Erbium doped fibre amplifier (EDFA) before being transmitted over 50-km single mode fiber (SMF).Unless otherwise stated, the signal launch power into the fiber was 10 dBm.At the receiver, the optical signal was detected by a photodiode.A variable optical attenuator (VOA) was used to fix the received power at −3 dBm for all schemes.The detected signal was electrically amplified, sampled by a 50-GS/s oscilloscope, and processed by digital signal processing, as discussed in Section 2. Around 1 million bits were measured and the bit error rate (BER) was obtained by direct error counting.We firstly investigated the back-to-back performance.The PAPR and the bias for intensity modulation were optimized for three schemes.The optimal values in offset-QAM OFDM and conventional OFDM were the same and found to be 9 dB and 2.4 V, respectively.The optimal PAPR of multi-band CAP was slightly lower and was ~8.5 dB.These values were used in all measurements at back-to-back.Figure 5(a) shows the BER versus the signal data rate of adaptively loaded conventional offset-QAM OFDM (using Chow's algorithm) and SPoffset-QAM OFDM (using the algorithm of Eqs. ( 2) and ( 3)).The performances of offset-8QAM and offset-16QAM for all subcarriers are also shown, for comparison.In these two cases, 54 out of 64 data subcarriers were modulated so that the data rates were ~30 Gbit/s and 40 Gbit/s for offset-8QAM and offset-16QAM, respectively.At back-to-back, the channel response was flat without spectral nulls.Therefore, the system with adaptively loaded conventional offset-QAM only got slight performance improvement compared to systems with a single format for all subcarriers.Adaptive loading of the SP-offset-QAM formats greatly improved the performance, with one order of magnitude reduction in the BER.

Back-to-back performance
Figure 5(b) illustrates the performances of multi-band CAP and the proposed SP-offset-QAM OFDM.Adaptive loading was employed in all cases.In multi-band CAP, the spectral guard band was 6.25% of the symbol rate per sub-band; the roll-off factor of the spectral shape was 0.05; and the memory length of the FIR filters was 40.On the other hand, in SPoffset-QAM OFDM, there was no spectral guard band; the roll-off factor of the spectrum was 0.5; and the memory length was the same as that in multi-band CAP.Due to the spectral guard band, the average number of bits per sub-bands in multi-band CAP was larger than that in SP-offset-QAM OFDM (by 6.25%), in order to achieve the same data rate.From Fig. 5(b), we can see that the SP-QAM formats, using the algorithm of Eqs. ( 2) and ( 3), also resulted in improved performance in multi-band CAP.SP-QAM based multi-band CAP had similar performance as the proposed SP-offset-QAM OFDM.We further compared SP-offset-QAM OFDM and SP-QAM based multi-band CAP. Figure 6(a) shows the BER versus the roll-off factor of the signal spectrum at 40 Gbit/s.The memory length of the FIR filters was fixed as 40.In SP-offset-QAM OFDM, the phase of the crosstalk from adjacent subcarriers is orthogonal to that of the signal (see Eq. ( 10)).Therefore, the orthogonality was maintained despite the overlapped spectrum, and the performance was insensitive to the roll-off factor of the signal spectrum.In contrast, multiband CAP with 6.25% guard band exhibited significantly degraded performance when the roll-off factor exceeded 0.15, due to the crosstalk between sub-bands.Reducing the roll-off factor eliminated the spectral overlap.However, as the roll-off factors were reduced, the signal pulse approached to the sinc function with infinite tails, and a fixed memory length of 40 was not sufficient to get the desirable spectral profile.Therefore, there was an optimal rolloff factor of 0.05. Figure 6(b) shows the BER versus the memory length of the FIR filters for SP-offset-QAM OFDM with a roll-off factor of 0.5 and SP-QAM based multi-band CAP with a roll-off factor of 0.05.It is seen that multi-band CAP required a long memory length (> 30) to achieve the optimal performance.This length was greatly reduced in SP-offset-QAM OFDM, which still gave an acceptable penalty when the memory length was reduced to 2. Also note that the complexity of multi-band CAP is ~O{(J/2 + 1)⋅N 2 }, while the parallelized SP-offset-QAM OFDM has the complexity of ~O{N/2•log 2 (N) + (J/2 + 1)⋅N}.Therefore, the proposed scheme has significantly reduced complexity, compared to multi-band CAP.
Next, we compared the back-to-back performance of SP-QAM based conventional OFDM and the proposed scheme.Figure 7(a) shows the BER versus the signal data rate of conventional OFDM, SP-QAM based conventional OFDM, and SP-offset-QAM OFDM.In the former two schemes, two cases were investigated and the lengths of CP were 0 and 8, respectively.On the other hand, CP was not required in SP-offset-QAM OFDM.Note that the average number of bits per subcarrier in conventional OFDM with a CP length of 8 was larger due to the CP-induced overhead.From the figure, it is seen that the performance of conventional OFDM was also improved by using the adaptively loaded SP-QAM formats.However, SP-QAM based conventional OFDM still exhibited a penalty, compared to the proposed scheme, regardless of the length of CP.In order to see this, Fig. 7(b) shows the performance versus the length of CP in conventional OFDM under either a fixed average number of bits per subcarrier (i.e. a fixed 40-Gbit/s raw data rate including the CP) or a fixed net data rate excluding the CP.The BER of 40-Gbit/s SP-offset-QAM OFDM without any CP is also shown.Conventional OFDM uses the sinc function with infinite spectral tails in the frequency domain.The low-pass filtering effects in the system cut off the spectral tails of subcarriers, thus breaking the orthogonality and inducing inter-symbol interference (ISI)/inter-carrier interference (ICI).As shown by the triangles in Fig. 7(b), increasing the length of CP could mitigate the impairment but it also reduced the net data rate.In order to get the same net data rate as in SP-offset-QAM OFDM, the number of bits per subcarrier should be larger, which in turn increased the BER under fixed SNRs.Therefore, the overall performance could not be enhanced by increasing the length of CP under a fixed net data rate, as shown by the squares in Fig. 7(b).These results imply that SP-offset-QAM OFDM has better performance than SP-QAM based conventional OFDM.

Performance after the transmission
In this subsection, we investigated the performance after 50-km SMF transmission.Unless otherwise stated, the signal launch power into the fiber was 10 dBm.The PAPR and the bias for intensity modulation were re-optimized.The optimal values of offset-QAM OFDM and conventional OFDM were still the same and found to be ~10 dB and 2.4 V, respectively.This optimal PAPR was slightly higher than that at back-to-back.This was because the signal after transmission was spread due to dispersion and the DC power was also reduced due to the Rayleigh scattering, resulting in a higher modulation index after transmission.Therefore, the PAPR was set higher to enable the optimal performance.On the other hand, the optimal PAPR in multi-band CAP was slightly lower than that of OFDM and was ~9.5 dB.We firstly investigated the performance of offset-QAM OFDM. Figure 8(a) shows the BER versus the signal data rate after transmission.Figure 8(b) depicts the allocated SE over subcarriers at 40 Gbit/s, as well as the measured SNR profile.It is clearly seen that the dispersion resulted in a spectral null.The position of nulls, fnull, could be estimated by cos(β 2 L/2 × (2πf null ) 2 ) = 0 and was calculated to be ~9 GHz, where β 2 was assumed to be 20 ps 2 /km and L was 50 km.When a single format was used for all subcarriers, the performance of subcarriers around the spectral null was significantly degraded, resulting in very poor overall performance.Conventional adaptive algorithm allocated formats according to the SNR with low-level formats around the spectral null.Consequently, the performance was improved.However, the supported data rate was still limited to 35 Gbit/s at the BER of 3.8 × 10 −3 .The proposed SP-offset-QAM OFDM further improved the performance and 42.5 Gbit/s could be achieved at the BER of 3.8 × 10 −3 .We then compared the proposed scheme with multi-band CAP, as shown in Fig. 9(a).Similar to back-to-back, adaptive loading of SP-QAM formats improved the performance of multi-band CAP system.SP-QAM based multi-band CAP had similar performance as the proposed SP-offset-QAM OFDM.This was in contrast to conventional OFDM that exhibited poorer performance than the other two schemes.The spectra of multi-band CAP are concentrated without infinite spectral tails.Therefore, the orthogonality can be maintained provided that the spectra between sub-bands do not overlap.Note that the number of subbands in multi-band CAP was equal to that of subcarriers in OFDM for fair comparison.When a smaller number of sub-bands is used, the performance of multi-band CAP might be better than that of OFDM at back-to-back, due to a lower PAPR.However, a smaller number of sub-bands results in degraded transmission performance.Figure 9(b) depicts the BER of multi-band CAP when the number of sub-bands (after Hermitian extension) was 128, 64, and 32.We could notice that the performance degraded as the number of sub-bands decreased.At the BER of 3.8 × 10 −3 , the supported data rates were 42.5, 38, and 33 Gbit/s, when the number of sub-bands was 128, 64, and 32, respectively.
Figure 10(a) shows the performance versus the roll-off factor of the signal spectrum at 30 Gbit/s for SP-QAM based multi-band CAP and SP-offset-QAM OFDM.The memory length was set to be 40.This figure gives a similar conclusion, as in Fig. 6(a): the performance of SP-offset-QAM OFDM was insensitive to the roll-off factor of the signal spectrum; the performance of multi-band CAP degraded rapidly when the roll-off factor exceeded 0.15 and the optimal value was around 0.05. Figure 10(b) depicts the performance versus the memory length of the FIR filters.As expected, due to a small roll-off factor, multi-band CAP required a long memory length (> 30) to achieve the optimal performance.It is interesting to note that the performance of SP-offset-QAM OFDM after transmission was insensitive to the memory length, while there was still a visible penalty for the memory length of 2 at back-to-back, as shown in Fig. 6(b).It could be attributed to the fact that the signal has been degraded by other impairments in the transmission, which overwhelmed the effect of the memory length.One possible impairment arose from the rapid variations in the frequency response (induced by the spectral null), thus the SRRC function, used as the signal spectrum for orthogonality, could not be ideally maintained if the frequency response imposed on a subcarrier was no longer a constant.The results in Fig. 10 confirm the advantages of the proposed scheme over multiband CAP after transmission.Figure 11 illustrates the performance of conventional OFDM and SP-offset-QAM OFDM.Similar to Fig. 7, two cases were investigated in conventional OFDM, and the lengths of CP were 0 and 8, respectively.The average number of bits per subcarrier in OFDM with a CP length of 8 was larger due to the additional overhead.It was seen that the performance of SP-QAM based conventional OFDM was not as good as that of the proposed scheme, regardless of the length of GI.This was because offset-QAM OFDM was more tolerant to ISI and ICI by avoiding the long spectral tails of the sinc function.Figures 11(b  One interesting result in Fig. 11(a) shows that the performance of conventional OFDM with the CP length of 8 was better than that without the CP, no matter whether the SP-QAM formats were used.This is in contrast to Fig. 7(a), in which a longer CP resulted in slightly degraded performance.This phenomenon could be explained as follows.In Fig. 7(a), ISI was mainly induced by the low-pass filtering effects of devices and was not severe.Therefore, a longer length of CP did not bring more benefits but introduced a higher loss of data rate, resulting in a larger average number of bits per subcarrier.On the other hand, in Fig. 11(a), the effect of ISI increased after transmission.Therefore, the benefit of a longer length of CP exceeded the disadvantage of the loss of data rate, resulting in better performance.Figure 12(a) depicts the performance versus the length of CP in conventional OFDM under either a fixed average number of bits per subcarrier (i.e. a fixed 30-Gbit/s raw data rate including the CP) or a fixed net data rate excluding the CP.The BER of 30-Gbit/s SP-offset-QAM OFDM without any CP is also shown.Figure 12(b) depicts the estimated SNR versus the index of subcarriers at 50 km.It is seen from Fig. 12(b) that the SNR of SP-QAM based conventional OFDM was degraded when the length of GI was zero.It implied that the effect of ISI, induced by dispersion and low-pass responses of devices, was indeed visible.In Fig. 12(a), when the average number of bits was fixed (triangles), the BER reduced as the length of CP increased.On the other hand, when the net data rate was fixed, the number of bits on subcarriers increased as the length of CP increased.Therefore, there was an optimal value, beyond which a longer CP length did not bring more benefits but induced a larger overhead.However, even with the optimal length of CP, SP-QAM based conventional OFDM was still not as good as the proposed SP-offset-QAM OFDM.

Performance characterization of SP-offset-QAM OFDM
Finally, we characterized the performance of SP-offset-QAM OFDM with respect to some system parameters, in order to confirm its potential for optical access networks.Figure 13(a) shows the BER versus the signal launch power into the fiber when the algorithm estimated the SNR for each signal launch power (circles) or used a fixed SNR profile obtained at the launch power of 10 dBm (triangles).It is seen that fiber nonlinear effects, including selfphase modulation and intra-channel four-wave mixing, were negligible for 10-dBm launch power (as used in the results above) and became prominent as the power increased.The increasing nonlinear noise reduced the overall SNR of subcarriers.Therefore, when a fixed

Fig. 3 .
Fig. 3. Constellation points of SP-128QAM, which are divided into two subgroups represented by the solid and empty circles respectively.

Fig. 5 .
Fig. 5. (a) BER performance versus signal data rate at back-to-back when the signal formats are offset-8QAM, offset-16QAM, adaptively loaded conventional offset-QAM, and adaptively loaded SP-offset-QAM.(b) BER versus signal data rate when the signals are SP-offset-QAM OFDM, SP-QAM based multi-band CAP, and conventional multi-band CAP.

Fig. 6 .
Fig. 6.(a) BER performance versus the roll-off factor of the signal spectrum for SP-offset-QAM OFDM and SP-QAM based multi-band CAP at 40 Gbit/s.(b) Performance versus the memory length of the FIR filters at 40 Gbit/s.In (b), the roll-off factors of the signal spectrum in SP-offset-QAM OFDM and SP-QAM based multi-band CAP are 0.5 and 0.05, respectively.

Fig. 7 .
Fig. 7. (a) BER versus signal data rate for SP-offset-QAM OFDM, conventional OFDM, and SP-QAM based conventional OFDM with different lengths of CP.(b) Performance versus the length of CP for SP-QAM based conventional OFDM at 40 Gbit/s.

Fig. 8 .Fig. 9 .
Fig. 8. (a) BER versus signal data rate when the signal formats are offset-8QAM, offset-16QAM, adaptively loaded conventional offset-QAM, and adaptively loaded SP-offset-QAM.(b) SE versus the index of subcarriers at 40 Gbit/s.The dashed line represents the SNR profiles ( = SNR (dB) / 3).The inset is the electrical spectrum of the received signal.

Fig. 10 .Fig. 11 .
Fig. 10.(a) BER performance versus the roll-off factor of the signal spectrum for SP-offset-QAM OFDM and SP-QAM based multi-band CAP at 30 Gbit/s.(b) Performance versus the memory length of the FIR filters at 30 Gbit/s.In (b), the roll-off factors of the signal spectrum in SP-offset-QAM OFDM and SP-QAM based multi-band CAP are 0.5 and 0.05, respectively.
) and 11(c) depict the constellations of subcarriers allocated with SP-128QAM for SP-QAM based conventional OFDM and SP-offset-QAM OFDM, respectively.All experimental parameters were the same in Figs.11(b) and 11(c).It was seen that the latter indeed gave a clearer constellation.

Fig. 12 .
Fig. 12.(a) Performance versus the length of CP for SP-QAM based conventional OFDM at 30 Gbit/s.(b) SNR versus the index of subcarriers for SP-QAM based conventional OFDM and SP-offset-QAM OFDM.