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In this paper, an improved Flip-OFDM scheme is proposed for IM/DD optical systems, where the modulation/demodulation processing takes advantage of the fast Hartley transform (FHT) algorithm. We realize the improved scheme in one symbol period while conventional Flip-OFDM scheme based on fast Fourier transform (FFT) in two consecutive symbol periods. So the complexity of many operations in improved scheme is half of that in conventional scheme, such as CP operation, polarity inversion and symbol delay. Compared to FFT with complex input constellation, the complexity of FHT with real input constellation is halved. The transmission experiment over 50-km SSMF has been realized to verify the feasibility of improved scheme. In conclusion, the improved scheme has the same BER performance with conventional scheme, but great superiority on complexity.
© 2014 Optical Society of America
1. Introduction
Orthogonal frequency division multiplexing (OFDM) is often employed as a modulation scheme for high-speed optical transmission and access networks, due to its simple one tap equalizer, high spectrum efficiency (SE) and robustness against chromatic dispersion (CD) and polarization-mode dispersion (PMD) [1–5]. Among the proposed OFDM systems, intensity-modulation and direct-detection (IM/DD) technique inherently enjoys a low cost and brief structure, which is attractive for future cost-sensitive & short-range & high-speed transmission such as passive optical network (PON), indoor optical wireless communication and interconnections in data center [6–8].
The two most popular IM/DD OFDM systems are DC-offset OFDM (DCO-OFDM) and asymmetrically clipped optical OFDM (ACO-OFDM) [9–11]. Recently, as an alternative scheme, Flip-OFDM was presented for IM/DD optical systems [12–14]. The comparisons of three IM/DD OFDM systems are briefly described below:
- To decrease the clipping noise, DCO-OFDM needs a large DC-bias to generate positive time-domain signal because of its high peak-to-average power ratio (PAPR). However, the large DC-bias used in DCO-OFDM is inefficient in terms of optical power. Beyond that, the optimum DC-bias depends on the signal constellation. Thus, the design of DCOOFDM is not optimum for all constellation sizes, making DCO-OFDM not suited to adaptive systems [10].
- In ACO-OFDM systems, only the odd sub-carriers transmit data to generate the time-domain signal with anti-symmetry property. So the generated time-domain signal can be clipped at zero which results in a positive signal without losing any information. Compared to DCO-OFDM, ACO-OFDM has a better power efficiency and the same optimal designs for all constellation sizes due to the nonuse of DC-bias.
- In Flip-OFDM systems [12, 13], positive and negative parts are extracted from the bipolar OFDM signal. Then the polarity of negative part is inverted to form an independent OFDM symbol. The positive and negative parts are transmitted in two consecutive OFDM symbols. Flip-OFDM is similar to ACO-OFDM in spectral efficiency, power efficiency and BER performance. Flip-OFDM offers 50% saving in hardware complexity at the receiver and an enhanced detection over ACO-OFDM [13]. Due to double symbols transmitted in Flip-OFDM, many operations, such as cyclic prefix (CP) operation, polarity inversion and symbol delay, are doubled. Thus, there is room for further refinement in complexity of Flip-OFDM.
Fast Hartley transform (FHT) has been proposed as an alternative modulation/demodulation processing in IM/DD optical OFDM systems [15–17]. It is a real trigonometric transform. If the input constellations are real, the generated OFDM symbols are real. Therefore, FHT for IM/DD systems does not need Hermitian symmetry which is required in conventional fast Fourier transform (FFT). And the direct and inverse Hartley transforms are identical, so that the same algorithm can be applied for the OFDM modulation and demodulation. Moreover, the complexity of FHT with real input constellation is half of that of FFT with complex input constellation [18–20]. Thus, FHT is perfect for IM/DD systems due to its low complexity.
To take advantage of FHT algorithm and reduce the complexity of Flip scheme, we propose an improved FHT-based Flip-OFDM scheme for IM/DD systems. In the improved scheme, we transmit the positive and negative parts both in one OFDM symbol period. By this way, the complexity of system is further reduced. We compare the improved scheme with conventional FFT-based Flip-OFDM scheme in terms of spectral efficiency, BER performance and complexity. The feasibility of the improved scheme has been verified by the standard single mode fiber (SSMF) transmission experiment. Under the same spectral efficiency, our proposed scheme has the same transmission performance with the conventional scheme, but its complexity is halved.
2. Principle
The block diagram of improved FHT-based Flip-OFDM system is depicted in Fig. 1. The N-order Inverse FHT (IFHT) and FHT are defined by,
where cas(.) = cos(.) + sin(.). And x is the time-domain OFDM symbol and X is the frequency-domain input symbol.
Fig. 1 Experiment setup for improved FHT-based Flip-OFDM. MZM, Mach-Zehnder modulator; SSMF, standard single-mode fiber; VOA, variable optical attenuator; EDFA, erbium doped fiber amplifier; PD, photodiode.
Obviously, Hartley transform is a real trigonometric transform. Thus, if the real constellation is adopted for the modulation format, the generated OFDM samples are real. As Fig. 1 depicts, the data sequences are sent into the real constellation mapper and the output real constellations are assigned to even sub-carriers of FHT operation, i.e., X2k+1 = 0, k = 0, ..., N/2 − 1. The output of FHT, x has a half-wave even symmetry where the samples in the period from 0 to NT/2 are repeated again from NT/2 to NT, where N is the size of FHT and T is the sampling period. We demonstrate these OFDM samples as follows:
Thus, only half the symbol period is required to transmit this OFDM symbol. The outputs of FHT are sent into the Flip module to generate the unipolar symbols. Figure 2(a) shows the detailed step: at the beginning, we reserve only the first half-period of input symbols,
Then y can be decomposed into a positive part and a negative part, where the positive part y+ and negative part y− are defined as, And the positive part is still transmitted on original position while the flipped (inverted polarity) part delays NT/2. Finally, two parts are multiplexed to generate a positive symbol x̄ of a length N,As Fig. 3(a) depicts, the symbol before Flip module has a half-wave even symmetry. And Fig. 3(b) shows that positive Flip-OFDM symbol is generated by Flip module. After parallel-to-serial, CP Addition, DAC and LPF modules, the analog improved FHT-based Flip-OFDM signal is completed.
Fig. 3 (a) Half-wave even symmetrical OFDM symbol based on 64-order FHT; (b) Improved Flip-OFDM symbol based on 64-order FHT.
At receiver, the inverse operations of transmitter are realized. We introduce the De-Flip module in detail. As Fig. 2(b) depicts, firstly, the input symbol is divided into two sub-symbol, one is from 0 to NT/2, the other is from NT/2 to NT. We conduct delay operation of NT/2 to the first sub-symbol, and polarity inversion to the second sub-symbol. Then two sub-symbols make up one symbol with a period of NT/2. Finally, this symbol is extended by its copy to generate a half-wave even symmetrical frame with a period of NT. The output of De-Flip module is sent into FHT and De-Mapper modules to recover the transmitted data sequences.
3. Key parameters for comparison
3.1. Spectral efficiency
As Table 1 reveals, in conventional FFT-based Flip-OFDM scheme, half of the spectrum is sacrificed in order to have a real OFDM signal due to the Hermitian symmetry. The improved FHT-based Flip-OFDM scheme overcomes this drawback due to the real trigonometric Hartley transform. In the improved scheme, only even sub-carriers are used to transmit information and one symbol period is sufficient to extract the information. On the other hand, although conventional scheme uses both odd and even sub-carriers, it needs two symbol periods to extract the information. Figure 4 shows the frame structures of conventional scheme and improved scheme. Thus, if M is the size of complex constellation for conventional scheme, to achieve the same spectral efficiency, the size of real constellation for the improved scheme is only .
Table 1. Comparison between the improved FHT-based Flip-OFDM and conventional FFT-based Flip-OFDM. T denotes the sampling period, N denotes the FFT and FHT size
Fig. 4 OFDM frame structure used to compare conventional FFT-based Flip-OFDM and improved FHT-based Flip-OFDM. N denotes the FFT and FHT size for each case.
3.2. BER performance in AWGN channel
Figure 5 depicts the BER performance of conventional FFT-based Flip-OFDM scheme and improved FHT-based Flip-OFDM scheme in additive white gaussian noise (AWGN) channel. The size of FHT and FFT is 64. And when the same simulation parameters are adopted, the BER curve of BPSK (4ASK)-modulated improved scheme coincides to the BER curve of QPSK (16QAM)-modulated conventional scheme. As Section 3.1 depicts, BPSK (4-ASK)-modulated improved scheme has the same spectral efficiency with QPSK (16-QAM)-modulated conventional scheme. Thus, under the same spectral efficiency, the improved scheme can achieve the same BER performance compared to conventional scheme in AWGN channel.
Fig. 5 Comparison of BER performance between conventional FFT-based Flip-OFDM and improved FHT-based Flip-OFDM in AWGN channel. The size of FHT and FFT is 64.
3.3. Complexity
M. Vetterli and H. J. NussBaumer demonstrated a simple FFT algorithm in [18]. If the input data is real, the number of multiplications required by N-order FFT is N/2 · (log2(N) − 3) + 2 and the number of additions is N/2 · (3log2(N) − 5) + 4. But if the input data is complex, the real and imaginary parts of data are separately transformed (thus doubling the computational load) and the outputs are combined by 2N − 4 additions. So N-order FFT with complex input data needs N · (log2(N) − 3) + 4 multiplications and 3N · (log2(N) − 1) + 4 additions [18]. P. Duhamel and M. Vetterli proposed an improved FHT algorithm in [19, 20]. If the input data is real, FHT uses only two additions more than the FFT algorithms. Thus, N-order FHT with real input data requires N/2 · (log2(N) − 3) + 2 multiplications and N/2 · (3log2(N) − 5) + 6 additions [18–20]. As Table 1 depicts, the input constellations is real in the improved FHT-based Flip-OFDM and complex in the conventional FFT-based Flip-OFDM. Obviously, the complexity of FHT in improved scheme is the half of that of FFT in conventional scheme.
As Fig. 4 reveals, we implement the improved FHT-based Flip-OFDM in one symbol period while conventional FFT-based Flip-OFDM in two consecutive symbol periods. Thus, compared to conventional scheme, the complexity of many operations, such as CP operation, polarity inversion and symbol delay, is halved in improved scheme. As described above, the improved scheme offers nearly 50% saving in implement complexity over conventional scheme.
4. Experiment setup and results
4.1. Experiment setup
Figure 1 shows the experiment setup of improved FHT-based Flip-OFDM system. The improved FHT-based Flip-OFDM signal was encoded and decoded by matlab. The encoding block mainly consisted of real constellation mapper, 64-point FHT, Flip module, parallel-to-serial conversion and CP addition. In the generated symbols, only 30 sub-carriers were valid. Due to the AC-coupled devices, DC sub-carrier was not modulated. 4 cyclic prefix samples were employed. For every 256 symbols, 8 training symbols and 1 synchronization symbol were transmitted. The generated digital signal was then uploaded into an arbitrary waveform generator (Tektronix AWG7122C) operating at 10 GSa/s to generate analog signal. So the net symbol rate was about 4.2 Gbaud/s (10 G × 30/(64 + 4) × 256/(256 + 8 + 1) ≈ 4.2 G). A laser with 5 kHz line-width was used to generate the optical carrier. A Mach-Zehnder modulator (MZM) was adopted to modulate the optical carrier with the generated analog signal without DC bias. The Vpi of MZM was about 7 Vpp.
At the receiver, a variable optical attenuator (VOA) was used to vary the received optical power. We used an EDFA worked at power-controlled status to maintain a constant input power of photodiode (PD). The received optical signal can be converted into electrical signal using a 40 GHz PD. And the electrical signal was then filtered by a low-pass filter (LPF) with a 3 dB bandwidth of 10 GHz. The filtered electrical signal was captured by a 100 GS/s (20 GHz 3 dB bandwidth) real-time digital phosphor oscilloscope (Tektronix DPO72004C) to implement analog-to-digital conversion (ADC). The generated digital signal was decoded by offline processing in matlab. The decoding block consisted of CP-removal, serial-to-parallel conversion, channel estimation, De-Flip module, 64-point FHT, and constellation de-Mapper. The channel estimation was realized by the least square (LS) algorithm.
4.2. Experiment results
Figure 6 depicts that BERs versus received power for 4.2 Gbaud/s BPSK (4ASK)-modulated improved Flip-OFDM based on FHT after B2B, 25-km and 50-km SSMF transmission. In BPSK-modulated system, the required received power at the FEC limit was measured to be about −32.2 dBm, −31.9 dBm and −31.7 dBm for B2B, 25-km and 50-km SSMF transmission, respectively. The maximum power penalty for the case of 50-km SSMF was about 0.5 dB. In 4ASK-modulated system, the required received power at the FEC limit was measured to be about −24.1 dBm, −24.5 dBm and −24.8 dBm for B2B, 25-km and 50-km SSMF transmission, respectively. The maximum power penalty for the case of 50-km SSMF was about 0.7 dB. Compared with BPSK-modulated system, the maximum power penalty for the 4ASK-modulated system was about 7 dB. As Fig. 6 reveals, the improved FHT-based Flip-OFDM is available for high-speed IM/DD systems.
Fig. 6 BER versus received power for improved Flip-OFDM systems based on FHT after B2B, 25-km and 50-km SSMF transmission.
In Fig. 7, the transmission performance comparison between improved FHT-based Flip-OFDM and conventional FFT-based Flip-OFDM is illustrated. The size of FHT and FFT is 64. The insets show the recovered constellations near FEC limit after 50-km SSMF transmission. For a fair comparison, we transmit the same data sequence and employ the same synchronization and channel equalization in improved and conventional schemes. As Fig. 7 shows, under the same spectral efficiency and received power, almost the same BER can be obtained from the two schemes. It clearly reveals that improved scheme has the same transmission performance compared to conventional scheme in high-speed IM/DD systems over 50-km SSMF.
Fig. 7 Comparison of BER performance between conventional FFT-based Flip-OFDM and improved FHT-based Flip-OFDM over 50-km SSMF. The size of FHT and FFT is 64.
5. Conclusion
In this paper, we have proposed an improved FHT-based Flip-OFDM scheme for IM/DD optical systems. And the feasibility of the improved scheme has been verified by the SSMF transmission experiments. Because Hermitian symmetry is not required, if M is the size of complex constellation for conventional FFT-based Flip-OFDM scheme, to achieve the same spectral efficiency, the size of real constellation for the improved scheme is only . Compared to conventional scheme, under the same spectral efficiency, the improved scheme has the same BER performance, but its complexity is halved. This paper shows the great attraction of our proposed scheme for future cost-sensitive IM/DD optical systems.
Acknowledgments
This work was supported in part by National Natural Science Foundation of China ( 61271192, 61331010); National 863 Program of China ( 2013AA013401); Postgraduate Innovation Fund of SICE, BUPT, 2013 P. R. China.
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