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By multiplexing two OFDM signals with the same channel space and bit rate together in an interleaved mode, a novel optical multiplexing scheme is proposed and experimentally demonstrated. Since the channel space is halved, the spectral efficiency is doubled compared with conventional OFDM. It is proved that the orthogonality between the subcarriers is maintained as long as the data is real. With discrete Fourier transform, the proposed scheme has similar computational complexity as conventional OFDM and single sideband modulation is conveniently achieved. A 10 Gb/s transmission system is set up, and proves the feasibility and efficiency of the scheme experimentally.
©2010 Optical Society of America
1. Introduction
During the last decade, with the great development of communication technology and multimedia services, the demand for higher bandwidth is becoming increasing urgent [1–4]. Recently, optical orthogonal frequency division multiplexing (O-OFDM) has drawn more and more interest as a promising technology for future high-speed optical communication system [5–8]. It has high tolerance to chromatic dispersion (CD) and polarization mode dispersion (PMD) [9,10]. What is more, as a special frequency multiplexing method, in OFDM systems, the spectral of the subcarriers overlap with each other, making OFDM have a higher spectral efficiency (SE) than any other frequency multiplexing methods. Recently, a great effort has been done to analyze and further improve the SE of OFDM system [11–13].
A novel scheme called fast OFDM (F-OFDM) is proposed in reference [11], where the frequency gap between subcarriers is half reduced, and the orthogonality between the subcarriers is still maintained as long as the data are real numbers, based on which, the SE of conventional OFDM is increased twice. As a matter of fact, in frequency domain, halving the frequency gap between subcarriers is equivalent to join two OFDM signals with the same bit rate and channel space together, which is achieved by discrete cosine transform (DCT) in [11]. However, DCT is not a common processing method in communication systems, which may increase the computational complexity of the operations. Besides, it is known that the signals before and after DCT are all real numbers, which means double sideband (DSB) signals, so Hilbert Transform and optical filters is used to realize SSB modulation, making the system more complex.
In this paper, a completely new multiplexing method is proposed by multiplexing two OFDM signals with the same bit rate and channel space together in an interleaved mode, where the frequency gap between subcarriers is also halved which means the SE is doubled compared with conventional OFDM systems. As the most common algorithm, discrete Fourier transform (DFT) is employed in our scheme, so fast Fourier transform (FFT) can be applied to greatly decrease the computational complexity.
The structure of the paper is arranged as follows. In section 2, the principle and operations of the proposed scheme are explained, and the orthogonality is proved mathematically as well. Then, the setup of a 10Gb/s optical communication system based on the proposed scheme is introduced in section 3, followed by the analysis of the experiment data. At last, the conclusion is given.
2. OFDM interleaved multiplexing
The basic principle of our scheme is multiplexing two OFDM signals with same bit rate and channel space in an interleaved mode, whose mathematical expression is shown in Eq. (1) below:
Where n is the total number of the subcarriers, k is the index of the subcarriers, T equals to one frame period, and a0 ~an-1 are the baseband data. The first and second terms of Eq. (1) are just the expression of the conventional OFDM modulation, whose spectral are shown in insets (a) and (b) of Fig. 1 respectively. In Eq. (1), odd and even terms of the baseband data are multiplexed separately, which is solely to simplify the mathematical expression. The factor exp(jπ × t/T) in Eq. (1) presents the frequency shift between the two OFDM signals, which exactly equals to half of the channel space. Inset (c) of Fig. 1 shows the spectrum of the signal after multiplexing, and it is apparently that with the proposed scheme, the SE is doubled compared with the conventional OFDM. It is obvious in inset (c) of Fig. 1 that the subcarriers are disturbed terribly by each other, however, the following part of this section will prove that the subcarriers are still orthogonal with each other as long as the data carried by them are real numbers.The orthogonality of the conventional OFDM is mathematically shown below in Eq. (2):
Where the integral of the product of two subcarriers with different frequencies during one frame period is 0, while the integral of the product of two subcarriers with the same frequency is 1 (or a non-zero number). So the data carried on different subcarriers can be recovered.The two terms of Eq. (1) can be combined together as follows in Eq. (3):
Where the 1/2T presents the new frequency gap between subcarriers, which is only half of the conventional OFDM systems. The integral of the product of two arbitrary subcarriers during one frame period is written below in Eq. (4):Where m and n are the index of the subcarriers, and the symbol ‘*’ stands for the complex conjugate operation. Similar analysis is made for Eq. (4) in two cases where m equals n and m does not equal n. When the frequencies of the two subcarriers are the same, the result of the integral is 1 as shown below in Eq. (5):Which means the data can be recovered, and this is completely the same as conventional OFDM. But when the subcarrier pairs have different frequencies, the situation will be a little bit complex as Eq. (6) shows:Where the results depend on the relationship between m and n. When the difference between m and n is an even number, which is equivalent to the subcarrier pairs in conventional OFDM, the result of the integral will be 0. On the other hand, if the difference between m and n is an odd number, the result is not 0, which means the two subcarriers turn non-orthogonal. However, we find in Eq. (6), the result is a pure imaginary number, whose real part is still 0. If our attention is moved to the real part of the subcarriers, when the frequency gap is 1/2T, the subcarriers are still orthogonal. The analysis above is summarized as follows in Eq. (7):which is similar as the expression in Eq. (2) so the orthogonality between the subcarriers in the proposed scheme is mathematically proved. It is the same as the F-OFDM in [11], the data carried by the subcarriers must be real numbers since only the real part of the integral is orthogonal. And it can be predicted that the constellation of the signal will not be ‘points’ but ‘lines’. The special shape constellation will be shown in the following section of the paper.Like OFDM, in realistic operations, FFT is employed to discretize Eq. (1) and the discrete form of which is written below in Eq. (8):
Where p is the index of the sample points and n is the total number of the subcarriers which is also the length of IFFT. Equation (8) shows that, compared with the conventional OFDM, the proposed scheme divides a long FFT operation into two shorter ones, which will not increase the computational complexity. Furthermore, the proposed scheme is based on DFT, so the data after multiplexing is naturally SSB signal, avoiding extra processing.The demodulation is completely the inverse processing of the modulation, so similar operation as Eq. (8) is applied to recover the original data as Eq. (9) shows above, where S stands for the multiplexed data, a stands for baseband data and p is the index.
3. Experiment setup and results
The transmission experiment setup of the system is shown in Fig. 2 below.
Fig. 2 Experiment setup (ASK: Amplitude Shift Keying; ATT: attenuator; AWG: Arbitrary Waveform Generator; BPF: Band Pass Filter; BERT: bit error rate tester; DPO: Digital Phosphor Oscilloscope; EDFA: Erbium-Doped optical Fiber Amplifier; LPF: low pass filter; MZM: Mach-Zehnder Modulator; OFDM: Orthogonal Frequency Division Multiplexing; PD: Photon Detector; PRBS: Pseudo-Random Binary Sequence; SSMF: Standard Single Mode Fiber)
At the transmitter the pseudo-random binary sequence (PRBS) baseband signal is first modulated in 4-ASK format. After that, the total 10Gb/s baseband data is divided into two parts, and each is multiplexed with the conventional OFDM method, where the number of the subcarriers is 1024. It is known that OFDM signal is generated from frequency domain, and the sample rate of the system and AWG often do not match, so the length of the IFFT is usually larger than the number of the subcarriers. It is equivalent that there are some zero subcarriers in the OFDM signal. The spectral shape of the OFDM signal can be easily controlled by arranging the position of the zero subcarriers. In order to combat with the CD originated from the fiber transmission, 100 cyclic prefixes are added at the head of every frame. The two OFDM signals is combined after introducing a frequency shift, and then the real and imaginary part of the combined signal is carried by the cosine and sinusoidal form of a 4GHz intermediate frequency carrier respectively. The multiplexed electrical signal is generated by the Tektronix arbitrary waveform generator (AWG) 7122B with the sample rate of 20Gs/s and 3 dB bandwidth about 9GHz.
A tunable external cavity laser is used as the laser source, and a Mach-Zehnder Modulator (MZM) is used to modulate the signal onto optical carrier with the modulation index about 0.6. Then, the optical power of the signal is adjusted by an EDFA and an attenuator before coupling into the 80km SSMF. At the receiver, the power loss during the whole transmission link is compensated with the help of another EDFA. A band pass filter (BPF) is added here to suppress the ASE noise of EDFA and out of band noise generated from transmission. Before O/E conversion, the optical power is controlled by a second attenuator. The signal after photon detector (PD) detection is sampled by the Tektronix digital phosphor oscilloscope (DPO) 72004B with the sample rate of 50Gs/s and 3dB bandwidth 10GHz. The received signal is mixed with a same 4GHz intermediate frequency carrier and then the real and imaginary parts of the baseband signal are got after removing the high frequency component with a low pass filter (LPF). The demultiplexing processing is completely the same as multiplexing, and like conventional OFDM systems, the CD is compensated by utilizing cyclic prefixes and reference symbols. All these are processed off line on PC, including the calculation of the BER.
Figure 3 shows the electrical and optical spectral of the signal respectively. The bit rate of the baseband signal is 10Gb/s, so in conventional OFDM systems, after 4-ASK modulation, the bandwidth of the SSB signal should be 5GHz. As it is analyzed above, the proposed scheme has a double SE compared with the conventional OFDM, so the bandwidth of the signal should be reduced 50% at the same situation. Inset (a) of Fig. 3 shows that, with our scheme, the bandwidth of the electrical signal is indeed 2.5GHz, which matches the analysis completely. In inset (a), the higher frequency part of the signal is slightly attenuated due to the output character of the AWG. This effect will be compensated in the demodulation processing at the receiver by applying an inverse filter in the digital domain.
In order to emphasize the experiment system is SSB modulated, a asymmetry spectral structure is intentionally designed. It is clear in inset (a) that the 4GHz intermediate frequency is not in the center but at the edge of the spectrum. Apparently, this will not degrade the data transmission performance.
The spectrum of the corresponding optical signal after MZM modulation is also shown in inset (b), whose bandwidth is twice of the electrical signal.
Both back to back (B2B) and 80km transmission experiments are accomplished to evaluate the system performance. In both situations, the BER curves are depicted, where 1,048,576 bits is used. In Fig. 4 the red triangles present B2B situation while blue squares present transmission situation. The special shape constellations of both situations are also inserted in Fig. 4 beside the BER curves respectively. As predicted above, the constellations is totally different from the ones we know before. In horizontal, the point values are divided into four parts according to the 4-ASK modulation. While in vertical, the point values are disordered because the imaginary part of the subcarriers is not orthogonal. And this special shape is coincident with the analysis. The power penalty after 80km SSMF transmission at the BER of 2×10−3, which is the FEC limit, is less than 1dB.
4. Conclusion
In this paper, a novel OFDM interleaved multiplexing scheme with a double SE compared with the conventional OFDM is proposed and experimentally demonstrated. The principle of the proposed scheme is mathematically explained. What is more, with the utilization of DFT, the proposed scheme has nearly the same computational complexity with the conventional OFDM, and SSB modulation is also conveniently achieved. Besides, an 80km SSMF transmission system is set up. The bandwidth of the 10Gb/s 4-ASK signal is 2.5GHz, which is only half of the conventional OFDM systems. At last, the BER curves for both B2B and transmission situations are drawn and analyzed, it is shown that the power penalty after 80km SSMF transmission at the FEC limit is less than 1dB. The proposed scheme is proved feasible and effective theoretically and experimentally.
Although the experiment is based on a direct detect optical OFDM system, the proposed scheme is independent with the optical modulation style. Applying coherent transmitter and receiver, single optical sideband modulation will be easily realized, and our scheme will play a greater role in the optical communication systems.
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Contract 60736002, 60807026, 60932004, and by State Key Laboratory of Advanced Optical Communication Systems and Networks, China (2008SH03).
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