Diversity-combining technique for discreet Hartley transform-based asymmetrical clipping optical orthogonal frequency-division multiplexing

Zhuo Cai; Ji Zhou; Yaojun Qiao

doi:10.3788/COL201513.S20605

Abstract

In this Letter, we propose a scheme that integrates a diversity-combining technique with asymmetrical clipping optical orthogonal frequency-division multiplexing (ACO-OFDM) based on a discreet Hartley transform (DHT). Simulations are demonstrated for the DHT-based ACO-OFDM system with a diversity-combining technique. The simulation results indicate that when the optimal weighting factor is chosen, the bit error rate (BER) performance is improved by about 2 dB when the binary phase-shift keying (BPSK) is modulated and about 3 dB when the 16 pulse-amplitude modulation is modulated. Additionally, experiments are presented to verify the feasibility of diversity-combining DHT-based ACO-OFDM. In the transmission experiments, a BPSK-modulated DHT-based ACO-OFDM with a diversity-combining receiver is realized, which improves the BER performance by 1.5 and 1.3 dB for a span length of back-to-back and a 50 km standard single-mode fiber, respectively.

In recent years, orthogonal frequency-division multiplexing (OFDM) has become an important technique for future optical networks due to its high spectrum efficiency and resistance against chromatic dispersion and polarization mode dispersion. As a multicarrier modulation technology, OFDM is drawing extensive attention in research as well as in the fields of its potential applications^[1,2].

In coherent OFDM systems, bipolar and complex signals are transmitted, but such signals cannot be adopted in intensity modulated/direct detection (IM/DD) systems because the intensity of light is positive. Due to its advantages, such as low complexity, low cost, and a simple structure, IM/DD optical OFDM has become a promising candidate for future low-cost transmission systems. The application range of IM/DD optical OFDM is huge, such as passive optical networks and indoor optical wireless communication and interconnection in data centers^[3–7]. Among the various implementation schemes for IM/DD optical OFDM systems, asymmetrical clipped optical OFDM (ACO-OFDM) is among the most popular, and is receiving increased interest^[8].

If only odd subcarriers are used to carry data, the bipolar OFDM signal will have an anti-symmetrical property. So the negative part of the bipolar OFDM signal is redundant. The ACO-OFDM signal is generated by clipping the bipolar signal at zero. Though half of the signal’s amplitude is clipped, no information is lost in the odd subcarriers. But the non-use of even subcarriers causes inefficiency in terms of the spectrum. However, the ACO-OFDM has some unique advantages. An ACO-OFDM is more efficient in terms of optical power. Moreover, the non-use of the DC-bias makes the same optimal design suitable for all constellations, without any changes to the existing system scheme^[9].

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Recently, a discreet Hartley transform (DHT)-based ACO-OFDM was proposed as an alternative IM/DD scheme^[10]. DHT/inverse DHT (IDHT) is a real trigonometric transform and a one-dimensional real constellation, such as binary phase-shift keying (BPSK) or $M$ pulse-amplitude modulation (PAM), is adopted for real OFDM generation without a Hermitian symmetry (HS) operation^[11]. Moreover, DHT has a self-inversion property; consequently, the same algorithm can be used to calculate the forward and inverse operations, which will reduce the implementation complexity of the system^[12].

Among a number of existing approaches to improve the optical efficiency of IM/DD OFDM systems, Dr. Liang Chen et al. presented a diversity-combining system for a fast Fourier transform (FFT)-based ACO-OFDM^[13]. In the conventional receiver of an ACO-OFDM, the even subcarriers are discarded and not demodulated. However, in a diversity-combining receiver, the received signal on even subcarriers is combined with the signal on odd subcarriers, which can improve the receiving sensitivity performance of the system.

In this Letter, we propose a scheme that integrates a diversity-combining technique with a DHT-based ACO-OFDM, which is appropriate for IM/DD optical systems. Compared to a FFT-based ACO-OFDM, the implementation complexity of the DHT-based ACO-OFDM is reduced. Meanwhile, the diversity-combining technique can improve the performance of the DHT-based ACO-OFDM. The feasibility of a diversity-combining DHT-based ACO-OFDM is verified via transmission experiments, in which back-to-back (BTB) and a 50 km standard single-mode fiber (SSMF) are included. It is found that the proposed scheme can significantly improve the performance of IM/DD systems.

A block diagram of the proposed system is depicted in Fig. 1. The $N$ -order IDHT and DHT are defined as follows: $x_{n} = \frac{1}{\sqrt{N}} \sum_{k = 0}^{N - 1} X_{k} cas (\frac{2 π k n}{N}), n = 0, 1, \dots, N - 1,$ (1) $X_{k} = \frac{1}{\sqrt{N}} \sum_{n = 0}^{N - 1} x_{n} cas (\frac{2 π k n}{N}), k = 0, 1, \dots, N - 1,$ (2)where $x_{n}$ represents time-domain symbols, $X_{k}$ represents frequency-domain symbols, and $cas (\cdot) = \cos (\cdot) + \sin (\cdot)$ .

Figure 1.Block diagram of diversity-combining DHT-based ACO-OFDM.

In the proposed scheme, the data sequence after the serial-to-parallel operation is sent to the PAM mapping module to generate real PAM signal for the IDHT. Only the odd subcarriers of the IDHT operation are adopted to carry data symbols, so the input signal to the IDHT, $X$ , comprises only odd components such that $X = [0, X_{1}, 0, X_{3}, \dots, X_{N - 1}]$ . DHT/IDHT is a real trigonometric transform with no need for HS. As Fig. 2(a) shows, the resulting time signal after IDHT, $x$ , is real and has an anti-symmetrical property. Its anti-symmetrical property is shown as $x_{n + \frac{N}{2}} = \frac{1}{\sqrt{N}} \sum_{k = 0}^{N - 1} X_{k} cas (\frac{2 π k}{N} (n + \frac{N}{2})) = \frac{1}{\sqrt{N}} \sum_{n = 0}^{\frac{N}{2} - 1} X_{2 k + 1} cas (\frac{2 π (2 k + 1)}{N} (n + \frac{N}{2})) = - \frac{1}{\sqrt{N}} \sum_{n = 0}^{\frac{N}{2} - 1} X_{2 k + 1} cas (\frac{2 π n (2 k + 1)}{N}) = - \frac{1}{\sqrt{N}} \sum_{k^{'} = 0}^{N - 1} X_{k^{'}} cas (\frac{2 π k^{'} n}{N}) = - x_{n},$ (3)where $n$ is from 0 to $N / 2 - 1$ .

Figure 2.(a) BPSK-modulated OFDM based on the 32-order DHT and (b) corresponding ACO-OFDM.

The negative part of the DHT-based OFDM symbols can be clipped at the zero level without losing any information. In Fig. 2(b), the corresponding DHT-based ACO-OFDM symbol is given. After the clipping module, the clipped signal can be denoted as $x_{n, c}$ , which is defined as $x_{n, c} = {\begin{matrix} x_{n}, & x_{n} > 0 \\ 0, & x_{n} \leq 0 \end{matrix} 0 \leq n \leq N - 1 .$ (4)

Subsequently, the clipped time-domain signal is transmitted to the receiver end. The time-domain signal can be separated into two parts that are obtained from the odd and even subcarriers, which can be given by $x_{n, c} = x_{n, c}^{odd} + x_{n, c}^{even}, n = 0, 1, \dots, N - 1 .$ (5)

The recovered signal $X_{k}^{'}$ can be obtained using $X_{k}^{'} = \sum_{n = 0}^{N - 1} x_{n, c} cas (\frac{2 π k n}{N}), n = 0, 1, \dots, N - 1,$ (6)

The frequency-domain counterpart of $x_{n, c}^{odd}$ and $x_{n, c}^{even}$ can be denoted as $X_{k, odd}^{'}$ and $X_{k, even}^{'}$ , respectively. $X_{k, odd}^{'}$ and $X_{k, even}^{'}$ remain the odd subcarriers and even subcarriers of $X_{k}^{'}$ , respectively. So, the relationship between the time-domain and frequency-domain symbols on the odd and even subcarriers can be given by $x_{n, c}^{odd} = \sum_{k = 0}^{N - 1} X_{k, odd}^{'} cas (\frac{2 π k n}{N}),$ (7) $x_{n, c}^{even} = \sum_{k = 0}^{N - 1} X_{k, even}^{'} cas (\frac{2 π k n}{N}),$ (8)

Consequently, $x_{n, c}^{odd}$ is equal to $x_{n} / 2$ and $x_{n, c}^{even}$ can be obtained from $x_{n, c}^{even} = x_{n, c} - x_{n, c}^{odd} = x_{n, c} -= \frac{1}{2} | x_{n} | = | x_{n, c}^{odd} | .$ (9)

So the noise component on the even carriers is highly relative to the signals on the odd subcarriers. Therefore, despite the noise component, it can be utilized to further improve the bit error rate (BER) performance of the system. And a diversity-combining module, which can be used in the receiver end, can take advantage of the noise component to fulfill this purpose. The block diagram of the diversity combining module is shown in Fig. 3.

Figure 3.Diversity-combining module, where $sgn (\cdot)$ represents the sign function.

Taking noise into consideration, we can suppose that the two aforementioned highly correlated signals are transmitted by two independent subcarriers, because the frequency-domain noise $N$ (the time-domain counterpart of which is $n$ ) has a low correlation between odd and even subcarriers. So we can denote the signal on the odd subcarriers and even subcarriers as $Y_{k, odd} = X_{k, odd}^{'} + N_{k, odd},$ (10) $Y_{k, even} = X_{k, even}^{'} + N_{k, even} .$ (11)

Through two separate IDHT processes of the odd and even subcarriers, we can regenerate $y_{k, odd}$ and $y_{k, even}$ , which are depicted in Figs. 4(a) and 4(b). $y_{n, odd} = x_{n, c}^{odd} + n_{n, odd},$ (12) $y_{n, even} = | x_{n, c}^{odd} | + n_{n, even} .$ (13)

Figure 4.(a) Symbol on odd subcarrier; (b) symbol on even subcarrier; and (c) under the circumstances of no noise, the regenerated signal from the symbol on the even subcarrier indicated by the polarity of the symbol on the odd subcarrier.

In this diversity-combining module, as shown in Fig. 3, $y_{n, odd}$ is the polarity indicator to decide whether to flip the value of $y_{n, even}$ on the even subcarriers, which is no less than zero. Thus, besides $y_{n, odd}$ , a new anti-periodic signal, $y_{n, even}^{'}$ , is generated, which will contribute to restoring the original sequence in the diversity-combining module. $y_{n, even}^{'}$ is shown in Fig. 4(c). $y_{n, even}^{'}$ is defined as $y_{n, even}^{'} = sgn (y_{n, odd}) \times y_{n, even},$ (14)where $sgn (\cdot)$ represents the sign function.

Due to the influence of noise, incorrect polarity information might be extracted, subsequently leading to corresponding errors in $y_{n, even}^{'}$ . Such situations are more likely to happen with small-power signals, because polarity information errors should only occur when noise has opposite polarity and the amplitude of noise is larger than signal simultaneously. Thus, the probability of a serious error in $y_{n, even}^{'}$ should be low, which would not hurt the performance much.

Finally, $y_{n, even}^{'}$ and $y_{n, odd}$ are combined for recovering the original sequence as ${\hat{y}}_{n} = α \times y_{n, even}^{'} + (1 - α) \times y_{n, odd},$ (15)where alpha is a weighting factor, ranging from 0 to 1. By selecting a proper $α$ , we can achieve the optimal performance of the system.

With the purpose of elaborating on the performance of the proposed scheme, we conducted a series of simulations with MATLAB.

Figure 5 presents the influence of $α$ on the Eb/N0 gain for different modulation constellations at the forward error correction (FEC) limit. In our simulations, the adopted modulation constellations include BPSK, 4-PAM, 8-PAM, and 16-PAM. Meanwhile, to select a proper $α$ more accurately, we choose $α$ from 0 to 1 with a step of 0.05. According to our simulation results, which are shown in Fig. 5, the optimal value of $α$ is approximately 0.45, at which the system has a relatively better performance in terms of $α$ gain. When $α = 0.45$ , the $α$ gain is around 1.9, 2.3, 2.8, and 3.2 dB for BPSK, 4-PAM, 8-PAM, and 16-PAM, respectively.

Figure 5.Eb/N0 gain versus $α$ for diversity-combining technique in DHT-based ACO-OFDM with BPSK, 4-PAM, 8-PAM, and 16-PAM modulated.

Figure 6 shows the comparison of the BER performances of the conventional DHT-based ACO-OFDM and the optimal diversity-combining DHT-based ACO-OFDM with different given modulation constellations. According to the aforementioned deductions, if $α$ is 0, the system is equivalent to a conventional DHT-based ACO-OFDM without the diversity-combining module. So, as shown in Fig. 6, we set $α$ to 0 to generate the original signals for comparison. For a given modulation constellation, compared to the DHT-based ACO-OFDM, the BER performance of the optimal diversity-combining DHT-based ACO-OFDM is clearly improved. As revealed in Fig. 6, the improvement of the required Eb/N0 for the BER limit of $10^{- 3}$ is approximately 1.9, 2.3, 2.8, and 3.2 dB for BPSK, 4-PAM, 8-PAM, and 16-PAM, respectively. Therefore, an improvement in Eb/N0 can be achieved by employing the proper $α$ in this scheme.

Figure 6.Comparison of BER performance between conventional DHT-based ACO-OFDM without diversity-combining module and optimal diversity-combining DHT-based ACO-OFDM with different given modulation formats, where original means conventional DHT-based ACO-OFDM without diversity-combining module.

We present the experiments to verify the feasibility of diversity-combining DHT-based ACO-OFDM.

The experiment setup is depicted in Fig. 1. In this experiment, the coding and decoding of the signal are realized through MATLAB. The number of OFDM subcarriers is 64, and eight cyclical prefix samples are employed. Sixteen training symbols and one synchronization symbol should be transmitted every 256 OFDM symbols. The generated digital signal is sent to an arbitrary waveform generator (AWG, Tektronix AWG7122C), which can be used to realize the digital-to-analog converter operating at 10 GS/s. Therefore, the overall link bit rate is 10 Gb/s, and the net bit rate is nearly 4.2 Gb/s $(1 \times 10 G \times 64 / (64 + 8) \times 256 / (256 + 16 + 1) ∖ \approx 4.2 Gb / s)$ . We utilize a 5 kHz linewidth laser to generate the optical carrier, and a Mach–Zehnder modulator is applied to modulate the optical carrier with the analog signals generated by the AWG. The launch power is set at 0 dBm.

At the receiver end, we use a variable optical attenuator to vary the received optical power. In addition, an erbium-doped fiber amplifier working at the power-control status is used to maintain the input optical power of the photodiode (PD) to be constant. The received optical signal is converted to an electrical signal via the PD. After going through a low-pass filter with a 3 dB width of 10 GHz, the signal is captured by a real-time digital phosphor oscilloscope (Tektronix DPO72004C), which performs as an analog-to-digital converter. Finally, the captured signal is processed offline by MATLAB.

Figure 7 depicts the BERs versus the received power for the diversity-combining DHT-based ACO-OFDM system after BTB and 50 km SSMF transmission with an $α$ of 0 and 0.45. For a BTB system where $α = 0$ and $α = 0.45$ , the required received power at the FEC limit is about $- 31.2$ and $- 32.6 dBm$ , respectively. After transmission on a 50 km SSMF, the required received powers at the FEC limit under the conditions of $α = 0$ and $α = 0.45$ are about $- 30.7$ and $- 32 dBm$ , respectively. Therefore, compared to a conventional DHT-based ACO-OFDM, the optimal diversity-combining DHT-based ACO-OFDM improves the BER performance by nearly 1.5 dB in a BTB system, and in a 50 km SSMF transmission system, the BER performance should be improved by around 1.3 dB.

Figure 7.BER versus received power for diversity-combining DHT-based ACO-OFDM systems after BTB and 50 km SSMF transmission.

In conclusion, we propose a scheme of a diversity-combining DHT-based ACO-OFDM and theoretically analyzed its principles. From the simulation performance analyses, we discover the approximate optimal weighting factor for diversity combining. Compared to a conventional DHT-based ACO-OFDM, the BER performance of the proposed scheme can be improved in the additive white Gaussian noise channel. Meanwhile, we perform experiments to verify the feasibility and study the transmission performance of the proposed scheme. When the optimal weighting factor is chosen, in the BTB system, the BER performance is improved by nearly 1.5 dB compared to the conventional scheme, and in the 50 km SSMF transmission system, the BER performance is improved by nearly 1.3 dB. In conclusion, a diversity-combining DHT-based ACO-OFDM can be a valuable alternative to IM/DD optical OFDM systems.

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