A spectrally efficient modified asymmetrically and symmetrically clipped optical (mASCO)-OFDM for IM/DD systems

A novel spectrally efficient modified asymmetrically and symmetrically clipped optical (mASCO)-OFDM for intensity modulated direct detection (IM/DD) systems is presented. The conventional ASCO-OFDM systems use two frames to transmit the conventional asymmetrically clipped optical (ACO)-OFDM and symmetrically clipped optical (SCO)-OFDM system. The proposed mASCO-OFDM system replaces the two frame SCO-OFDM by a single frame modified SCO (mSCO)-OFDM. The mSCO-OFDM clips the data on only one side of the symmetry and performs an absolute function on the other side of the symmetry. This allows mASCO-OFDM to be 1.333 times more spectrally efficient than the conventional ASCO-OFDM. The mASCO-OFDM reduces its receiver’s complexity by estimating and eliminating the clipping noise distortion in time domain. Overall, this system has 43% lower complexity in comparison to ASCO-OFDM system. The mASCO-OFDM shows a better BER performance and a lower Peak Average Power Ratio (PAPR) than ASCO-OFDM. The proposed system also shows better BER performance than ACO-OFDM for the same spectral efficiency.


Introduction
Orthogonal frequency division multiplexing (OFDM) has many inherent advantages such as high spectral efficiency and low-cost implementation, due to which it is increasingly being used for intensity modulated/direct detection (IM/DD) systems. DC-bias optical OFDM (DCO-OFDM) (Dissanayake and Armstrong 2013;Armstrong and Schmidt 2008;Armstrong and Lowery 2006) and asymmetrically clipped optical OFDM (ACO-OFDM) (Dissanayake and Armstrong 2013; Armstrong and Schmidt 2008;Armstrong et al. 2006) are basic forms of optical OFDM (O-OFDM) techniques that generate real and unipolar signals required for (IM/DD) transmission mediums. High spectral efficiency of DCO-OFDM is a result of optimum subcarriers utilization to process its information (Dissanayake and Armstrong 2013). However, the DC bias in DCO-OFDM is inefficient in terms of optical power (Wu and Bar-Ness 2015). As ACO-OFDM is more power efficient, it is generally preferred over DCO-OFDM for IM/DD applications. The SE of ACO-OFDM is 50% of SE of DCO-OFDM, as ACO-OFDM processes its data only on its odd subcarriers.
This motivated the researchers to enhance the SE of ACO-OFDM. A hybrid scheme named ADO-OFDM was developed in (Dissanayake and Armstrong 2013), that utilized all subcarriers by combining ACO-OFDM on its odd subcarriers and DCO-OFDM on even sub-carriers. Another hybrid technique known as Hybrid ACO-OFDM (HACO-OFDM) (Ranjha and Kavehrad 2014) combined ACO-OFDM on odd subcarriers and PAM-DMT on the imaginary parts of the even ones. This scheme is spectrally inefficient, as the real parts of even subcarriers remain unused. To overcome this disadvantage, Enhanced hybrid asymmetrically clipped optical OFDM (EHACO-OFDM) (Guan et al. 2016) added a third path of DCO-OFDM on the unused real parts of even subcarriers of HACO-OFDM. EHACO-OFDM achieved higher power efficiency than ADO-OFDM and DCO-OFDM, however it was still optically inefficient due to DCO-OFDM.
The power inefficient DCO-OFDM was replaced by a technique known as symmetrically clipped optical OFDM (SCO-OFDM) that used two frame flip type processing to carry the negative and positive information in ASCO-OFDM (Wu and Bar-Ness 2015). Clipping directly on even subcarriers resulting in loss of information due to even symmetry, is prevented by the two frame SCO-OFDM in ASCO-OFDM. This processing also requires a two frame ACO-OFDM to process its information, thereby increasing its bandwidth and complex processing at the receiver. ASCO-OFDM achieved better symbol error rate (SER) performance and lower optical power per bit in comparison to ADO-OFDM (Wu and Bar-Ness 2015) at the expense of a large bandwidth with increased complexity at the receiver. The SE of ASCO-OFDM is 75% of SE of DCO-OFDM.
It has been proven that the clipping distortion of ACO-OFDM falls on the even subcarriers without effecting its data on odd subcarriers. The conventional receivers in (Dissanayake and Armstrong 2013;Wu and Bar-Ness 2015;Wang et al. 2014;Lowery 2016) use complex signal processing by combining both frequency-domain and time-domain processing to estimate and cancel the clipping distortion of ACO-OFDM. This process becomes more significant when subsequent streams of even subcarriers carry additional information, as its BER performance depends on the accurate estimation and cancellation of clipping distortion of ACO-OFDM. Many iterative procedures have also been used to cancel the clipping distortion, that have shown to improve the BER performance but at the cost of increased complexity (Wang et al. 2014).
In this paper, modified ASCO-OFDM (mASCO-OFDM) system is proposed for IM/DD optical wireless systems. The proposed mASCO-OFDM utilizes all the subcarriers and has the same SE of DCO-OFDM. The simplified model mASCO-OFDM replaces the two frame SCO-OFDM by a proposed single frame modified SCO (mSCO)-OFDM signal, that clips only one side of the symmetry and performs an absolute function of the data on the other side of the symmetry. The clipped data contains both the data and the clipping distortion (represented by the absolute function of the data) on the even subcarriers. The absolute function on the other side of the symmetry will help eliminate the clipping distortion and accurately recover the data at the receiver. This system additionally applies the concept of time domain clipping noise estimation (TD-CNE) (Wang et al. 2018) to its receiver, to recover its signal information through time-domain signal processing that reduces the receiver complexity and further improves the overall BER performance of mASCO-OFDM signal.
2 System modeling Figure 1 shows the transmitter of mASCO-OFDM system. The serial to parallel (S/P) data are mapped using QAM symbols and then constrained to Hermitian symmetry. The resulting signal X K is divided into odd and even stream of subcarriers, where where X odd,K = X K is a complex QAM symbol for K = 1,3 . . . , N 2 − 1 and N is the number of subcarriers. The Hermitian constrained X odd input block to the IFFT block generates real time domain signal x odd,n has an anti-symmetric property (Armstrong and Schmidt 2008;Armstrong et al. 2006).This signal is zero clipped to yield the unipolar conventional ACO-OFDM signal generated from odd subcarriers denoted as x ACO odd generated as where x odd, n c = max {x odd, n , 0} ( . c denotes the zero bias clipping operation) (Ranjha and Kavehrad 2014;Wang et al. 2015) and can also be represented as where the clipping distortion |x odd,n | falls on the even subcarriers and does not affect the data x odd,n on the odd subcarriers (Dissanayake and Armstrong 2013;Armstrong et al. 2006). The even stream of subcarriers X even are represented as where X even,K = (X K ) is a complex QAM symbol for K = 0,2, 4 . . . , N 2 − 2. The first and N 2 th subcarriers are not modulated to fulfill the Hermitian symmetry requirements. This resultant signal when input to the IFFT block generates real time domain signal x even and has a symmetric property as As, it has a symmetric property, direct negative clipping of this signal causes loss of information (Wu and Bar-Ness 2015). Alternatively, across the symmetry, clipping is done only one side of the symmetry. The absolute value of the data is performed at the other side of the symmetry and is scaled by half. The resulting signal x mSCO even is given as, where |x even,n−N/2 | represents the absolute value function (|.|) and x even, n c = max {x even, n , 0} (zero bias clipping operation) is also expressed as x even, n c = 1 2 (x even, n + |x even, n |) where the data x even,n and the clipping distortion (| x even,n |) are present on the even subcarriers. The generated real time domain signals x ACO odd and x mSCO even are combined to yield a real valued non-negative signal x mASCO,m given as The combined signal x mASCO,n consists of the undistorted ACO-OFDM signal on the odd subcarriers. The even subcarriers on one side of the symmetry contains the mSCO-OFDM data and the clipping distortions of ACO-OFDM and mSCO-OFDM, while the other side contains only the absolute value of mSCO-OFDM data and clipping distortion of ACO-OFDM.
The combined signal x mASCO,n in Eq. (8) is appended with a Cyclic Prefix (CP) and converted from parallel to serial (P/S). This is followed by the optical modulation process across a flat channel as in (Dissanayake and Armstrong 2013;Wu and Bar-Ness 2015;Baig et al. 2022). The shot noise and thermal noise are modeled as additive white Gaussian noise (AWGN) as in (Dissanayake and Armstrong 2013;Wu and Bar-Ness 2015;Lowery 2016;Yang et al. 2011;Baig et al. 2022).
At the Receiver (Fig. 2), the received signal is first converted from an optical to electrical signal using a photodiode and then converted from analog to digital (A/D). The resulting received signal after removing the CP and parallel to serial conversion (P/S) is given as where w n is modeled as the AWGN. The mASCO-OFDM receiver implements TD-CNE (Wang et al. 2018) so that the data retrieval from the even subcarriers can be done independently. y mASCO, n = x odd, n c + x even, n c + w odd, n + w even, n where w odd,n and w even,n are the AWGN that contribute to the odd and even subcarriers respectively. Considering a flat channel and due to even symmetry w even,n = w even,n− N 2 . Inserting Eqs. (3) and (7) into Eq. (10), and scaling by a factor of 2, yields y mASCO,n =    x odd,n + |x odd,n +x even,n + |x even,n + w odd1,n + w even,n 0 ≤ n ≤ N 2 − 1 (−x odd,n− N 2 + | − x odd,n− N 2 +|x even,n ) + w odd2,n + w even,n N 2 ≤ n ≤ N − 1 As no clipping distortion falls on odd subcarriers, it can be directly estimated from y mASCO odd,n as y odd,n = y mASCO odd,n = x odd,n + w odd,n

Fig. 2 mASCO-OFDM Receiver
This is then input to the FFT and equalized to recover the odd subcarriers symbols Y odd of QAM constellation. The even subcarriers of scaled version of received signal y mASCO,n (represented by Eq. (11)) is split into y mASCO even1,n and y mASCO even2,n where y mASCO even1,n = y mASCO even,n = |x odd,n | + x even,n + |x even,n | + w even,n y mASCO even2,n = y mASCO even,n+N/2 = | − x odd,n− N 2 | + |x even,n | + w even,n Equation (14) can be re-written as y mASCO even2,n = y mASCO even,n+N/2 = |x odd,n | + |x even,n | + w even,n Subtracting Eqs. (13) and (15), yields the even signal in time domain as y even,n = y mASCO even1,n − y mASCO even2,n = |x odd,n | + x even,n + |x even,n | + w even,n −|x odd,n −|x even,n − w even,n = x even,n This noiseless signal is then transformed into frequency domain, from which the even symbols of QAM constellation are recovered.

Complexity analysis
The complexity of the system is determined by the number of complex multiplications of FFT/IFFT operations (Islim and Haas 2016). The computational complexity for ASCO-OFDM transmitter is3O (Nlog 2 N) as it requires two IFFT's for the stream of odd subcarrier, and one IFFT for even subcarriers. The computational complexity of ASCO-OFDM receiver is4O (Nlog 2 N) as it requires two FFT's and IFFT's for the demodulation of its signals.
The computational complexity for the proposed model mASCO-OFDM transmitter is 2O (Nlog 2 N), as it requires two N-point IFFT for its odd and even stream of subcarriers. The computational complexity for the proposed receiver of mASCO-OFDM is2O (Nlog 2 N).
The complexity analysis for mASCO-OFDM and ASCO-OFDM is summarized in Table 1.
The complexity reduction ratio is evaluated to determine the improvement for the proposed system in comparison to the conventional system. The Cr is evaluated as mASCO achieves 33% lower complexity at the transmitter and 50% lower complexity at the receiver. Thus, the overall complexity of mASCO-OFDM reduces to about 43% in comparison to the conventional ASCO-OFDM.

Spectral efficiency
The SE for ACO-OFDM for a large 'N' IFFT size without the CP can be approximated as where Q ACO represent the constellation sizes. The SE approximation for ASCO-OFDM for a large 'N' IFFT size is given by where Q ACO and Q SCO represent the constellation sizes of ACO-OFDM and SCO-OFDM respectively. For a large 'N' IFFT size, the SE approximation for the proposed model is given as where Q ACO and Q mSCO represent the constellation sizes of the ACO-OFDM and mSCO-OFDM streams respectively. The SE's for a large N are evaluated and compared against different QAM constellations for ACO-OFDM, ASCO-OFDM and mASCO-OFDM as shown in Fig. 3.
For this analysis, same constellation size and equal optical power were used for both odd and even subcarriers for the above-mentioned systems. In general, mASCO-OFDM requires a lower order QAM modulation to achieve the same spectral efficiency in comparison to ASCO-OFDM and ACO-OFDM. For example, mASCO-OFDM requires 16-QAM (applied to both odd and even streams) and ACO-OFDM requires 256-QAM to achieve same SE   (17) and (18). Theoretically, compared to ACO-OFDM, mASCO-OFDM requires 16 times lower order QAM, which means it requires lower bandwidth to achieve the same SE. Comparing with ASCO-OFDM, mASCO-OFDM requires 4 times lower order QAM to achieve the same SE. Analyzing for the same QAM, mASCO-OFDM achieves respectively 2 and 1.333 times higher SE than ACO-OFDM and ASCO-OFDM.

Results
The simulation results presented in this section were based on the assumption of a perfect synchronization over an AWGN channel.

Peak average power ratio (PAPR)
The non-linear characteristics of optical devices in IM/DD optical system can cause high PAPR that can deteriorate the system. Hence, PAPR is an important parameter in evaluation of an O-OFDM system (Yang et al. 2011). Some of the precoding techniques mentioned in (Mohammed et al. 2021) have reduced the PAPR, without affecting the bit error rate (BER) performance. The performance of PAPR is evaluated by the complimentary cumulative distribution function (CCDF), which is given as which denotes the probability that the PAPR of an OFDM symbol exceeds a threshold P AP R . Figure 4 shows the comparison of CCDF vs. PAPR curves for mASCO-OFDM and ASCO-OFDM. The total average optical power of each OFDM scheme is normalized to unity as demonstrated in (Dissanayake and Armstrong 2013;Yang et al. 2011) for the schemes in Fig. 4. The simulations were performed for 16-QAM on the odd and even subcar- riers for conventional ASCO-OFDM and mASCO-OFDM respectively. The conventional ACO-OFDM was also simulated for 16-QAM and is used as a reference baseline model. As observed from Fig. 4, the CCDF of the PAPR for mASCO-OFDM is about 0.65 dB and 1.34 dB lower than ASCO-OFDM and the conventional ACO-OFDM respectively. This shows that the proposed mASCO-OFDM has a better resilience to the system non-linearity. Figure 5 shows BER against optical bit energy to noise power ratio (E b(opt) /N o ). The simulation results were verified with Monte-Carlo simulations for 16-QAM and 1024-QAM, and the same constellations were used for both odd and even streams as in (Baig et al. 2018(Baig et al. , 2022. The E b(opt) /N o is expressed as E b(opt) /N o = P opt /b , where 'Popt ' is the optical power of the transmitted signal and ' b ' is the bit rate. The average optical power P opt is set to unity for all the models presented in Fig. 5. The size of the IFFT/FFT is N=1024 and 256 symbols were used.

Bit-error-rate (BER)
As evident in Fig. 5, the proposed mASCO-OFDM has a superior BER performance than ASCO-OFDM. At the BER of 10 −3 , mASCO-OFDM gains 1.73dB and 3.12dB lower E b(opt) /N o than conventional ASCO-OFDM for 16-QAM and 1024-QAM respectively. The performance improvement is significantly due to the reduction of errors in mSCO-OFDM, which was evident by the implementation of TD-CNE, as it did not require the estimation and cancellation of the clipping noise of ACO-OFDM.
From this result, it is observed that the proposed mASCO-OFDM showed better BER performance than ASCO-OFDM for the same QAM and SE. However, in comparison to ACO-OFDM this advantage could only be seen for the same SE, and not for the same QAM

Conclusion
A novel mASCO-OFDM has been successfully presented. The proposed system achieves an overall lower computational complexity and higher SE in comparison to conventional ASCO-OFDM. By exhibiting a better BER performance and lower PAPR in comparison to the conventional ASCO-OFDM, the proposed mASCO-OFDM can be a better alternative for IM/DD systems. The performance of mASCO-OFDM were carried out assuming an ideal flat AWGN channel. The proposed model will be further investigated and analyzed in the case of multipath channel in the future work.