Impact of clipping noise on the sum rate of NOMA with PD-DCO-OFDM and conventional DCO-OFDM.

sIn visible light communication (VLC) systems, a non-orthogonal multiple access (NOMA) scheme is deemed promising technology to offer better spectral efficiency than the Orthogonal multiple access (OMA) scheme. The feasibility of power domain NOMA for VLC system has been studied with different variants of unipolar OFDM schemes. However, few research works have been presented on the impact of clipping noise on the achievable sum rate of NOMA with DC-biased optical OFDM (DCO-OFDM) and polarity divided DCO-OFDM (PD-DCO-OFDM). This paper presents the impact of clipping noise on the achievable sum rate of NOMA-DCO-OFDM and NOMA-PD-DCO-OFDM VLC systems. Moreover, NOMA-DCO-OFDM and NOMA-PD-DCO-OFDM systems are compared based on achievable sum rates for different total power constraints and signal clipping levels. For the two-user scenario, Simulation results have confirmed that NOMA-PD-DCO-OFDM can offer a better sum rate compared to NOMA-DCO-OFDM system.

Introduction

Visible light communication (VLC) is thought to be a promising complement for conventional RF wireless communication to tackle the challenge of the inevitable spectrum crunch in the conventional RF band [1, 2]. The recent huge deployments of LEDs for lighting purposes have created significant motivation towards simultaneous functionalities of LEDs for both lighting and communication purposes. However, the issue of low modulation bandwidth of LEDs is a well-known challenge towards the implementation of practical VLC. Therefore, spectrally efficient modulation and multiple access schemes are highly needed to maximize the capacity of LED-based VLC systems [3, 4]. To accommodate high-speed communication and massive connectivity in cases of internet of things (IoT) and overly growing mobile internet, VLC should adopt spectrally efficient multiple access and modulation schemes such as NOMA and DCO-OFDM, respectively. NOMA is mostly implemented with OFDM to utilize the inherent advantages of OFDM such as resistance to inter symbol interference (ISI), high spectral efficiency, and the possibility of flexible bandwidth allocation [5, 6, 7]. Different variants of OFDM schemes such as asymmetrically clipped optical OFDM (ACO-OFDM), DCO-OFDM, and PD-DCO-OFDM have been proposed for optical wireless communications [8, 9, 10, 11].

Different alternatives of NOMA (power domain NOMA and code domain NOMA) [2, 12] have been adopted recently to improve the spectral efficiency of DCO-OFDM based VLC system. NOMA improves the spectral efficiency of VLC by enabling the sharing of the same frequency resource for multiple users at the same time. In NOMA, users' data are superimposed with the aid of superposition coding at the transmitter. Successive interference cancelation (SCI) is also performed at the receiver to separate the user's information signal.

In those [13, 14] previous works, NOMA has been studied for VLC without consideration of double-sided clipping noise. In [15], the effect of clipping on the achievable rate of NOMA-DCO-OFDM system was presented in comparisons to the performance of orthogonal multiple access (OMA) scheme. In [11], polarity division DCO-OFDM (PD-DCO-OFDM) was introduced with code domain NOMA to reduce the effect of clipping noise. However, it lacks the analytical modeling of clipping noise when power domain NOMA is implemented with PD-DCO-OFDM.

The goal of this paper is to analyze the impact of clipping distortion on the achievable sum rate of power domain NOMA VLC systems implemented with DCO-OFDM and PD-DCO-OFDM schemes. Analytical frameworks are presented for clipping distortions of NOMA PD-DCO-OFDEM VLC system. Moreover, performances of NOMA DCO-OFDM and NOMA PD-DCO-OFDEM VLC systems are compared based on achievable sum rates.

The other parts of this paper are organized in the following format. Section 2 covers the system model and clipping noise analysis of PD-DCO-OFDM NOMA. Section 3 reviews the system model and clipping noise analysis of DCO-OFDM NOMA. Simulation results are discussed in Section 4 and conclusions are drawn at last in Section 5.

System model of NOMA PD-DCO-OFDM

In this paper, downlink transmission NOMA for a total of two users is considered. Hence, a maximum of two users is sharing the same time-frequency resources to reduce the receiver complexity and error propagation due to imperfect successive interference cancelation (SCI). As shown in Figure 1, the information bits of both users are given as input to the serial and parallel converters and later mapped to QAM symbols and allocated to the available subcarriers.

Figure 1

NOMA PD-DCO-OFDM transmitter block diagram.

Assuming subcarriers are available in the system, the QAM symbol of user at subcarrier is represented as , , . Hermitian symmetry is imposed to obtain real bipolar time-domain signal at the output of the IFFT modules. The QAM symbols which are mapped to subcarriers satisfy the conditions ( and ) [8]. According to the central limit theorem (for enough number of available subcarriers, ), The time-domain signal at the output of the IFFT module follows a zero-mean Gaussian distribution with variance .

As illustrated in Figure 1, superposition of the bipolar signal of the two users is done in power domain. Let is the available electrical power for transmission of both users information signals, the superimposed time-domain signal can be written in the following form [15, 16]:where and are power allocation factors for user-1 and user-2 respectively. Assuming normalized variances for both users (), becomes a zero-mean Gaussian random signal with variance . Let and are the optical channel gains of user-1 and user-2 respectively. Assuming user-1 is the nearest user to the transmitter, the power allocation factors can be obtained from normalized gain power allocation (NGDPA) method as [16]:

For large number of users in the case of indoor multi-users VLC, user grouping strategies based on their channel gains along with different power allocation algorithms can be used to reduce both interference and receiver complexity [1, 17, 18].

In PD-DCO-OFDM NOMA system, positive unipolar and negative unipolar signals are constructed by the polarity divider as:

A DC-offset is added only on to obtain a positive unipolar signal to fulfill the requirement of IM/DD system. Let and , respectively, are the upper and lower dynamic ranges of the LED. Assuming , both and will experience a single-sided clipping, i.e. upper sided clipping on at the point and lower sided clipping on at point .

Clipping distortion of PD-DCO-OFDM

The exact distribution of the time domain clipping noise for practical clipping bounds is yet to be investigated. However, different pieces of literature [19, 20, 21] have modeled the time domain clipping noise in OFDM based OWC as a Gaussian random variable with the aid of Bussgag theorem. The main assumption of this approach is that the time domain signal remains Gaussian after clipping is performed. On the contrary, the assumption of clipping noise as Gaussian distribution is claimed to be valid only for particular conditions [22]. In [22], Kurtosis function is used to measure the normality of the clipped signal distribution and the authors have claimed that the assumption of the time domain clipping noise as Gaussian distribution is accurate only if the range of truncation is wide enough to assure the better part of the signal untouched.

In this paper, the time domain clipping noise has been assumed to be Gaussian and the truncation rages are kept large enough to satisfy the claims on [22]. After clipping has been performed on lower side of and upper side of , the clipped signal and can be written by using Bussgang theorem as [8, 20]:Where and are attenuation coefficients and and are clipping noise components uncorrelated with . Since the input to both processes represented in Eqs. (5) and (6) is the zero-mean Gaussian process, the clipping operator and for and respectively, can be given as [23]:

In PD-DCO-OFDM, the assumption is, the two LEDs are located near to each other and signals from both LEDs merge in the air after propagating a negligible distance. Therefore the clipped signal after the merging of and can be rewritten as:Where is the overall attenuation coefficient and is the total clipping noise component which is uncorrelated with . The clipping operator of can be obtained from Eqs. (7) and (8) by combing and as:

As presented in [20, 23], the attenuation factor can be expressed as:Where , , is covariance operator, and denotes error function.

The variance of the clipping noise can be calculated as:Where is the mean of the clipping noise.

The electrical power of the clipped signal is also calculated from Eq. (12) as:

From Eqs. (12) and (13), the variance of the clipping noise is given by:Where is the 2nd moment of the truncated Gaussian random signal with lower truncation point at and upper truncation point at . Therefore, the term in Eq. (14) is obtained as [24, 25]:Where and are probability distribution function (PDF) and communicative distribution function (CDF) of standard normal distribution respectively. The term in Eq. (14) can also be calculated as the square of the mean of the truncated Gaussian random signal :

Received signal and achievable rate

After removing the DC bias, the received signal of user-1 and user-2, and respectively, can be written as:

Since user-1 has higher channel gain compared to user-2, user -1 should decode the information bits of user-2 and remove the contribution of user-2 signal from before decoding its information bits. With an assumption of perfect SIC, the achievable rate of user-1 and of user-2 become [15, 18]:

The total achievable sum rate can be obtained from Eqs. (19) and (20) as:

The system model of NOMA DCO-OFDM

The system model of downlink NOMA DCO-OFDM is shown in Figure 2 for the two-user scenario. After the information bits of both users mapped to QAM symbols, each QAM symbol is mapped to subcarriers. Let be the QAM symbol of user at subcarrier, Hermitian symmetry is imposed on half of the subcarriers to obtain real bipolar signal at the output of the IFFT module, i.e. and for available subcarriers in the system. Power domain superposition coding is performed on the bipolar time-domain signals and of user-1 and user-2 respectively. For total available power for transmission and power allocation factors and for user-1 and user-2 respectively, the superimposed signal can be written as:

Figure 2

NOMA DCO-OFDM transmitter block diagram.

Since is a bipolar signal, a DC-offset should be added on to obtain a positive unipolar signal. Due to the limited dynamic range of LED, the bipolar signal will experience a double-sided clipping at from the top and at from the bottom.

Clipping noise and achievable rate of NOMA DCO-OFDM

According to Bussgang theorem, the clipped signal can be modeled as:Where is the attenuation coefficient and is the clipping noise component which is uncorrelated with . The clipping distortion operator can also be obtained based on Bussgang theorem as [15]:

The variance of the clipping noise can be obtained as:WhereAnd and

The achievable rate and of NOMA DCO-OFDM for user-1 and user-2 respectively can be obtained by using (19) and (20) respectively. The details of the effect of clipping noise in DCO-OFDM NOMA system can be obtained in [15].

Simulation results

In this part, the achievable sum-rates of NOMA PD-DCO-OFDM and NOMA DCO-OFDM systems are compared with the aid of simulation results for two-user scenario. The following Simulation parameters listed in Table 1 are used for both PD-DCO-OFDM and DCO-OFDM based NOMA VLC systems.

Table 1

Simulation parameters.

P_T	26 W, 30 W, 36 W
λ_b	0
λ_t	28, 32, 35
h_1	1
h_2	0.6

To avoid complete clipping of the non-negative samples of the bipolar signal , a DC bias is set to be less than , i.e. . The dc bias can be defined in relative to the standard deviation of the unclipped signal as [8]:And the DC-offset can be defined in dB as. Due to the equal added DC biases on PD-DCO-OFDM NOMA and DCO-OFDM NOMA schemes, both have comparable power efficiencies. The performance gaps between the two schemes are originated from the unequal achieved SNIR value which is emerged from the unequal magnitudes of the clipping noise on the two schemes. A normalized gain power allocation (NGDPA) method [16] has been adopted throughout all simulations.

The performances of PD-DCO-OFDM NOMA and DCO-OFDM NOMA systems are presented in Figure 3 for , , and . The simulation results show that PD-DCO-OFDM NOMA offers superior performance compared to DCO-OFDM NOMA. It is noted that a DC-bias is not added on the positive samples of PD-DCO-OFDM NOMA. As a result, the upper side clipping noise is reduced and better performance is achieved with PD-DCO-OFDM. For lower DC bias (3–5 dB), the increment in SINR is insignificant when is increased since the magnitude of the clipping noise increases for larger. As a consequence, the performance improvements of NOMA DCO-OFDM is insignificant when is increased in the lower Dc-bias region. When is increased in the DC-bias region beyond 5dB for NOMA DCO-OFDM, the positive and negative samples of the time domain signal will have large peaks and more clipping will be experienced especially on positive valued samples. As a result, the increment in is dominated by the increment in the clipping noise which in turn reduces the SNIR, and consequently, the performance of NOMA DCO-OFDM shows a reverse relation with for DC-biases beyond 5 dB. Contrarily, the performance of PD-DCO-OFDM NOMA is improved when is increased for DC-biases beyond 5 dB. This is because is large enough to avoid upper sided clipping since DC bias is avoided on samples having a positive polarity. Therefore, when the DC bias is increased, the lower side clipping will be negligible and larger SNIR will be achieved for larger.

Figure 3

The achievable sum rate of PD-DCO-OFDM and DCO-OFDM NOMA.

From Figure 3, it is also shown that NOMA DCO-OFDM has reached its peak performances at optimum DC bias of 6 dB, 7 dB, and 8 dB for values of 26 W, 30 W, and 36 W respectively. When the DC bias is increased beyond those optimum values, the performance has declined due to the larger upper side clipping noise.

As illustrated in Figures 4 and 5, for lower DC bias (5–7 dB) and large values (& 35), NOMA DCO-OFDM with larger has shown a slightly better sum rate compared to the NOMA DCO-OFDM system with lower . On the contrary, when the DC bias is large (beyond 7 dB), the larger the , the lower the sum rate of NOMA DCO-OFDM system since the upper side clipping noise increases because of the positive valued samples having large peaks.

Figure 4

The achievable sum rate of PD-DCO-OFDM and DCO-OFDM NOMA.

Figure 5

The achievable sum rate of PD-DCO-OFDM and DCO-OFDM NOMA.

Besides, From Figures 3, 4, and 5, it is shown that for fixed DC bias, for example at 9 dB, the sum rate performance gap between PD-DCO-OFDM NOMA and DCO-OFDM NOMA at the same values has been reduced as increases. This is because both PD-DCO-OFDM and DCO-OFDM experience equal lower side clipping noise for the same transmitted power and the performance gap is mostly due to the unequal upper side clipping nose in the two schemes. However, the upper side clipping noise of NOMA DCO-OFDM can also be minimized when is large enough. When is large, the simulation results show that the gap of the performance between the PD-DCO-OFDM NOMA and DCO-OFDM is reduced for the fixed and DC bias.

Conclusions

In this paper, the analytical framework of double-sided asymmetrical clipping noise has been presented for PD DCO-OFDM NOMA with a two-user scenario. Closed-form formulas for both attenuation factor and clipping noise variance have been given for the case of double-sided clipping in PD-DCO-OFDM NOMA. The impact of clipping noise on the achievable sum rate of NOMA PD-DCO-OFDM has also been presented with the aid of simulation results. Moreover, performance comparisons of DCO-OFDM NOMA and PD-DCO-OFDM NOMA have been presented based on the achievable sum-rate for the case of equal transmitted power and DC bias. The obtained simulation result confirmed that PD-DCO-OFDM NOMA has superior performance compared to DCO-OFDM NOMA.

Declarations

Author contribution statement

Zelalem Hailu Gebeyehu: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Competing interest statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.