I Introduction
Lightemitting diode (LED)based communications, typical for shortrange optical wireless systems, has attracted much attention in recent research due to its many advantages over radiofrequency (RF) communications. By using LEDs as transmitters, visible light communications (VLC) and infrared (IR) communications are immune to RF interference, have low power consumption, low impact on human health, can offer higher security, and can provide potentially highdatarate transmission. In this paper, we compare two popular modulation schemes often used with LEDbased systems: ary pulse amplitude modulation (MPAM) and orthogonal frequency division multiplexing (OFDM).
Recently, OFDM has been employed in optical wireless communication (OWC) systems due to its resistance to intersymbol interference (ISI) and high spectral efficiency [1]. Since intensity modulation and direct detection are used in OWC systems, the transmitted signal should be nonnegative. Therefore, conventional OFDM cannot be applied directly in OWC. DCbiased optical OFDM (DCOOFDM) is a popular optical OFDM technique that can be applied in OWC that use incoherent light [2]. Hermitian symmetric data is used to make the DCOOFDM signal real. Because of the nonlinear response of LEDs, the DCOOFDM signal must be clipped, distorting the signal.
Alternatively, pulsebased MPAM has been explored to yield a ()fold increase in the data rate compared with onoff keying (OOK) [3]. However, the transmitted data rate is still limited by the low rise time of LEDs. When the transmitted symbol rate is high, ISI can affect the system performance. Equalization is an effective way to reduce the ISI caused by the low LED bandwidth [4]. Some researchers have discussed pre/postequalization, software equalization and hardware equalization methods for VLC [5, 6, 7, 8, 9].
In this paper, we compare the performance of DCOOFDM and MPAM techniques for OWC systems. For DCOOFDM, we model the clipping noise caused by the LEDs’ nonlinearity (clipping at both zero and peak current). We optimize the modulation index and the bits loaded on each subcarrier to maximize the transmitted bit rate despite the limited LED bandwidth. For MPAM, although there is no clipping, the ISI limits the data rate severely. Recently, some researchers proposed a joint waveform design and minimum mean squared error (MMSE) equalization algorithm to combat ISI and multiple access interference in [10]. In this work, the joint optimal waveform design, referred to as JOW, is used to reduce the ISI assuming a single user. We compare the DCOOFDM with bit loading and MPAM with JOW for the same bandwidth LED. From numerical results, the MPAM modulation scheme using the JOW algorithm can support a higher data rate than the optimized DCOOFDM with the same bit error rate (BER) performance.
A comparison between optical OFDM and PAM was discussed in [11]. MPAM with a minimum mean squared error (MMSE) decision feedback equalizer was shown to have a better performance than optical OFDM. However, only zero clipping for optical OFDM is modeled in [11], and preequalization is not considered.
Ii Optimized DCOOFDM
In this section, we describe how we optimize the DCOOFDM system. Due to the LED nonlinearity, the signals may be clipped prior to the LED. The optimized DCOOFDM scheme maximizes the transmitted bit rate by optimizing the modulation index and the bits loaded on all subcarriers.
A block diagram of the optimized DCOOFDM is shown in Fig. 1. To simplify the notation, we analyze the signal in one symbol time. In this diagram, is the data to be modulated on the th subcarrier after ary quadrature amplitude modulation (QAM). We assume that there are subcarriers. To make the OFDM signal real, is the conjugate of , .
After the IFFT, the real OFDM signal for the th component, , can be represented as
(1) 
After converting the parallel data to a serial stream and adding a DC offset, the th sample of the transmitted signal can be represented as where the term is referred to as the modulation index. is the DC bias, which is set to , where is the saturation current to drive the LEDs.
In order to prevent the LEDs from damage, the drive current should remain in the range of . Considering the bandlimited characteristic of LEDs, we model the LED as a clipping component and a lowpass filter in series as shown in Fig. 1. In reality, the signal outside the range is clipped. However, the clipping effect can be modeled as a scaling function plus clipping noise.
After matched filtering and sampling at the receiver, the received signal can be modeled as [12]
(2) 
where is the discrete time version of the impulse response of the LED. is the additive Gaussian noise with power spectral density . When is large (usually greater than 64), the analog signal can be modeled as a Gaussian random process. Since the clipping effect is a nonlinear operator, the constant coefficient can be found by using the Bussagang theorem. [12]
(3) 
where , and
is the variance of the discretetime OFDM signal,
. We model the clipping noise,, as a zero mean Gaussian variable with a variance estimated using
(4) 
where
is the probability density function (pdf) of the samples
.In this paper, we assume the 3 dB modulation bandwidth of the LEDs is limited to a few MHz [8], and the frequency response can be modeled as a first order lowpass filter. Therefore, the channel amplitude for each subcarrier is not the same. At the receiver, the signal to noise ratio (SNR) for the th subcarrier can be calculated as
(5) 
where is the LED response for the th subcarrier. represents the expectation operation, and , is the variance of the receiver additive Gaussian noise over one subcarrier. is the symbol time. Given the SNR, we can calculate the bit error rate (BER) for each subcarrier by using the approximate expression [13]
(6) 
where is the modulation constellation size for the QAM used in the th subcarrier.
The throughput for the DCOOFDM can be calculated as
(7) 
To optimize the throughput, we can choose the optimal , , and the number of bits loaded onto each subcarrier. In this paper, for each subcarrier, the subcarrier bit loading is constrained only by the BER requirement, .
Iii Optimized MPAM
In this section, an optimized MPAM algorithm using a temporal waveform design at the transmitter and MMSE equalization at the receiver is described. This joint optimal waveform (JOW) design algorithm is based on a precoding technique that was proposed recently in [10]. In JOW, the waveforms and MMSE filters can be optimally designed to reduce ISI and support highspeed data transmission rates.
A block diagram of the system is shown in Fig. 2. is the th data after MPAM, where is the modulation constellation size. The discrete time transmitted signal after waveform design can be represented as
(8) 
where is the designed waveform, and is the number of samples describing the waveform, which is a design parameter. Considering the peak drive current constraint, , should be in the range . We assume that the sampling rate, , for the waveform design and at the receiver are the same.
After rectangular matched filtering and sampling, the received signals can be represented as
(9) 
where , is the discrete time version of the truncated impulse response of the LED. is the additive receiver noise. After applying the MMSE filter, , the estimated data can be written in matrix form as
(10) 
where is a Toeplitz matrix that can be represented as , where and are functions that operate as circular shifts of
to the left and right, respectively. The vector of transmitted samples that affect
is denoted, , where , which describes the length of successive samples that blur together. and represent past and future samples that contribute to ISI, respectively.The MMSE filter can be obtained as
(11) 
where , and . The additive constant term is needed for filtering the nonzeromean signal.
is the identity matrix, and
is the noise variance that can be calculated as , where and are noise spectral density and sampling rate, respectively [10]. can be calculated as , with the th element of given by(12) 
After the MMSE filter, the power of the ISI plus noise can be estimated as
(13) 
Thus, the signal to interference plus noise ratio (SINR) can be calculated as [14]
(14) 
After substituting (11) and (13) into (14), we can find that , and are the only variables needed to find . Denoting the SINR as , the BER can be approximately calculated as [13].
(15) 
For different sampling rates and modulation constellation sizes, the waveform design algorithm can adaptively adjust the waveforms to minimize the ISI. For a given sampling chip rate and modulation constellation size, the optimized waveforms can be obtained by maximizing the SINR. The optimization cost function is
(16) 
where is the optimal value for .
Since the transmission bit rate can be calculated as , we need to solve the following problem to maximize the bit rate:
(17) 
where is the required BER, and can be solved using (16) for a given and .
Iv Simulation Results and Comparison
In this section, numerical results of the comparison between DCOOFDM and MPAM are shown. To obtain a fair comparison, the same parameters are used for DCOOFDM and MPAM. Unless otherwise noted, the parameters used to obtain the numerical results are shown in Table I. To simplify the problem, an ideal channel (zero loss) is considered in this paper. In addition, the forward current to optical power conversion ratio of the LED is assumed to be unity. Thus, the LED drive current constraint imposes a constraint on the peak transmitted optical power.
3 dB bandwidth of LEDs,  20 MHz 

Number of subcarriers,  64 
Noise spectral density,  mW/Hz 
BER requirement, 
For DCOOFDM, a compromise is reached between the signal power and clipping noise power by adjusting the modulation index. In Fig. 3, the throughput with different modulation indexes using bit loading is shown. From the results, the number of subcarriers does not seem to affect the maximum throughput.
Fig. 4 shows a comparison between the optimized DCOOFDM and the optimized MPAM using JOW. In this figure, is used to measure the spectral efficiency. MPAM and DCOOFDM can both use more than the 3 dB bandwidth of the LED. However, the clipping distortion caused by the nonlinearity of the LED can affect the performance of the DCOOFDM; therefore, using MPAM with JOW can provide a better performance than DCOOFDM. From the results, the MPAM using JOW can support an higher transmitted bit rate than the optimized DCOOFDM for the parameters tested. With the help of waveform design, JOW can also surpass MPAM that uses only the MMSE equalizer. If there is no equalization technique for MPAM, the optimized DCOOFDM can support about five times higher data rate than MPAM when the transmitted power is 8 mW.
V Conclusion
In this paper, we compare the performance of DCOOFDM and MPAM for LEDbased communication systems. We consider the bandlimited characteristic and the constrained transmitted power of LEDs. We propose an optimized DCOOFDM by choosing the modulation index that maximizes the data rate with bit loading. For MPAM, a joint optimization of the waveform and the receiver filter is proposed to reduce the ISI caused by the bandlimited LED. From numerical results, we conclude that MPAM with waveform design and MMSE equalization can provide a significantly higher data transmission rate than DCOOFDM with bit loading and an optimal modulation index.
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