2. OFDM principles

This section gives a brief introduction on the principles of OFDM in radio frequency communication which serves as a basis for further reading. The baseband diagram of OFDM is shown in Figure 1. At the transmitter side, coded information bits are first mapped to symbols through digital modulation such as pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), and phase shift keying (PSK). Typically, complex-valued QAM modulation is used

OFDM Systems for Optical Communication with Intensity Modulation and Direct Detection http://dx.doi.org/10.5772/intechopen.68199 87

Figure 1. The "IFFT" module at the receiver side should be "FFT" module.

In IM/DD channel, there are still some non-ideal factors that may deteriorate the quality of communication. One key factor is the multipath effect. This effect is caused by several mechanisms. First, in wireless communications, the light could be reflected at multiple locations and by many times by the surroundings before arriving at the receiver side. Second, the modulation bandwidth of LED is limited, typically below 100 MHz. When the bandwidth of signal exceeds the modulation bandwidth of LED, multipath effect occurs. Third, in fiber communication, light components of different wavelength propagate through different paths, which also cause multipath effect. Therefore, effective means of mitigating the multipath effect are

In RF communication, orthogonal frequency division multiplexing (OFDM) is a powerful multi-carrier modulation scheme to combat the multipath effect. Compared to the singlecarrier modulation schemes, OFDM avoids the usage of a complicated high-order timedomain equalizer. Instead, it employs frequency domain equalizer that only has a single tap. This greatly simplifies the equalization task and can perfectly resolves the multipath effects without any residual errors at high signal-to-noise ratio (SNR) region. Thus, introducing OFDM to IM/DD optical communication is a natural choice. However, different from RF communication, IM/DD requires that the transmitted signal must be real and positive, which imposes strict constraint on the modulation scheme and the original OFDM transceiver must be modified carefully to satisfy the new scenario. In addition, different applications may have diverse emphasis such as spectral efficiency, power efficiency, detection capability, as well as

Within such perspectives, the purpose of this chapter was to analyze the potential forms of OFDM that are suitable for IM/DD transmission as well as various receiver designs in optical communication. We first study the concepts and basic modulation schemes of OFDM systems in IM/DD optical communication. They can be generally classified into three categories: directcurrent-biased optical OFDM (DCO-OFDM), non-DC-biased optical OFDM, and hybrid optical OFDM. We will elaborate the system models and explain the validity of some fancy designs in those systems through analysis. Second, we investigate the preliminary receivers of those OFDM systems. Besides, we will propose a new receiver that is capable of improving the detection performance based on the inherent signal structures of the specific transmitted signal. Third, the spectral efficiencies and computational complexities of different systems and receivers are analyzed and compared. Finally, the bit error rate (BER) performance of different systems is compared through computer simulations to give the reader a whole

picture of different candidate OFDM systems in IM/DD optical communication.

This section gives a brief introduction on the principles of OFDM in radio frequency communication which serves as a basis for further reading. The baseband diagram of OFDM is shown in Figure 1. At the transmitter side, coded information bits are first mapped to symbols through digital modulation such as pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), and phase shift keying (PSK). Typically, complex-valued QAM modulation is used

necessary in IM/DD optical communications.

86 Optical Fiber and Wireless Communications

computational complexity.

2. OFDM principles

in OFDM. Then, the modulated symbols are divided into multiple groups and each group consists of N-modulated symbols, defined as <sup>X</sup> ¼ ½Xð0Þ,Xð1Þ,…,Xð<sup>N</sup> � <sup>1</sup>Þ�<sup>T</sup>, where the group index is omitted here for simplicity. In OFDM, each modulated symbol XðkÞ is loaded on a subcarrier with center frequency <sup>2</sup><sup>π</sup> <sup>N</sup> k and there are N subcarriers in total. All the symbols are transmitted on their subcarriers simultaneously. Mathematically, this is equivalent to transform the vector X by an N-point inverse fast Fourier transform (IFFT) module, resulting in a new vector <sup>x</sup> ¼ ½xð0Þ,xð1Þ,…,xð<sup>N</sup> � <sup>1</sup>Þ�<sup>T</sup>, that is,

$$\mathbf{x}(n) = \frac{1}{\sqrt{N}} \sum\_{k=0}^{N-1} \mathbf{X}(k) e^{\frac{2\pi k n}{N}}.\tag{1}$$

In OFDM, X is generally considered as frequency domain signal and x is viewed as time-domain signal. In addition, x is typically called an OFDM symbol, which is different with the modulated symbol aforementioned. Finally, x is appended at its head with a cyclic prefix (CP), which is just the copy of the last few samples of x. In general, the length of CP is no smaller than the length of transmission channel to avoid inter-symbol interference (ISI) between adjacent OFDM symbols.

Assuming the impulse response of the multipath channel is denoted by <sup>h</sup> ¼ ½hð0Þ, <sup>h</sup>ð1Þ,…, <sup>h</sup>ð<sup>L</sup> � <sup>1</sup>Þ�<sup>T</sup> ; then, the received signal at the receiver after channel transmission is given by

$$r(n) = h(n) \* \mathbb{x}\_{\varepsilon}(n) + \varepsilon(n),\tag{2}$$

where xcðnÞ is the CP-appended version of the time-domain transmitted signal, zðnÞ is the additive white Gaussian noise (AWGN) with zero mean, and \* denotes linear convolution. The receiver first removes the CP parts of received signal, which results in a new vector y of length N, which can be rewritten as

$$\mathbf{y}(n) = h(n) \otimes \mathbf{x}(n) + \mathbf{z}(n),\tag{3}$$

where ⊗ denotes cyclic convolution. We can see that due to the insertion and removal of CP, the linear convolution is now transformed to a cyclic one, which would be beneficial for equalization, as will be shown in the following text.

From signal processing theory, cyclic convolution in time domain is equivalent to product in frequency domain. Based on this fact, by defining YðkÞ, HðkÞ, and ZðkÞ as the N-point fast Fourier transform of yðnÞ, hðnÞ, and zðnÞ, respectively, one has

$$Y(k) = H(k)X(k) + Z(k), \\ k = 0, 1, \ldots, N - 1. \tag{4}$$

As we can see, each frequency-domain symbol XðkÞ is transmitted as if in a flat channel of response HðkÞ and different symbols transmit in different subchannels (subcarriers) without interfering with each other. This greatly simplifies the equalization task. For example, both zero forcing (ZF) and minimum mean square error (MMSE) equalization can be performed to recover XðkÞ which only involves single-tap equalizer per subcarrier:

$$\widehat{X}(k) = \begin{cases} \frac{Y(k)}{H(k)} & \text{' } \quad \text{ZF} \\\\ \frac{H^\*(k)Y(k)}{\left|H(k)\right|^2 + \sigma\_n^{-2}}, & \text{MMSE} \end{cases} \tag{5}$$

where σ<sup>n</sup> <sup>2</sup> is the variance of noise. The processing in Eqs. (4) and (5) can be realized by performing FFT and per-subcarrier equalization, as shown in Figure 1.

#### 3. Optical OFDM systems for IM/DD channel

#### 3.1. Preliminaries

In IM/DD channel, there is a key difference with RF channel: the transmitted signal must be real and positive. This results from the fact that the intensity of light must be a real and positive quantity. Therefore, the structure for OFDM shown in Figure 1 cannot be directly used in IM/ DD optical channel. Necessary changes must be made instead. A common approach is to generate a real time-domain signal first. This can be realized by imposing Hermitian symmetry on the frequency domain signal X, which is defined as follows:

$$X(N-k) = X^\*(k), \\ k = 1, \ldots, N-1, \\ X(0) = X(N/2) = 0. \tag{6}$$

It can be easily shown that the IFFT of X having property Eq. (6) is a pure real-valued signal x. Based on this real signal, one can further generate a positive signal to drive the optical source by various means. Those resultant new OFDM systems are typically referred to as optical OFDM systems.

#### 3.2. DC-biased optical OFDM

The most straightforward approach to generate a positive signal from a real signal is to impose a proper DC bias. In optical communication, the DC bias is typically chosen such that the mean value of the positive signal just lies on the center point of the linear range of the optical source. This system is called direct current-biased optical OFDM, or DCO-OFDM, whose transmitter is shown in Figure 2.

The clipping module shown in Figure 2 is necessary. Since xðnÞ is Gaussian distributed, it is possible that xðnÞ plus a DC bias is still out of the linear range of the optical source. For example, if an LED accepts driving current within the range of [a, b], where 0 ≤ a < b, then the OFDM Systems for Optical Communication with Intensity Modulation and Direct Detection http://dx.doi.org/10.5772/intechopen.68199 89

Figure 2. Diagram of DCO-OFDM transmitter.

clipping is needed to confine xðnÞ plus a DC bias into this range. Otherwise, the LED could not be illumined due to under-driving or even be damaged due to over-driving.

#### 3.3. Non-DC-biased optical OFDM

Besides DCO-OFDM, there are many forms of optical OFDM systems that are not relying on DC bias. The most famous ones are introduced in this subsection.

#### 3.3.1. ACO-OFDM

YðkÞ ¼ HðkÞXðkÞ þ ZðkÞ, k ¼ 0, 1, …, N � 1: ð4Þ

ðkÞ, k ¼ 1, …, N � 1, Xð0Þ ¼ XðN=2Þ ¼ 0: ð6Þ

ð5Þ

As we can see, each frequency-domain symbol XðkÞ is transmitted as if in a flat channel of response HðkÞ and different symbols transmit in different subchannels (subcarriers) without interfering with each other. This greatly simplifies the equalization task. For example, both zero forcing (ZF) and minimum mean square error (MMSE) equalization can be performed to

YðkÞ

ðkÞYðkÞ

In IM/DD channel, there is a key difference with RF channel: the transmitted signal must be real and positive. This results from the fact that the intensity of light must be a real and positive quantity. Therefore, the structure for OFDM shown in Figure 1 cannot be directly used in IM/ DD optical channel. Necessary changes must be made instead. A common approach is to generate a real time-domain signal first. This can be realized by imposing Hermitian symmetry

It can be easily shown that the IFFT of X having property Eq. (6) is a pure real-valued signal x. Based on this real signal, one can further generate a positive signal to drive the optical source by various means. Those resultant new OFDM systems are typically referred to as optical

The most straightforward approach to generate a positive signal from a real signal is to impose a proper DC bias. In optical communication, the DC bias is typically chosen such that the mean value of the positive signal just lies on the center point of the linear range of the optical source. This system is called direct current-biased optical OFDM, or DCO-OFDM, whose transmitter is

The clipping module shown in Figure 2 is necessary. Since xðnÞ is Gaussian distributed, it is possible that xðnÞ plus a DC bias is still out of the linear range of the optical source. For example, if an LED accepts driving current within the range of [a, b], where 0 ≤ a < b, then the

H�

<sup>H</sup>ðk<sup>Þ</sup> , ZF

<sup>j</sup>HðkÞj<sup>2</sup> <sup>þ</sup> <sup>σ</sup>n<sup>2</sup> , MMSE

<sup>2</sup> is the variance of noise. The processing in Eqs. (4) and (5) can be realized by

recover XðkÞ which only involves single-tap equalizer per subcarrier:

8 >>><

>>>:

performing FFT and per-subcarrier equalization, as shown in Figure 1.

X \_ ðkÞ ¼

3. Optical OFDM systems for IM/DD channel

on the frequency domain signal X, which is defined as follows:

XðN � kÞ ¼ X�

where σ<sup>n</sup>

3.1. Preliminaries

88 Optical Fiber and Wireless Communications

OFDM systems.

shown in Figure 2.

3.2. DC-biased optical OFDM

Asymmetrically clipped optical OFDM (ACO-OFDM) is the most famous non-DC-biased optical OFDM system and has been extensively studied in literature [1]. The basic idea of ACO-OFDM is to generate an asymmetrically structured time-domain signal such that direct clipping at zero (without adding DC bias) is allowed without any information loss. To do so, the frequency-domain input symbol X has a special structure besides satisfying Hermitian symmetry. Specifically, the odd components of X contain useful information U but the even components of X are set to zeros. This is shown in Figure 3.

After IFFT, the time-domain signal x has an asymmetrical structure:

$$\mathbf{x}(n) = -\mathbf{x}\left(n + \frac{N}{2}\right), n = 0, 1, \dots, N/2. \tag{7}$$

As shown in Figure 4, signal x can be directly clipped at zero without adding any DC bias, yet the information is kept after clipping thanks to the asymmetrical structure.

Figure 3. Diagram of ACO-OFDM transmitter.

Figure 4. Asymmetrical structure before and after clipping at zero in ACO-OFDM.

#### 3.3.2. PAM-DMT

Pulse amplitude modulation-discrete multi-tone (PAM-DMT) is another non-DC-biased optical OFDM system [2]. It is similar to ACO-OFDM, in that direct clipping is used. However, the difference is that in PAM-DMT, only the imaginary part of subcarrier input X carries useful information U while the real part is set to zero, as shown in Figure 5. Note that PAM modulation should be used in PAM-DMT rather than QAM in DCO-OFDM and ACO-OFDM.

It can be easily shown that the resultant time-domain signal x also has an asymmetric structure but is slightly different with that of ACO-OFDM, which is shown in Eq. (8) and Figure 6:

$$\mathbf{x}(n) = -\mathbf{x}(N-n), n = 1, 2, \dots, \frac{N}{2}, \mathbf{x}(0) = \mathbf{x}\left(\frac{N}{2}\right) = 0. \tag{8}$$

Figure 5. Diagram of PAM-DMT transmitter.

Figure 6. Asymmetrical structure before and after clipping at zero in PAM-DMT.

#### 3.3.3. Flip-OFDM

3.3.2. PAM-DMT

90 Optical Fiber and Wireless Communications

Figure 5. Diagram of PAM-DMT transmitter.

Pulse amplitude modulation-discrete multi-tone (PAM-DMT) is another non-DC-biased optical OFDM system [2]. It is similar to ACO-OFDM, in that direct clipping is used. However, the difference is that in PAM-DMT, only the imaginary part of subcarrier input X carries useful information U while the real part is set to zero, as shown in Figure 5. Note that PAM modulation should be used in PAM-DMT rather than QAM in DCO-OFDM and ACO-OFDM. It can be easily shown that the resultant time-domain signal x also has an asymmetric structure but is slightly different with that of ACO-OFDM, which is shown in Eq. (8) and Figure 6:

�me

(a) unclipped signal (b) clipped signal

N/2 N-1

Figure 6. Asymmetrical structure before and after clipping at zero in PAM-DMT.

amplitude amplitude

�me

N

<sup>2</sup> , xð0Þ ¼ <sup>x</sup>

N 2 

(b) clipped signal

N/2 N-1

¼ 0: ð8Þ

�me

N/2 N-1

�me

xðn޼�xðN � nÞ, n ¼ 1, 2,…,

(a) unclipped signal

Figure 4. Asymmetrical structure before and after clipping at zero in ACO-OFDM.

N/2 N-1

amplitude amplitude

Both ACO-OFDM and PAM-DMT rely on specially designed signal structures on the frequencyand time-domain signals. In contrast, flip-OFDM employs a simpler way such that a general frequency-domain signal X without any fancy structure is accepted [3]. Instead, the real timedomain signal x, without any symmetry, is split into two parts: the first part only contains the samples of positive ones in x, the negative ones are set to zeros; the second part only contains the samples of negative ones, but with flipped signs, and leaves the positive ones as zeros. This is shown in Figure 7.

Mathematically, the first and second parts of the flipped signal are given by

$$\mathbf{x}\_1(n) = \frac{\mathbf{x}(n) + |\mathbf{x}(n)|}{2}, \mathbf{x}\_2(n) = \frac{-\mathbf{x}(n) + |\mathbf{x}(n)|}{2}, n = 0, 1, \dots, N - 1. \tag{9}$$

After flip processing, the two signal parts are appended with CP, respectively, and are transmitted on channel consecutively. In some literature, flip-OFDM is also referred to as unipolar OFDM (U-OFDM).

Figure 7. Signal structure before and after flipping processing in flip-OFDM.

#### 3.4. Duality of non-DC-biased optical OFDM systems

This section gives a brief introduction on the duality of the non-DC-biased optical OFDM systems. Based on this duality, many receiver design methods could be easily extended from one system to other systems.

For ACO-OFDM, the transmitted signal is given by

$$\mathbf{x}\_c = (\mathbf{x} + |\mathbf{x}|)/2,\tag{10}$$

and x can be written as x ¼ ½x1; � x1� <sup>T</sup>, where x<sup>1</sup> is the first half of x. Therefore, the first and second halves of x<sup>c</sup> can be written as

$$\mathbf{x}\_{c,1}(n) = \frac{\mathbf{x}\_1(n) + |\mathbf{x}\_1(n)|}{2}, \mathbf{x}\_{c,2}(n) = \frac{-\mathbf{x}\_1(n) + |\mathbf{x}\_1(n)|}{2}, \tag{11}$$

which is exactly the same as the model in Eq. (9) except that the size is changed from N to N/2. For PAM-DMT, the transmitted signal is also given by Eq. (10). However, the unclipped signal x is slightly different, that is, x ¼ ½x1;x2� <sup>T</sup>, where <sup>x</sup><sup>2</sup> ¼ �Jx<sup>1</sup> with <sup>J</sup> being a matrix whose anti-diagonal elements are 1s and other elements are all 0s. Now, the first and second halves of the transmitted signal are given by

$$\mathbf{x}\_{c,1} = \frac{\mathbf{x}\_1 + |\mathbf{x}\_1|}{2}, \mathbf{x}\_{c,2} = \frac{-f\mathbf{x}\_1 + f|\mathbf{x}\_1|}{2}. \tag{12}$$

However, JJ = I; therefore, by defining xc,<sup>3</sup> ¼ Jxc,2, we have

$$\mathbf{x}\_{c,1} = \frac{\mathbf{x}\_1 + |\mathbf{x}\_1|}{2}, \mathbf{x}\_{c,3} = \frac{-\mathbf{x}\_1 + |\mathbf{x}\_1|}{2}. \tag{13}$$

Now, Eq. (13) is exactly the same as Eqs. (9) and (11).

Therefore, we can see that ACO-OFDM, PAM-DMT, and flip-OFDM essentially share the same signal structure and there is a duality between them. Based on this fact, the receivers designed for one system can be readily extended to other systems with simple substitution of variables.

#### 3.5. Hybrid systems

Beside the basic forms of DC and non-DC-biased optical OFDM systems, there also exist some hybrid ones where multiple basic systems are superimposed in a specially designed fashion. In general, hybrid systems can be further classified into three categories.

#### 3.5.1. Hybrid optical OFDM based on DCO-OFDM and a non-DC-biased one

A representative for this kind of system is ADO-OFDM, which combines DCO-OFDM and ACO-OFDM in a special way [4]. Specifically, in ACO-OFDM, the useful data are only loaded on the odd subcarriers, as illustrated in Figure 3, the even subcarriers are forced to be zero. After clipping in time domain, the clipping noise only falls onto even subcarriers and the odd subcarriers are not affected by the clipping noise. At the receiver side, the data could be recovered by using only the odd subcarriers. With the recovered data, one can further perfectly reconstruct the clipping noise on even subcarriers. Therefore, in ACO-OFDM, the even subcarriers can be exploited to load more data, which is the basic idea of ADO-OFDM.

In ADO-OFDM, the odd subcarriers are performed exactly the same as the ACO-OFDM. For the even subcarriers, a modified DCO-OFDM signal is generated, in which only the even subcarriers are used. Then, the signals generated from ACO-OFDM and DCO-OFDM are added together to obtain the ADO-OFDM signal. At the receiver side, ACO-OFDM signal, which is on odd subcarriers, are first detected. Then, the clipping noise on even subcarriers is estimated and subtracted. After that, the even subcarriers contain only DCO-OFDM signal, which is finally decoded.

#### 3.5.2. Hybrid optical OFDM based on two different non-DC-biased ones

HACO-OFDM, or hybrid ACO-OFDM, combines ACO-OFDM and PAM-DMT in one system [5]. The basic idea is similar to that of ADO-OFDM, that is, the odd subcarriers are used for ACO-OFDM transmission while the even subcarriers are used for PAM-DMT transmission. At the receiver side, interference cancellation is used for even subcarriers before decoding PAM-DMT signal. An alternative form for HACO-OFDM is also proposed [6].

#### 3.5.3. Hybrid optical OFDM based on a same non-DC-biased one

anti-diagonal elements are 1s and other elements are all 0s. Now, the first and second halves of

<sup>2</sup> , xc,<sup>2</sup> <sup>¼</sup> �Jx<sup>1</sup> <sup>þ</sup> <sup>J</sup>jx1<sup>j</sup>

<sup>2</sup> , xc,<sup>3</sup> <sup>¼</sup> �x<sup>1</sup> þ jx1<sup>j</sup>

Therefore, we can see that ACO-OFDM, PAM-DMT, and flip-OFDM essentially share the same signal structure and there is a duality between them. Based on this fact, the receivers designed for one system can be readily extended to other systems with simple substitution of variables.

Beside the basic forms of DC and non-DC-biased optical OFDM systems, there also exist some hybrid ones where multiple basic systems are superimposed in a specially designed fashion. In

A representative for this kind of system is ADO-OFDM, which combines DCO-OFDM and ACO-OFDM in a special way [4]. Specifically, in ACO-OFDM, the useful data are only loaded on the odd subcarriers, as illustrated in Figure 3, the even subcarriers are forced to be zero. After clipping in time domain, the clipping noise only falls onto even subcarriers and the odd subcarriers are not affected by the clipping noise. At the receiver side, the data could be recovered by using only the odd subcarriers. With the recovered data, one can further perfectly reconstruct the clipping noise on even subcarriers. Therefore, in ACO-OFDM, the even subcarriers can be exploited to load more data, which is the basic idea of ADO-OFDM.

In ADO-OFDM, the odd subcarriers are performed exactly the same as the ACO-OFDM. For the even subcarriers, a modified DCO-OFDM signal is generated, in which only the even subcarriers are used. Then, the signals generated from ACO-OFDM and DCO-OFDM are added together to obtain the ADO-OFDM signal. At the receiver side, ACO-OFDM signal, which is on odd subcarriers, are first detected. Then, the clipping noise on even subcarriers is estimated and subtracted. After that, the even subcarriers contain only DCO-OFDM signal,

HACO-OFDM, or hybrid ACO-OFDM, combines ACO-OFDM and PAM-DMT in one system [5]. The basic idea is similar to that of ADO-OFDM, that is, the odd subcarriers are used for ACO-OFDM transmission while the even subcarriers are used for PAM-DMT transmission.

<sup>2</sup> : <sup>ð</sup>12<sup>Þ</sup>

<sup>2</sup> : <sup>ð</sup>13<sup>Þ</sup>

xc,<sup>1</sup> <sup>¼</sup> <sup>x</sup><sup>1</sup> þ jx1<sup>j</sup>

xc,<sup>1</sup> <sup>¼</sup> <sup>x</sup><sup>1</sup> þ jx1<sup>j</sup>

general, hybrid systems can be further classified into three categories.

3.5.2. Hybrid optical OFDM based on two different non-DC-biased ones

3.5.1. Hybrid optical OFDM based on DCO-OFDM and a non-DC-biased one

However, JJ = I; therefore, by defining xc,<sup>3</sup> ¼ Jxc,2, we have

Now, Eq. (13) is exactly the same as Eqs. (9) and (11).

the transmitted signal are given by

92 Optical Fiber and Wireless Communications

3.5. Hybrid systems

which is finally decoded.

Another form of hybrid optical OFDM is to superimpose multiple blocks of signals from a same non-DC-biased OFDM system. For example, enhanced unipolar OFDM (eU-OFDM) involves multiple blocks of signals from flip-OFDM [7]. Figure 8 shows its time-domain structure with three layers [8], where the symbols x<sup>þ</sup> i,j and x� i,j denote, respectively, the positive and flipped negative parts of the original j-th bipolar signal xi,j from layer-i. Each layer is just a repetition of flip-OFDM time-domain signal. We can see that for the first layer, four normal flip-OFDM symbols are used. For the second layer, two normal flip-OFDM symbols are repeated two times. For the third layer, one normal flip-OFDM symbol is repeated four times. Then, all the time symbols from three layers are added for transmission.

The receiver detection is very simple. The first layer is firstly decoded using normal subtraction. The second and third layers do not interfere in this procedure due to perfect selfcancellation. After the first layer is decoded, its impact is subtracted from the received signal. Then, the second layer is decoded subsequently. Then, the second layer signal is subtracted from the received signal and the third layer is decoded finally.

Besides eU-OFDM, the overlapping of ACO-OFDM or PAM-DMT is also proposed in literatures [9–11]. They all share similar idea with eU-OFDM and the receiver is based on layer-bylayer decoding.


Figure 8. Illustration of a three-layer eU-OFDM time-domain signal components.
