## Abstract

In this paper, we theoretically analyze and demonstrate that spectral efficiency of a conventional direct detection based optical OFDM system (DDO-OFDM) can be improved significantly using frequency interleaving of adjacent DDO-OFDM channels where OFDM signal band of one channel occupies the spectral gap of other channel and vice versa. We show that, at optimum operating condition, the proposed technique can effectively improve the spectral efficiency of the conventional DDO-OFDM system as much as 50%. We also show that such a frequency interleaved DDO-OFDM system, with a bit rate of 48 Gb/s within 25 GHz bandwidth, achieves sufficient power budget after transmission over 25 km single mode fiber to be used in next-generation time-division-multiplexed passive optical networks (TDM-PON). Moreover, by applying 64- quadrature amplitude modulation (QAM), the system can be further scaled up to 96 Gb/s with a power budget sufficient for 1:16 split TDM-PON.

©2010 Optical Society of America

## 1. Introduction

Optical orthogonal frequency division multiplexing (O-OFDM) brings the benefit of electronic equalization and robustness against multi-path fading of legacy wireless-OFDM systems into the optical domain to combat against fiber impairments, such as chromatic dispersion and polarization mode dispersion (PMD) and achieved impairments-tolerant ultra high speed optical systems [1–3]. Depending on the detection mechanisms, O-OFDM systems can be broadly categorized into two sub-groups namely, coherent O-OFDM (CO-OFDM) and directly detected (incoherent) O-OFDM (DDO-OFDM). Among them, CO-OFDM systems are found to be more complex and expensive, as they require additional signal conditioning devices both in the transmitting and receiving ends [4]. On the other hand, a DDO-OFDM system [5] offers simpler transmitter and receiver architectures; therefore, has the potential to

be used in next-generation 40 Gb/s and 100 Gb/s optical access systems, which expect to avoid inline optical amplification and dispersion compensation for simplicity and low-cost [6–9]. Since a DDO-OFDM system directly detects the signal using a square law photodetector (PD), it must have a spectral gap between the optical carrier and OFDM signal band to accommodate subcarrier-to-subcarrier beat interference (beat noise), which otherwise would contaminate the actual data. At optimum operating condition, this required spectral gap needs to be either equal to or greater than the OFDM signal bandwidth [10, 11]. Therefore, in a DDO-OFDM system, at least half of the signal bandwidth remains unused, reducing the effective optical spectral efficiency (SE) enormously [12, 13].

Different approaches have been proposed recently to increase the spectral efficiency of DDO-OFDM systems [12–15]. The first approach [12] introduces techniques to either avoid or use less spectral gap by applying an iterative signal processing algorithm that reduces the beat noise from the detected signal. This iterative signal processing algorithm is computationally intensive and requires additional fast Fourier transform (FFT) and inverse-FFT (IFFT) operations in every iteration, which is complex and time consuming; therefore, may not be suitable for high speed communications, such as 100 Gb/s. The second [13, 14] and third [15] approaches apply polarization division multiplexing (POLMUX) scheme, and respectively self-coherent [16] and direct-detection schemes to achieve spectrally efficient 100 Gb/s O-OFDM in long-haul communications. POLMUX systems are however, quite complex and expensive while considered for short haul communications, such as passive optical network (PON).

In order to resolve these issues in short-haul communications, such as PON, a frequency interleaving method has been proposed where two neighboring DDO-OFDM channels are overlapped in such a way that the mandatory spectral gap of a channel is being occupied by the OFDM signal band of its neighbor and vice versa. This overlapping enhances the spectral efficiency of a conventional DDO-OFDM system significantly, as shown in Fig. 1 [17–19]. In this paper, we extend the previous work and demonstrate such a frequency interleaved DDO-OFDM system both by theoretical analysis and numerical simulations. The system is developed by focusing the delivery of next-generation 40 Gb/s and 100 Gb/s optical access systems over current time-division-multiplexed passive optical networks (TDM-PON) architectures, where inline optical amplification and dispersion compensation are avoided for simplicity and low-cost. Our results show that, at optimum operating condition, frequency interleaving of two adjacent DDO-OFDM channels can increase the spectral efficiency up to 50% over a standard DDO-OFDM system. It is also found that such a frequency interleaved DDO-OFDM system, with a bit rate of 48 Gb/s within 25 GHz bandwidth, achieves sufficient power budget after transmission over 25 km single mode fiber (SMF) to be used in already deployed TDM-PONs with a split ratio of 1:32/64/128. Moreover, instead of 8-quadrature amplitude modulation (QAM), by applying 64-QAM, the system capacity can be further increased to 96 Gb/s with a power budget sufficient for 1:16 split TDM-PON.

The paper is organized as follows. Section 2.1 describes the theory of operation of the proposed system, Section 2.2 explains the effective spectral efficiency of the system, Section 3 illustrates the simulation setup, Section 4 discusses the simulation results and Section 5 is the conclusion.

## 2. System description

Shown in Fig. 1, we propose that a conventional DDO-OFDM channel modulated in optical single sideband with carrier (OSSB + C) format with an effective bandwidth of *B* can be redesigned by frequency interleaving of two adjacent OSSB + C formatted DDO-OFDM channels, where upper sideband (Band-1) of one channel falls within the mandatory spectral gap between the lower sideband (Band-2) and optical carrier of other channel and vice versa. The theory of operation and effective spectral efficiency of the proposed system is explained in the following subsections.

#### 2.1 Theory of operation

A baseband OFDM signal with cyclic prefix can be represented mathematically [20] as,

*i*-th information symbol at

*k*-th subcarrier, ${T}_{s}$ is the symbol duration at subcarrier level, ${f}_{k}=\frac{k-1}{{T}_{s}}$ is the subcarrier frequency, ${T}_{CP}$ is the guard interval due to cyclic prefix (CP) extension, and $f\left(t\right)$ is the rectangular pulse waveform expressed as $f(t)=\{\begin{array}{c}1,\text{}\left(-{T}_{CP}\text{}t\text{}\text{}{T}_{s}-{T}_{CP}\right)\\ 0,\text{}\left(t\text{}\le \text{}{T}_{CP},\text{}t{T}_{s}-{T}_{CP}\right)\end{array}$.

For simplicity, Eq. (1) is considered for the first information symbol (*i* = 0) at time ${t}_{0}$ where $-{T}_{CP}<{t}_{0}<\text{}{T}_{s}-{T}_{CP}$ and expressed as:

Eq. (2) is then up-converted by a radio frequency (RF) carrier, ${E}_{RF1}{e}^{j\left[2\pi {f}_{RF1}{t}_{0}+{\phi}_{RF1}\left({t}_{0}\right)\right]}$:

*E*is the amplitude, ${f}_{RF1}$ is the frequency, and ${\varphi}_{RF1}\left({t}_{0}\right)$ is the phase noise of RF carrier respectively.

_{RF1}Eq. (3) was then multiplied by an optical carrier (${E}_{1}{e}^{j\left[2\pi {f}_{1}{t}_{0}+{\phi}_{1}\left({t}_{0}\right)\right]}$) to generate O-OFDM signal and expressed as:

*E*is the amplitude, ${\phi}_{1}\left({t}_{0}\right)$ is the phase noise and ${f}_{1}$ is the frequency of the optical carrier respectively. Also in Eq. (4), ${m}_{1}$ and ${\theta}_{1}\left({t}_{0}\right)$denote modulation index and modulator bias phase shift respectively. For simplicity, Eq. (4) assumed values for

_{1}*E*and

_{RF1}*E*as unity.

_{1}After Taylor series expansion of Eq. (4) we get,

Eq. (5) shows two OFDM sidebands generated at (${f}_{1}+{f}_{RF1}$) and (${f}_{1}-{f}_{RF1}$). Taking only the upper sideband and the respective optical carrier into consideration, the OSSB + C formatted O-OFDM signal (channel-1) can be simplified as:

Instead of upper sideband, considering the lower sideband of a second O-OFDM signal (channel-2), Eq. (6) can be re-written as:

*p*-th subcarrier, frequency of RF carrier, phase noise of RF carrier, frequency of optical carrier, phase noise of optical carrier, modulation index, and modulator bias phase shift of second O-OFDM channel. For clarity, Eq. (6) and Eq. (7) can be simplified respectively to:

Now, after interleaving, the schematic optical spectra of these signals can be drawn as Fig. 2 (a)
. In order to detect the desired signal ${A}_{1}({t}_{0})$ at the receiver, we assume that the interleaved channel ${A}_{2}({t}_{0})$ is suppressed by a factor *V,* where *V* is defined as the ratio of the attenuated signal to the original signal before attenuation. After square law PD, the detected output can be expressed as:

*R*is the responsivity of the PD and (.)* denotes the complex conjugate of (.) term.

Real signal components of Eq. (8) are shown schematically in Fig. 2 (b). It shows that the desired OFDM signal ${A}_{1\_data}({t}_{0}){A}_{1\_carrier}^{*}({t}_{0})$ is interfered by the beating products $V{A}_{1\_data}({t}_{0}){A}_{2\_data}^{*}({t}_{0})$ and ${V}^{2}{A}_{2\_data}({t}_{0}){A}_{2\_carrier}^{*}({t}_{0})$, unless the unwanted signal components are suppressed sufficiently. It also shows that the subcarriers closer to the null are more affected than the remaining subcarriers.

Now if we consider the detected OFDM signal as well as the in-band interfering components, Eq. (8) simplifies to Eq. (9).

Shown in Eq. (9), the first component denotes the desired OFDM signal (${I}_{sig}$), whereas the second and the third components denote unwanted OFDM band-OFDM band beat noise (${I}_{SSBI}$), multiplied by the factor *V* and unwanted adjacent channel interference (${I}_{ACI}$) multiplied by the factor *V*
^{2} respectively. Therefore Eq. (9) confirms that, with sufficient suppression of the unwanted signal components (smaller value for *V*), the effects of ${I}_{SSBI}$ and ${I}_{ACI}$ will be negligible and error free recovery of the desired signal will be achieved.

#### 2.2 Effective spectral efficiency

In order to facilitate demultiplexing at the receiver, each OFDM signal band requires sufficient guard bands, as shown in Fig. 3 (a)
. Let us assume that each OFDM signal band occupies a signal bandwidth of α*B*, where *B* is the total system bandwidth and α is a multiplication factor. To ensure the mandatory spectral gap in a DDO-OFDM system, value of α can be as large as ½. However, the expected increase in spectral utilization due to interleaving limits the lower value of α to ¼. Therefore, the guard band (β) within an optical

carrier and the adjacent OFDM band can be expressed as $\left(\text{\xbd}B-\alpha B\right)/2$, as shown in Fig. 3 (a).

Now, the increase in spectral efficiency (SE) due to interleaving, γ, can be expressed as:

Fig. 3 (b) shows the relationships among γ, α, and β. It shows that the plots γ vs. α and β vs. α intersect at a point where α is 0.375. This point offers an increased spectral efficiency of 50%. This efficiency can be further increased if guard band requirement of the filters can be reduced. This may however impose stringent requirements on filter’s response. Potential technologies for such filters are microring resonators [21, 22] and fiber Bragg gratings (FBG) [23] with temperature control [24] or athermal filter design [25].

## 3. Simulation setup

To verify the effectiveness of the frequency interleaving scheme, we assume an optical grid with a channel spacing of 25 GHz. In such a system a conventional DDO-OFDM channel can have a maximum OFDM bandwidth of 12.5 GHz. Instead, by applying frequency interleaving technique, we have chosen two OFDM channels each with a bandwidth of 9.5 GHz resulting in a total OFDM bandwidth of 19 GHz within the same 25 GHz available system bandwidth. This improves the overall spectral efficiency of the system by 50%. The system is modeled using VPItransmissionMaker^{TM}7.6 [26] as shown in Fig. 4
, where each of the DDO-OFDM channels comprises of a zero filled centre subcarrier, surrounded by 194 orthogonal subcarriers. Among these subcarriers, 186 subcarriers carry 8-quadrature amplitude modulation encoded PRBS data and 8 (eight) equally spaced pilot subcarriers carry binary phase shift keyed (BPSK) encoded pilot symbols. Then the OFDM signal with necessary oversampling is generated by a 256 point inverse fast Fourier transform (IFFT) module by filling the remaining subcarriers with zeros. The last 32 samples of each OFDM symbol (12.5% of the IFFT size) are added in the beginning of the symbol as a cyclic prefix. The generated block of complex valued OFDM symbols are then serialized, separated into in-phase (*I*) and quadrature (*Q*) components, and converted to analog wave forms using two digital-to-analog (DAC) modules with a sampling rate of 12.5 GS/s such that after up-converting these *I* and *Q* signals to an intermediate RF frequency (18.75 GHz), an OFDM signal with a bandwidth of 9.5 GHz ($195\text{}\times \text{}43.4\text{}\times \text{}{10}^{6}\text{}\times \text{}1.125$) is generated carrying 24 Gb/s ($\text{186}\times \text{43 .4}\times {\text{10}}^{\text{6}}\times \text{3}$) of data. The peak-to-peak amplitude of the RF oscillator (*Vpp*) was 2

a.u. and the root-mean-square amplitude of the electrical OFDM signal (*Vrms*) was calculated to be 0.2. Then this RF modulated OFDM signal is modulated over an optical carrier using a Mach-Zehnder modulator (MZM) with an insertion loss of 4 dB and a bias voltage (*VpiDC* = 4.5 V) close to its transmission null (*VpiDC* = 5 V) [10, 11]. The optical modulation index (OMI) of the O-OFDM system was therefore 0.4, which can be defined as *Vpp* / *VpiRF* (*VpiRF* = 5 V in this case). The first O-OFDM transmitter then generates a double sideband with career (ODSB + C) formatted optical signal using a laser module with 100 kHz linewidth (LLW), relative intensity noise (RIN) of −140 dB/Hz and 3 mW average power at an emission frequency of 193.1 THz, whereas the second transmitter generates a similar ODSB + C signal using a similar laser module with an emission frequency 25 GHz apart from the first place. After generating the ODSB + C formatted O-OFDM signals, lower side band of the first channel and the upper side of the second channel are then removed using suitably tuned optical band pass filters (OBPF) and amplified to 0 dBm to offset modulation losses. Two such 24 Gb/s OSSB + C formatted signals are then combined using an optical power combiner to generate the desired frequency interleaved 48 Gb/s DDO-OFDM signal. The composite signal is then transmitted over 25 km single mode fiber (SMF) with a dispersion of 17 ps/nm/km, attenuation of 0.2 dB/km, nonlinear index of $2.6\times {10}^{-20}$m^{2}/W, and PMD of 0.1 ps/√km. At the receiver, the signal is divided in two halves by using a 1:2 optical splitter. Each of these halves is then demultiplexed using two cascaded 12.5 GHz rectangular type optical band stop filters with a suppression ratio of 30 dB [18] and directly detected using a PIN photodetector with a responsivity of 0.7 A/W, thermal noise of 1e-12 A/√Hz and shot-noise enabled. After amplification of the detected signal using an amplifier with a noise value of 5e-12 A/√Hz, signal was then down-converted to baseband using a RF *I-Q* down-converter. The baseband *I, Q* signals are then digitized using two analog-to-digital-converters (ADCs) and passed through the electrical OFDM receiver to recover transmitted data bits. The electrical OFDM receiver performs the necessary digital signal processing including cyclic prefix removal, FFT processing, channel equalization and phase noise compensation [4, 20]. A total of 200 OFDM symbols are transmitted in the simulation among which first two symbols are used for channel estimation and zero-forcing equalization. Performance of the system is measured in terms of the error vector magnitude (EVM), expressed in decibles (dB), as calculated using Eq. (11) [27, 28].

*L*is the total number of OFDM symbols, and

_{p}*N*is the number of data subcarriers in the OFDM system. For an 8-QAM O-OFDM system, EVM of −15 dB is required to achieve a bit error ratio (BER) of 10

_{DS}^{−3}which is the usual forward error correction (FEC) limit [27].

## 4. Simulation results

The optical spectra of the system are shown in Fig. 5 , where the OSSB + C formatted DDO-OFDM channels (channel-1 and channel-2) are shown in Fig. 5 (a) and 5 (b). As shown in Fig. 5 (a), each DDO-OFDM channel has an OFDM signal bandwidth of 9.5 GHz. Fig. 5 (c) shows the optical spectrum of the proposed frequency interleaved DDO-OFDM system occupying a total optical bandwidth of 25 GHz. The demultiplexed DDO-OFDM channel-1 and channel-2 are shown in Fig. 5 (d) and 5 (e) respectively. Finally Fig. 5 (f) shows the RF spectrum of channel-1 after direct detection. Performance of channel-1 is investigated only to avoid duplicity of results. Fig. 6 (a) shows the EVM vs. received optical power curve for channel-1 after transmission over 25 km SMF, with back-to-back (no fiber) performance plot as a reference. It shows that the proposed interleaved DDO-OFDM system exhibits similar performances for both ‘25 km SMF’ and ‘no fiber (back-to-back)’ configurations. It also confirms that the receiver’s sensitivity of the interleaved DDO-OFDM system is −27.5 dBm at the FEC limit. Therefore, the system exhibits a power margin of 16.5 dB after 25 km SMF, as the received optical power after 25 km SMF was −11 dBm that considered attenuations of signal by 5 dB in fiber and 5.8 dB in coupler and optical filters. This power margin can however be increased to approximately 22 dB by simply replacing the filtering arrangements with an optical circulator followed by a double notch optical filter [29]. The system thus has the potential to implement in a 25 km passive optical network (PON) with a split ratio up to 1:128. Fig. 6 (b) shows the EVM performance of channel-1 with and without the presence of channel-2 in the interleaving scheme. The overlapped points in the plots confirm that at optimum operating condition frequency interleaving has very little effect on the overall performance of the system.The effects of various demultiplexing filter profiles on the overall performance of the interleaved channels are characterized and shown in Fig. 7 (a) and 7 (b). Fig. 7 (a) shows four different filter profiles each with 0 dB and 30 dB bandwidths of 12.5 GHz and 10 GHz respectively. A ripple magnitude of 0.5 dB was set for Chebyshev and Elliptic filters. Corresponding filter orders for Butterworth, Elliptic and Chebyshev filters were calculated to be around 15, 7 and 7 respectively. The overall EVM performance of the proposed interleaved system with the presence of these filter profiles are measured and shown in Fig. 7 (b). It shows that, as long as the filter’s suppression bandwidth is sufficient (e.g. 10 GHz) to suppress the unwanted OFDM signal band, the overall performance of the system varies only as little as 0.3 dB irrespective of filter types. To investigate the effects of filter orders, the performance of the system was measured with Chebyshev type filters with varying filter orders as shown in Fig. 8 (a) . It shows that at the FEC limit, 4th order Chebyshev filters exhibit 2 dB additional power penalty in compare to 7th order filters. This is due to the inability of the 4th order filters to suppress the unwanted signal components sufficiently. With filter orders lower than 4, the system is unable to recover error free (at the FEC limit) data. This situation could potentially be avoided if larger guard band was chosen with a compromise with overall spectral efficiency. Fig. 8 (b) shows the corresponding receivers sensitivities at the FEC limit with respect to different filter orders and confirms that filter orders higher than 7 contribute very little in overall system performance.

To investigate the effect of laser linewidth on the system, performance of the interleaved channels are characterized with different laser linewidths as shown in Fig. 9(a) . It shows that performance of the system remains unchanged if laser linewidth is increased from 100 kHz to 1 MHz. However, for an increase to 10 MHz a system penalty of 0.5 dB is observed. Besides, higher order modulation formats are expected to be more sensitive to laser phase noise as

explained in [30]. This means that special care has to be taken about LLW while designing such links practically.

In order to achieve higher bit rates, the performance of the system is measured with higher order modulation formats such as 16, 32 and 64-QAMs that result in data rates of 54 Gb/s, 80 Gb/s and 96 Gb/s respectively. Fig. 9 (b) shows the receivers’ sensitivities as a function of modulation orders or bit rates. As expected, sensitivity of the system decreases with the increase of modulation orders or bit rates. Instead of using 8-QAM, if 64-QAM signal is used, sensitivity of the system reduces from −27 dBm to −18 dBm, which eventually reduces the overall power margin to 12 dB, sufficient for 1:16 TDM-PON. Therefore, the proposed frequency interleaved DDO-OFDM system can be considered in next generation optical access system at bit rates as much as 96 Gb/s with a compromise with the desired split ratio.

## 5. Conclusion

Theoretical analysis and simulation results suggest that two DDO-OFDM channels can be frequency interleaved such that mandatory spectral gap of one channel is being occupied by the data band of other channel and vice versa to improve the spectral efficiency of a conventional DDO-OFDM system significantly. We show that, at optimum operating condition, proposed interleaved technique can offer as much as 50% additional spectral efficiency, irrespective of system configurations. The concept is demonstrated by modeling an 8-QAM 48 Gb/s system (within 25 GHz optical bandwidth) in 25 km uncompensated passive optical link, suitable for easy upgrade of current low-cost TDM-PONs to next-generation 40 Gb/s and 100 Gb/s optical access systems. The system is also scaled up to 96 Gb/s by

replacing 8-QAM with 64-QAM, and found to offer error free transmission (within FEC limit) with a power budget sufficient for 1:16 TDM-PON. Therefore the proposed spectrally efficient DDO-OFDM system has the potential to be used in next generation high speed optical access networks.

## Acknowledgment

NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.

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