WO2019196095A1

WO2019196095A1 - Radio frequency pilot assisted carrier recovery in digital communication

Info

Publication number: WO2019196095A1
Application number: PCT/CN2018/082978
Authority: WO
Inventors: Jianjun Yu; Rui DENG; Xiangjun Xin; Yufei Chen; Yun Zhang
Original assignee: Zte Corporation
Priority date: 2018-04-13
Filing date: 2018-04-13
Publication date: 2019-10-17

Abstract

A heterodyne Mm-wave fiber-wireless system using twin single-side-band orthogonal frequency division multiplexing (Twin-SSB-OFDM) transmission scheme with low-cost electrical filters is described. Because the signal generation is based on optical heterodyne with non-ideal laser sources, there is a time-varying carrier frequency offset (CFO) in the system. To mitigate the CFO effect and simultaneously realize down-conversion, a blind carrier recovery method is described.

Description

RADIO FREQUENCY PILOT ASSISTED CARRIER RECOVERY IN DIGITAL COMMUNICATION

TECHNICAL FIELD

This patent application relates to optical communications.

BACKGROUND

With the emergence of a variety of network applications, such as high-quality Internet protocol television (IPTV) , video sharing, virtual reality, cloud computing, and peer-to-peer multimedia services, the demand for higher transmission data rate and capacity of wired and wireless communications continues to grow.

SUMMARY

This patent document described, among other things, transmitter-side and receiver-side techniques for transmission/reception of dual single sideband (SSB) signals with orthogonal frequency division multiplexing based modulation being used for each SSB signal. For example, discrete multitone transform (DMT) modulation may be used by the SSB signals.

In one example aspect, a method for optical communication, implemented by an optical transmitter, is disclosed. The method includes generating, by the optical transmitter, an optical signal carrying modulated data bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme. The method further includes transmitting the optical signal over a communication channel.

In another example aspect, a receiver-side method of optical communication is disclosed. The method includes receiving an optical signal carrying modulated data bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme, converting the optical signal into a digital signal in an electrical domain, processing the digital signal through a coarse carrier recovery step in which a first approximation of carrier frequency is used to generate a baseband signal, processing the baseband signal through a second step in which a fine carrier recovery is performed to improve the first approximation of carrier frequency, and reconstructing the information bits by further processing an output of the second step.

In another example aspect, an optical communication apparatus comprising a processor configured to implement the above-described methods is disclosed.

In yet another example aspect, an optical communication network comprising a transmitter apparatus that implements the above-described transmission method, and a receiver that implements the above-described reception method are disclosed.

These, and other, features are described in greater detail throughout this document.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A and 1B are block diagrams showing functional flow of an example twin-SSB-DMT generation scheme based on single OFDM modulation.

FIG. 2A shows an example scheme for twin-SSB-OFDM transmission over heterodyne Mm-wave system.

FIG. 2B shows expected signal spectrum evolution in an example of a Twin-SSB-OFDM transmission scheme.

FIG. 2C shows the expected signal spectrum evolution before and after the digital mixing in a lower sideband (LSB) OFDM demodulation process.

FIG. 3A shows an example of a structure for implementing carrier recovery.

FIG. 3B shows an example of frequency magnitude response of a filter used in carrier recovery.

FIG. 3C shows a block diagram of example functional blocks used in the carrier recover scheme.

FIG. 4A depicts an experimental Twin-SSB-OFDM Mm-wave fiber-wireless transmission system. Inset (1) : the spectrum of the optical signal received by the PD. Inset (2) : the time-domain signal received by the DSO. ①: the heterodyne Mm-wave fiber-wireless system.

FIG. 4B shows a digital signal processing (DSP) flowchart of an implementation of a Twin-SSB-OFDM transmitter.

FIG. 4C shows a DSP flowchart of an implementation of a Twin-SSB-OFDM receiver, in which Sync. : Synchronization; Est. : Estimation; Eq. : Equalization.

FIG. 5 shows an example of recorded signal power spectral density (PSD) evolution at the receiver side.

FIG. 6A shows an example structure of the first step of the clock recovery module applied in the LSB-OFDM demodulation.

FIG. 6B shows an example structure of the first step of the clock recovery module applied in the right sideband RSB-OFDM demodulation.

FIG. 6C shows graphs (i) ～ (vii) of the recorded signal spectrum evolution of the RSB-OFDM/LSB-OFDM signal before and after the clock recovery.

FIG. 7 is a graph showing the measured bit error rate (BER) performance in an example implementation.

FIG. 8A shows an experimental setup for the additional real-time experiment. ①: the heterodyne Mm-wave fiber-wireless system.

FIG. 8B shows an example of an applied scheme for demodulating the LSB-OFDM signal in the additional experiment.

FIG. 8C shows an example of the recorded spectrum of the signal before using receiver-side LPF.

FIG. 8D shows an example of the recorded spectrum of the signal after using receiver-side LPF.

FIG. 8E shows an example of the probability distribution of the frequency of the IF carrier in the positive frequency domain.

FIG. 8F shows an example of the probability distribution of the frequency of the IF carrier in the negative frequency domain.

FIG 8G pictorially depicts the relation between the carrier frequency and time recorded within a continuous period of time.

FIG. 8H shows the calculated spectrum of the signal before carrier recovery.

FIG. 8I shows the calculated spectrum of the signal after carrier recovery.

FIG. 9 shows the measured BER performance of the LSB-OFDM transmission in the additional experiment.

FIG. 10 shows the diagram of the hardware architecture of the real-time clock recovery module.

FIG. 11 shows an example structure of the Np-parallel Nt-tap MAF.

FIG. 12 shows an example of the hardware utilization of the real-time carrier recovery module estimated by FPGA design tool.

FIG. 13 shows an example of a communication system.

FIG. 14 is a flowchart for an example of a transmitter-side communication method.

FIG. 15 is a flowchart for an example of a receiver-side communication method.

FIG. 16 is a block diagram of an example of an optical communication apparatus.

DETAILED DESCRIPTION

Future networks are expected to provide broadband services and support mobility simultaneously. Hence, radio over fiber or fiber wireless integration, combining the advantages of broadband (optical communication) and mobility (wireless communication) , has been regarded as a promising candidate for future access networks. Meanwhile, due to the scarcity of wireless spectrum resources, it is expected to utilize the millimeter-wave (mm-wave) band with large unregulated bandwidth to provide exceeding 10 Gb/s data transmission at the wireless level in the future. Therefore, mm-wave fiber wireless system is being extensively studied all over the world. Moreover, among some millimeter-wave frequency bands of interest, Mm-wave (75-110 GHz) recently is attracting increasing attention since it has relatively lower atmospheric propagation loss and broader transmission bandwidth compared to its adjacent mm-wave bands, including the regions around 60-GHz and 120-GHz. Nevertheless, it is a challenge to directly modulate Mm-wave radio signals on an optical carrier with pure electrical components due to the electronic bandwidth bottleneck. Fortunately, there is a relatively simple and attractive solution, i.e., the employment of photonics techniques. The solution would contribute to the breakthrough of the electronic bandwidth bottleneck. Meanwhile, by using photonics techniques and electrical techniques simultaneously, the seamless integration of wireless communication and optical communication can be realized easily. Thus, it can facilitate the realization of fiber wireless integration.

Nowadays, a widely used photonics technique for Mm-wave signal generation is optical heterodyne mixing of two free-running lasers. The technique is simple and cost-efficient. At present, a quite number of Mm-wave fiber-wireless transmission schemes based on optical heterodyne have been proposed. Moreover, according to the detection mode, these schemes can be mainly categorized into two types. One is based on direct detection with envelope detector (ED) , and the other is based on heterodyne detection with radio frequency (RF) mixer. Compared with direct detection, the heterodyne detection is more spectrally efficient because the amplitude and phase information of the received signal both can be used for data transmission. Besides, heterodyne detection possesses a higher receiver sensitivity and is more suitable for long-distance transmission. Nevertheless, in general, there is a time-varying carrier frequency offset (CFO) in the heterodyne Mm-wave fiber-wireless system due to the frequency swing of the transmitter-side lasers and the receiver-side sinusoidal RF source, potentially reducing the efficiency of transmission.

Orthogonal frequency division multiplexing (OFDM) has become one of the most popular modulation techniques for fiber wireless system due to its high tolerance to optical dispersion effect and wireless multipath fading effect. Moreover, owing to the advantages of the technique, such as high spectrum utilization and flexible bandwidth allocation, it is also one of the most effective methods to increase the data rate of the Mm-wave fiber wireless system. At present, a number of high-speed heterodyne Mm-wave OFDM systems have been demonstrated. However, in the most of the prior demonstrations, since the received signal is an intermediate frequency (IF) OFDM signal, to capture the signal completely without using coherent receiver, the sampling rate of the OFDM receiver should be more than two times of that of the OFDM transmitter. However, higher sampling-rate OFDM receiver requires higher sampling-rate ADC in real applications. And the cost of the high-sampling-rate ADC is much expensive. Thus, it can greatly increase the implementation cost of the high-speed heterodyne Mm-wave OFDM system. Recently, twin single-side-band discrete multi-tone (Twin-SSB-DMT) transmission scheme has been proposed in direct detection (DD) optical fiber system. It can increase the data rate of the DD optical fiber system and meanwhile decrease the requirement of the ADC's sampling rate. Nevertheless, additional Twin-SSB-DMT transmission scheme may not be suitable for single-PD-based heterodyne Mm-wave fiber-wireless OFDM system since it normally requires two PDs and also requires two optical filters. In addition, heterodyne Mm-wave fiber-wireless OFDM system inherits the disadvantage of common OFDM systems and is sensitive to CFO. Therefore, CFO mitigation is inevitable in the heterodyne Mm-wave fiber-wireless OFDM system. Some have proposed a simple RF-pilot-assisted carrier recovery method to mitigate CFO in CO-OFDM system. It can mitigate the CFO effect and the phase noise simultaneously. Nevertheless, the method should be performed with extra preamble-based CFO estimation after timing synchronization. The extra preamble-based CFO estimation would increase the implementation complexity and thereby increase the implementation cost to some extent.

In this document, techniques are described that can be implemented at the transmitter-side or the receiver-side in a digital communication system. In some disclosed embodiments, a twin-SSB-OFDM transmission scheme over heterodyne Mm-wave fiber-wireless system can be implemented without optical filters. The usefulness of the disclosed techniques is investigated in an experimental heterodyne Mm-wave fiber-wireless system employing optical heterodyne generation and RF heterodyne detection. The disclosed transmission scheme can be implemented entirely in the electrical domain, e.g., just based on low-cost electrical filters. Meanwhile, to mitigate the CFO effect, a blind carrier recovery method may be used.

To validate the approach, some experiments were performed. First, a 12-GSa/s two-channel arbitrary waveform generator (AWG) and a 25-GSa/s digital storage oscilloscope (DSO) are used as the signal transmitter and receiver respectively in the experimental system for an offline experiment. The offline experimental result shows that the system with the proposed schemes can successfully achieve a high data rate up to 40.07 Gb/s with a bit-error-ratio (BER) below 3.8 × 10 ^-3. These results preliminarily verify the effectiveness of the disclosed schemes. Second, an additional semi-real-time experiment is carried out by setting the AWG sampling rate at 5 GSa/s and using a field programmable gate array (FPGA) -based real-time platform equipped with a 5-GSa/s analog-to-digital (ADC) as the left side-band (LSB) -OFDM receiver. The additional experimental result shows that although the frequency swing of the intermediate frequency (IF) carrier of the received LSB-OFDM signal is up to ～300 MHz, the LSB-OFDM transmission of the system can still achieve a relatively stable BER (bit error rate) performance. It further verifies the effectiveness of the blind carrier recovery scheme. Meanwhile, because the carrier recovery scheme is implemented in the real-time platform and performed in a real-time way, this additional experimental result also verifies the feasibility of implementing the blind carrier recovery scheme by hardware in real applications.

A. Single OFDM modulator for Twin-SSB-DMT generation

Twin-SSB-DMT can effectively increase the data rate of the DD optical fiber system. FIG. 1A shows the traditional Twin-SSB-DMT transmitter 100 and it utilizes two OFDM modulators. Hence, the generated Twin-SSB-DMT signal (104) can be expressed as

where N is the total amount of the subcarriers. For example, N is equal to the length of inverse fast Fourier transform (IFFT) , N _l1～N _l2 is the region of the valid data-carrying subcarriers of the left side-band (LSB) DMT signal (N _l1<N/2, N _l2<N/2) , N _r1～N _r2 is the region of the valid data-carrying subcarriers of the right side-band (RSB) DMT signal (N _r1<N/2, N _r2<N/2) . According to the Hermitian symmetry property of the IFFT, there is the following equation

Hence, Eq. (1) can be transformed as

where

N _d= [N _l1, N _l2] ∪ [N-N _r2, N-N _r1] (4)

and

As depicted in FIG. 1A, the two QAM modulated outputs are transformed through N point inverse Fast Fourier Transform (IFFT) transform, a cyclic prefix is added to the output of IFFT and a parallel to serial conversion is performed to generate real and imaginary values of the resulting OFDM signal. These values are differenced fed into an I/Q modulator as described in the equations (1) to (5) .

The above equations 2 to 5 show the Twin-SSB-DMT generation can be realized by using the equivalent process with single OFDM modulator, as shown in FIG. 1B, reference numeral 102. The RSB and LSB data are used for generating QAM symbols, that are then converted into OFDM symbols by mapping to subcarriers, N-point IFFT transform, followed by adding a CP, followed by parallel to serial conversion. The real and imaginary parts of the output symbols are modulated using an IQ modulator, resulting in a signal that is mathematically equivalent to the output 104 described with respect to FIG. 1A.

The term Discrete Multitone Transform (DMT) normally refers to a baseband wireline multicarrier communication, while OFDM refers to wireless multicarrier communication. Hence, Twin-SSB-DMT is also termed as Twin-SSB-OFDM for the fiber-wireless system in this document.

Examples of transmission schemes of Twin-SSB-OFDM signal over heterodyne Mm-wave Fiber-Wireless system

In DD optical fiber system, the realization of the Twin-SSB-DMT transmission is normally based on optical filters. As mentioned previously, this document describes a Twin-SSB-OFDM transmission scheme based on electrical filters is proposed for heterodyne Mm-wave fiber-wireless system. An embodiment of this scheme is illustrated in FIGs. 2A, 2B and 2C. In the scheme, after modulating the Twin-SSB-OFDM signal onto the optical carrier from the ECL-1 via the IQ modulator, the optical Twin-SSB-OFDM signal 202 can be expressed as

where ω ₁ and Φ ₁ are the frequency and phase of the optical carrier from ECL-1, S _LSB (t) and S _RSB (t) are the LSB and RSB optical OFDM signal respectively, and S _DC1 is the amplitude of the optical carrier. When the optical heterodyne is realized by mixing the optical signal and another optical carrier from the ECL-2 via a photodetector (PD) after fiber transmission, without considering the channel effect, the IF Twin-SSB-OFDM signal 204 can be obtained as

where ω ₂ and Φ ₂ are the frequency and phase of the optical carrier from ECL-2, and S _DC2 is the amplitude of the optical carrier from ECL-2. When the frequency offset between the optical carriers from ECL-1 and ECL-2 is 75～110 GHz, i.e., ω ₂ –ω ₁∈ [75, 110] GHz, the obtained IF Twin-SSB-OFDM signal would be a Mm-wave signal. By using RF heterodyne mixing further, the signal can be down-converted as (signal 206) :

where ω _RF and Φ _RF are the frequency and phase of the sinusoidal signal from the clock source used for mixing.

Whenω ₁-ω ₂-ω _RF equals f _c GHz and the bandwidths of the LSB OFDM signal and RSB OFDM signal are both lower than f _c GHz, the frequency range of the LSB OFDM signal and RSB OFDM signal will be located within (0, f _c) GHz and (f _c, 2f _c) GHz respectively. In frequency domain, the signal after RF heterodyne mixing can be expressed as

where F _LSB (ω) , F _RSB (ω) and F _carrier (ω) are the LSB signal, the RSB signal and the IF carrier signal respectively in frequency domain.

Hence, in theory, the LSB-OFDM signal can be extracted by using an analog low-pass filter (LPF 208) with cutoff frequency at f _c, and the RSB-OFDM signal can be extracted by using an analog high-pass filter (HPF) with cutoff frequency at also f _c. After that, the two side-band OFDM signals can be separated and captured by two OFDM receivers. In detail, the LSB-OFDM signal can be received by a 2f _c GSa/s ADC directly. Nevertheless, because the frequency range of the RSB-OFDM signal is from f _c GHz to 2f _c GHz while the Nyquist bandwidth of the 2f _c GSa/s ADC is limited at f _c GHz, to receive the RSB signal by using the 2f _c GSa/s ADC, an extra mixer and an extra LPF with cutoff frequency at f _l (f _l ∈ [f _c , 2f _c] ) should be used to make down-conversion for the RSB-OFDM signal in advance as shown in FIG. 2A. In this way, the entire Twin-SSB-OFDM signal with frequency range (0, 2f _c) can be demodulated by two 2f _c GS/s receiver rather than a 4f _c GS/s receiver.

FIG. 2B shows the expected signal spectrum evolution in the disclosed Twin-SSB-OFDM transmission scheme. In FIG. 2B, from left to right, the graphs show spectrum of the original twin SSB OFDM signal, where the LSB and the RSB are spectrally disjoint and symmetrically situated around the central carrier frequency. The next graph shows the spectrum after optical heterodyning. The next graph shows the spectrum after RF heterodyning. After LPF, the LSB spectrum is depicted in the upper branch and the RSB spectrum is depicted in the lower branch. The LSB goes through a sampling to generate digital signals in electrical domain. The RSB signal goes through a mixing and filtering operation (downsampling) to generate a baseband RSB spectrum. In addition, it should be mentioned that although the LSB-OFDM signal can be received by the 2f _c GSa/s ADC directly after LPF filtering, the received signal is still an IF signal. Hence, in the demodulation of the LSB-OFDM signal, a digital mixing with f _c-frequency carrier should be used to make a frequency conversion for the received LSB-OFDM.

FIG. 2C shows the expected signal spectrum evolution before and after the digital mixing in the LSB-OFDM demodulation process. The principle of the digital mixing is to shift the usable negative frequency-domain part of the received LSB-OFDM signal into the positive frequency domain. In such a way, the received IF LSB-OFDM signal can be recovered to a baseband OFDM signal and thereby can be demodulated by OFDM demodulation. As depicted in FIG. 2C, from left to right, first, the result of spectral unfolding is depicted, then the digital mixing operation is depicted, followed by the resulting spectrum, which is then further processed for OFDM demodulation to recover information bits from the modulation symbols.

EXAMPLE EMBODIMENTS OF A BLIND CARRIER RECOVER SCHEME

In real applications, the frequency and phase of the optical carriers from the lasers are not absolutely stable. Meanwhile, the frequency and phase of the sinusoidal signal used for RF mixing are also unstable in general. Hence, in fact, in the proposed transmission scheme as mentioned above, the obtained IF signal after RF heterodyne mixing should be expressed as

where △ω +ω’ (t) is the frequency of the IF carrier, △Φ +Φ’ (t) is the phase of the IF carrier, △ω is the expected frequency of the IF carrier and ω’ (t) is the time-varying carrier frequency offset, and Φ’ (t) is the time-varying phase noise.

It means that the frequency of the IF carrier of the obtained signal may swing within a limit represented by [△ω +ω’ _min, △ω +ω’ _max] , where ω’ _min means the minimum value of ω’ (t) , and ω’ _max means the maximum value of ω’ (t) . In non-realtime data recovery schemes, implementations can just use large-size FFT to estimate the frequency and phase of the IF carrier and then realize a carrier recovery. However, in practical applications, the large-size FFT would lead to a large overhead of hardware resources, thus increasing the implementation complexity and cost. One approach is to perform a simple RF-pilot-assisted carrier recovery method. This method includes performing of a coarse CFO mitigation using preamble and a residual CFO mitigation based on a multiplierless multi-stage decimation and interpolation filter (MDIF) /moving average filter (MAF) . However, to be of benefit, the preamble-based coarse CFO mitigation should be performed after timing synchronization. Meanwhile, timing synchronization requires preamble-based CFO estimation.

Accordingly, in some embodiments, a method of signal reception, that can be divided into two logical steps for the sake of explanation, may be implemented. In the first step, a coarse carrier recovery is realized by using the proposed structure as shown in FIG. 3A. Initially, a preliminary frequency-conversion operation is realized as

R _d1 (n) =R (n) exp (-jω _d1n) (11)

where R (n) is the received signal, ω _d1 is the estimated value of △ω+ω’ _min and R _d1 (n) is the obtained signal after the frequency-conversion operation. This operation can be used to make a frequency conversion for the received IF signal in the LSB-OFDM demodulation. Nevertheless, it should be mentioned that, in the RSB-OFDM demodulation, if the frequency of the IF carrier is relatively low, this preliminary frequency-conversion operation can be removed (not implemented) .

Subsequently, a coarse CFO mitigation is realized based on a processing which consists of multiple operations, including LPF filtering, decimation, FFT, averaging, etc., as shown in FIG. 3A. The coarse CFO mitigation can be operated with single stage or multiple stages, arranged such that output of a previous stage is used as input of a next stage. The output of the final stage is used for further processing, as described herein. When the coarse CFO mitigation is based on 1 stage, the obtained signal R _d1 (n) after the preliminary frequency-conversion is firstly filtered by a digital LPF as

where h is the impulse response sequence of the LPF. In actual application, the LPF can be implemented by using a simple moving average filter (MAF) as

where N _maf is the averaging length. Noted that, when N _maf is the integer power of 2, Eq. (14) can be realized in hardware platform by using only adders and shift registers without requiring multipliers. Secondly, a decimation operation is realized as

R _dec (n) =R _lpf (N _dec·n) (12)

where N _dec is the decimation ratio. N _dec >0 and N _dec∈ Z. Thirdly, by using N _f1-point FFT and averaging operation, a frequency-domain amplitude metric sequence can be obtained as

where N _aver is the average times. At last, by seeking for the index of the maximum value of the frequency-domain metric sequence, a further digital mixing can be realized as

R _d1 (n) =R _d0 (n) exp [-jn2π· (f'-1) /N _f1·1/N _dec] (16)

where

f'=arg max (M) (17)

where argmax ( ^. ) stands for argument of the maxima.

Eq. (12) ～ (17) illustrate the all operations of the 1-stage coarse CFO mitigation. When m stages are used in the coarse CFO mitigation, each stage would be based on a similar structure with the 1-stage coarse CFO mitigation as shown in FIG. 3A.

After the first step, the captured IF signal can be approximately down-converted to a baseband signal. However, there still will be a small residual CFO. Then, the second step is realized for mitigating the small residual CFO. The second step is based on MDIF/MAF, as shown in FIG. 3C. The applied residual CFO mitigation example, depicted in FIG. 3C, possesses a specific form which consists of an MDIF (6/2/16) and two 32-point MAFs. The normalized frequency response of the MDIF/MAF module is shown in FIG. 3B. In such a way, the disclosed carrier recovery method can be accomplished after the two steps. As depicted in FIG. 3C, the process may include the following operations performed on the signal -a 16-point moving average filter, followed by a decimation, followed by a 16-point moving average filter, followed by a decimation, followed by a 16-point moving average filter, followed by interpolation, 16-point moving average filter, followed by interpolation, followed by two stages of 32 point moving average filters.

One advantageous aspect of the first step is to use FFT to estimate the frequency of the IF carrier roughly and then realizing a coarse down-conversion according to the estimated frequency. Compared with using a large-size FFT to directly estimate the frequency of the IF carrier, embodiments using the first step can effectively reduce the size of the required FFT by using decimation and thereby decrease the implementation complexity. Although carrier recovery could be performed with the assistance of the IF carrier, it can also be termed as a blind method because the IF carrier is inherently existing in the heterodyne Mm-wave system and implementations do not require any prior information.

Examples of Experimental Demonstrations

Experimental setup

FIG. 4A shows the experimental setup of the heterodyne Mm-wave fiber-wireless system employing the Twin-SSB-OFDM transmission scheme. One optical carrier (linewidth: ～100 kHz) is generated by a commercial and tunable ECL (ECL-1) . Then, the optical carrier can be modulated with the Twin-SSB-OFDM signal via an optical IQ modulator. The I and Q components of the Twin-SSB-OFDM signal are firstly generated by a 12-GSa/s two-channel AWG (Tektronix AWG7122B) and then filtered and amplified by using two identical anti-imaging filters (Mini-Circuits VLF-5000+) and two identical electrical amplifiers (EA-1, EA-2) . The optical carrier modulated with Twin-SSB-OFDM signal is amplified by a polarization maintaining Erbium-doped optical fiber amplifier (PM-EDFA) . After that, another optical carrier (linewidth: 100 kHz) is generated by another commercial and tunable ECL (ECL-2) . With an optical coupler (OC) , the two optical carriers can be transmitted together over single 22-km SSMF. A tunable optical attenuator (ATT) is used at the end of the fiber to adjust the received optical power (ROP) . Then, a photodetector (PD) is used for optical heterodyne. Since the frequency spacing of the two optical carriers is about 82 GHz as shown in FIG. 4A, inset (1) , the generated RF signal after optical heterodyne is a 82-GHz Mm-wave signal. Subsequently, a Mm-wave electrical amplifier (EA-3) is used to amplify the generated Mm-wave signal. Then, by using two Mm-wave horn antennas further, 1-m wireless transmission of the Mm-wave signal can be realized. After wireless transmission, the Mm-wave signal is received by an RF mixer integrated with a 77-GHz local oscillation source. Thus, RF heterodyne can be realized and a 5-GHz IF signal can be obtained further. Eventually, the obtained IF signal is amplified by a low-noise electrical amplifier (EA-4) and then is captured by a 25 GSa/s DSO (Tektronix DPO72004B) .

TABLE I

KEYPARAMETERS OF THE SINGLE OFDM MODULATION FOR TWIN- SSB-OFDM GENERATION

The digital signal processing (DSP) flowchart for generating the Twin-SSB-OFDM signal based on single OFDM modulation is shown in FIG. 4B. It may include the following seven processings: (1) pseudo-random binary sequence (PRBS) generation; (2) QAM mapping; (3) Discrete Fourier transformation (DFT) precoding. DFT-spread technique used for peak to average power reduction (PAPR) ; (4) 512-point IFFT; (5) 16-point CP addition; (6) Inserting training symbols (TS) . The parameters for the twin-SSB-OFDM generation are shown in Table 1. There are two PRBS generation modules in the transmitter. The two PRBS generation modules are used to generate the original binary data for LSB-OFDM and RSB-OFDM generation respectively. In practical transmitters, information bits that include application layer user data or control data used for network traffic such as overheads of maintenance and signaling, may be used.

Depending on channel and data, different QAM mapping formats are applied for the two side-band OFDM. For the generation of the RSB-OFDM signal, 16-QAM mapping is applied and the 16-QAM mapped data are modulated onto the 16 ^th～226 ^th subcarriers. For the generation of the LSB-OFDM signal, 32-QAM mapping is applied and the 32-QAM mapped data are modulated onto the 308 ^th～498 ^th subcarriers. Moreover, after DFT-spread precoding, conjugating, multiplying with imaginary number j and inverse operation are performed to realize the process depicted in Eq. (2) for the LSB-OFDM generation.

Correspondingly, the Twin-SSB-OFDM receiver is implemented as shown in FIG. 4C. As shown in FIG. 4C, the left SSB and the right SSB may be processed initially through different processing blocks (due to their spectrum separation) , but after digital signals are produced representing each SSB, the subsequent processing is identical in both cases. In practical systems, the “BER Analyzer” function may not be implemented, or may be implemented to provide feedback to the transmitter regarding the quality of the optical channel over which the signal was received.

In an experiment, the entire processes of the Twin-SSB-OFDM reception and demodulation are emulated and processed by offline calculation in personal computer (PC) in this experiment. In the receiver, the signal captured by DSO is resampled from 25 GSa/s to 24 GSa/s at first. One sample of the time-domain signal captured by the DSO is shown in FIG. 4A as inset (2) . Then, based on the proposed Twin-SSB-OFDM reception scheme, two OFDM receivers are used to receive the resampled signal for the LSB-OFDM demodulation and RSB-OFDM demodulation respectively. In the LSB-OFDM demodulation, an analog LPF with cutoff frequency at 5.5 GHz and a 12 GSa/s ADC are emulated to capture the LSB-OFDM signal. In the RSB-OFDM demodulation, an analog HPF with cutoff frequency at 4.6 GHz, a mixer with a 4.6-GHz local oscillation source, a LPF with 6-GHz cutoff frequency and a 12 GSa/s ADC are emulated to capture the RSB-OFDM. Then, the remaining DSP processes of the LSB-OFDM demodulation and the RSB-OFDM demodulation are almost the same.

The remaining processes include the following 10 stages: (1) Coarse timing synchronization. Here, the coarse timing synchronization is realized just based on the fact that the intensity of the received signal in the gap between two OFDM frames is relatively low. It is used to find the head of one OFDM frame and then enable the following carrier recovery. In the coarse timing synchronization, a timing metric by detecting the intensity of the received signal is obtained firstly with the following equation

where r (n) is the received signal, N _sum is an integer constant. Then, according to the timing metric, the synchronization point is obtained by

d'=arg min [M _pro (k) ] *N _sum (19)

where argmin (. ) stands for argument of the minimum; (2) Carrier recovery, which is based on the techniques described in the present document; (3) Fine timing synchronization. The fine synchronization scheme could be implemented as described in M. Chen et al., "Symbol synchronization and sampling frequency synchronization techniques in real-time DDO-OFDM systems, " Optics Communications, vol. 326, no. 1, pp. 80-87, Sep. 2014, which is incorporated by reference in its entirety herein. (4) CP removal; (5) 512-point FFT; (6) Channel estimation. In some embodiments, an Intra-symbol frequency-domain averaging (ISFA) may be used in the estimation to improve the estimation precision. The ISFA may be as described in Q. Yang et al., "Demonstration of Frequency-Domain Averaging Based Channel Estimation for 40-Gb/s CO-OFDM With High PMD, " IEEE Photonics Technology Letters, vol. 21, no. 20, pp. 1544-1546, Oct. 2009, which is incorporated by reference in entirety herein. The utilized tap number for ISFA may be 4; (7) Channel equalization; (8) IDFT decoding; (9) QAM demapping; (10) BER analyzer (e.g., recovering information bits and comparing with the information bits sent from the transmitter-side) .

Corresponding experimental results and discussions

In the experiment, as described with reference to FIG. 4A-4C, firstly, the signal power spectral density (PSD) evolution at the receiver side is recorded as shown in FIG. 5. Graph (a) shows the PSD of the captured signal in the receiver. After filtered by the emulated LPF, the PSD of the signal is changed as shown in graph (b) . Similarly, after filtered by the emulated HPF, the PSD of the signal is changed as shown in graph (c) . In this way, LSB-OFDM and RSB-OFDM signals can be separated and demodulated respectively. Then, the LSB-OFDM can be received directly by the emulated 12-GSa/s ADC. The PSD of the LSB-OFDM signal captured by the ADC is shown in graph (d) . Meanwhile, the RSB-OFDM is mixed with a 4.6 GHz sinusoidal signal and then captured by the emulated 12-GSa/s ADC. Then, the PSD of the RSB-OFDM signal captured by the ADC is shown in graph (e) .

Secondly, in the demodulation process, the spectrum of the signal before and after clock recovery is captured as shown in FIG. 6C. In addition, in the LSB-OFDM demodulation, the applied structure for the first step of the clock recovery is shown in FIG. 6A. In RSB-OFDM demodulation, the applied structure for the first step of the clock recovery is shown in FIG. 6B. In the RSB-OFDM demodulation, initialized frequency-conversion is removed as the frequency of the IF carrier of the RSB-OFDM signal is relatively low. Moreover, -5.5-GHz carrier is used for initialized frequency-conversion in the first step of the clock recovery in the LSB-OFDM demodulation. In detail, insets (i) , (ii) and (iii) in FIG. 6C show the spectrum of the RSB-OFDM signal before clock recovery, the spectrum of the RSB-OFDM signal after the first step of the clock recovery, and the spectrum of the RSB-OFDM signal after the second step of the clock recovery.

Insets (iv) , (v) , (vi) and (vii) in FIG. 6C show the spectrum of the LSB-OFDM signal before clock recovery, the spectrum of the LSB-OFDM signal after initialized frequency-conversion, the spectrum of the LSB-OFDM signal after the first step of the clock recovery, and the spectrum of the LSB-OFDM signal after the second step of the clock recovery. After the first step of the clock recovery, the IF carrier of the LSB-OFDM and RSB-OFDM signal can be effectively converted into the frequency region around zero frequency. Nevertheless, there is still a small CFO after the first step as shown in the inset (1) in inset (ii) / (vi) . After the second step of the clock recovery, the IF carrier can be almost shifted to be zero frequency as shown in in the inset (1) in inset (iii) / (vii) in FIG. 6C.

The result depicted in FIG. 7 verifies the effectiveness of the one example embodiment of the carrier recovery method. At last, the BER performance of the system is measured and the result is shown in FIG. 7. When the received optical power (ROP) is beyond about -3 dBm, the RSB-OFDM transmission can achieve a BER below 3.8e-3, the hard decision forward error correction (HD-FEC) limit. Meanwhile, when the ROP is about -1 dBm, the LSB-OFDM transmission can also achieve a BER around the HD-FEC limit. By aggregating the BER of the RSB-OFDM and the LSB-OFDM transmission, the BER performance of the overall system can be obtained as shown in FIG. 7. When the received optical power (ROP) is beyond -2 dBm, the overall system can achieve a BER below the HD-FEC limit. Meanwhile, it is calculated that the overall system can achieve a data rate up to 40.07 Gb/s ( (211*4+191*5) /512*12*49/50*512/ (512+16) ) . The results preliminarily show the feasibility of the scheme for the Twin-SSB-OFDM transmission over heterodyne Mm-wave system with the blind clock recovery method.

Semi-Real-Time Experimental Verification

An additional semi-real-time experiment is carried out to further verify the effectiveness and feasibility of the proposed blind carrier recovery. The corresponding experimental setup is shown in FIG. 8A. Being different from the experiment setup depicted in last section, the frequency spacing of the optical carriers from the ECL-1 and ECL-2 is adjusted to ～79.3 GHz as shown in inset (1) in FIG. 8A. Meanwhile, the sampling rate of the AWG is changed to 5 GSa/s. Moreover, two analog LPFs (Mini-Circuits VLF-2250+) are used instead of the original analog LPFs (Mini-Circuits VLF-5000+) as the anti-imaging filters. In addition, a real analog LPF (Mini-Circuits VLF-1800+) is used at the receiver side to extract the LSB-OFDM signal. Most importantly, a high-performance FPGA board (Xilinx VC707) equipped with a 10-bit@5-GSa/s ADC is used instead of the DSO to receive the LSB-OFDM signal and realize LSB-OFDM demodulation.

FIG. 8B shows the applied scheme for demodulating the LSB-OFDM signal in the additional experiment. In the scheme, the blind carrier recovery is implemented in the real-time FPGA platform and performed in a real-time way. The remaining DSP processes for demodulation are performed by offline processing. In detail, in the LSB-OFDM demodulation process, the data from the ADC interface are first processed by the blind carrier recovery module in FPGA. Then, the obtained data after carrier recovery is sent to a first-in-first-out (FIFO) module and subsequently uploaded to a personal computer (PC) via Ethernet connection. After that, the remaining DSP processes for demodulation, including timing synchronization, CP removal, etc., are performed in MATLAB. In this way, the transmission performance of the LSB-OFDM transmission can be effectively measured and simultaneously the validity and resource consumption of the blind clock recovery can be evaluated by using FPGA tool.

In this experiment, first, the spectrums of the signal at the receiver side are recorded by the DSO. FIG. 8C shows the recorded spectrum of the signal before using receiver-side LPF. FIG. 8D shows the recorded spectrum of the signal after using receiver-side LPF. Obviously, the LSB signal is extracted successfully after using the filter. Meanwhile, it can be found that the frequency of the IF carrier of the signal in the positive/negative frequency domain becomes about 2.25/-2.25 GHz. Secondly, a statistics is made for the frequency of the IF carrier of the signal by using the FPGA-based real-time platform and the result is shown in FIG. 8E to 8G. FIG. 8E shows the probability distribution of the frequency of the IF carrier in the positive frequency domain. FIG. 8F shows the corresponding probability distribution of the frequency of the IF carrier in the negative frequency domain. Besides, FIG. 8G shows the recorded carrier frequency be found that the frequency swing of the IF carrier is up to ～300 MHz. And the carrier frequency would change about 3.4 MHz within 5.28 us. Thirdly, in the LSB-OFDM demodulation, the data before and after the real-time carrier recovery are captured and uploaded to the PC. Then, the corresponding spectrums of the signal before and after carrier recovery are calculated. FIG. 8H shows the calculated spectrum of the signal before carrier recovery. FIG. 8I shows the calculated spectrum of the signal after carrier recovery. Apparently, the real-time carrier recovery works effectively as the negative frequency-domain IF carrier has been shifted to zero frequency after using the carrier recovery.

At last, the BER performance is measured via statistics within a relatively long period of time. The result is shown in FIG. 9. Although the CFO is time-varying and the frequency swing of the IF carrier is up to ～300 MHz, the LSB transmission can still achieve a relatively stable BER below 2.4 × 10 ^-2, the soft decision forward error correction (SD-FEC) limit, even when the ROP is as low as -6 dBm. When the ROP is beyond -2 dBm, the LSB transmission can also achieve a relatively low BER below 6 × 10 ^-3. The result further verifies the effectiveness of the disclosed blind carrier recovery method.

In addition, the sampling rate of the ADC used in the real-time receiver is up to 5-GSa/s. However, the state-of-the-art FPGA can only operate at about a few hundred megahertz. Instead of serial data processing, the parallel signal processing technique is used to reduce operation frequency. In an example implementation of a real-time receiver, the clock frequency for digital signal processing is 156.25MHz by utilizing 32-channel parallel ADC interface. Meanwhile, the clock recovery is implemented based on a parallel architecture in FPGA. The diagram of the architecture of the real-time clock recovery is illustrated in FIG. 10. The main modules in the real-time clock recovery is the N _p-parallel N _t-tap MAF and the 4-parallel 32-point FFT, which are further described in the present document. The other modules in the real-time clock recovery, including exponent (exp) operation, bit shifting, etc., can be easily realized by using look-up tables (LUTs) . Furthermore, Random Access Memory RAM-based shifted registers may be used to control the delay of the signal in the clock recovery, and the first step of the clock recovery may be enabled according to an enable signal from the coarse timing synchronization, which means that the first step of the clock recovery can be just enabled only after the coarse timing synchronization is done.

FIG. 11 shows the detailed structure of the N _p-parallel N _t-tap MAF. It can be found that only adders and shift operations are required in this kind of module. The 4-parallel 32-point FFT is a radix-4 FFT and it is based on a web edition Spiral DFT/FFT IP core [34-35] . It only uses 20 multipliers and 50 adders. Furthermore, by using FPGA design tool, the detailed hardware resource utilization of the entire real-time carrier recovery module can be estimated. The estimated result is shown in FIG. 11. It can be found that, although the number of the maximum parallel channels for implementing the clock recovery in FPGA is up to 32, the resource consumption is relatively low. It intuitively verifies the feasibility of implementing the proposed carrier recovery method in real applications.

FIG. 12 illustrates an example optical communication network 1200 in which an optical signal transmitter 1212 and an optical signal receiver 1216 communicate with each other via an optical transmission channel 1214. The optical signal transmitter 1212 may include circuitry configured to convert electrical input signals to optical signals. The optical transmission channel 1214 may include optical fibers that extend in length from several hundred feet (e.g., last mile drop) to several thousands of kilometers (e.g., long haul networks) . The optical signals that have passed the optical transmission channel 1214 may be transmitted through intermediate optical equipment such as amplifiers, repeaters, switches, etc., which are not shown in FIG. 12 for clarity. The optical signal receiver 1216 may include circuitry configured to perform the actual reception of the optical signals and convert the optical signals into electrical signals.

FIG. 13 shows a tabular representation of device utilization during implementation of the various signal processing tasks described herein.

FIG. 14 is a flowchart showing an example method 1400 of generating and transmitting an optical signal. The method 1400 includes generating (1402) , by an optical transmitter, an optical signal carrying modulated data bits. The optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme. The method 1400 further includes transmitting (1404) the optical signal. Advantageously, this optical signal may be transmittable either over a wired medium such as optical fiber, or over a wireless channel.

The method 1400 may perform the optical signal generation operation 1402 as described with reference to FIGs. 1A and 1B. The generated spectrum may include first sideband signal and a second sideband signal that carry independent data bits and have spectra that are symmetric around a center frequency. As described with reference to FIGs. 1B, 2B and 2C, each sideband may include less than all subcarriers of an OFDM scheme and therefore the spectrum may not fully extend to the carrier frequency (e.g., spectrum is attenuated with greater than 25 dB attenuation at the carrier frequency) . As described with respect to FIG. 1B, a single OFDM modulator may be used for the generation of the signal. Equation (3) shows a mathematical representation of a signal generated by the method 1400.

FIG. 15 is a flowchart of an example method 1500 of receiver-side processing performed on an optical signal. The method 1500 may be performed by a communication apparatus (e.g., as described in FIG. 16) for receiving twin-SSB-OFDM signals and extracting data bits from the received signals. While the method 1500 is described in the context of optical communication, a similar method may also be implemented for receiving other wireline (e.g., copper or coaxial) or wireless signals.

The method 1500 includes receiving (1502) an optical signal carrying modulated data bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme.

The method 1500 includes converting (1504) the optical signal into a digital signal in an electrical domain. The converting operation may include, first, converting from optical domain to the electrical domain (e.g., by using a photo-diode) and then by sampling the signal using an analog to digital conversion circuit that operates using sampling frequency and bandwidth as described in the present document.

The method 1500 includes processing the digital signal through a coarse carrier recovery step in which a first approximation of carrier frequency is used to generate a baseband signal. As described in this document, the coarse carrier recover may be performed using multiple stages, wherein in each stage, wherein each stage includes processing an input signal of the stage through a low pass filtering operation, followed by a decimation operation, followed by a fast Fourier transform operation, followed by an averaging operation followed by a argmax operation to generate an output signal of the stage. For example, the argmax operation may select a maxima of the signal upon which the argmax operation is performed. Additional details of the coarse carrier recover step are described with respect to FIG. 3A, FIG. 6A, and so on.

The method 1500 includes processing (1506) the baseband signal through a second step in which a fine carrier recovery is performed to improve the first approximation of carrier frequency. As further described with respect to FIG. 3C, the second step may include processing an input signal using a multi-stage decimation filter and a moving average filter to produce an output of the second step. The decimation operation may be performed in two (or more) stages, effectively providing a decimation by factor of 12 in each stage.

The method 1500 includes reconstructing (1508) the information bits by further processing an output of the second step. The recovery of information bits is performed by demodulating the OFDM symbols for both the first sideband signal and the second sideband signal.

FIG. 16 is a block diagram showing an example implementation of an optical communication apparatus 1600. The apparatus includes processor electronics 1602, communicatively coupled with an optical transceiver 1606 that is used to transmit or receive optical signal. The processor electronics 1602 may be programmed to implement various signal processing tasks described in the present document. In some embodiments, processor electronics 1602 may use external hardware, such as signal processing circuitry 1604, for accelerating certain tasks, e.g., IFFT, and filter implementations.

In some embodiments, an optical transmission apparatus (e.g., the apparatus 1600) includes a processor and an optical transmitter, wherein the processor receives information bits and generates an optical signal carrying modulated data bits generated from the information bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme, and the optical transmitter is configured to transmit the optical signal over an optical transmission medium.

In some embodiments, an apparatus for optical communication includes an optical receiver (e.g., 1606) , an opto-electrical convertor (may be a part of 1606) , and a processor (e.g., 1602) . The optical receiver is configured to receive an optical signal carrying modulated data bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme. The opto-electric converter (e.g., a photo-diode) is configured to convert the optical signal into a digital signal in an electrical domain. The processor is configured for processing the digital signal through a coarse carrier recovery step in which a first approximation of carrier frequency is used to generate a baseband signal; processing the baseband signal through a second step in which a fine carrier recovery is performed to improve the first approximation of carrier frequency; and reconstructing the information bits by further processing an output of the second step

Concluding Remarks

In this document, we have disclosed a TWIN-SSB-OFDM Mm-wave fiber-wireless transmission system using optical heterodyne generation and RF heterodyne detection. Meanwhile, a simple blind carrier recovery method based on FFT and MDIF&MAF is proposed in this paper. First, in an offline experiment, by using a 12-GSa/s two-channel AWG as transmitter and a 25-GSa/s DSO as receiver, the performance of the system is measured. The result shows that the system can achieve a data rate up to 40.07 Gb/s with a BER below the HD- FEC limit. It preliminarily verifies the effectiveness of the proposed carrier recovery method and verifies the feasibility of the TWIN-SSB-OFDM transmission scheme over heterodyne Mm-wave fiber-wireless system. Second, in an additional experiment, by using a 5-GSa/s real-time platform as LSB-OFDM receiver and setting the sampling rate of the AWG at 5-GSa/s, the performance of the LSB-OFDM transmission is investigated separately. Besides, the carrier recovery module is implemented in the real-time platform and the hardware resource utilization of the carrier recovery module is estimated correspondingly. The corresponding experimental results show that the LSB-OFDM transmission can also achieve a relative stable BER performance although the measured frequency swing of the IF carrier of the received signal is up to ～300 MHz. In addition, the results also show that the estimated value of the hardware resource of the carrier recovery module is relatively low. All of these verified the effectiveness of the carrier recovery method and the feasibility of implementing the proposed carrier recovery method by hardware in practical applications. The apparatus 1600 may be incorporated with the transmitter 1212 or the receiver 1216, as described herein.

The processes and logic flows described in this document can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit) .

Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

While this document contains many specifics, these should not be construed as limitations on the scope of an invention that is claimed or of what may be claimed, but rather as descriptions of features specific to particular embodiments. Certain features that are described in this document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or a variation of a sub-combination. Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results.

Only a few examples and implementations are disclosed. Variations, modifications, and enhancements to the described examples and implementations and other implementations can be made based on what is disclosed.

Claims

A method of optical communications, comprising:

generating, by an optical transmitter, an optical signal carrying modulated data bits,

wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme; and

transmitting the optical signal over a communication channel.
The method of claim 1, wherein a first spectrum occupied by the first sideband signal and a second spectrum occupied by the second sideband signal are symmetric around a center frequency.
The method of claim 2, wherein the center frequency is separated from the first spectrum and the second spectrum by a spectral gap.
The method of claims 1 to 3, wherein the first sideband signal and the second sideband signal are generated using a single OFDM modulator.
The method of claim 1, wherein the optical signal is represented as

wherein x (n) represents the optical signal, N is number of subcarriers in the OFDM modulation scheme, N _l1～N _l2 is the region of the valid data-carrying subcarriers of the first sideband signal, wherein N _l1<N/2, N _l2<N/2, wherein N _r1～N _r2 is the region of the valid data-carrying subcarriers of the second sideband signal, wherein (N _r1<N/2, N _r2<N/2) .
A method of optical communication, comprising:

receiving an optical signal carrying modulated data bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme;

converting the optical signal into a digital signal in an electrical domain;

processing the digital signal through a coarse carrier recovery step in which a first approximation of carrier frequency is used to generate a baseband signal;

processing the baseband signal through a second step in which a fine carrier recovery is performed to improve the first approximation of carrier frequency; and

reconstructing the information bits by further processing an output of the second step.
The method of optical communication of claim 6, wherein the coarse carrier recovery step comprises one or more stages wherein each stage comprises:

processing an input signal of the stage through a low pass filtering operation, followed by a decimation operation, followed by a fast Fourier transform operation, followed by an averaging operation followed by a argmax operation to generate an output signal of the stage.
The method of optical communication of claim 6, wherein the second step comprises:

processing an input signal using a multi-stage decimation filter and a moving average filter to produce an output of the second step.
The method of claim 8, wherein a number of stages in the multi-stage decimation filter includes at least two stages of decimation.
The method of claim 6, wherein the further processing includes performing demodulation of the first sideband signal and the second sideband signal to recover the information bits.
An optical transmission apparatus comprising a processor and an optical transmitter, wherein the processor receives information bits and generates an optical signal carrying modulated data bits generated from the information bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme, and

the optical transmitter is configured to transmit the optical signal over an optical transmission medium.
The apparatus of claim 11, wherein a first spectrum occupied by the first sideband signal and a second spectrum occupied by the second sideband signal are symmetric around a center frequency.
The apparatus of claim 12, wherein the center frequency is separated from the first spectrum and the second spectrum by a spectral gap.
The apparatus of claims 11 to 13, wherein the first sideband signal and the second sideband signal are generated using a single OFDM modulator.
The apparatus of claim 11, wherein the optical signal is represented as

wherein x (n) represents the optical signal, N is number of subcarriers in the OFDM modulation scheme, N _l1～N _l2 is the region of the valid data-carrying subcarriers of the first sideband signal, wherein N _l1<N/2, N _l2<N/2, wherein N _r1～N _r2 is the region of the valid data-carrying subcarriers of the second sideband signal, wherein (N _r1<N/2, N _r2<N/2) .
An apparatus for optical communication, comprising:

an optical receiver configured to receive an optical signal carrying modulated data bits, wherein the optical signal includes a first sideband signal that comprising a first portion of the data bits modulated using an orthogonal frequency division multiplexing (OFDM) modulation scheme and a second sideband signal that comprises a second portion of the data bits modulated using the OFDM modulation scheme;

an opto-electric converter configured to convert the optical signal into a digital signal in an electrical domain; and

a processor configured for:

processing the digital signal through a coarse carrier recovery step in which a first approximation of carrier frequency is used to generate a baseband signal;

processing the baseband signal through a second step in which a fine carrier recovery is performed to improve the first approximation of carrier frequency; and

reconstructing the information bits by further processing an output of the second step.
The apparatus of claim 16, wherein the coarse carrier recovery step comprises one or more stages wherein each stage comprises:

processing an input signal of the stage through a low pass filtering operation, followed by a decimation operation, followed by a fast Fourier transform operation, followed by an averaging operation followed by a argmax operation to generate an output signal of the stage.
The apparatus of optical communication of claim 16, wherein the second step comprises:

processing an input signal using a multi-stage decimation filter and a moving average filter to produce an output of the second step.
The apparatus of claim 18, wherein a number of stages in the multi-stage decimation filter includes at least two stages of decimation.
The apparatus of claim 16, wherein the further processing includes performing demodulation of the first sideband signal and the second sideband signal to recover the information bits.