CN108631879B - A kind of light orthogonal frequency division multiplexing communication method and system based on probability shaping mapping - Google Patents
A kind of light orthogonal frequency division multiplexing communication method and system based on probability shaping mapping Download PDFInfo
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- 238000007493 shaping process Methods 0.000 title claims abstract description 23
- 238000013507 mapping Methods 0.000 title claims abstract description 20
- 238000000034 method Methods 0.000 title claims abstract description 19
- 238000006243 chemical reaction Methods 0.000 claims abstract description 37
- 239000013307 optical fiber Substances 0.000 claims abstract description 26
- 125000004122 cyclic group Chemical group 0.000 claims abstract description 20
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- 230000005540 biological transmission Effects 0.000 claims description 7
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/50—Transmitters
- H04B10/516—Details of coding or modulation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/50—Transmitters
- H04B10/516—Details of coding or modulation
- H04B10/548—Phase or frequency modulation
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
- H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
- H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
- H04L27/36—Modulator circuits; Transmitter circuits
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
- H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
- H04L27/38—Demodulator circuits; Receiver circuits
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Abstract
The present invention relates to a kind of light orthogonal frequency division multiplexing communication method and system based on probability shaping mapping, method includes: to generate pseudo-random binary bit stream PRBS signal；PRBS signal is modulated and obtains PS-QAM complex signal；PS-QAM complex signal is subjected to serial/parallel conversion, inverse fast Fourier transform and parallel/serial conversion and obtains base band OFDM signal, and obtains the OFDM baseband signal of addition cyclic prefix；Acquisition PS-OOFDM signal on light carrier is modulated to after carrying out D/A switch to OFDM baseband signal and is transferred to optical fiber；PS-OOFDM signal on optical fiber is transformed into simulation OFDM electric signal；Simulation OFDM electric signal is subjected to analog/digital conversion and obtains digital OFDM signal, removes cyclic prefix, Fast Fourier Transform (FFT) is carried out after parallel/serial conversion and obtains PS-QAM complex signal；The real part imaginary part of PS-QAM complex signal is separated, demapping restores corresponding PRBS signal.The present invention can obtain reshaping gain and improve the spectrum efficiency of fiber optic communication.
Description
Technical Field
The invention relates to a digital modulation technology in the field of optical fiber communication, in particular to an optical orthogonal frequency division multiplexing communication method and system based on probability shaping mapping.
Background
With the increase of transmission demand of users, optical fiber communication is becoming a main direction of communication as a long-distance and large-capacity transmission mode. The Optical Orthogonal Frequency Division Multiplexing (OOFDM) technology combines the traditional OFDM technology with the optical fiber communication technology, has the advantages of high-speed OFDM access, large information capacity, good dispersion resistance of optical fiber transmission and polarization mode dispersion, and has wide application prospect.
Quadrature Amplitude Modulation (Quadrature Amplitude Modulation) higher spectral efficiency can be obtained by joint Modulation of phase and Amplitude. The constellation diagram of the common QAM is distributed in a rectangular grid, the more points in the constellation diagram, the larger the information amount transmitted by each symbol, but the smaller the distance between the constellation points, the higher the requirement on a demodulation algorithm and the higher the error rate.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an optical orthogonal frequency division multiplexing communication method and system based on probability shaping mapping, which can obtain shaping gain and improve the spectral efficiency of optical fiber communication.
In order to achieve the purpose, the technical scheme of the invention is as follows:
on one hand, the invention discloses an optical orthogonal frequency division multiplexing communication method based on probability shaping mapping, which comprises the following steps:
generating a pseudo random binary bit stream (PRBS) signal by a pseudo random binary encoder;
modulating the PRBS signal to obtain a PS-QAM complex signal;
performing serial/parallel conversion on the PS-QAM complex signal to obtain N paths of parallel complex signals, performing fast Fourier inverse transformation on the N paths of parallel complex signals, and performing parallel/serial conversion to obtain a baseband OFDM signal; adding a cyclic prefix in a baseband OFDM signal to obtain an OFDM baseband signal added with the cyclic prefix; performing digital/analog conversion on the OFDM baseband signal to obtain an OFDM analog signal; modulating the OFDM analog signal to an optical carrier to obtain a PS-OOFDM signal; transmitting the PS-OOFDM signals to an optical fiber;
converting the PS-OOFDM signals on the optical fiber into analog OFDM electrical signals; performing analog/digital conversion on the analog OFDM electric signal to obtain a digital OFDM signal, removing a cyclic prefix, performing fast Fourier transform after parallel/serial conversion to obtain a PS-QAM complex signal; and separating the real part and the imaginary part of the PS-QAM complex signal, and demapping to recover a corresponding PRBS signal.
Preferably, modulating the PRBS signal to obtain a PS-QAM complex signal includes:
generating a length of 2 from a Maxwell-Boltzmann distributionn+1The offline probability codebook of (a);
dividing the binary bit stream PRBS signal into two paths of bit sequences with equal length;
one path of bit sequence generates 2 every n +1 code elementsn+1Carrying out a system symbol L, acquiring an L-th symbol from an offline probability codebook to generate a real part of a PS-QAM signal; make another path of bit sequence generate a 2 every n +1 code elementsn+1A binary system symbol L, wherein the symbol of the L-th bit is acquired in an offline probability codebook to generate an imaginary part of the PS-QAM signal; whereinM is an even power of 2 and represents the order of the QAM modulation format.
Preferably, the real part and the imaginary part of the PS-QAM complex signal are separated, and demapping is performed to recover the corresponding PRBS signal, specifically:
and separating the real part and the imaginary part of the PS-QAM complex signal, and respectively demapping and recovering the corresponding PRBS signal according to the offline probability codebook.
Preferably, the generating method of the offline probability codebook specifically includes:
according to Maxwell-Boltzmann distributionProduce a length of 2n+1The offline probability codebook of (a); wherein,and v represents a probability factor, belongs to R, and is valued according to corresponding parameters in practical application.
Preferably, the PS-OOFDM signal on the optical fiber is converted into an analog OFDM electrical signal, specifically:
and the PS-OOFDM signals on the optical fibers are subjected to photoelectric conversion into analog OFDM electric signals by adopting a photoelectric detector.
In another aspect, the present invention provides an optical orthogonal frequency division multiplexing communication system based on probability shaping mapping, comprising:
a data generation module for generating a pseudo random binary bit stream PRBS signal through a pseudo random binary encoder;
the probability shaping module is used for modulating the PRBS signal to obtain a PS-QAM complex signal;
the PS-OOFDM signal modulation module is used for performing serial/parallel conversion on the PS-QAM complex signal to obtain N paths of parallel complex signals, performing fast Fourier inverse transformation on the N paths of parallel complex signals, and performing parallel/serial conversion to obtain a baseband OFDM signal; adding a cyclic prefix in a baseband OFDM signal to obtain an OFDM baseband signal added with the cyclic prefix; performing digital/analog conversion on the OFDM baseband signal to obtain an OFDM analog signal; modulating the OFDM analog signal to an optical carrier to obtain a PS-OOFDM signal; transmitting the PS-OOFDM signals to an optical fiber;
the PS-OFDM transmission module is used for converting the PS-OOFDM signals on the optical fiber into analog OFDM electric signals; performing analog/digital conversion on the analog OFDM electric signal to obtain a digital OFDM signal, removing a cyclic prefix, performing fast Fourier transform after parallel/serial conversion to obtain a PS-QAM complex signal; and separating the real part and the imaginary part of the PS-QAM complex signal, and demapping to recover a corresponding PRBS signal.
Preferably, the modulating the PRBS signal to obtain a PS-QAM complex signal specifically includes:
generating a length of 2 from a Maxwell-Boltzmann distributionn+1The offline probability codebook of (a);
dividing the binary bit stream PRBS signal into two paths of bit sequences with equal length;
one path of bit sequence generates 2 every n +1 code elementsn+1Carrying out a system symbol L, acquiring an L-th symbol from an offline probability codebook to generate a PS-QAM signalThe real part of (a); make another path of bit sequence generate a 2 every n +1 code elementsn+1A binary system symbol L, wherein the symbol of the L-th bit is acquired in an offline probability codebook to generate an imaginary part of the PS-QAM signal; whereinM is an even power of 2 and represents the order of the QAM modulation format.
Preferably, the real part and the imaginary part of the PS-QAM complex signal are separated, and demapping is performed to recover the corresponding PRBS signal, specifically:
and separating the real part and the imaginary part of the PS-QAM complex signal, and respectively demapping and recovering the corresponding PRBS signal according to the offline probability codebook.
Preferably, the generating method of the offline probability codebook specifically includes:
according to Maxwell-Boltzmann distributionProduce a length of 2n+1The offline probability codebook of (a); wherein,and v represents a probability factor, belongs to R, and is valued according to corresponding parameters in practical application.
Preferably, the PS-OOFDM signal on the optical fiber is converted into an analog OFDM electrical signal, specifically:
and the PS-OOFDM signals on the optical fibers are subjected to photoelectric conversion into analog OFDM electric signals by adopting a photoelectric detector.
The invention has the following beneficial effects:
the invention relates to an optical orthogonal frequency division multiplexing communication method and system based on probability shaping mapping, which obtains a signal with higher quality and enables a demodulation algorithm to have higher universality by using a probability mapping method; meanwhile, an off-line probability codebook of probability mapping is calculated according to Maxwell-Boltzmann distribution, so that the signal quality is obviously improved. In addition, the generated binary bit stream PRBS signal is divided into two paths of bit sequences with equal length, so that higher sensitivity of the optical receiver can be realized.
The present invention will be described in further detail with reference to the accompanying drawings and embodiments, but the method and system for optical orthogonal frequency division multiplexing communication based on probability shaping mapping according to the present invention are not limited to the embodiments.
Drawings
Fig. 1 is a flow chart of OOFDM signal modulation in an embodiment of the present invention;
FIG. 2 is a block diagram of a PS-OOFDM signal demodulation process according to an embodiment of the invention;
FIG. 3 is a constellation probability distribution diagram according to an embodiment of the present invention;
FIG. 4 is a Maxwell-Boltzmann distribution histogram of an embodiment of the present invention;
FIG. 5 is a diagram of signal point distribution of a PS-16-QAM constellation diagram according to an embodiment of the present invention;
FIG. 6 is a probability codebook map according to an embodiment of the present invention;
fig. 7 is a flow chart of a PS-OOFDM system according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
Referring to fig. 1 to 6, in one aspect, the present invention is an optical orthogonal frequency division multiplexing (PS-OOFDM) communication method based on probability shaping (probability mapping), taking 16-QAM as an example, and the method includes:
step 1) according to Maxwell-Boltzmann distribution(xi＝[-3,-1,1,3]Taking v ═ 0.384) to generate an optimal Lookup table (Lookup table) of length 8, see fig. 6, i.e. an offline probability codebook, whose probability distribution is shown in fig. 4.
Step 2) generating a pseudo-random binary bit stream (PRBS signal) by a pseudo-random binary encoder. Generating a new 8-ary symbol L by each 3-bit binary code of one path of PRBS signal, generating a real part of a QAM signal according to the symbol of the L-th bit in a lookup table, generating an imaginary part of the QAM signal by the other path of PRBS signal in the same way, mapping the two paths of signals into a complete PS-16-QAM complex signal, and referring to a constellation diagram in FIG. 5 and probability distribution in FIG. 3.
And 3) carrying out fast Fourier inverse transformation on the PS-16-QAM complex signal and carrying out parallel/serial conversion to obtain a baseband OFDM signal. And adding a cyclic prefix in the baseband OFDM signal to obtain an OFDM baseband signal added with the cyclic prefix, and performing digital-to-analog conversion on the OFDM baseband signal to obtain an OFDM analog signal. An OFDM analog signal is modulated onto an optical carrier by using a Mach-Zehnder modulator (MZM), and the obtained PS-OOFDM signal is transmitted through an SSMF optical fiber.
And 4) performing photoelectric conversion on the PS-OOFDM signal by using a photodiode to obtain an analog OFDM signal, performing analog/digital conversion on the analog OFDM signal to obtain a digital OFDM signal, removing a cyclic prefix in the digital OFDM signal, and performing fast Fourier transform on the digital OFDM signal to obtain a PS-QAM complex signal.
And 5) separating the PS-16-QAM complex signal to obtain a real part signal and an imaginary part signal, and respectively demodulating and recovering the corresponding PRBS sequence according to the probability codebook.
Referring to fig. 7, in another aspect, an optical orthogonal frequency division multiplexing communication system based on probability shaping mapping according to the present invention includes: the device comprises a data generation module, a probability shaping module, a PS-OOFDM signal modulation module and a PS-OFDM transmission module.
The data generation module is used for generating a PRBS signal of a pseudo-random binary bit stream with the length of 10w bits.
The probability shaping module is used for shaping the probability of the target,
first, the distribution is based on Maxwell-Boltzmann distribution Produce a length of 2n+1Offline probability codebook (Lookup table).
Secondly, the binary bit stream PRBS signal is divided into two paths of bit sequences with equal length. One path of PRBS signal generates one 2 per n +1 bit binary coden+1Carry systemAnd a symbol L, acquiring the symbol of the L-th bit in the offline probability codebook to generate a real part of the PS-QAM signal. The other PRBS signal generates the imaginary part of the PS-QAM signal in the same way.
The PS-OOFDM signal modulation module:
the device is used for performing serial/parallel conversion on the PS-QAM complex signal to obtain N paths of parallel complex signals, performing fast Fourier inverse transformation on the N paths of parallel signals, and performing parallel/serial conversion to obtain a baseband OFDM signal. And adding a cyclic prefix in the baseband OFDM signal to obtain an OFDM baseband signal added with the cyclic prefix, and performing digital-to-analog conversion on the OFDM baseband signal to obtain an OFDM analog signal. Modulating the OFDM analog signal to an optical carrier to obtain a PS-OOFDM signal, and transmitting the PS-OOFDM signal to an optical fiber.
The PS-OFDM transmission module:
the system is used for transmitting the PS-OOFDM signals through single-mode optical fibers of a 50km SSMF standard, photoelectric conversion is carried out on the PS-OOFDM signals through a photodiode at a system receiving end to obtain analog OFDM electric signals, the analog OFDM signals are subjected to analog/digital conversion to obtain digital OFDM signals, cyclic prefixes in the digital OFDM signals are removed in the DSP, then the real parts and imaginary parts of the PS-QAM complex signals are obtained through fast Fourier transform, the real parts and the imaginary parts of the PS-QAM complex signals are separated, and the real parts and the imaginary parts of the PS-OOFDM signals are demodulated and recovered according to a probability codebook.
The above is only one preferred embodiment of the present invention. However, the present invention is not limited to the above embodiments, and any equivalent changes and modifications made according to the present invention, which do not bring out the functional effects beyond the scope of the present invention, belong to the protection scope of the present invention.
Claims (8)
1. An optical orthogonal frequency division multiplexing communication method based on probability shaping mapping, comprising:
generating a pseudo random binary bit stream (PRBS) signal by a pseudo random binary encoder;
modulating the PRBS signal to obtain a PS-QAM complex signal;
performing serial/parallel conversion on the PS-QAM complex signal to obtain N paths of parallel complex signals, performing fast Fourier inverse transformation on the N paths of parallel complex signals, and performing parallel/serial conversion to obtain a baseband OFDM signal; adding a cyclic prefix in a baseband OFDM signal to obtain an OFDM baseband signal added with the cyclic prefix; performing digital/analog conversion on the OFDM baseband signal to obtain an OFDM analog signal; modulating the OFDM analog signal to an optical carrier to obtain a PS-OOFDM signal; transmitting the PS-OOFDM signals to an optical fiber;
converting the PS-OOFDM signals on the optical fiber into analog OFDM electrical signals; performing analog/digital conversion on the analog OFDM electric signal to obtain a digital OFDM signal, removing a cyclic prefix, performing fast Fourier transform after parallel/serial conversion to obtain a PS-QAM complex signal; separating the real part and the imaginary part of the PS-QAM complex signal, and demapping to recover a corresponding PRBS signal;
modulating the PRBS signal to obtain a PS-QAM complex signal, specifically comprising:
generating a length of 2 from a Maxwell-Boltzmann distributionn+1The offline probability codebook of (a);
dividing the binary bit stream PRBS signal into two paths of bit sequences with equal length;
one path of bit sequence generates 2 every n +1 code elementsn+1Carrying out a system symbol L, acquiring an L-th symbol from an offline probability codebook to generate a real part of a PS-QAM signal; make another path of bit sequence generate a 2 every n +1 code elementsn+1A binary system symbol L, wherein the symbol of the L-th bit is acquired in an offline probability codebook to generate an imaginary part of the PS-QAM signal; whereinM is an even power of 2 and represents the order of the QAM modulation format.
2. The optical orthogonal frequency division multiplexing communication method based on probability shaping mapping according to claim 1, wherein the real part and the imaginary part of the PS-QAM complex signal are separated, and demapping is performed to recover the corresponding PRBS signal, specifically:
and separating the real part and the imaginary part of the PS-QAM complex signal, and respectively demapping and recovering the corresponding PRBS signal according to the offline probability codebook.
3. The method according to claim 1, wherein the generating of the offline probability codebook specifically comprises:
according to Maxwell-Boltzmann distributionProduce a length of 2n+1The offline probability codebook of (a); wherein,nu represents a probability factor, and nu belongs to R.
4. The method according to claim 1, wherein the PS-OOFDM signal on the optical fiber is converted into an analog OFDM electrical signal, specifically:
and the PS-OOFDM signals on the optical fibers are subjected to photoelectric conversion into analog OFDM electric signals by adopting a photoelectric detector.
5. An optical orthogonal frequency division multiplexing communication system based on probability shaping mapping, comprising:
a data generation module for generating a pseudo random binary bit stream PRBS signal through a pseudo random binary encoder;
the probability shaping module is used for modulating the PRBS signal to obtain a PS-QAM complex signal;
the PS-OOFDM signal modulation module is used for performing serial/parallel conversion on the PS-QAM complex signal to obtain N paths of parallel complex signals, performing fast Fourier inverse transformation on the N paths of parallel complex signals, and performing parallel/serial conversion to obtain a baseband OFDM signal; adding a cyclic prefix in a baseband OFDM signal to obtain an OFDM baseband signal added with the cyclic prefix; performing digital/analog conversion on the OFDM baseband signal to obtain an OFDM analog signal; modulating the OFDM analog signal to an optical carrier to obtain a PS-OOFDM signal; transmitting the PS-OOFDM signals to an optical fiber;
the PS-OFDM transmission module is used for converting the PS-OOFDM signals on the optical fiber into analog OFDM electric signals; performing analog/digital conversion on the analog OFDM electric signal to obtain a digital OFDM signal, removing a cyclic prefix, performing fast Fourier transform after parallel/serial conversion to obtain a PS-QAM complex signal; separating the real part and the imaginary part of the PS-QAM complex signal, and demapping to recover a corresponding PRBS signal;
modulating the PRBS signal to obtain a PS-QAM complex signal, specifically comprising:
generating a length of 2 from a Maxwell-Boltzmann distributionn+1The offline probability codebook of (a);
dividing the binary bit stream PRBS signal into two paths of bit sequences with equal length;
one path of bit sequence generates 2 every n +1 code elementsn+1Carrying out a system symbol L, acquiring an L-th symbol from an offline probability codebook to generate a real part of a PS-QAM signal; make another path of bit sequence generate a 2 every n +1 code elementsn+1A binary system symbol L, wherein the symbol of the L-th bit is acquired in an offline probability codebook to generate an imaginary part of the PS-QAM signal; whereinM is an even power of 2 and represents the order of the QAM modulation format.
6. The optical orthogonal frequency division multiplexing communication system based on probability shaping mapping according to claim 5, wherein the real part and the imaginary part of the PS-QAM complex signal are separated, and the corresponding PRBS signal is recovered by demapping, specifically:
and separating the real part and the imaginary part of the PS-QAM complex signal, and respectively demapping and recovering the corresponding PRBS signal according to the offline probability codebook.
7. The optical orthogonal frequency division multiplexing communication system based on probability shaping mapping as claimed in claim 5, wherein the generation manner of the offline probability codebook specifically comprises:
according to Maxwell-Boltzmann distributionProduce a length of 2n+1The offline probability codebook of (a); wherein,nu represents a probability factor, and nu belongs to R.
8. The optical orthogonal frequency division multiplexing communication system based on probability-shaping mapping of claim 5, wherein the PS-OOFDM signal on the optical fiber is converted into an analog OFDM electrical signal, specifically:
and the PS-OOFDM signals on the optical fibers are subjected to photoelectric conversion into analog OFDM electric signals by adopting a photoelectric detector.
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| CN109217933B (en) * | 2018-09-03 | 2021-06-11 | 南京信息工程大学 | Carrier-free amplitude and phase modulation method and demodulation method based on probability forming |
| CN109104250B (en) * | 2018-10-11 | 2021-04-13 | 南京信息工程大学 | Star 24QAM mapping-based optical probability forming coding method |
| CN109412999B (en) * | 2018-12-24 | 2020-04-17 | 北京邮电大学 | Mapping method and device for probability modeling |
| CN111371530B (en) * | 2018-12-26 | 2022-03-25 | 海思光电子有限公司 | Quadrature Amplitude Modulation (QAM) signal modulation and demodulation method and device |
| CN109756438B (en) * | 2019-02-01 | 2021-06-29 | 华侨大学 | OOFDM method and system based on LDPC coding probability shaping mapping |
| CN110278031A (en) * | 2019-06-10 | 2019-09-24 | 华侨大学 | Direct detection optical fiber telecommunications system and communication means based on many-one mapping PS-PAM4 |
| CN110311732A (en) * | 2019-06-10 | 2019-10-08 | 华侨大学 | A kind of WDM-PON system and communication means based on PS-PAM4 |
| CN111092663B (en) * | 2019-12-05 | 2022-07-01 | 华侨大学 | Optical orthogonal frequency division multiplexing system and communication method based on bit weighted distribution |
| CN111083078B (en) * | 2019-12-11 | 2020-11-17 | 华中科技大学 | Probability shaping quadrature amplitude modulation format blind identification method and system |
| CN111641438B (en) * | 2020-04-27 | 2021-03-23 | 苏州大学 | System, method and processor readable medium for estimating number of RFID tags |
| CN115567162A (en) * | 2022-09-29 | 2023-01-03 | 南京信息工程大学 | Probability constellation shaping method and system, and optical communication method and system |
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| US9300407B2 (en) * | 2012-09-07 | 2016-03-29 | Futurewei Technologies, Inc. | Channel estimation for optical orthogonal frequency division multiplexing systems |
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