Study on the Influence of optical fiber nonlinear effects on optical OFDM signals (1)

Study on the Influence of optical fiber nonlinear effects on optical OFDM signals (1)

Optical Orthogonal Frequency Di-vision Multiplexing (O-OFDM) is a new type of Optical transmission technology that has been developed in recent years, it applies Orthogonal Fre-quency Division Multiplexing (OFDM) technology to optical fiber channels. Transmitting OFDM Signals in optical fiber channels can improve the spectrum utilization and resist dispersion and various noise interference, with higher transmission rate and bandwidth. However, because the OFDM signal is composed of multiple modulated sub-carrier signals, a larger peak-to-average ratio (PAPR) may be generated ), it will directly bring about non-linear effects of the optical fiber, including self-phase modulation (SPM), cross-bit modulation (XPM) and four-wave mixing (FWM. By studying the influence of nonlinear effects of optical fiber on the transmission of OFDM Signals in optical fiber, we can obtain the signal variation pattern, so as to find an appropriate signal compensation method.

1. Basic principles of optical OFDM

The basic O-OFDM System Structure 1 is shown. The original binary sequence is mapped to N parallel sub-carrier channels through string/and conversion. At this time, the data cycle of each modulated sub-carrier is expanded to N times that of the original sequence, latency expansion and the numeric ratio of the symbol period are also reduced by N times.

After the QAM modulation is performed on the sequence of each sub-carrier channel, the Fourier inversion IFFT is performed. At this time, the expression in the data frequency domain is transformed to the time domain, the transmitted bits are mapped to the subcarrier's amplitude and phase. Then, the signal is converted into a serial signal, and then the I/Q conversion and upper frequency conversion are performed on the signal. After going through the mahzeng demodulated modulation, the electrical signal is converted into a optical signal, it is sent to the optical fiber for transmission. After optical detection, downconversion, And I/Q demodulation, the signal is restored to an electrical signal and then mapped to N parallel sub-carrier channels through string/conversion, after Fourier transform FFT, the signals in the time domain are converted to the frequency domain. After the signals are demodulated and converted in string, the signals are restored to a serial output sequence.

O-OFDM Working Principle

2. Optical OFDM signal transmission in Optical Fiber

The model of OFDM signal transmitted in optical fiber can be described using the nonlinear schörördinr equation (NLSE:

Nonlinear schörör Equation

Formula: A (z, T) is the slow amplitude of the pulse envelope, z is the distance of the Pulse Propagation Along the optical fiber, T = t-β 1 z, β 1 = 1 Vg, vg is the group speed, α is the fiber loss coefficient, β1, β2 are the first order and second order dispersion coefficient, and gamma is the non-linear coefficient. Normalized amplitude: U = A (z, T) P0, P0 is the peak power of the incident pulse. The formula (1) can be written as follows:

Since the non-linear schödnex equation generally cannot directly find the analytical solution, it is necessary to obtain the numerical solution. Step-by-step Fourier transformation is one of the methods. The idea of the distributed Fourier transformation method is to select a optical signal transmission distance h. When h is very small, the influence of dispersion and nonlinear effects on the pulse can be calculated separately, and an approximate result is obtained. When the optical pulse transmits h 2 in the optical fiber, the dispersion is calculated, and then the nonlinear function is calculated in z + h 2. When the optical pulse continues to transmit h 2, the dispersion is calculated, obtain the approximate solution with the transmission distance of h. Finally, the approximate solution is obtained when the optical pulse signal is transmitted at h distance in the optical fiber based on the results of dispersion and nonlinear effects.

3. Simulation results and analysis

3.1 simulation process

(1) generation of OFDM electrical signals: Set the QAM modulation index and the number of sub-carriers, and form a random sequence into an OFDM signal.

(2) modulation light source: Use the OFDM signal obtained in the previous step to modulated the light source to obtain the optical OFDM signal.

(3) step-by-step Fourier Method Solution: Set the fiber channel parameters and algorithm step size, use the step-by-step Fourier method to solve the non-linear schödörör equation, and simulate the process of optical OFDM signal passing through the fiber, obtain the signal transmitted through the optical fiber.

(4) photoelectric detection: Convert the signals transmitted through optical fiber into electrical signals.

(5) signal compensation processing: compensate the corresponding signal amplitude and phase based on the OFDM signal parameters and the optical fiber parameters to eliminate the influence of the dispersion and attenuation of the optical fiber.

(6) OFDM demodulation: Based on the QAM modulation index and the number of sub-carriers of the OFDM signal, the OFDM signal is demodulated to restore the original signal sequence.

(7) Error Analysis: Compare the input sequence of the sender and the output sequence of the receiver, and analyze the system error characteristics.

For the sake of simplification, other devices are considered as ideal devices, and only the influence of Optical Fiber on signal is considered.

3.2 simulation results

3.2.1 Bit Error Rate Calculation

For an input sequence, refer to the process to obtain the transmitted sequence to obtain the error characteristics. Through a large number of randomly generated input sequences, we can calculate the average peak-to-peak distribution of signals and the error rate at the same time, so that we can obtain the distribution of system error rates and the average system error rate.

The calculation method is as follows:

The average peak-to-peak probability distribution of recorded signals is recorded as p (PAPR), and the error rate distribution of the corresponding peak-to-peak ratio is recorded as PAPR. Then, the system error rate distribution is p (PAPR) * BER (PAPR), the average system error rate is Σ (p (PAPR) * BER (PAPR )).