Binary Review Optical Signal System

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Signal Optical Power

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Modulation formats for optical communications

10.7.1 Power budgeting

In an optical system without inline optical amplifiers, receiver sensitivity is defined as the minimum signal optical power at the receiver to obtain the specified BER, as has been discussed in Section 8.3 . In such a system, link budgeting is essentially a power budgeting to find the power margin between the receiver sensitivity and the signal optical power that actually reaches the receiver.

Fig. 10.7.1 shows an example of an optical system consisting of an optical transmitter, and a direct detection receiver. The fiber has five sections, linked together by four fiber connectors and three fiber splices. There is also a fiber tap in the system which taps out a portion of the optical power for monitoring purpose. Assume the signal optical power emitted by the transmitter is Ptx, and the loss of each fiber section is αiLi where αi is the attenuation coefficient and Li is the length of the ith fiber section, with i = 1, 2, 3, 4, 5. The loss of each fiber coupler is Ac, the loss of each fiber splice is As, and the loss of the fiber tap is Atap. The signal optical power that reaches the receiver is then,

Fig. 10.7.1 . Example of an optical system with five fiber sections, four couplers, three splices, and one fiber tap.

where the optical power is in dBm, and the losses of different components are all in dB. If the receiver sensitivity is Psen, then the system power margin is Pmargin = PsPsen which has to be positive for the system to have a BER lower than the specified value. It is important to note that receiver sensitivity Psen is determined by the target BER level of the receiver, which depends on the coding technique used in the system. Traditionally, BER levels of 10 − 12 –10 − 15 are required for most of the long-distance optical transmission systems. With the advance of forward error correction (FEC) coding, the required pre-FEC BER level can be much relaxed, to the level around 10 − 3 depending on the FEC coding strength. This helps reducing the power level of Psen, and improving system power margin.

In the example shown in Fig. 10.7.1 , assume attenuation coefficients of fiber sections are α1 = 0.22 dB/km, α2 = 0.25 dB/km, α3 = 0.21 dB/km, α4 = 0.28 dB/km, α5 = 0.27 dB/km, fiber lengths are L1 = 2.2 km, L2 = 3.5 km, L3 = 15 km, L4 = 21 km, and L5 = 12 km, loss of each connector is Ac = 0.3 dB, loss of each splice is As = 0.1 dB, and the loss of the fiber tap is Atap = 1.5 dB. The total system loss is 16.63 dB. If the transmitter power is Ptx = 2 mW, which is 3 dBm, and the receiver sensitivity is Psen =−20 dBm, the system margin is Pmargin = 6.37dB. This means that the system can tolerate an additional 6.37 dB loss.

In practical system design, at least 3 dB margin is usually reserved to ensure the reliability of the system against unexpected events and system aging over the life time.

Optical performance monitoring in optical long-haul transmission systems

Receiver Sensitivity

Receiver sensitivity, the traditional measure of receiver performance, is defined as the minimum received optical signal power at a specific BER (e.g., 10 −9 ) 4 in the back-to-back configuration. This parameter shows the quality of receiver design. The better the receiver sensitivity, the better the system performance in terms of longer transmission distance and the greater the tolerance to fiber impairments.

However, receiver sensitivity is not the critical measure for long-haul systems that consist of many optical amplifiers. In the optically amplified long-haul system, receiver sensitivity is replaced by optical signal-to-noise ratio (OSNR) as the base for performance comparison. Nevertheless, back-to-back receiver sensitivity itself is still a good measure of performance for high-speed receiver design.

Unrepeatered Transmission

7.2.3 Line fiber with larger effective area

The line fiber is also impacting the channel count, especially over long unrepeatered distances where the optical signal powers launched into the fiber are high. Fibers with large effective area (quantitative measure of the area that a fiber mode effectively covers in the transverse dimensions) are tolerant to higher launched power, delaying the onset of nonlinearities occurring during signal propagation. While standard G.652 fibers typically offer an 80 μm 2 effective area, single-mode fibers with effective area of about 110 μm 2 , 130 μm 2 and even 150 μm 2 [10] became available in the last decade.

If large effective area is beneficial from a signal nonlinearities perspective, distributed Raman amplification is, however, more efficient in smaller effective area fiber as discussed in subsection 7.4.2.1 . Achieving the same Raman gain in a large effective area fiber as in a smaller effective area fiber requires more Raman pump power but, when the same level of Raman gain is obtained, the optical transmission benefits offered by Raman amplification are the same for both types of fiber. Furthermore, the higher tolerance from large effective area fibers to launched signal power, combined with their lower attenuation, results, despite the lower Raman gain coefficient gr, in Raman gain further into the line. The longest unrepeatered transmission demonstrations have been achieved on large effective area fibers (see subsection 7.4.3.6 for a more detailed discussion).

Photodetectors

4.4.1 APD used as a linear detector

For application in optical communication systems, an APD is usually used as a linear detector in which the photocurrent is linearly proportional to the received signal optical power . The contribution of the avalanche process is that each input photon may generate multiple free electrons and holes. Thus, the responsivity expression of an APD has to include the effect of carrier multiplication,

where MAPD is defined as the APD gain, and is the responsivity of a PIN photodiode defined by Eq. (4.2.1) . Since the avalanche process depends on the electrical field in the avalanche region, the APD gain strongly depends on the voltage of the reverse bias. A simplified expression commonly used for APD gain is

where nB is a parameter that depends on the device structure and the material. VB is the applied reverse bias voltage and VBD is defined as the breakdown voltage of the APD, and Eq. (4.4.2) is valid only for VB (4.4.3) M APD ω = M APD , 0 1 + ωτ e M APD , 0 2

where MAPD, 0 = MAPD(0) is the APD gain at DC as shown in Eq. (4.4.2) and τe is an effective transient time, which depends on the thickness of the avalanche region and the speed of the carrier drift. Therefore, the 3-dB bandwidth of APD gain is

In practical applications, the frequency bandwidth requirement has to be taken into account when choosing APD gain.

Due to the effect of carrier multiplication in an APD, signal photocurrent is

As far as the noises are concerned, since the thermal noise is generated in the load resistor RL, it is not affected by the APD gain. However, both shot noise and the dark current noise are generated within the photodiode, and they will be enhanced by the APD gain ( Fyath and O’Reilly, 1989 ). Within a receiver bandwidth B, the mean-square shot noise current in an APD is

The dark current noise in an APD is

In both Eqs. (4.4.6) and (4.4.7) , F(MAPD) is a noise figure associated with the random nature of carrier multiplication process in the APD. This noise figure is proportional to the APD gain MAPD. The following simple expression is found to fit well with measured data for most practical APDs:

where 0 ≤ x ≤ 1, depending on the material. For often used semiconductor materials, x = 0.3 for Si, x = 0.7 for InGaAs, and x = 1 for Ge APDs.

From a practical application point of view, APD has advantages compared to conventional PIN when the received optical signal is very weak and the receiver SNR is limited by thermal noise. In quantum-noise-limited optical receivers, such as coherent detection receivers, APD should, in general, not be used, because it would only increase noise level and introduce extra limitations in the electrical bandwidth.

Introduction

1.1.1.3 Optical Fiber Transmission Characteristics

Attenuation and dispersion are two important parameters that influence the optical fiber transmission performance.

Attenuation is a phenomenon that, when light travels in the optical fibers, the optical signal power will decay with the transmission distance increasing according to the exponential law. The attenuation value of the optical fiber largely determines the distance between repeaters in an optical fiber communication system.

There are three main causes of optical signal attenuation: absorption loss, scattering loss, and radiation loss: a.

Absorption loss refers to the loss caused by the absorption of light energy in the optical fiber. It can be divided into intrinsic absorption and impurity absorption. The former is caused by pure quartz; the latter is caused by impurities.

Scattering loss refers to the loss of the light in the process of scattering, which ascribes to the fluctuation of the refractive index, due to unevenness in the internal density of the material that is caused by the thermal disturbances of the molten quartz glass molecules during the heating process.

Radiation loss refers to the radiation loss caused by the leaking out of light energy to the cladding when the fiber is bent by external forces. Sometimes the surface of the optical fiber will be molded with a layer of a compression jacket in the optical fiber manufacturing process. When the optical fiber bears external force and bends, the jacket will deform, but the optical fiber will still keep straight.

Dispersion refers to the extension of pulse when the optical signal transits in the optical fiber. In the optical fiber communication system, the optical signal will be distorted when dispersion reaches a certain point and further lead to intersymbol interference caused by the overlapping of the front and rear pulse. Optical fiber dispersion limits the bandwidth and distance of fiber-optic communications.

The reasons for optical fiber dispersion include fiber material, waveguide structure, mode structure, and optical signal structure. According to different causes, dispersion is generally divided into material dispersion, waveguide dispersion, mode dispersion, and polarization mode dispersion. In general, multimode fiber is mainly mode dispersion, and single-mode fiber is mainly material dispersion and polarization mode dispersion.

Optical transmission system design

8.3.2 Required OSNR

In the systems discussed earlier, optical noise is not accompanied with the optical signal that reaches the optical receiver, and therefore, BER can be reduced by increasing the level of signal optical power . On the other hand, in a long-distance optical transmission system employing multiple inline optical amplifiers, the level of optical power at the receiver can always be increased by increasing the gain of optical amplifiers. But the accumulated ASE noise generated by these optical amplifiers may become significant when the number of inline optical amplifiers is large. When the OSNR at the input of the receiver is too low, increasing optical power at the receiver may not result in the improvement of BER performance. In this type of systems, the performance is no longer limited by the signal optical power that reaches the receiver; rather, it is limited by the OSNR.

Fig. 8.3.4 illustrates a fiber-optic transmission system with N optically amplified fiber spans. In this system, if the transmission loss of each fiber span is exactly compensated by the gain of the inline optical amplifier in that span, the average signal optical power that reaches the receiver is equal to that emitted from the transmitter. Meanwhile, each EDFA generates an optical noise power spectral density ρASE, i = 2nsp(hc/λ)(Gi − 1), with i = 1, 2, …, N. As the ASE noise generated by each EDFA is also attenuated by the fibers and amplified by the EDFAs along the following fiber spans, the accumulated ASE noise power spectral density at the input of the receiver will be simply the addition of contributions from all inline EDFAs: ρ ASE = ∑ i = 1 N ρ ASE , i . Then, OSNR at the input of the optical receiver is defined as the ratio between the average optical signal power, Pave, and the power spectral density of the accumulated noise ρASE, that is

Fig. 8.3.4 . Fiber-optic transmission system with N optically amplified fiber spans.

Since the unit of the signal average power is [W] and the unit of optical noise power spectral density is [W/Hz], the unit of OSNR should be [Hz], or [dB·Hz]. In practice, the optical noise power spectral density is measured by an optical spectrum analyzer (OSA) with a certain resolution bandwidth, RB, and the OSA reports the measured noise power within a resolution bandwidth with the unit of [W/RB]. Whereas, assume the spectral linewidth of the optical signal itself is narrower than the OSA resolution bandwidth, the OSA actually measures the total power of the optical signal. Thus, [dB·RB] is often used as the unit to specify OSNR.

In the system with multiple optical amplifiers, since the level of optical power arriving at the receiver is usually high enough, signal-independent noises such as thermal noise and dark current noise can be neglected in comparison with signal-dependent noises, that include shot noise, signal-ASE beat noise, and ASE-ASE beat noise. If we only consider shot noise, signal-ASE beat noise, and ASE-ASE beat noise, and neglect waveform distortion, Q-value can be calculated by

This can be expressed as the function of OSNR as

Fig. 8.3.5 shows the calculated receiver Q-value as the function of the signal OSNR for a 10 Gb/s binary system based on Eq. (8.3.10) , where waveform distortion is not considered (A = 1 and B = 0). The OSNR, based on a resolution bandwidth of 0.1 nm, is the signal optical power divided by the noise power within 0.1 nm optical bandwidth. Other system parameters are Pave = 0 dBm, = 0.85mA/mW, Bo = 25 GHz, Be = 7.5 GHz, and λ = 1550 nm. Contributions due to shot noise, ASE-ASE beat noise and signal-ASE beat noise are shown in the same figure. In the vicinity of BER = 10 − 12 (Q = 8.45 dB), the Q-value is mainly determined by the contribution from signal-ASE beat noise, and the required OSNR (ROSNR) to achieve the targeted BER of 10 − 12 is approximately 16 dB.

Fig. 8.3.5 . Q-value as the function of signal OSNR (curve marked with total) considering contributions from shot noise, ASE-ASE beat noise, and signal-ASE beat noise.

Since SAE-ASE beat noise can be reduced by further reducing the bandwidth of the optical filter, the dominant noise in most of the long-distance optical systems employing multiple inline optical amplifiers are signal-ASE beat noise. If we only consider signal-ASE beat noise and also take into account the effect of waveform distortion, the Q-value will be

which is similar to that described in Eq. (8.3.7) , but here Pave and ρASE are input optical signal average power and noise power spectral density, respectively, at the receiver, and their ratio represents the OSNR.

Eq. (8.3.11) indicates that the Q-value of the receiver is not determined by the received signal optical power level, but rather it is linearly proportional to the square root of the OSNR. If we set a target value of Q = 7 (for BER = 10 − 12 ), the required OSNR, or ROSNR is simply

Fundamentals of Optical Devices

Rongqing Hui, Maurice O’Sullivan, in Fiber Optic Measurement Techniques , 2009

1.4.3.3.2 EDFAs with AGC and APC

Automatic gain control (AGC) and automatic power control (APC) are important features in practical EDFAs that are used in optical communication systems and networks. Since the optical gain of an EDFA depends on the signal optical power , system performance will be affected by signal optical power fluctuation and add/drop of optical channels. Therefore, AGC and APC are usually used in in-line optical amplifiers to regulate the optical gain and the output signal optical power of an EDFA. Because both the optical gain and the output signal optical power are dependent on the power of the pump, the automatic control can be accomplished by adjusting the pump power.

Figure 1.4.16 shows an EDFA design with AGC in which two photodetectors, PDI and PDO, are used to detect the input and the output signal optical powers. An electronic circuit compares these two power levels, calculates the optical gain of the EDFA, and generates an error signal to control the injection current of the pump laser if the EDFA gain is different from the target value. If the EDFA carries multiple WDM channels and we assume that the responsivity of each photodetector is wavelength independent within the EDFA bandwidth, this AGC configuration controls the overall gain of the total optical power such that

Figure 1.4.16 . Configuration of an EDFA with both automatic gain control. PDI: input photodiode, PDO: output photodiode.

where N is the number of wavelength channels. In this case, although the gain of the total optical power is fixed by the feedback control, the optical gain of each individual wavelength channel may vary, depending on the gain flatness over the EDFA bandwidth.

In long distance optical transmission, many in-line optical amplifiers may be concatenated along the system. If the optical gain of each EDFA is automatically controlled to a fixed level, any loss fluctuation along the fiber system will make the output optical power fluctuate and therefore the optical system may become unstable.

APC, on the other hand, regulates the total output optical power of an EDFA, as shown in Figure 1.4.17 . In this configuration, only one photodetector is used to detect the total output signal optical power. The injection current of the pump laser is controlled to ensure that this measured power is equal to the desired level such that

Figure 1.4.17 . Configuration of an EDFA with automatic power control.

The advantage of APC is that it isolates optical power fluctuations along the system, because the variation of fiber loss in one span does not affect other spans. However, since the total power is regulated, channel add/drop in WDM systems will affect the optical power of each individual channel. Therefore, in advanced optical communication systems, EDFAs are controlled by intelligent systems taking into account the number of wavelength channels, optical signal-to-noise ratio, and other important system parameters.

Optical System Performance Measurements

Rongqing Hui, Maurice O’Sullivan, in Fiber Optic Measurement Techniques , 2009

5.2.1 Receiver Sensitivity and Power Margin

Receiver sensitivity is one of the most widely used specifications of optical receivers in fiber-optic systems. It is defined as the minimum signal optical power level required at the receiver to achieve a certain BER performance. For example, in a specific optical system, for the BER to be less than 10 −12 , the minimum signal optical power reaching the receiver has to be no less than −35 dBm; therefore the receiver sensitivity is −35 dBm. Obviously the definition of receiver sensitivity depends on the targeted BER level and the signal data rate. However, signal waveform distortion and optical SNR are, in general, not clearly specified in the receiver sensitivity definition. In fact, the receiver sensitivity measurement assumes that the noise generated in the receiver is the major limiting factor of receiver performance.

Neglecting waveform distortion and the impact of crosstalk in the optical signal for a moment, the Q-value will only depend on the signal power and the noise generated by the receiver. For example, in an intensity-modulated system with direct detection, if no optical amplifier is used in the system, the receiver sensitivity is mainly limited by receiver thermal noise, shot noise, and photodiode dark current noise. In this case, Equation 5.1.19 can be written as

Figure 5.2.1 shows the calculated receiver Q-value as a function of the received average signal optical power Pave. This is a 10 Gb/s binary system with direct detection, and the electrical bandwidth of the receiver is Be = 7.5 GHz. Other parameters used are ℜ = 0.85mA/mW, RL = 50Ω, Id = 5nA, and T = 300K. Figure 5.2.1 indicates that to achieve a targeted BER of 10 −12 , or equivalently Q = 7 (10log(Q) = 8.45 dB), the received average signal optical power has to be no less than −19 dBm. Therefore the sensitivity of this 10 Gb/s receiver is −19 dBm. Every dB decrease in signal optical power will result in a dB decrease of the Q-value, as indicated in Figure 5.2.1 .

Figure 5.2.1 . Receiver sensitivity plot for a 10 Gb/s system using a PIN photodiode.

Another type of optical receiver employs an optical preamplifier before the PIN photodiode as illustrated in Figure 5.2.2(b) . The optical preamplifier increases the signal optical power before it reaches the photodiode, while at the same time introducing ASE noise. In this case, the level of the ASE noise is proportional to the gain of the optical preamplifier; therefore the receiver Q-value still decreases with the decrease of the input signal optical power. In the preamplified optical receiver, the Q-value can be calculated by

Figure 5.2.2 . Direct detection receivers with and without optical preamplifier.

where the parameters are defined by Table 5.1.2 . Again, the waveform distortion is neglected and the average signal power is equal to ½ of the instantaneous power at signal digital 1. Suppose the amplified signal optical power that reaches the PIN photodiode is fixed at Pr = −3 dBm; the gain of the optical preamplifier becomes a function of the input signal optical power, as does the ASE noise level. For an optical amplifier with an F = 5 dB noise figure which corresponds to nsp = 1.58, the ASE noise spectral density is

in the unit of Watt per Hertz. Figure 5.2.3 shows the calculated receiver Q-value as a function of the received average signal optical power Pave at the input of the EDFA preamplifier. The parameters used in the calculation are RL = 50Ω, Id = 5 nA, T = 300 K, Bo = 25 GHz, Be = 7.5 GHz, and λ = 1550 nm. In this case the receiver sensitivity is Psen = −37.1 dBm, which is approximately 18 dB better than the direct detection without the EDFA preamplifier.

Figure 5.2.3 . Receiver sensitivity plot for a 10 Gb/s system with an optically preamplified PIN receiver.

For every dB signal optical power decrease, there is only half a dB decrease in 10log(Q). The reason is that the optically preamplified receiver is dominated by the signal-ASE beat noise, which is signal-dependent. In fact, the dashed line in Figure 5.2.3 shows the Q values only considering signal-ASE beat noise, which is obviously a good approximation. Except when the signal optical power is too high or too low, where the signal-ASE beat noise is comparable to or lower than the PIN thermal noise or the ASE-ASE beat noise, then the linear approximation becomes inaccurate.

Figure 5.2.4 shows the measurement setup to characterize the receiver sensitivity in an optical transmission system. A variable optical attenuator (VOA) is used to change the level of signal optical power that reaches the receiver. The optical power is monitored by a power meter through a fiber tap. The optical transmitter is modulated by a digital signal generated from a BER test set and the signal recovered by the optical receiver is analyzed by the error detector of the same BER test set. The Q-value of the receiver can be calculated through the BER measurement using Q = 2 ⋅ e r f c − 1 ( 2 × B E R ) , where erfc −1 is the inverse complementary error function. By scanning the value of the VOA and thus the optical power level at the receiver, the Q-value as the function of signal optical power can be obtained systematically, and the receiver sensitivity can be derived. This is more accurate than only measuring a single power level corresponding to the targeted BER.

Figure 5.2.4 . Schematic diagram of experimental setup to characterize receiver sensitivity.

Figure 5.2.5 shows a comparison between the calculated and the measured BER as a function of the input signal optical power at the receiver. The 10Gb/s receiver has an optical preamplifier with a 5 dB noise figure. The corresponding Q-value is also indicated along the right-side vertical axis in the figure. It is noticeable that the measured sensitivity at BER = 10 −12 is approximately 3 dB worse than the calculated results. This is caused by the waveform distortion and eye closure penalty, which are not considered in the calculation. The curve of BER versus signal optical power as shown in Figure 5.2.5 is sometimes referred to as a waterfall curve because of its waterfall-like shape.

Figure 5.2.5 . Illustration of the calculated and measured receiver BER plot.

Accurate prediction of receiver sensitivity must take into account the eye closure penalty caused by waveform distortion, as illustrated in Figure 5.1.6 , where A 0. More accurately, Equations 5.1.15 and 5.1.16 have to be used to take into account the pattern-dependent waveform distortion effect. In general, the measured receiver sensitivity can be affected by a number of factors. First, different eye openings of the received optical signal may result in different waterfall plots; therefore it has to be precisely specified when reporting the measured sensitivity values. Second, if the optical system has inline optical amplifiers, the accumulated ASE noise in the system will certainly have significant impact in the measured sensitivity at the receiver.

Figure 5.2.6 . Receiver Q as the function of signal OSNR with and without eye closure penalty. Solid lines were obtained using Equation 5.2.5 and dashed lines were obtained considering signal-ASE beat noise only using Equation 5.2.6 .

Receiver sensitivity is a useful parameter to find the performance margin of a transmission system. The power margin of a system is defined as the ratio between the available signal optical power and the receiver sensitivity.

where Pactual is the actual optical power arrives at the receiver, and Psen is the receiver sensitivity. For example, in a transmission system, if the actual signal optical power that reaches the receiver is −25 dBm while the receiver sensitivity is −32 dBm, the power margin is 7 dB. Generally, in optical system design and implementation, a certain power margin has to be budgeted at the time of system installation. This is reserved for system aging and other unexpected degradations during the lifetime of the system. Power margin consideration is an important issue in system design, both technically and economically. If the margin is too small, the integrity of the system transmission performance may not be guaranteed, whereas if the margin is too large, it would be a waste of resources that results in unnecessarily high cost.

Receiver sensitivity and power margin have been widely used to specify the performance of optical receivers and optical transmission systems. In a traditional optical system without inline optical amplifiers, noise generated in the receiver is the dominant source of transmission performance degradation. Therefore, receiver sensitivity and power margins are the perfect measures of the receiver and the system performance with minimum ambiguity. On the other hand, in long-distance and high-speed optical systems using multiple optical amplifiers, signal optical power levels at the photodiode may not be the most important limiting factor in terms of the system performance. For example, the signal optical power can be easily increased by increasing the gain of inline optical amplifiers. In these systems, optical SNR of the signal is more important than the level of signal optical power. Therefore the power margin may no longer be the best performance measure of amplified optical systems. Instead, optical SNR margins may be more relevant.

Coherent optical communication systems

Problems

In a coherent detection optical receiver, assume the power coupling coefficient of the 2 × 2 coupler is ɛ. Find the optimum coupling coefficient ɛ to achieve the highest coherent detection efficiency.

Does this optimum coupling coefficient depend on the power ratio between the LO and the received optical signal?

In order for a coherent receiver to operate properly, the power of the LO has to be high enough so that shot noise generated by the LO is much higher than thermal noise. What is the LO power required for the LO-induced shot noise to be 10 times the thermal noise at room temperature? Assume receiver load resistance is RL = 50 Ω and photodiode responsivity is = 1mA/mW.

Consider a coherent homodyne receiver with 0 dBm phase-locked LO, and a direct detection receiver shown in the following figure. Both receivers use PIN photodiodes with 0.75 A/W responsivity and a negligible dark current at the room temperature, and 40 GHz electrical bandwidth. The load resistor is 50 Ω.

Please find the signal optical power required to achieve the electrical SNR of 20 dB for coherent detection and direct detection, respectively.

What is the signal optical power level below which coherent detection provides better SNR compared to direct detection?

All parameters are the same as in problem 2, but now consider an on-off key binary modulated optical signal in which Ps,1 = 2Ps,ave, with Ps,1 and Ps,ave signal optical power at signal “1” and average signal optical power, respectively. Assume there is no signal waveform distortion. (a)

Please find the average signal optical power required to achieve the receiver Q = 8 for coherent homodyne detection and direct detection, respectively.

What is the average signal optical power level at which coherent detection has the same Q value as direct detection?

Consider an on-off key binary modulated optical system without waveform distortion. Both coherent homodyne receiver and optically preamplified direct detection can be used as shown in the following figure. Operating wavelength is 1550 nm and photodiode has 100% quantum efficiency. For the coherent detection, assume LO is strong enough so that LO-induced shot noise is the dominate noise. For optically preamplified receiver, assume signal ASE beat noise is the dominate noise source, and the optical gain of the amplifier is very high so that G ≫ 1.

What would be the noise figure of the optical preamplifier for these two receivers to have the same SNR for at the same average signal optical power?

(Note: SNR is evaluated at signal “1,” and assume that signal power at “1” is twice the average signal power Ps,ave)

Consider a coherent homodyne receiver used in a binary intensity modulated system with multiple inline optical amplifiers at 1550 nm wavelength. Assume the modulation data rate is 40 Gb/s and the receiver electrical bandwidth is 40 GHz. Neglect signal waveform distortion, and only consider LO-ASE beat noise, what is the required OSNR in [dB ⋅ 0.1nm] to achieve a Q value of 7?

Consider an optical system with inline optical amplifiers, the signal optical power is Ps and the optical noise power spectral density is ρASE. If a coherent homodyne receiver is used, Eq. (9.2.14) indicates that the electrical SNR at the receiver output is SNR = OSNR/Be. Now an optical preamplifier is inserted as shown in the following figure with an optical gain G. Assume that the LO power is high enough so that the major noise source is due to the mixing between LO and ASE.

Does this optical preamplifier help improve system performance? Please explain the reason by deriving necessary equations.

For a coherent receiver, the relative intensive noise (RIN) of the LO is − 140 dB/Hz within the receiver bandwidth. If the photodiode responsivity is 1 mA/mW, what the LO power such that the RIN noise is equal to the shot noise generated by the LO.

Consider coherent homodyne detection based on a 2 × 4 90 degree hybrid coupler as shown in Fig. 9.4.3 . If the actual value of the 90 degree optical phase shifter is 90°+ δ, where δ = 10° is a fabrication error, what is the maximum percentage of signal power variation ΔiI 2 + ΔiQ 2 with the random variation of Δφ [reference to Eqs. (9.4.19) and (9.4.20) ]?

Same coherent homodyne receiver as in problem 9, but the optical signal is QPSK modulated with four constellation points at (π/4, 3π/4, 5π/4, 7π/4). Because of the δ = 10° error of the 90° phase shifter, what are the angles of the detected constellation points by this I/Q receiver?

Optical amplifiers

5.4.4 Additional considerations in EDFA design

EDFA performance depends on the spectral shapes of emission and absorption cross sections, pumping configuration and power, and EDF length. In general, an EDFA can have either a forward pump or a backward pump, or both of them as illustrated in Fig. 5.4.8 . Forward pumping refers to the pump that propagates in the same direction as the signals, whereas in backward pumping scheme the pump travels in the opposite direction of the optical signal.

Fig. 5.4.8 . Configuration of an EDFA with both a forward pump and a backward pump.

An EDFA with a forward pump alone usually has relatively low signal output optical power, but at the same time the forward ASE noise level is also relatively low. However, the backward propagated ASE noise level at the input side of the EDF may become quite high. The reason is that although the pump power can be strong at the fiber input, its level is significantly reduced at the fiber output because the pump energy is converted to the amplified signal along the fiber. Because of the weak pump at the EDF output, the carrier inversion level is low as well; therefore, the differential gain reduces monotonically along the EDF and the output optical signal power is limited. On the other hand, since the carrier inversion level is very strong near the fiber input side, the backward propagated spontaneous emission noise meets high amplification in that region, and thus the backward ASE noise power is strong at the fiber input side. An example of the EDFA performance using only a forward bump is shown in Fig. 5.4.6 .

With backward pumping, the pump power is strong near the fiber output side and its level is significantly reduced when it reaches to the input side. Because of the strong pump power and the relatively high carrier inversion at the EDF output, the output optical signal power can be higher than the forward pumping configuration at the same pump power. But the forward ASE noise level can also be high because of the high differential gain near the output port. Bidirectional pumping can be used to increase both optical gain and output signal optical power for an EDFA. In such a case, pump power distribution along the EDF is more uniform compared to unidirectional pumping. Fig. 5.4.9 shows the power levels of pump and signal channels along the EDF in a bidirectional pumping scheme with 100 mW pump in each direction, and the output PSD. The variation of the combined pump power is less than 5 dB along the EDF. Because of the increase of the total pump power, the optical gain and the total output optical signal power are also increased in comparison to the case of forward pumping as shown in Fig. 5.4.6 .

Fig. 5.4.9 . Performance of EDFA with bidirectional pumping and 25 m EDF length. 100-mW pump power is used in each direction, and there are six signal wavelength channels each with − 20 dBm input power. (A) Power evolution along the EDF for forward pump (squares), backward pump (circles), total pump (stars), and optical signal channels (solid lines). (B) Output optical power spectral density.

Because the optical gain and the shape of the gain spectrum of an EDFA can be affected by the variation of the signal optical power through gain saturation, optical gain has to be stabilized to ensure the stability of the optical system. Automatic gain control (AGC) and automatic power control (APC) are important features in practical EDFAs that are used in optical communication systems and networks. AGC and APC are usually used in in-line optical amplifiers to regulate the optical gain and the output signal optical power of an EDFA. Because both the optical gain and the output signal optical power are dependent on the power of the pump, the automatic control can be accomplished by adjusting the pump power.

Fig. 5.4.10 shows an EDFA design with AGC in which two photodetectors, PDI and PDO, are used to detect the input and the output signal optical powers. An electronic circuit compares these two power levels, calculates the optical gain of the EDFA, and generates an error signal to control the injection current of the pump laser if the EDFA gain is different from the target value. If the EDFA carries multiple WDM channels and we assume that the responsivity of each photodetector is wavelength independent within the EDFA bandwidth, this AGC configuration controls the overall gain of the total optical power such that

Fig. 5.4.10 . Configuration of an EDFA with both automatic gain control. PDI: input photodiode and PDO: output photodiode.

where N is the number of wavelength channels. In this case, although the gain of the total optical power is fixed by the feedback control, the optical gain of each individual wavelength channel may vary, depending on the spectral shape of the optical gain over the EDFA bandwidth.

In long-distance optical transmission, many in-line optical amplifiers may be concatenated along a system. If the optical gain of each EDFA is automatically controlled to a fixed level, any signal power fluctuation, for example, through dynamic wavelength channel add/drop, along the fiber system will make the output optical power variation throughout the system.

APC, on the other hand, regulates the total output optical power of an EDFA, as shown in Fig. 5.4.11 . In this configuration, only one photodetector is used to detect the total output signal optical power. The injection current of the pump laser is controlled to ensure that this measured power is equal to the desired level such that

Fig. 5.4.11 . Configuration of an EDFA with automatic power control.

The advantage of APC is that it isolates signal optical power fluctuations along the system because loss change in one span does not propagate to other spans. However, since the total power is regulated, channel add/drop in WDM systems will affect the optical power of each individual channel. Therefore, in advanced optical communication systems, EDFAs are controlled by intelligent systems taking into account the number of wavelength channels, OSNR, and other important system parameters.

In a multiwavelength optical system, the wavelength-dependent gain characteristic of EDFAs shown in Fig. 5.4.7 makes transmission performance different from channel to channel and thus greatly complicates system design and provisioning. In addition, the shape of the optical gain spectrum also changes with the signal optical power as illustrated in Fig. 5.4.7 which is known as dynamic gain tilt. Considering signal power level variations and wavelength add/drop in optical networks, the dynamic gain tilt may also significantly affect transmission performance, and needs to be taking into EDFA design.

In high-end optical amplifiers for long distance and multiwavelength optical systems, gain variation vs. wavelength can be compensated by passive optical filters, as shown in Fig. 5.4.12 A. To flatten the gain spectrum, an optical filter with the transfer function complementing to the original EDFA gain spectrum is used with the EDFA so that the overall optical gain does not vary with the wavelength, and this is illustrated in Fig. 5.4.13 . However, the passive gain flattening is effective only with one particular optical gain of the amplifier. Any change of EDFA operation condition, such as signal optical power, would change the spectral shape of the gain spectrum and therefore, require a different filter.

Fig. 5.4.12 . EDFA gain flattening using (A) a passive filter and (B) a spatial light modulator.

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