The present invention relates generally to optical communication systems, and more specifically to a method and system for determining receiver power for a required bit error rate (BER).
In optical communication systems, it is often desirable to determine the minimum power at a receiver to achieve a required or a specified bit error rate (or bit error ratio, where the bit error ratio is defined as the number of erroneously transmitted bits divided by the number of correct bits). Many optical communication systems must operate within a specified BER. The BER is generally dependent, among others, on the receiver power. The BER decreases as the receiver power is increased and the BER increases as the receiver power is decreased. The BER is a measure of an optical communication system's performance and reliability. A low BER generally indicates superior system performance while a high BER indicates inferior system performance.
The source signal Ss 105 is a digital signal having a binary data stream.
The signal Ss 105 is received by an optical transmitter 108 that converts the signal Ss 105 into an optical signal So 109. The signal So 109 is transmitted over a fiber channel 112 to an optical receiver 116. The optical receiver 116 converts the optical signal So 109 into an electrical signal Sr 117.
If CS represents the number of bits in SS and CRE represents the number of error bits in SR, then, BER can be defined by the following equation:
Where CRE is defined as
And where SS(n) represents the nth bit of the signal Ss and SR(n) represents the nth bit of signal received by a BER tester 120 shown in
In addition to the receiver power, the BER is dependent on the sampling phase and decision threshold at the receiver. The relationship of the BER to the sampling phase and the decision threshold is represented by a BER contour diagram. A BER contour diagram is created by measuring a plurality of BERs for various values of sampling phases and decision thresholds. The measured sampling phases and decision thresholds corresponding to a common BER is plotted to create the BER contour diagram.
A sampling phase indicates where in time a signal is sampled. For example, an optical signal may have a pulse width of 10 ns. The optical signal may be sampled 1 ns, 0.1 ns or at any other arbitrary time less than 10 ns from the origin of the pulse.
A decision threshold is a numerical value used to determine if the sampled bit is a mark (i.e., “1”) or a space (i.e., “0”). For example, if the decision threshold is 0.7, then sampled values greater than 0.7 are considered marks and sampled values less than 0.7 are considered spaces.
A plurality of BER contours are used to create a BER contour diagram.
As discussed before, the BER depends on the power, the sampling phase and the decision threshold. In optical communication systems, signals degrade due to nonlinear effects such as chromatic dispersion, polarization mode dispersion, fiber characteristics and LASER characteristics. The nonlinear effects shift the optimum decision threshold for a sampling phase away from the mid point between the marks and the spaces causing the optimum BER to be difficult to measure. Also, if the required BER is low, it may require a long time to determine the minimum power required at the receiver, which is typically specified during system or equipment calibration. Accordingly, there is a need for a method and system for efficiently determining the minimum power at the receiver in order to achieve a specified BER.
The present invention is directed to a method and system for determining a receiver power for a required bit error rate (BER) in optical communication systems. According to one aspect of the invention, a BER contour diagram is created by measuring high BER values and approximating low BER values from the high BER values. The low BER values are approximated using error functions. The optimum decision threshold is determined from the contour diagram and the BER is calculated at the optimum decision threshold. The measured BER is compared to the required or specified BER. If the measured BER is not close to or equal to the required BER, the power at a transmitter is adjusted until the measured BER is close to or equal to the required BER. The receiver power can then be calculated from the transmitter power or directly from the received signal.
In one embodiment of the invention, a BER contour diagram is created to locate the optimum decision threshold for a sampling phase. The BER is measured or calculated at the optimum decision threshold, and the minimum power at the receiver is determined for the BER at the optimum decision threshold.
When BER values are relatively high (e.g., >10e-5), they can be easily measured using selected sampling phases and decision thresholds. However, when BER values are low (e.g., <10e-8), it may require an unreasonably long time to measure the BER. In one embodiment, high BER values are measured, and then, low BER values are approximated from the high BER values to create a BER contour diagram.
When BER is relatively high, it is practical to measure BER at all sampling phases that a receiver may viably sample. The BER measurements may be taken, for example, at decision thresholds close to mark level (e.g., 0.8, 0.9) and space level (e.g., 0.1, 0.2) at all available sampling phases, because measurements close to mark and space levels will likely result in high BER. The sampling phases can be distributed evenly or unevenly. Also the decision thresholds can be distributed evenly or unevenly.
When the decision threshold is set near an optimum level for detection, the BER can be low, and it may take an unreasonably long time to measure the BER. In order to complete the BER contour diagram where the BER is low, an equation provided below representing BER as a function of decision threshold D at a selected sampling phase is used.
Where μ1 and μ0 represent the mean of the marks and spaces, respectively, σ1 and σ0 represent the standard deviation of the marks and spaces, respectively, and erfc is the complementary error function defined by the following equation:
Equation (3) takes into consideration both the marks and spaces. However, where actual measurements are made for high BER, the decision level D is close to either the mark or the space level, and for those cases, equation (3) is simplified as follows:
Next, the logarithm base 10 of equation (5) yields:
The parameters μ1, μ0, σ1 and σ0 are derived by using a polynomial fit in equations (6a) and (6b). Next, an approximation is used for marks from equation (6a) to obtain equation (7).
Where
y=1.192−0.6681(log 10(BER(D)))−0.0162(log 10(BER(D)))2 (8)
The error term is minimized as follows:
Where yi is obtained from equation (8) for each decision threshold Di where BER(Di) has been measured (BER is high at those decision thresholds). After further modifications, the equations (10) and (11) are obtained.
Similar equations can be derived for μ0, and σ0 where yis and Dis are calculated from the measurements obtained by decreasing the Dis closer to the space level. Once the parameters μ1, μ0, σ1 and σ0 are obtained, BER(D) can be approximated using equation (3).
The foregoing procedures are repeated for all viable sampling phases and the decision thresholds and the BER values are calculated. The sampling phases and decision thresholds for each specific BER value are plotted to create the BER contour diagrams.
The optimum decision threshold for a sampling phase occurs when the BER due to the marks is equal to the BER due to the spaces. The BERs due to the marks and spaces are equal when equation (6a) is equal to equation (6b).
The optimum decision threshold and sampling phase is associated to the smallest BER(D) across the BER contour.
As discussed before, it is desirable to determine the minimum power at the receiver to achieve a required BER. However, it may require a long time to determine the minimum power at the receiver if the required BER is low.
According to one embodiment of the invention, BER is measured by moving the decision threshold closer to the marks and the spaces for each available sampling phase for a given transmitter (TX) power. Next, using the method described above, the optimum decision threshold and sampling phase is determined. If the calculated BER at the optimum decision threshold and sampling phase is less than the required BER, the TX power is decreased. If the measured BER at the optimum decision threshold and sampling phase is greater than the required BER, the TX power is increased. The TX power is varied until the measured BER value is equal to or close to the required BER value. Finally, the corresponding receiver (RX) power is calculated from the TX power or is directly calculated from the receiver signal.
By way of example, suppose the required BER value is 1.0e-15 and the fiber channel attenuation is −30 dB. The TX power is initially set to 5 mW and a BER contour diagram is drawn. The BER is measured corresponding to the optimum decision threshold and sampling phase using the foregoing method. The measured BER corresponding to 5 mW TX power is 1.0e-10.
Since the measured BER (i.e., 1.0e-10) corresponding to TX power=5 mW is higher than the required BER (i.e., 1.0 e-15), the TX power is increased to 7.5 mW. A BER contour diagram is drawn and the BER is measured corresponding to the optimum decision threshold and sampling phase. The measured BER corresponding to 7.5 mW TX power is 1.0e-14.
Since the measured BER (i.e., 1.0e-14) corresponding to 7.5 mW TX power is still higher then the required BER value, the TX power is increased to 8.75 mW and the corresponding BER is measured. The measured BER corresponding to 8.75 mW TX power is 1.0e-18.
Since the measured BER corresponding to 8.75 mW TX power is less than the required BER value, the TX power is now decreased to 8 mW. The measured BER corresponding to 8 mW TX power is 1.5e-15. Since the measured BER value (1.5e-15) at 8 mW TX power is close to the required BER value (1.0e-15), the measured BER value is considered approximately equal to the required BER value.
Next, the RX power is calculated from the TX power (8 mW) using methods well known to those skilled in the art. Since the fiber channel attenuation is −30 dB, the calculated RX power corresponding to 8 mW TX power is 8 uW. Thus, the minimum RX power is set at 8 uW to achieve the required BER value of ≦1.0e-15.
In one embodiment, the invention can be utilized in testing of optical communication devices or systems. For example, during testing of optical communication devices or systems in a test environment such as a laboratory the invention can be used to determine a receiver power for a required BER. It will be obvious to those skilled in the art how to implement the invention during testing of optical communication devices or systems.
In one embodiment of the invention, the receiver power for a required BER can be determined by varying power to the receiver by changing the attenuation of the transmitted signal through the transmission medium (e.g., fiber link or channel) with an optical attenuator rather than changing the TX power. It will be obvious to those skilled in the art how to vary power to the receiver by changing attenuation through the transmission medium with an optical attenuator.
It is to be understood that even though various embodiments and advantages of the present invention have been set forth in the foregoing description, the above disclosure is illustrative only, and changes may be made in detail, and yet remain within the broad principles of the invention. For example, many of the components described above may be implemented using either digital or analog circuitry, or a combination of both, and also, where appropriate, may be realized through software executing on suitable processing circuitry.
This application is related to an application entitled “BIT ERROR RATE CONTOUR-BASED OPTIMUM DECISION THRESHOLD AND SAMPLING PHASE SELECTION”, attorney docket number 185940/US, filed concurrently.