# Patent

## Title
Method and circuit for statistical estimation

## Abstract

A method for determining a quality indication, such as a bit error rate or a signal to noise ratio, of a photonic signal is described. The photonic signal is sampled, and then an estimated quality indication, such as the bit error rate, is calculated utilizing statisical analysis of the sampled photonic signal.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
The present patent application claims priority to the Provisional Patent Application identified by U.S. Ser. No. 60/475,668, filed on Jun. 4, 2003, the entire content of which is hereby incorporated herein by reference.


STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not applicable.
THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT
Not applicable
INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC
Not applicable
BACKGROUND OF THE INVENTION
In telecommunication, the incoming information signal is corrupted with noise and jitter. The noise and jitter sources are many, a full description of which is beyond the realm of this application. However, what is important here is that noise and jitter degrades the quality of signal. It is very important the received signal is at a predetermined quality, measured in bit-error rate (BER), Q-Factor (Q), and signal to noise ratio (SNR); BER and SNR are two key parameters used to determine the channel performance.
The quality of signal impacts several transmission and network parameters, such as quality of service, link length, protection strategy, channel reassignment, bandwidth utilization, cost, etc.
In optical communications, because the fiber spans are long and the bit rates are high, channel performance increases in importance and links are more difficult to engineer.
In telecommunications, the current art relies on sophisticated error detecting and correcting codes, known as forward error correction (FEC), that have been added to each information frame. Thus, FEC adds overhead to and ups the line bit-rate of the information channel. Based on the FEC method, typically up to sixteen errors are detected and up to eight are corrected within a frame. From the detected error, the bit error rate (BER) is calculated and thus the channel performance.
However, this method requires several frames (or packets) to estimate the bit error rate and channel performance and thus a long time that compromises the overall system and network responsiveness to remedial action.
BRIEF SUMMARY OF THE INVENTION
In one aspect, the present invention is a method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of: sampling the photonic signal without disrupting the transmission of the photonic signal; and calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal.
In another aspect, the present invention is a method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of: sampling the photonic signal without disrupting the integrity of the photonic signal; and calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal.
Moreover, another aspect of the present invention is a method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of: sampling the photonic signal without introducing a test signal; and calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal.



BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
FIG. 1 is a block diagram of a prior art or “current art” forward error correction (FEC) system.
FIG. 2 is a diagram illustrating Bit Error Rate (BER) estimation based on eye diagram and statistical tables.
FIG. 3 is a block diagram of a circuit, constructed in accordance with the present invention, for statistical estimation of Bit Error Rate and Signal to Noise Ratio based on pulse sampling.
FIG. 4 is a block diagram of another circuit, constructed in accordance with the present invention, for statistical estimation of Bit Error Rate and Signal to Noise Ratio based on pulse sampling.



DETAILED DESCRIPTION OF THE INVENTION
Introduction:
In telecommunications, the incoming information signal is corrupted with noise and jitter. The noise and jitter sources are many, a full description of which is beyond the realm of this application. However, what is important here is that noise and jitter degrades the quality of signal.
It is very important that the received signal is at a predetermined quality, measured in bit-error rate (BER), Q-factor (Q), and signal to noise ratio (SNR); BER and SNR are two key parameters used to determine the channel performance.
The quality of signal impacts several transmission and network parameters, such as quality of service, link length, protection strategy, channel re-assignment, bandwidth utilization, cost, etc.
In optical communications, because the fiber spans are long and the bit rates are high, channel performance increases in importance and links are more difficult to engineer.
Current Art:
In telecommunications, the current art relies on sophisticated error detecting and correcting codes, known as forward error correction (FEC), that have been added to each information frame. Thus, FEC adds overhead to and ups the line bit-rate of the information channel. Based on the FEC method, typically up to sixteen errors are detected and up to eight are corrected within a frame. From the detected errors, the bit error rate (BER) is calculated and thus the channel performance.
However, this method requires several frames (or packets) to estimate the bit error rate and channel performance and thus a long time that compromises the overall system and network responsiveness to remedial action. For example, at a line rate of 10 Gb/s and for an objective of 10−15 BER (meaning one error in 1015 bits), it may take up to 26 hrs, for 10−12 BER it may take 1.7 min, and for 10−10 it may take 1 s. Even 1 s is long time for networks that have hundreds or thousands of data streams.
In FIG. 1, the following abbreviations mean the following:
PD=Photodetector
LPF=Low pass filter
DEC=Decision threshold; determines logic “1” and logic “0”.
FEC=Forward error detection and correction function
BER=Bit error rate performance function
Function of the Circuit in FIG. 1:
The incoming photonic signal is detected by a photodetector (PD), which converts it in an electronic signal; this is passed through a low pass filter (LPF) to remove high frequency noise. The filtered signal is then passed through a decision threshold circuit, which at periodic intervals determines, based on the threshold level, whether the signal at that instant is a logic “1” or logic “0”. The timing circuitry extracts timing from the line rate and supplies “clock” to the decision and to subsequent digital circuitry. The binary signal passes through a framer and forward error detection and correction function (Framer & FEC). The latter detects the start of frame and it reads the FEC code in the frame overhead. It then detects errors and corrects errors, and it provides a signal to the bit error rate (BER) function for each error found. Thus, many frames are required to determine the bit error rate and the performance of the signal; this, depending on the performance targets, may take a long time.
New Art:
As shown graphically in FIG. 2, the noise and jitter in the signal degrades its quality which is manifested with closure of the “eye diagram”. The eye diagram method is used to manually provide a qualitative visual observation of the signal quality; however, it requires costly equipment that makes it cost-prohibitive to incorporate in communications systems on a per channel basis.
Herein, we describe a method and a circuit that automatically (and without human intervention) estimates the BER, SNR, and Q-factor of the incoming signal. The method is based on statistical sampling and therefore the estimates may be made in a much shorter time than the current art. In addition, the method lends itself to implementation with a VLSI and/or microprocessor. We describe two implementations, FIG. 3 and FIG. 4, although this method is not limited to the two implementations described.
The Bit Error Rate can be estimated based on the eye diagram and statistical tables set forth in FIG. 2, as follows:














1. Measure:
2. Calculate:









σ0 = std deviation for “0”
Eeye = I1, min − I0, max



σ1 = std deviation for “1”
Q = Emax {square root over (σ12 + σ02)}



Eeye, Emax
BER = 1⁄2 erfc (Q/{square root over (2)})










Standard Deviation Based on Statistical Tables (Histograms):

The standard deviation, σ, is calculated from an ensemble of measured values, with which a histogram is made (see previous FIG. 2), from:

σ=√{square root over (Σ(fjX2j)/N−(ΣfjXj/N)2)}{square root over (Σ(fjX2j)/N−(ΣfjXj/N)2)}=√{square root over (X2−X2)}

Where  is the mean of the squares of various values of X, and  is the square of the mean of the values of X, N is the number of samples, and fj is the frequency of occurrence of a value Xj.
Similarly, the mean value, ΣfjXj/N, is calculated by summing the product of frequency of occurrence by the value of the variable X and divide by the sample. The following example demonstrates this:
Numerical Example:
Consider 65 samples with values Xj and frequencies of occurrence fj as in the table:












Xj
fj
fjXj

















55
8
440


65
10
650


75
16
1200


85
14
1190


95
10
950


105
5
525


115
2
230



N = 65
ΣfX = 5185









From this, the mean value is, ΣfX/N=5185/65=83.50. Based on the f, X, fX, and fX2 values, the standard deviation is easily measured.
SNR:
Based on the eye diagram method, and assuming that the measured value Emax corresponds to the received signal+noise, ES+EN, and that the measured value Eeye corresponds to the received signal minus noise, ES−EN, then an approximated signal to the noise ratio is derived as:

SNR=ES/EN=(ρ+1)/(ρ−1),

where ρ=Emax/Eeye.

The received signal may contain overshoot due to a number of mechanisms and therefore Emax and Eeye are not exact. Then, an approximated E*max value may be used to compensate for it, E*max=E1, mean+k1σ1, where k1=1, 2, or 3 and E1, mean is the value for logic “1”. Similarly, E*eye=(E1, mean−k1σ1)−(E0, mean+k0σ0), where k0=1, 2, or 3, and E0, mean is the mean value for logic 0.
Function of the Circuit, FIG. 3:
The incoming photonic signal is detected by a photodetector (PD), which converts it in an electronic signal. The electronic signal is routed to a sample and hold (S&H) function that samples periodically the signal and holds for one period the voltage value (Vs). The voltage Vs is sent to a voltage comparator which compares it with a reference voltage (Vref). It is also sent to an analog to digital (A/D) converter function, where it is converted into digital codes.
The binary or digital codes from the A/D is sent to two functions, one that receives those that are greater than Vs, named “1s std dev”, and another that receives those that are smaller than Vs, named “0s std dev”; this is controlled by the comparator that generates two enabling signals, Vs>Vref and Vs<Vref, respectively. The “1s std dev” function builds statistical tables for those codes that correspond to Vs>Vref and from their distribution it determines the standard deviation for the “fs”. Similarly, the “0s std dev” function builds statistical tables for those codes that correspond to Vs<Vref and from their distribution it determines the standard deviation for the “0s”. The two standard deviation functions provide inputs to a functional block that calculates the Q factor and passes information signals to two functions labeled SNR and BER which calculate the estimated signal to noise ratio and the bit error rate, respectively. Because of the statistical nature of this method, a relatively small sample of periods, few thousands, are required. At 10 Gb/s, 10,000 periods correspond to 1 μs.
Implementation of Circuit, FIG. 3:
The circuit consists of few functional blocks that may be implemented with one VLSI or with a VLSI and a low-cost microprocessor (shown in previous FIG. 3); the actual design implementation depends on designer preference and cost.
In one embodiment, the circuit in FIG. 3 may be implemented with a VLSI and a microprocessor. The VLSI consists of timing function, S&H, comparator, A/D and part of the “1s std dev” and “0s std dev” functions. The microprocessor includes the standard deviation calculation function for both “1s” and “0s”, the Q, SNR and the BER functions.
In another embodiment, the VLSI consists of the S&H, Comparator, A/D and the “1s std dev” and “0s std dev” functions. The microprocessor includes the Q, SNR and the BER functions.
In another embodiment, a VLSI may contain all functions, including a microprocessor.
Function of the Circuit, FIG. 4:
The incoming photonic signal is detected by a photodetector (PD), which converts it into an electronic signal. The electronic signal is routed to a sample and hold (S&H) and analog to digital (A/D) converter function that converts periodically the sampled signal into digital codes. The binary or digital codes from the A/D is sent to a binary comparator that compares them with a reference code. Those codes that correspond to Vs>Vref are sent to the “1s std dev” function and those to Vs<Vref to “0s std dev” function.
The “1s std dev” function builds statistical tables for those codes that correspond to Vs>Vref and from their distribution it determines the “1s” standard deviation. Similarly, the “0s std dev” function builds statistical tables for those codes that correspond to Vs<Vref and from their distribution it determines the “0s” standard deviation.
The two standard deviation function provide inputs to a functional block that calculates the Q factor and it passes information signals to the SNR and BER functions which calculate the estimated signal to noise ratio and the bit error rate, respectively. Like in circuit of FIG. 3, because of the statistical nature of this method, a relatively small sample of periods, few thousands, are required. At 10 Gb/s, 10,000 periods corresponds to 1 μs.
Implementation of Circuit, FIG. 4:
Like the circuit of FIG. 3, the circuit in FIG. 4 consists of few functional blocks that may be implemented with one VLSI or with a VLSI and a low-cost microprocessor; the actual design implementation depends on designer preference and cost.
In one embodiment, the circuit in FIG. 4 may be implemented with a VLSI and a microprocessor. The VLSI consists of the timing and S&H+A/D functions. The microprocessor includes the comparator, the standard deviation calculation function for both “1s” and “0s”, the Q, SNR and the BER functions.
In another embodiment, a VLSI may contain all function, including a microprocessor.
The circuit in FIG. 3 is based on a bus architecture and thus it is better embodied in a microprocessor architecture.
Cost Reduction of Circuit in FIGS. 3 and 4:
The circuit in FIG. 3 and FIG. 4 contains a S&H and an A/D function. Assuming a line rate at 10 Gb/s, it means that the function must perform 109 samples and conversions per second; similarly, the remainder of the circuit must operate at the same speed to cope with the data flow in the circuit. To accomplish this, state of the art electronic circuit is required because of the high operational speed of electronics. However, this function may be slowed down by a large factor, for example 1000 times, if one of every 1000 pulses are sampled. Although this does not compromise the accuracy of the method, it does slow it down 1000 times. Assuming that 1000 samples is an adequate statistical ensemble, then a total of 1000×1000 (1,000,000) samples are required. At 10 Gb/s, one million pulses will enter the circuit in 0.1 ms, that is, still a very short time. Thus, slowing down the sampling rate by 1000 allows for lower speed electronics implementable with conventional low cost and low power electronic circuitry. Depending on line rate, other sampling rates may be considered.
Benefits
The method and the circuit described has several benefits to quickly provide a statistical estimate of the SNR and BER.

    
    
        It is based on statistical sampling of the analog incoming signal
        It provides fast estimate of BER based on statistical sampling
        It provides fast estimate of SNR and Q based on statistical sampling
        It lends itself to easy implementation with integrated IC and/or mu-P
        VLSI allows for per channel low cost implementation
    
    


REFERENCES


    1. S. V. Kartalopoulos, “DWDM: Networks, Devices and Technology”, IEEE/Wiley 2003 (to be avail. 9/2002).
    2. S. V. Kartalopoulos, “Fault Detectability in DWDM: Toward Higher Signal Quality & System Reliability”, IEEE 2001.
    3. S. V. Kartalopoulos, “On the Performance of Multi-wavelength Optical Paths in High Capacity DWDM Optical Networks”, To be submitted for publication.
    4. Possible Simulation Tools (for optical physical layer): OpNet, OptiWave Corporation, LinkSim by Rsoft.
    5. Possible Simulation Tools (for electronic circuitry): Existing VLSI synthesis and simulation tools.

Potential Interest
    
        Instrumentation manufacturers
        Equipment Manufacturers
        VLSI Manufacturers
        Software simulation developers
    
    


It should be understood that the foregoing is intended to be illustrative of the invention, and that the invention is not confined to the particular embodiments set forth herein, but embraces all such modified forms thereof as come within the scope of the following claims.

## Claims

1. A method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of:
synchronously sampling the photonic signal without disrupting the transmission of the photonic signal; and
calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal; and storing at least one of the calculated estimated bit error rate and the calculated signal to noise ratio.

2. The method of claim 1, wherein the step of synchronously sampling the photonic signal is defined further as the steps of converting the photonic signal into an electrical signal indicative of the photonic signal, and sampling the electric signal.

3. The method of claim 2, wherein the electric signal has a Vs and wherein the step of calculating an estimated bit error rate is defined further as the steps of building a first statistical table for codes within the electric signal having Vs>Vref.

4. The method of claim 3, wherein the step of calculating the estimated bit error rate is defined further as the step of building a second statistical table for codes within the electrical signal having Vs<Vref.

5. A method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of:
synchronously sampling the photonic signal without disrupting the integrity of the photonic signal; and
calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal; and storing at least one of the calculated estimated bit error rate and the calculated signal to noise ratio.

6. The method of claim 5, wherein the step of synchronously sampling the photonic signal is defined further as the steps of converting the photonic signal into an electrical signal indicative of the photonic signal, and sampling the electric signal.

7. The method of claim 6, wherein the electric signal has a Vs and wherein the step of calculating an estimated bit error rate is defined further as the steps of building a first statistical table for codes within the electric signal having Vs>Vref.

8. The method in claim 7, wherein the step of calculating the estimated bit error rate is defined further as the step of building a second statistical table for codes within the electrical signal having Vs<Vref.

9. A method for determining one of a bit error rate
and a signal to noise ratio rate of a photonic signal, comprising the step of:
synchronously sampling the photonic signal without introducing a test signal; and
calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal; and storing at least one of the calculated estimated bit error rate and the calculated signal to noise ratio.

10. The method of claim 9, wherein the step of synchronously sampling the photonic signal is defined further as the steps of converting the photonic signal into an electrical signal indicative of the photonic signal, and sampling the electric signal.

11. The method of claim 10, wherein the electric signal has a Vs and wherein the step of calculating an estimated bit error rate is defined further as the steps of building a first statistical table for codes within the electric signal having Vs>Vref.

12. The method of claim 11, wherein the step of calculating the estimated bit error rate is defined further as the step of building a second statistical table for codes within the electrical signal having Vs<Vref.

13. A method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of:
sampling the photonic signal without disrupting the transmission of the photonic signal;
calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal;
and storing at least one of the calculated estimated bit error rate and the calculated signal to noise ratio;
wherein the step of sampling the photonic signal is defined further as the steps of converting the photonic signal into an electrical signal indicative of the photonic signal, and sampling the electric signal; and
wherein the electric signal has a Vs and wherein the step of calculating an estimated bit error rate is defined further as the steps of building a first statistical table for codes within the electric signal having Vs>Vref.

14. The method of claim 13, wherein the step of calculating the estimated bit error rate is defined further as the step of building a second statistical table for codes within the electrical signal having Vs<Vref.

15. A method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of:
sampling the photonic signal without disrupting the integrity of the photonic signal;
calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal;
and storing at least one of the calculated estimated bit error rate and the calculated signal to noise ratio;
wherein the step of sampling the photonic signal is defined further as the steps of converting the photonic signal into an electrical signal indicative of the photonic signal, and sampling the electric signal; and
wherein the electric signal has a Vs and wherein the step of calculating an estimated bit error rate is defined further as the steps of building a first statistical table for codes within the electric signal having Vs>Vref.

16. The method of claim 15, wherein the step of calculating the estimated bit error rate is defined further as the step of building a second statistical table for codes within the electrical signal having Vs<Vref.

17. A method for determining one of a bit error rate and a signal to noise ratio rate of a photonic signal, comprising the step of:
sampling the photonic signal without introducing a test signal;
calculating at least one of an estimated bit error rate and a signal to noise ratio rate utilizing statistical analysis of the sampled photonic signal;
and storing at least one of the calculated estimated bit error rate and the calculated signal to noise ratio;
wherein the step of sampling the photonic signal is defined further as the steps of converting the photonic signal into an electrical signal indicative of the photonic signal, and sampling the electric signal; and
wherein the electric signal has a Vs and wherein the step of calculating an estimated bit error rate is defined further as the steps of building a first statistical table for codes within the electric signal having Vs>Vref.

18. The method of claim 17, wherein the step of calculating the estimated bit error rate is defined further as the step of building a second statistical table for codes within the electrical signal having Vs<Vref.