PT108740B - LOW COMPLEXITY DIGITAL FILTER FOR THE COMPENSATION OF CHROMATIC DISPERSION IN THE FIELD OF TIME - Google Patents

Abstract

THE INVENTION HERE PRESENTED IS BASED ON THE APPLICATION OF A NEW METHOD OF DIGITAL EQUALIZATION, INTENDED FOR THE COMPENSATION OF CHROMATIC DISPERSION IN COHERENT OPTICAL COMMUNICATION SYSTEMS. THIS METHOD HAS ON THE BASIS AN ANALYTICAL DECOMPOSITION OF FIR FILTER COEFFICIENTS IN DISCRETE VALUES, DATA IN POTENCES OF 2. THIS DECOMPOSITION ALLOWS TO EXPLOIT THE REPLICATION OF THE COEFFICIENTS AND TO TAKE PART OF THE DISTRIBUTIVE PROPERTY OF THE MULTIPLICATION TO THE ADDITION, REDUCING SIGNIFICANTLY THE NUMBER OF MULTIPLICATIONS NECESSARY TO THE FILTER FIR. IN ADDITION, THE BREAKDOWN OF 2 OF THE COEFFICIENTS ALLOWS THE IMPLEMENTATION OF THE MULTIPLICATIONS ONLY WITH ADDITION AND BINARY SHIFT OPERATIONS. THE COMBINATION OF THESE CHARACTERISTICS GAVE ORIGIN TO A NEW AND EFFICIENT ARCHITECTURE FIR DISTRIBUTIVE, OPTIMIZED FOR REAL TIME.

Description

DESCRIPTION

Low Complexity Digital Filter for Time Domain Chromatic Dispersion Compensation

Technical Field of the Invention

The present invention relates to the field of optical communications and describes a method for egualizing the effects of chromatic dispersion in optical systems. high speed optical communication ,. using digital ET.R filters and providing for multiplier-free implementation.

Description of the prior art

The chromatic dispersion present in fiber optic communication systems strongly limits signal range and throughput. For most of the optical connections currently installed in the field, chromatic dispersion compensation is carried out in the optical domain by the inclusion of Dispersion Compensation Fiber (DGF - _: Dispersion Gompensafirg Fíher) sections. However, the use of dispersion compensating fibers has several disadvantages, notably the degradation of the signal-to-noise ratio (due to additional amplifiers and nonlinear distortions caused by the PCEs) and the inflatability to optical pathway changes and / or on the transmission signal.

The recent introduction of new digital modulation and coherent detection technologies combined with a Digital Bigngl Processing (DSE) component has sparked a revolution: in commercial optical communication systems, these new systems retrieve amplitude information, phase and polarization of the optical field, thus allowing the compensation of transmission distortions and signal propagation in the digital domain after signal detection, reducing the need for optical domain compensation.

Given the linear and time-invariant character of the chromatic dispersion, it can be compensated through linear digital filters, allowing the DGFs to be removed from the communication system, and consequently to avoid the performance penalties mentioned above. Digital equalization of chromatic dispersion can be realized in the time domain using either finite or infinite impulse response filters (CFiR / IlR Finite / Infinite impulse Response) or alternatively in the frequency domain where it is applied to the inverse frequency transfer function. linear response of fiber.

A frequency domain or time domain implementation will depend on the final system in question. Time domain equalization is generally simpler to implement in real time, avoiding the use of Fourier transforms and consequent block processing. However, for long-range, high-symbol transmission systems, the accumulated chromatic dispersion values tend to be very high, creating long memory effects. Under these conditions, frequency domain equalization tends to be more advantageous as it requires fewer computational requirements compared to time domain equalization. In fact, the computational effort imposed by FIR filter compensation evolves with N '^; , where N represents the number of filter coefficients, while the computational effort associated with frequency domain equalization evolved with Niclogfiferj, where Nifv represents the minimum number of samples required: for each transform (FFT) :. Given that similarly with increasing chromatic dispersion, the disadvantage of conventional FIR filters for long-range systems with high accumulated dispersion is evident. The computational effort required by these algorithms emerges as: a very limiting factor in terms of energy supply and energy consumption, which leads to the need for. develop simplified methods for digital color dispersion compensation. The development of new simplified methods of digital equalization should take into account a compromise between performance and computational effort, with the possibility of adjusting to the optical communication system in question and the respective computational and energy resources available.

Detailed Description of the Invention

Since chromatic dispersion is a deterministic effect, known a priori and independent of polarization, it can be eliminated by applying the inverse transfer function of the channel propagation. For this purpose, Finite Impulse Response} digital finite impulse response filters can be used, where the equalized FIR filter outputs are obtained by evolving the input signal with the filter coefficients. Of the structure and general formula of the FIP filter. it turns out that this: is exolusivably made up of multiplication, addition and delay operations.

These filters need to be implemented in reconfigurable hafdware devices, such as Field Programmable Gate Arrays (PPGAs), and their optimization is essential to make them faster, simpler and more energy efficient. A critical parameter of the filters currently used for linear equalization is the number of multiplications required for its implementation. More specifically, the number of multiplications required for the filter evolves quadratically with the accumulated dispersion, making it difficult to implement on resource-limited hardware devices. That said, the optimization of the algorithm basically involves a reduction of the multiplication operations,

Considering a point-to-point static optical connection, where the fiber dispersion parameter is well known, FIR filter coefficients can be obtained by using the four-way inverse transform of the linear transfer function or by simple analytical formulas. Since the coefficients are constant, it is possible to determine them at the time of system initialization. If the system is changed © :, the network control plan shall indicate to the receiver that the network has been modified so that it can be re-adapted to the new system.

In order to meet the above requirements, a new digital filter architecture of reduced complexity has been proposed. The block diagram of Figure 1 illustrates the basic operations required to implement the new linear equation algorithm. The structure of this filter is divided into four parts :: sum _: symmetrical (E1), control units (S2), distributive sum (S3) and multiplication with binary displacements and; additions (sbiftard-add.) <E4J

Given the symmetries observed in the coefficients, the symmetric filter positions are summed, input samples obtained, thus obtaining an optimized realization of the filter (E1). This optimization allows for a reduction of approximately 50% in the number of multiplications initially required. The result of the symmetric sum is later: directed to the control units (E2). At this stage, the real and imaginary components of the coefficients: are analyzed separately, as can be seen from Figure 1. The control units are prrorr instructed to take advantage of the distributive property of multiplication over addition and thus to avoid replication. operations of mui tip 1 i cation / sh í - and - aâ <3. This is based on information from the process of decomposing coefficients into discrete values. After quantization, the coefficients are defined by a set of 2 Δ possible values> c ·), not null, each with a certain multiplicity. Thus, for each possible value: ο ', the control unit determines a: set: of input signals whose coefficient values are identical, thus obtaining 2 & sets. Next are:

after the sum of the sets obtained, according to the pairs, _cia and its symmetric (c ~ _s; ) (E3), It is important to highlight the presence of a negative sign in some of the adders, in order to accommodate the negative coefficients. Finally, the block sbí f t-and-add performs the corresponding multiplications on the results of the distributive sums:, which are then summed, finally producing the equated output signal y (n} ^Q (Ei).

Figure 2 shows the sequence of Preprocessing Operations performed on the filter coefficients: The coefficients are initially calculated using the inverse of the fiber impulse response (101). Subsequently, these are normalized between ~ 1 and 1 and uniquely quantized (102), giving rise to an output signal (104) defined by a set of discrete values. The fundamental parameter in this process is represented by the Constant Δ (1030, which imposes a set of 2Δ + 1 possible values, {ChO, for the filter coefficients. Thus, in the quantization process the precision is controlled by the value of Δ. Quantization: The coefficients have 2.1 + 1 possible values with a certain number of: repetitions (multiplicity} in the real and imaginary component. The coefficients are separated into real part (106) and imaginary part (10: 7) using block 105. Finally, for each possible value, Cm, block 108 determines the indices (taking into account the sign) for which: multiplicity of coefficients occurs, acting independently for the real (100) and imaginary (110} components, and it also determines the absolute values of the quantized coefficients (111) where: the symmetrical possible values, c ..- r = ~ cv and the always null values, the absolute values are: given: by Á values, fç;, ... , you?> Õ signs 109, / 110 to 111 obtained allow us to take advantage of the distributive property of the many significantly reducing the number of ghlf & - axâ-ad operations.

Figures 3 and 4 show the sequence of operations performed on the input samples. Initially, the input signals 201 at the symmetrical positions of the filter 202 are summed to explore the symmetry of the coefficients. 0 symmetric result of summing (203) is then sent to the control unit block (E2) which comprises two control units corresponding to the _part: real and imaginary quantized coefficients. The control unit E2, by means of index sets (109/110) where multiplicity of coefficients occurs, will be able to (from block: 3 01) select the input samples corresponding to these indices and direct them to their respective exit (sornador). Thus, at the output of block 301 are obtained sets of values that will be later. accumulated to obtain the sum of the input values for which the coefficients are equal. The adder can be implemented using a tree structure, where for each set of values is obtained _: an output. Finally, the obtained values are summed according to the pairs of coefficients (c, Ca-tca) and their symmetrical (.cu, c-, su. E-, a), (E3).

The results obtained from the sums are then multiplied by the respective absolute values (111) in blocks 302. Since the value of Δ is a power of 2, the possible values obtained, ('oj, can be represented as the power of 2. It becomes feasible to decompose these values into binary displacement operations and additions using a digital representation (SD), as exemplified in Figure 5. For this, each block 302 takes into account the information from signal 111, to contain the information of the absolute values of the coefficients present in the filter, and finally make the respective SD representation for each coefficient, thus obtaining a free implementation of real multipliers, using only multipliers shiít-and-add ( msa).

After multiplying the input signal by the filter coefficients the various contributions are summed, and the output signal 304 still requires an additional multiplication by the imaginary unit. The time domain equalized samples (306) are finally obtained by summing the contributions of filter freckle from complex signals 303 is 305 (S4),

Preferred Embodiment of the Invention

As an example, we present below a scenario of implementation of the chromatic dispersion equalization method proposed here. Some simulation results and their comparison with the equalization method using FIE filters are also provided.

Thus, the experimental results obtained are considered: for a PN-QPSK signal (Polarírafei on Multíplexing Quadrature Ffease ^ Shíffc Feyíng) operating at a rate of 100 Gb / s and spread over 4000 km single-mode fiber (SSMF 5 Cau da rd Single Node Fiher) with the parameter, 32 = -20.4 psVkm, Figures 6 and 7 present experimental results. Figure 6 shows the evolution of bit error rate (BER) as a function of the number of coefficients required to implement the FIE filter for chromatic dispersion compensation. For the scenario in question, it is found that although the theoretical value obtained through the physical model is 1341 coefficients, it is possible to reduce the number of coefficients to about 60% of this value (819 coefficients} with a penalty in factor p ² of 0.1 dB This value can be considered as the lower limit for the number of coefficients needed for color dispersion compensation to be effective, without significantly changing system performance.This optimization allows a substantial reduction in the computational effort required by Figure 7 shows the evolution of BER as a function of the constant Δ used in the coefficient quantification, considering only 60% of the coefficients, it is possible to reduce the value of Δ to 4, resulting in an additional penalty of only 0.2 dB in Q factor ^2. This process illustrates the additional flexibility provided by the proposed equalization technique.

for the purpose of commitment en t r e p r e c i s â o at how much coefficients and the play global of obtained. The results obtained demonst ram experimenting that by applying the architecture of £ liter F1R

distributive to reduced fi values, it is possible to significantly reduce the number of shfft-andadd operations required by the filter without significantly compromising equalization performance. For the previous example, using 819 coefficients and an A ~ i, a complexity reduction of about 90% multi-shift / shift-and-add and 37% additions relative to the BlR filter is achieved for a loss of performance less than 0.3 dB in factor p ² .

The implementation of this technique allows a significant reduction in the complexity of the algorithm. In this way, it becomes possible to minimize hardmare requirements and energy consumption: of electronic devices, used for their real-time implementation. Depending on the tired transmission system, this new technique allows to optimize the compromise between computational performance by adjusting the precision of the filter coefficients.

and quantification effort

Description of the Figures

Figure 1: Ά Figure 1 represents the block diagram for the implementation of the proposed method for chromatic dispersion equalization,

Reference Signals of Figure 1:

x (n.> - nth input sample ytn) '-' - nth equal sample

M-S - A - shift-and-add multiplier

El - symmetric sum of input samples

E2 - control units, where the various subsets of values with common coefficients are determined, one subset for each possible value

The distributive sum of the various subsets obtained in section E2

E <~ shift-and-add multiplication and sum of the contributions to the equalized sign of the real and imaginary part of coefficients and obtaining the equal sample

Figure 2: In Figure 2 and schematically represented © pre-processing process of the a priori coefficients determined. The coefficient quantitation is effected, e.g. Then the indices of the occurrence of the multiplicity of the obtainable values obtained are determined.

Reference Signals of Figure 2:

101 -filter coefficients. A priori determined.

102 - uniform quantity

103 - quantization parameter

104 - quantized coefficients for a given quantization parameter

105 - separates the real and imaginary part of the complex signal. 100 - real part of qualified coefficients

107 - Imaginary Part of Quantitative Coefficients

108 ~ determines the indices for which multiplicity of coefficients occurs is the corresponding absolute values

109 ~ indices of the occurrence of multiplicity of each possible value in the real part of coefficients

110 - Indices of the occurrence of multiplicity of each possible value in the imaginary part of coefficients

111 - absolute values

Figure 3; In Figure 3 is presented schematically a possible process of symmetrical sum of the input samples.

Reference Signals of Figure 3:

201 - input samples

202 - sum of input samples at symmetrical positions

203 ~ result of symmetrical sum of input samples

Figure 4: In Figure 4 is presented schematically a process of operations on symmetrically summed samples, to obtain equalized samples.

Reference Signals of Figure 4:

Z - accumulator

301 - control unit for determining the various subsets of values with common coefficients

302 - shift-and-add multiplier, which can be a priori set to each absolute value

303 - contribution of the real part of coefficients to obtain the equalized signal

304 ~ contribution of the imaginary part of coefficients to obtain the equalized signal

Contribution of the imaginary part of coefficients for obtaining the signal that is often mixed by the complex number

06 - Equalized sample

Figure 5: Figure 5 shows the internal structure of a possible implementation of the shif t-and-adcl multi-donor.

Reference Signals of Figure 5:

Shift - shift ieft./right

Figure 6: In Figure 6 a graph with a. evolution of the BER as a function of the number of substances, using the FIR filter. It is noted that it is possible to remove the accumulated dispersion in the fiber by reducing the number of coefficients up to about 60% / theoretical for a penalty. 0.1 dB maximum rating :.

Figure 7; Figure 10 shows a graph with: the evolution of the SER as a function of the quantization parameter, Δ, using the proposed method for 819 coefficients. For Δ-4, a complexity reduction of about 99% of multiples / shif t-and-add e is obtained. 37% of additions for the FIR filter for a performance loss of less than 0.3 dB by factor

Claims (6)

Claims 1, A chromatic dispersion digital equalization method for optical transmission based systems was coherent detection, implemented in the time domain using a distributive architecture of the multiplier free FIR filter 2 A digital equalization method of the chromatic dispersion to system optical transmission based was coherent detection according to claim ^paragraphs 1 ized character by the number of different coefficient of the FIR filter to be reduced through a quantization process, or reduction to a finite set of discrete levels. 3. A digital equalization method of chromatic dispersion for coherent detection based optical transmission systems according to the preceding claims characterized in that the real and imaginary part of the coefficients is separated in order to increase their multiplicity. 4. A method of. digital equalization of. Chromatic dispersion for coherent detection based optical transmission systems according to the preceding claims, characterized in that the distributive property of multiplication over addition is used, which is applied separately to the real part and the imaginary part of the FIR filter coefficients. A method of digital chromatic dispersion equalization for coherent detection based optical transmission systems of: according to the preceding claims characterized in that the multiplications are implemented only using addition and displacement: binary operations. A chromatic dispersion digital equalizing method for coherent detection based optical transmission systems according to the preceding claims is characterized in that it comprises the following steps; definition of the number of discrete levels for the filter coefficients, fSrl, where Δ is one. power of two ϊ sum of input samples at the symmetrical positions of the filter to take advantage of the fact that the impulse response of the filter is symmetrical; ~ routing: from the result of the symmetrical sum to two units of: control acting in parallel; one of the units in control < s responsible fur processing taking in tell to real part of coef.roient.es; the other. unity in control is responsible fur processing by having in tells the imaginary part of coefficients; The 2Δ results obtained after the distributive sum are processed using 2Δ multipliers, implemented st. only with shift and add operations, taking advantage of the fact that Δ is a power of two; the results of the addition and displacement operations are summed in two adders, one for the real part of the coefficients :, and another for the imaginary part of the coefficients, with the result of the adder corresponding to the imaginary part of the coefficients, further multiplied by the unit: imaginary j. _z before the final sum.