PT108740A - 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

; "Complexity Compensation Filter for the Compensation of the Dodiní in the Group:

TECHNICAL FIELD OF THE INVENTION The present invention relates to the field of optical communications and describes a. method to equalize the effects of color dispersion in high-speed optical communication systems using digital FIR filters and providing a free implementation of multipliers.

Description of the state of the art The chromatic dispersion present in optical fiber communication systems strongly limits the signal's range and throughput. In a large part of the optic connections currently installed in the field, the compensation of the chromatic dispersion I is re-established in the domain of the. I, II, III, III, III, IV, IV, IV, IV, IV, IV, F, ||| rll: Nil; Ib: tB: | ov | Ia | | | | | | | | | | | | | Dispersion of lithium and lithium derivatives of lithium and lithium derivatives of lithium and lithium derivatives.

(1), (2) and (3) and (4) and (4) and (4) 1. by the | | § | 1 || a. IPBIlll! Exemplary polypropylene copolymer.

Ipil rii |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| f. The invention relates to a process for the preparation of a compound of formula (II): ## STR1 ## |||||||||||||||||||||| flig | til d: ff | l ||| (1) (1) (1) (1) (1): a novelty of the compounds of formula (II): ## STR1 ## wherein R 1 and R 2 are as defined in formula (I). the optical field, thus allowing the compensation of distortions ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ ϋ digital domain, after signal detection, reducing the need for compensation in the optical domain.

Given the linear and time-invariant character of the chromatic dispersion, its compensation can be realized through linear digital filters, allowing to remove the DCFs from the communication system, and consequently to avoid the i4eps !!! i | is; of the invention; The digital equalization of the chromatic dispersion can be realized in the time domain, by means of filters of the same color; {f ||||| §i ~ .............. End: i | §: lIi | Í | ni: §él J | i |||se Response), Sllfi the frequency domain, where the inverse transfer function of the linear response of the fiber is applied.

An implementation in the frequency domain or in the time domain will depend on the end system in question. Time domain equalization is usually simpler to implement in real-time * avoiding the use of Fourier transform and consequent block processing. However, for long-distance and high symbol rate transmission systems, accumulated chromatic dispersion values tend to be very high, creating long temporal memory effects. Under these conditions, frequency domain equalization tends to be more advantageous, since it requires fewer computational requirements when compared to time domain equalization. In fact, the computational effort imposed by FIR filters evolves with iV2, where N represents the number of filter coefficients, while the computational effort associated with equalization in the domain of f requence evolves with ΝρϊτΙορϊΝρρτ), where minimum number of samples required: parameter each fast-Fourier transform {FFT}. Since N and Nm increase from one to the other, | . I: I, I, I, I, I, I, I, I, I, I, I, I, I, . ............. lii.

ILLUSTRATION. Lldtf required ......... by ............... these 1 | algorithms thus appears as a very limiting factor in terms of hardware requirements and energy consumption, which leads to the need to develop simplified methods for digital compensation of chromatic dispersion. The promotion of new simplified digital equalization methods should take into account a compromise between performance: and computational effort, with possibility of adjustment to the optical communication system in question and its computational and energetic resources. 11111;

Detailed Description of the Invention

Since the chromatic dispersion is a deterministic effect, known a priori and independent of polarization, it can be eliminated by applying the reverse propagation function of the channel. For this purpose, FIR (Finite Impulse Response) digital filters can be used, where the equalized outputs of the FIR filter are obtained by convolution of the input signal with the coefficients of the filter. From the structure and general formula of the FIR filter it is verified that it is exclusively composed of operations of multiplication, addition and delays.

Given the need to implement these filters in reconfigurable hardware devices, such as Field Programmable Gate Arrays (FPGAs), it becomes indispensable to optimize them in order 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 by the filter evolves quadratically with the accumulated dispersion, making it difficult to implement in hardware devices with limited resources. Therefore, the optimization of the algorithm passes fundamentally by a reduction of multiplication operations.

Considering a static optical point-to-point connection, where the fiber dispersion parameter is well known: FIR filter coefficients can be obtained using the inverse Fourier transform of the linear transfer function or through simple analytical formulas . Since the coefficients are constant, it is possible to determine them at the time of initial systemization. If the system | ièp3 :: i i || plan ||||||||||||||||||||||||||||||||||||||| give .................. indication to the recipient that the network has been modified so that it can be readjusted to the new system.

In order to meet the above mentioned requirements is here. proposed a new digital filter architecture of reduced complexity. The block diagram of Figure 1 illustrates the basic operations required to implement the new linear equalization algorithm. The structure of this filter is divided into four parts; symmetric sum (El), control units (E2), distributive sum (E3) and multiplication with binary displacements and additions (shift-and-add) {E4) <Given the symmetries observed in the coefficients, input samples at the symmetrical positions of the filter, thus providing an optimized filter performance (Ei). This optimization allows a reduction of approximately 50% of the number of multiplications initially required. The result of the symmetric sum is subsequently directed to the control units (E2). At this stage, the real and imaginary components of the coefficients are analyzed separately, as can be seen in Figure 1. The control units are a priori instructed to take advantage of the distributive property of multiplication over addition and thus avoid replication of multiply / shfc-and-add operations. This instruction is based on the information coming from the process of decomposition of the coefficients were discrete values. After quantization, the coefficients are defined by a set of 2Δ possible values {cw}, not null, each with a certain multiplicity. Thus, for each possible value: ..., the control unit determines a set of input whose coefficient values are identical, thus obtaining 2Δ sets. Then, sums of the sets obtained are obtained, according to the pairs, c 'and respective symmetric (c-m) (E3). It is important to emphasize the presence of negative signal in part to the adders, in order to accommodate the negative coefficients. Finally, the shift ~ and ~ add block performs the corresponding multiplications on the results of the distributive sums, which are then summed, finally producing the equalized output signal and (n) ΰ (E4>).

Figure 2 shows the sequence of preprocessing operations performed on the coefficients of the -filter *

The coefficients are initially calculated, using the inverse of the impulse response of the fiber (101). Subsequently, these are normalized between -1 and 1 and uniformly quantzized (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 (103), which imposes a set of 2Δ + 1 possible values, {c *), for the filter coefficients. Thus, in the quantization process the precision is controlled by the value of Λ. After quantization, the coefficients present 2Δ + 1 possible values "with a given number of repetitions (multiplicity) in the real and imaginary component." The coefficients: are separate real part (106) and imaginary part (107), using the bioco 105 Finally, for each possible value, Cm, the bin 108 determines the indices (taking into account the signal) for which multiplicity of coefficients occurs, acting independently for the real (109) and imaginary (110) components, and the absolute values of the quantyzed coefficients (111), where the possible values are symmetric, and are always null, the absolute values are given: pd || p ;: val: i || s: ||||| i: | ..., § $} Ips sinaii !,: l! L! L! L! Lll! || obtained allow us to take advantage of the distributive property of multiplication over addition, signi fi cantly reducing the number of operations of shift-and-add.

Figures 3 and 4 show the sequence of operations performed under the inlet samples. Initially the input signals 201 at the symmetrical positions of the filter 202 are summed in order to explore the symmetry of the coefficients. The result of the symmetric summation (203) is then sent to the control unit block (E2) which is composed of two control units corresponding to the real and imaginary part of the quantum coefficients. The control unit E2, through sets of indices {109/110} where multiplicity of coefficients occurs, will be able to (from block 301) select the input samples corresponding to those indices and direct them to their output ( Thus, at the output of block 301 2Δ are obtained with values of values that will be later accumulated in order to obtain the sum of the input values for which the coefficients are islandfij: j § | the sum of the coefficients of the coefficients: (1) For the purposes of this Article, the following definitions shall apply: s. fo | if pairs c ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ê || ..... respect iifób. f pf tiefr ic os ... ||llf .............. || {.slit '.......... llllllllllllllllllll ..... .. i: 0; || (a) and (b) (b) (b) (b) (b) The following is a list of the most widely used examples of this kind: "Pli: ......! l || bcosi || 2, 3, 4, 5, 6, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, These values in operations of binary displacements and | ádíç || sf {{ffi | | | | | | | | | | | | | | | | | | | In the same manner as in the present invention, the present invention provides a process for the preparation of a compound of the formula: ## STR1 ## in which: ## STR4 ## The compounds of the present invention may be prepared by the method of the invention in which the compound of formula (I): wherein R 1 is as defined in formula (I): wherein R 1 is as defined in formula (I) the filtering of the coefficients present in the filter and, finally, effecting the respective SD representation for each coefficient, thus obtaining a free implementation of real multipliers, using only shift-and-add multipliers (MS-A5,

After multiplication of the input signal by the coefficients of the filter the various contributions are summed, the output signal 304 still requiring an additional multiplication by the imaginary unit, = v ~ 1. Time domain equalized samples (306) are finally obtained by summing the filter output contributions from the signals ci3: iiliili: 03 and CB4). za9âo As an example, we present below an implementation scenario of the chromatic dispersion equalization method proposed here. We also provided some simulation results and their comparison with the equalization method using FIR filters.

Thus, experimental results obtained for a PM-QPSK signal (Polarization Multiplexing

Quadrature Phase-Shift Keying) operating at a rate of 100 Gb / s and propagated over 4000 km of single mode fiber (SSMF -Standard Single Mode Fiber) with the parameter, 02 = -20.4 ps2 / km. Figures 6 and 7 show experimental results obtained. In Figure 6, the evolution of the bit error rate (BER Bit Error Rate) can be observed as a function of the number of coefficients required to implement the FIR filter to compensate the chromatic dispersion. For the scenario in question, it should be noted 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 that value (819 1) i.e., in the form of an aliphatic compound of the formula: ## STR1 ## in which: for the number of coefficients needed to effectively compensate the chromatic dispersion, without the system performance changing significantly.This optimization allows a substantial reduction of the required computational effort the coefficients of the coefficients can be observed in Figure 7. Considering only 60% of the coefficients, it is possible to reduce the value of Δ to 4, resulting in an additional penalty This process illustrates the additional flexibility provided by the technique of equalization. the proposal to optimize the compromise between precision in the quantisation of the coefficients and the overall performance of the obtained filter. The results obtained demonstrate experimentally that by applying the distributive FIR filter architecture to reduced Δ values, it is possible to significantly reduce the number of operations necessary for the use of the IFR filter without "S1 cdl ^ lomedirlisiss signi fi t ca t ivãlph te ...... © ......... des empébflii ..... 'id ....... equal i. zation., l | The present invention relates to a process for the preparation of a compound of the general formulas (II): ## STR1 ## in which: ## STR2 ## in which R 1 is as defined in formula (I) many 'typologies / shi ft -and- add ....... lllle' '1111 ...... 37'% llllllllde '................ ádl The performance of this technique allows a significant reduction of the performance of the filter, complexity of the algorithm. In this way, it becomes possible to minimize the hardware requirements and the energy consumption of the devices and latrically used for real-time implementation. Depending on the transmission system in question, this new technique makes it possible to optimize the compromise between performance and computational effort by adjusting the accuracy in the quantization of the filter coefficients.

Description of Figures

Figure 1: Figure 1 represents the block diagram for the implementation of the proposed method for the equation of chromatic dispersion.

Figure 1: x (n) - is the input sample y (n): the nth equal sample - multiplying shif t ~ and-add El - symmetric sum of the input samples E2 ~ control units> where we determine the various subsets of values with coefficients in common, a subset for each possible value E3 - distributive sum, of the various subsets obtained in section E2 E - shift-and-add multiplication and sum of contributions l ^ ... -i'm real li! imaginary

Jidil: icientil | è obtain: | | | | airh3stra eqi | il íádáPP

Figure 2: In Figure 2 is schematic diagram and Fig. dlls::::::::::::::::::::::::::::::::::::::::::::::::: ... the quantification .... c ||| .. ||||: | p: l: is: n: t.ÍÍj | ....... l; l || The compounds of the present invention may be prepared by the following methods: Bacterial fillips can be obtained by the following methods:

Reference Signals of Figure 2: 0P $! ρ: ipl lP; Pi || ^ al ^ ul || dSbpp:.,: | ΪΡ0Ρ3ίΙΙΙΡ ::; :: Ρ ^^^ § § § §::::

PIPPPPs: PIPPPPs: P: P: P: PIPPPPII PIPPPPs: PIPPPPs PIPPPPs: PIPPPPs PIPPPPs PIPPPPs PIPPPPs PIPPPPs: ||| ||: ||| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||| | ;: | - the imaginary part of quantized coefficients 108 - determines the indices for which it occurs, multiplicity of coefficients and the corresponding absolute values 109 - indices of the occurrence of multiplicity of each value possible in the real part of coefficients 110 - indices of occurrence of multiplicity of each possible value in the imaginary part of coefficients 111 - absolute values

Figure 3: A possible process of the symmetric sum of the input samples is schematically shown in Figure 3.

Reference Signals of Figure 3; 201 - input samples 202 - sum of the input samples at the symmetrical positions 203 - result of the symmetric sum of the input samples

Figure 4: A process of operations on symmetrically added samples is shown schematically in order to obtain equalized samples.

Reference Signals of Figure 4: Σ. - accumulator; A control unit for determination of diluvolophosphate in the presence of a diluent in the presence of a compound of the formula: ## STR1 ## 302 - shift-and-add multiplier, where it can be a priori configured for 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 3 05 - the contribution of. an imaginary part of coefficients for i; In this example, the complex is the same as the one in which the sample is the same as the one in the sample.

Figure 5: In Figure. 5, the internal structure of the structure is presented as follows: (1) (1).

Reference Signals of Figure 5:

Shift - shift left / right.

Figure 6: Figure 6 shows a graph with the evolution of B.ER as a function of the number of coefficients, using FIR filter. Note that it is possible to remove the accumulated dispersion in the fiber by reducing the number of coefficients to about 60% of the theoretical value, for a penalty: / sd 1;

Figure 7: A graph showing the evolution of the BER as a function of the quantization parameter, Δ, is presented in Figure 10, using a proposed method for 819 coefficients. For Δ = 4, a reduction of complexity is obtained in about 99% of multiples / shif t.-and-add e. 37% of additions, relative to the FIR filter, for a loss of less than 0.3 dB in Q-factor. (i.e.

Claims (5)

Claims A method of digital equalization of the chromatic dispersion for optical transmission systems based on coherent detection characterized by being implemented in the time domain using a distributive architecture of the FIR filter || Bq A method of digital equalization of the chromatic dispersion for optical transmission systems based on coherent detection according to claim 1, characterized in that the method is based on the decomposition of the complex multiplication between input signals and coefficients, which input signal multiplies the real and imaginary part of the coefficients separately " A method of digital equalization of the chromatic dispersion for optical transmission systems based on coherent detection according to the preceding claims characterized in that the distributive property of multiplication is applied to the addition to the real and imaginary part of the quantized coefficients separately (109,110), thus eliminating the replication of multiplication operations, A method of digital equalization of the chromatic dispersion for optical transmission systems based on coherent detection according to the previous claims and characterized in that the FIR filter coefficients are preprocessed according to the following steps: normalization coefficients between -1 and i (1), (2) and (2). parci; SUBSTITUTE SHEET::::::::::::::::::::::::::::::::::::::::::: I, II, II, III, I, II, I, II, II, III, dt: dt: dt: dt: dt: dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt dt In addition, the invention relates to a process for the preparation of a compound of formula (I) pailf | able A method of digital equalization of the chromatic dispersion for optical transmission systems based on coherent detection according to the preceding claims characterized in that its structure if divided into four parts which are symmetric sum (E1), control units (E2 ), distributive sum (E3), and shift-and-multiplication multiplication ... i! f) !! i ..... ............. !! 'U ||||||||||||||||||||||||||||||||||||||||||||||||||| | The invention relates to a method according to any of the preceding claims, characterized in that it is constituted by pearls the following steps: - the sum of the input samples in the symmetrical positions d i ......... ilit r ©, iiiiiii ..............: i: - the first control unit is used to take advantage of the control unit, - the first control unit is used to take advantage of the control unit, - the first control unit is used to take advantage of of the multiplicity of the real part of coefficients, the second control unit is used to take out the coefficients of the coefficient For each set of values obtained from the symmetric sum in EI, each control unit determines 2Δ set of values, in which each set corresponds to a set of values, which is the value of the respective values of the set, - sums of the sets obtained, according to the ares, c * and respective symmetric (c-m) (S3), the shift-and-add multiplier block performs the corresponding: multiplications on the results of the distributive sums, the signal (304) being multiplied | i Ipétlb núméiillld ompl exo j> j | fj | - for each equalized sample a maximum of 2Δ shift-shift operations is performed for each equalized sample: (1) and-add, each corresponding to the absolute values (111), after applying the distributive property,