US9503293B2 - Coefficient error robust feed forward equalizer - Google Patents
Coefficient error robust feed forward equalizer Download PDFInfo
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- US9503293B2 US9503293B2 US14/889,814 US201414889814A US9503293B2 US 9503293 B2 US9503293 B2 US 9503293B2 US 201414889814 A US201414889814 A US 201414889814A US 9503293 B2 US9503293 B2 US 9503293B2
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03878—Line equalisers; line build-out devices
- H04L25/03885—Line equalisers; line build-out devices adaptive
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
- H04L25/03019—Arrangements for removing intersymbol interference operating in the time domain adaptive, i.e. capable of adjustment during data reception
- H04L25/03038—Arrangements for removing intersymbol interference operating in the time domain adaptive, i.e. capable of adjustment during data reception with a non-recursive structure
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- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03343—Arrangements at the transmitter end
Definitions
- the present invention relates to a coefficient error robust feed forward equalizing transmitter, and more particularly, to a feed forward equalizing transmitter based on baseband wired communication for preventing the influence of a coefficient error.
- a feed forward equalizer is a channel compensation scheme that is widely used in high-speed baseband interconnection.
- CMOS complementary metal-oxide semiconductor
- FFE transmitter may acquire a high data rate in a limited bandwidth.
- CMOS technology has developed on a nano scale.
- variation in devices has increased due to distortion, random variables, temperature fluctuation, aging, etc., and great coefficient errors occur due to variations in nano devices, and such coefficient errors degrade performance of and interrupt communication in a feed forward equalizer circuit.
- the present invention is proposed to solve the above problems and is directed to providing a feed forward equalizer that responds more robustly to a coefficient error while operating like a feed forward equalizing transmitter having a general structure in a normal state.
- the data change detection filter ( 120 ) may be disposed between the input terminal and a first delay unit (D) connected adjacent to the input terminal, between two adjacent delay units (D) among the N delay units (D), or between the first calculator ( 110 ) and a last delay unit (D) connected adjacent to the first calculator ( 110 ).
- D first delay unit
- D last delay unit
- the data change detection filter ( 120 ) may include one delay unit ( 122 ) and a second calculator ( 121 ) connected with the delay unit ( 122 ), and the second calculator ( 121 ) may calculate the data transition value (b[n ⁇ m]) based on a previous value (x[n ⁇ m+1]) input to the delay unit ( 122 ) and a current value (x[n ⁇ m]) output from the delay unit ( 122 ).
- the data transition value (b[n ⁇ m]) may be calculated through logic circuit combination of a plurality of consecutive digital bit values in a data stream.
- the data change detection filter ( 120 ) may be a high-pass filter (HPF).
- HPF high-pass filter
- each of the tap signals may include a feed forward equalizer coefficient (a), and the feed forward equalizer coefficient (a) may be adjustable by a user.
- the coefficient error robust feed forward equalizing transmitter operates identically to a general feed forward equalizer (FFE) when there is no coefficient error and also includes a simple logic circuit element and thus can improve robustness to a coefficient error with a small additional cost.
- FFE feed forward equalizer
- a high-pass transition detection filter installed in the coefficient error robust feed forward equalizer according to the present invention can reduce perturbation of a signal caused by a coefficient error and improve an eye diagram sensitivity indicating robustness of an interconnector by a factor of 7 to 17.
- coefficient error robust feed forward equalizer according to the present invention can be easily applied to high-speed interconnect because an improvement rate of an eye sensitivity increases as the data rate and the channel loss increase.
- FIG. 1 is a conceptual view of a high-speed interconnect system including a conventional feed forward equalizing transmitter.
- FIG. 2 is an exemplary view showing a conventional feed forward equalizer.
- FIG. 3 is a conceptual view of a conventional 3-tap feed forward equalizer.
- FIG. 8 is a graph comparing spectra between a conventional feed forward equalizer and a coefficient error robust feed forward equalizer according to the present invention.
- FIG. 9 is a graph showing the eye sensitivities of a conventional 2-tap feed forward equalizer for a primary RC channel and a coefficient error robust feed forward equalizer according to the present invention.
- FIG. 12 is a graph showing an eye diagram for each data transmission rate of FIG. 11 .
- FIG. 13 is a graph showing the eye sensitivities of a conventional 3-tap feed forward equalizer and a feed forward equalizer according to the present invention in a 3.5 cm silicon interposer package.
- FIG. 14 is a graph showing eye diagrams for data transmission rates of FIG. 13 .
- a conventional general feed forward equalizer for high-speed interconnect is configured to include a channel, a feed forward equalizing transmitter (FFE Tx), and a 1-bit quantizing receiver (Rx).
- the channel includes a coaxial cable, a backplane, a printed circuit board (PCB), a package, and on-chip wires, and has a typical length from several centimeters to several tens of meters.
- the channel When the data rate is in the range from several Gb/s to several tens of Gb/s, the channel usually serves as a low-pass filter (LPF), and inter-symbol interference (ISI) is generated in the channel.
- LPF low-pass filter
- ISI inter-symbol interference
- the channel loss When the channel loss is large at the Nyquist frequency, the inter-symbol interference seriously interrupts communication.
- the channel loss is determined to be small in the range of 0 to 10 dB, large in the range of 10 to 20 dB, and very large in the range of 20 to 30 dB. Accordingly, it is known that there are few cases in which a channel has a channel loss greater than 30 dB, and communication through such a channel is extremely difficult.
- FFE feed forward equalizing
- the feed forward equalizing transmitter (FFE Tx) is used to compensate for the channel loss and secure a data rate.
- the feed forward equalizer (FFE) having an appropriate tap coefficient w operates as a high-pass filter that compensates for the channel loss in order to convert a signal y[n] reaching the receiver (Rx) into a 2-level pulse amplitude modulation (PAM 2 ) signal.
- y[n] corresponds to a value when x[n ⁇ m] reaches the receiver (Rx).
- x[n] is a transmitted data sequence and has a signal level of 1 (a bit of ‘1’) or ⁇ 1 (a bit of ‘0’).
- m denotes a delay time until x[n] is received by the receiver through the channel.
- the 1-bit quantizing device of the receiver samples y[n] with a period T and then determines a value of ⁇ [n] on the basis of zero (0). In this case, ⁇ [n] has a value of 1 when ⁇ [n] is greater than zero and a value of ⁇ 1 otherwise.
- a general receiver depends on an eye diagram acquired through the feed forward equalizer (FFE).
- FFE feed forward equalizer
- ISI inter-symbol interference
- FIG. 2A is an exemplary diagram of the simplest and most general structure of a 2-tap feed forward equalizer (2-tap FFE).
- Equation (1) when n ⁇ 1, h[n] decreases exponentially by h[n ⁇ 1]e ⁇ T/ ⁇ .
- ISI inter-symbol interference
- 2-tap FFE 2-tap feed forward equalizer
- a least square method (least square error (LSE)) is used to determine a coefficient of the feed forward equalizer (FFE) in various channels.
- Equation (4) may be approximated to Equation (5) using a vector and a matrix in order to find a value of the least square method.
- w lse and h are truncated vectors of w lse [n] and h[n], respectively.
- h k and ⁇ ⁇ m are column vectors having h[n+k ⁇ 1] and ⁇ [n ⁇ m ⁇ 1] as nth elements, respectively.
- C-FFE feed forward equalizing transmitter
- B-FFE equalizing transmitter for preventing the influence of a coefficient error according to the present invention
- a differential current logic (CML) circuit of FIG. 3B determines a direction of tail current
- V Tx between Txp and Txn is a Thevenin-equivalent differential voltage corresponding to v[n] of FIG. 1 .
- which are shown in FIG. 3C , are sensitive to the variation caused by nanoscale technology.
- the variation cannot secure the robustness because the variation is not easy to control through micrometer technology.
- the influence caused by variation of the nano device may be modeled as the constant random variable ⁇ w added to the coefficient w .
- the variation is caused by the distortion, random variables, temperature fluctuation, aging, etc., during the process. The causes occur very slowly over several minutes to years because of a manufacturing process, a change in circuit operation, etc.
- the random number modeling such as ⁇ w is suitable for a coefficient error that has occurred during transmission.
- FIG. 4A is a block diagram of a high-speed interconnect system including a coefficient error robust feed forward equalizer (B-FFE) 100 according to an embodiment of the present invention
- FIG. 4B is a block diagram specifically showing a coefficient error robust feed forward equalizer (B-FFE) 100 according to an embodiment of the present invention.
- the high-speed interconnect system including the coefficient error robust feed forward equalizer (B-FFE) 100 is configured to include a feed forward equalizer (B-FFE) 100 , a receiver 300 configured to receive an output of the feed forward equalizer (B-FFE) 100 , and a channel 200 for communication between the feed forward equalizer (B-FFE) 100 and the receiver 300 .
- the data change detection filter 120 performs a function of outputting a data transition value b on the basis of the change in input data x.
- the coefficient error robust feed forward equalizer (B-FFE) 100 according to an embodiment of the present invention will be described in detail below, focusing on the data change detection filter 120 .
- the data change detection filter 120 includes one delay unit 122 and a second calculator 121 connected with the delay unit 122 .
- the second calculator 121 performs a function of calculating the data transition value b[n ⁇ m] on the basis of a previous value x[n ⁇ m+1] input to the delay unit 122 and a current value x[n ⁇ m] output from the delay unit 122 .
- x[n] is a value indicating input data
- b[n ⁇ m] is a value indicating data transition of x[n].
- c[n] is a high-pass filter (HPF) that detects the change in data.
- HPF high-pass filter
- b[n ⁇ m] may have a value of ⁇ 1, 0, or 1.
- x[n] changes from 1 to ⁇ 1.
- x[n] changes from ⁇ 1 to 1.
- b[n ⁇ m] is 0, x[n] does not change. That is, b[n ⁇ m] includes information about the change in x[n].
- the data transition value that is calculated and output using the above Equation (9) becomes ⁇ 1 when data input to the data change detection filter 120 is changed from 1 to ⁇ 1, becomes 1 when the data input to the data change detection filter 120 is changed from ⁇ 1 to 1, and becomes 0 when the input data does not change.
- the coefficient error robust feed forward equalizer can calculate the data transition value b[n ⁇ m] through logic circuit combination of a plurality of consecutive digital bit values in a data stream.
- FIG. 5A is a truth table that represents Equation (9) of the 3-tap coefficient error robust feed forward equalizer (B-FFE) according to an embodiment of the present invention and a table showing a value of b[n ⁇ i ⁇ 1] using two digital bits D pn-i-1 and D nn-i-1 .
- the two digital bits D pn-i-1 and D nn-i-1 are formed using AND gates, as shown in FIG. 5B .
- FIG. 5C is a block diagram of a circuit for calculating a sum and coefficient product of the 3-tap coefficient error robust feed forward equalizer (B-FFE) according to an embodiment of the present invention.
- the calculation circuit is of the same type as the conventional feed forward equalizer (C-FFE) CML circuit. Since the cost of the AND gate is very low, nanoscale CMOS technology is economically beneficial when the B-FFE according to embodiments of the present invention is implemented.
- tap signals are output from N delay units D of the coefficient error robust feed forward equalizer (B-FFE) 100 according to an embodiment of the present invention.
- the tap signal includes a feed forward equalizer coefficient a and a constant random coefficient error ⁇ a.
- the feed forward equalizer coefficient a is preferably configured to be adjusted by a user in order to mathematically map the coefficient error robust feed forward equalizer (B-FFE) according to an embodiment of the present invention to be the same as the conventional feed forward equalizer (C-FFE) in a normal state.
- Equation (9) when Equation (9) is rearranged using a vector and a matrix, b [n] may be represented as B x x [n].
- B x x x [n].
- b [n] [x[n] x[n ⁇ 1] . . . x[n ⁇ m+1], b[n ⁇ m] b[n ⁇ m ⁇ 1] . . . b[n ⁇ N]]T
- x [n] [x[n] x[n ⁇ 1] x[n ⁇ 2] . . . x[n ⁇ N]] T .
- B x is expressed as Equation (10) below (B x is an (N+1) ⁇ (N+1) matrix, and an identity matrix at the upper left corner of B x is an m ⁇ m matrix):
- v[n] of the conventional feed forward equalizer is x [n] T w .
- the feed forward equalizer coefficient a of the feed forward equalizing transmitter (B-FFE) 100 can be mapped to a feed forward equalizer coefficient w of the conventional feed forward equalizer (C-FFE), using the above Equation (11) and Equation (12).
- the feed forward equalizer (B-FFE) 100 may have functions of all conventional feed forward equalizers (C-FFEs) implemented therein as well as being more robust to a coefficient error than the conventional feed forward equalizer (C-FFE).
- the influence of variation of a device that occurs in the coefficient robust feed forward equalizer (B-FFE) according to the present invention is modeled in the form of the constant random coefficient error ⁇ a added to the feed forward equalizer coefficient a .
- a method of securing robustness of the coefficient error robust feed forward equalizer (B-FFE) according to the present invention will be described below.
- a 2-tap coefficient error robust feed forward equalizer in a primary RC channel according to an embodiment of the present invention will be described as an example.
- the feed forward equalizer is a linear time-invariant (LTI) system and thus may analyze the influence of a coefficient error from perturbation of a pulse response.
- Equation (13), which is associated with the conventional feed forward equalizer (C-FFE), may be derived by substituting w[n] shown in FIG. 1 with zero (0).
- Equation (13) denotes the influence of the coefficient error ⁇ w[m] to ⁇ y[n] when the input data x[n] is transmitted.
- Equation (14) the pulse response change ⁇ y[n] of the coefficient error robust feed forward equalizer (B-FFE) according to the present invention may be derived as shown in Equation (14) below:
- h ⁇ a[m] [n] is a coefficient error pulse response of ⁇ a[m].
- h ⁇ a[k] [n] is defined as ⁇ a[k]h[n ⁇ k].
- FIG. 6 is a view showing a simulation result of an influence of ⁇ w[ 0 ] in the conventional 2-tap feed forward equalizer (2-tap C-FFE) equipped to compensate for loss in the primary RC channel.
- a pulse response without the inter-symbol interference (ISI) may be checked as shown in FIG. 6A .
- the check result makes a perfect eye diagram as shown with a solid line in FIG. 6B .
- ⁇ v eye, ⁇ w[0] When the eye height decreased when there is only a ⁇ w[ 0 ] error is defined as ⁇ v eye, ⁇ w[0] , ⁇ v eye, ⁇ w[0] may be represented as 2max
- ⁇ w[ 0 ] is ⁇ 0.12 and is 20% of w[ 0 ], which is 0.6. Accordingly, when T is 0.4 ⁇ , max
- is 0.12, and the eye height ⁇ v eye, ⁇ w[0] decreased as shown in FIG. 6B is 0.4-0.16 2max
- the conventional feed forward equalizer (C-FFE) operates identically to the coefficient error robust feed forward equalizer (B-FFE) in a normal state, a pulse response without the inter-symbol interference (ISI) may be acquired as shown in 3 of FIG. 7A , and it may be checked that there is no spreading of an eye diagram as shown with a solid line in FIG. 7B .
- ISI inter-symbol interference
- ⁇ a[ 1 ] changes a pulse response, and spreads the eye diagram as shown with a dotted line of FIG. 7B .
- c[n] shown in FIG. 4 operates as a high-pass filter (HPF).
- HPF high-pass filter
- Equation (17) Equation (17) and Equation (18) below:
- LPF low-pass filter
- a[ 0 ] may be predicted within an error range of about 20%. It can be seen that a[ 0 ] is a much smaller value than other coefficients through Equation (19). In this embodiment, assuming the same coefficient error of 20%,
- 0.12,
- 0.08, and
- 0.16.
- Equation (20) and Equation (21) which represent the influence of ⁇ a[ 0 ] and ⁇ a[ 1 ]
- Equation 22 a continuous time perturbation function p ⁇ w[m] (t) of a pulse transmitted by ⁇ w[m] is derived as shown in Equation (22) below.
- ⁇ [n] is input to the conventional feed forward equalizer (C-FFE) as x[n]
- a spectrum P ⁇ w[m] (f) of p ⁇ w[m] (t) is derived as shown in Equation (23) below:
- Equation (22) the function ⁇ T (t) is defined as 1 when 0 ⁇ t ⁇ T and 0 otherwise.
- Equation 2 Equation 22
- Equation 223 Equation 234
- Equation 245 Equation 24
- H ⁇ w[m] ( f ) H ( f )
- P ⁇ w[m] ( f ) H ( f ) ⁇ ⁇ w[m],T ( f ) e ⁇ j2 ⁇ fmT .
- a continuous time transmission error pulse p ⁇ a[m] (t) of ⁇ a[m] and its spectrum in the coefficient error robust feed forward equalizer (B-FFE) according to the present invention are derived from Equation (26) and Equation (27) below:
- h ⁇ a[m] (t) of ⁇ a[m] is (h*p ⁇ a[m] )(t)
- a spectrum H ⁇ a[m] (f) of h ⁇ a[m] (t) may be derived from H(f) and P ⁇ a[m] (f), as shown in Equation (28) below:
- ⁇ ⁇ w[m],T (f) for the conventional feed forward equalizer (C-FFE) is filtered only by H(f) as shown in Equation (25) while ⁇ ⁇ a[n],T (f) (n ⁇ 0) for the coefficient error robust feed forward equalizer (B-FFE) according to the present invention is filtered by a high-pass filter (HPF) c(f) and a low-pass filter (LPF) H(f), as shown in Equation (28).
- HPF high-pass filter
- LPF low-pass filter
- FIGS. 8A to 8C are graphs for comparing various spectra of the conventional 2-tap feed forward equalizer (C-FFE) and the error robust feed forward equalizer (B-FFE) according to the present invention in a primary RC channel in which a loss of 18 dB occurs at f N .
- input-port-based coefficient error pulse spectra ⁇ ⁇ w[0],T (f), ⁇ ⁇ w[1],T (f), ⁇ ⁇ a[0],T (f), and ⁇ ⁇ a[1],T (f) of the conventional feed forward equalizer (C-FFE) and the coefficient error robust feed forward equalizer (B-FFE) according to an embodiment of the present invention has the form of a sinc function in which energy is focused on low frequencies.
- FIG. 8B shows a spectrum of C(f), which is a high-pass filter (HPF). As shown in FIG.
- H ⁇ a[0] (f) that is not filtered using a high-pass filter (HPF) c(f) is a value smaller than H ⁇ w[0] (f) or H ⁇ w[1] (f) according to Equation (19).
- FIG. 8D shows a simulation result of the spectrum of FIG. 8C in a 36 dB loss channel. Compared with H ⁇ w[0] (f) and H ⁇ w[1] (f), it can be seen that H ⁇ a[0] (f) and H ⁇ a[1] (f) are even smaller in FIG. 8D than in FIG. 8C . Accordingly, the coefficient error robust feed forward equalizer (B-FFE) according to the present invention provides a much better improvement effect for a high loss channel.
- the eye diagram is widely used to measure the quality of communication. Accordingly, in order to quantify the robustness of the feed forward equalizer (FFE), the number of coefficient errors that can be endured by the eye diagram is quantified using sensitivity S k[n] to an nth feed forward equalizer (FFE) coefficient ⁇ [n]. As shown in Equation (29), S k[n] may be derived by dividing a decreasing rate of an eye height decreasing value ⁇ v eye, ⁇ [n] of ⁇ [n] from an optimal eye height v eye by an error rate of ⁇ [n]. In this case, a different coefficient error is substituted with zero (0).
- the eye sensitivity of the feed forward equalizer FFE is high, the eye diagram of the feed forward equalizer (FFE) is further sensitive to the coefficient error. Accordingly, the eye sensitivity is useful as a method for measuring the robustness.
- a 2-tap feed forward equalizer (FFE) for a primary RC channel theoretically has a perfect eye.
- Equation (2) Equation 15
- Equation (16) Equation (31) and Equation (32) below:
- FIG. 9 is a graph showing the eye sensitivity and
- C-FFE 2-tap feed forward equalizer
- B-FFE coefficient error robust feed forward equalizer
- the w[ 0 ] error of 1.9% may reduce an eye height by 20%.
- the w[ 0 ] error of 12.6% reduces an eye height by the same percentage as above. Accordingly, a high cost is required to design the FFE in a very high loss channel with a loss of 30 dB or greater.
- Equation (14) max
- ⁇ v eye ⁇ 2max
- , ⁇ v eye ⁇ 2
- v eye 2a[ 0 ]. Accordingly, the eye sensitivity of ⁇ a[ 0 ] (S a[0] ) may be derived from Equation (36) below:
- B-FFE coefficient error robust feed forward equalizer
- Equation (37) max
- ⁇ a[ 1 ]
- (1 ⁇ e ⁇ T/ ⁇ ) is derived from Equation (14) and Equation (18), and ⁇ v eye, ⁇ a[1] ⁇ 2max
- 2
- FIG. 9 is a graph showing the eye sensitivities of the conventional feed forward equalizer (C-FFE) and the coefficient error robust feed forward equalizer (B-FFE) according to the present invention with respect to the data rate. It can be seen that the eye sensitivity of the conventional feed forward equalizer (C-FFE) increases to infinity, and the eye sensitivity of the coefficient error robust feed forward equalizer (B-FFE) according to the present invention converges to 1 or 2.
- the difference in eye sensitivity between the conventional feed forward equalizer (C-FFE) and the coefficient error robust feed forward equalizer (B-FFE) according to the present invention which is a degree of robustness enhancement, increases to infinity as the data increases.
- S a[1] 1.9, respectively, which are the worst eye sensitivities of the coefficient error robust feed forward equalizer (B-FFE) according to the present invention.
- C-FFE feed forward equalizer
- B-FFE coefficient error robust feed forward equalizer
- An actually used channel may be modeled as a lossy transmission line as shown in FIG. 10 .
- a transfer function of the lossy transmission line is derived using a telegrapher equation and a telegrapher equation including a secondary impact of a frequency dependent channel, as shown in Equation (38), Equation (39), Equation (40), and Equation (41) below:
- H(f) is a frequency response of a channel having a length of I
- Z c (f) is a characteristic impedance of a channel
- Z Tx (f) and Z Rx (f) are terminal impedances of a transmitter and a receiver, respectively
- R 0 , L 0 , G 0 , and C 0 are RLGC variables of the channel in DC
- R s and G d are variables that model a skin effect and dielectric loss, respectively.
- a frequency response of a printed circuit board (PCB) or package wire may be mathematically calculated from Equation (38), Equation (39), Equation (40), and Equation (41).
- FIG. 11 is a graph showing, in a 40-cm PCB channel, eye sensitivities and channel losses at the Nyquist frequency of the conventional 5-tap feed forward equalizer (C-FFE) and the 5-tap coefficient error robust feed forward equalizer (B-FFE) according to the present invention.
- C-FFE conventional 5-tap feed forward equalizer
- B-FFE 5-tap coefficient error robust feed forward equalizer
- w[ 1 ] should be controlled seven times more accurately than a[ 2 ]. If a decrease in eye size of 20% is allowed, w[ 1 ] requires accuracy of at least 0.77% while a[ 2 ] requires accuracy of 5.63%. Since a method of securing accuracy of 0.77% in nano technology is very expensive, the conventional feed forward equalizer operating at 10 Gb/s is not practical. However, the present invention requires an accuracy of just 5.63% under the same condition, and thus there is an effect of easily achieving 10 Gb/s.
- FIG. 12 is an eye diagram at 5 Gb/s, 7 Gb/s, and 8.5 Gb/s, which are selected from FIG. 11 .
- B-FFE coefficient robust feed forward equalizer
- Nyquist channel losses are 20 dB, 27.9 dB, and 33.6 dB, respectively.
- B-FFE coefficient robust feed forward equalizer
- C-FFE conventional feed forward equalizer
- FIG. 13 is a graph showing the channel loss at the Nyquist frequency and the eye sensitivities of the conventional feed forward equalizer (C-FFE) and the coefficient error robust feed forward equalizer (B-FFE) with respect to the data rate. Since the channel length is short as 3.5 cm, but the channel width is small, the channel loss at 10 Gb/s is large as 38.8 dB. In 10 Gb/s, the coefficient error robust feed forward equalizer (B-FFE) according to the present invention improves the eye sensitivity by a factor of 15 or more compared to the conventional feed forward equalizer (C-FFE).
- FIG. 14 is a graph for comparing 1-Gb/s, 5-Gb/s, 10-Gb/s eye diagrams of the coefficient error robust feed forward equalizer (B-FFE) according to the present invention and the conventional feed forward equalizer (C-FFE) in a normal state when the coefficient error of 10% has occurred.
- the Nyquist channel losses are 9 dB, 27.5 dB, and 38.8 dB at 1 Gb/s, 5 Gb/s, and 10 Gb/s, respectively.
- the eye diagram of the conventional feed forward equalizer (C-FFE) is quickly closed while the eye diagram of the coefficient error robust feed forward equalizer (B-FFE) according to the present invention is maintained open even when the data rate increases.
- FIGS. 13 and 14 there is an effect of improving robustness to the coefficient error, and in particular, an effect of securing robustness when the data rate is high and thus the issue of robustness is serious.
Abstract
Description
b[n−m]=0.5x[n−m+1]−0.5x[n−m],
where n and m are integers (n>m).
h[n]=0 if n≦0, or h[n]=(1−e −T/τ)e−(n−1)T/τ if n>0 [Equation 1]
where,
w opt=[1/(1+e −T/τ)−e −T/τ/(1+e −T/τ)]T [Equation 2]
where,
g opt [n]=(1−e −T/τ)/(1+e −T/τ) if n=1, or g[n]=0 if n≠1 [Equation 3]
max|v[n]|=|w[0]|+|w[1]|+|w[2]|+. . . +|w[N]|≦1 [Equation 6]
b[n−m]=0.5x[n−m+1]−0.5x[n−m]=c[n]*x[n] [Equation 9]
where,
w=B x T a [Equation 11]
a =(B x T)−1 w [Equation 12]
a[0]≈4|H(f N)|/π [Equation 19]
where,
p Δw[m](t)=Δw[m]Π T(t−MT) [Equation 22]
P Δw[m](f)=Δw[m]Λ T(f)e −j2πfmT=ΛΔw[m],T(f)e −j2πfmT. [Equation 23]
h Δw[m](t)=(h*p Δw[m])(t) [Equation 24]
H Δw[m](f)=H(f)P Δw[m](f)=H(f)ΛΔw[m],T(f)e −j2πfmT. [Equation 25]
v eye=2(1−e −T/τ)/(1+e −T/τ). [Equation 30]
a opt=(B x T)−1 w opt=[(1−e −T/τ)/(1+e −T/τ)2e −T/τ/(1+e −T/τ)]T. [Equation 35]
Claims (6)
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KR20140052097A KR20140132277A (en) | 2013-05-07 | 2014-04-30 | A coefficient error robust transmit feed forward equalization |
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US10243762B1 (en) | 2018-04-16 | 2019-03-26 | Macom Connectivity Solutions, Llc | Analog delay based fractionally spaced n-tap feed-forward equalizer for wireline and optical transmitters |
US11342907B2 (en) | 2019-09-30 | 2022-05-24 | Samsung Electronics Co., Ltd. | Electronic device including equalizing circuit and operating method of the electronic device |
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WO2019197897A1 (en) * | 2018-04-12 | 2019-10-17 | Rockley Photonic Limited | Optical engine |
US10924310B2 (en) | 2018-09-10 | 2021-02-16 | International Business Machines Corporation | Transmitter with fully re-assignable segments for reconfigurable FFE taps |
US20210126764A1 (en) * | 2019-10-29 | 2021-04-29 | International Business Machines Corporation | Time dependent line equalizer for data transmission systems |
KR102568428B1 (en) * | 2022-04-01 | 2023-08-18 | 한양대학교 산학협력단 | Transmitter comprising feed forward equalization |
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US10243762B1 (en) | 2018-04-16 | 2019-03-26 | Macom Connectivity Solutions, Llc | Analog delay based fractionally spaced n-tap feed-forward equalizer for wireline and optical transmitters |
US11342907B2 (en) | 2019-09-30 | 2022-05-24 | Samsung Electronics Co., Ltd. | Electronic device including equalizing circuit and operating method of the electronic device |
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