Ping-pong coefficients update scheme

The DFE architecture as shown in Fig. 2.8(b), the error can be calculated until the output of slicer is stable. The error or the sign of error will be passed to the adaptation block, and the adaptation block needs to calculate the new weights immediately if updating coefficients every bit. In real implementation, the clock period is too short to calculate so many operations.

A typical circuit implementation is to calculate the error or sign of error when the data is sampled in. Like the speculation technique, the circuit calculates two sign of error based on guessing the sampled data is high or low. When the sampled data is equalized, the sigh of error can also be chosen. Fig. 4.10 illustrates the concept of calculating sign of error speculatively.

Figure 4.10: Illustration of calculating sign of error speculatively.

In the architecture that we use in our model there are two parallel data paths. Each path has the same probability of processing high and low data for PRBS input pattern. That means these two calculated sign of error based on guessing the sampled data will be selected in equal probability in each data path.

Therefore, we can consider a mechanism that calculates one sign of error in each path. In the simulation we calculate the sign of error when the processed data is high in the upper data paths. On the other hand, the lower path calculates the sign of error when the processed data is low. If the sign of error is not calculated, the equalizer coefficients keep its current value. We simulate this mechanism under five different coefficient adaptation frequency. The simulation results are shown from Fig. 4.11 to Fig. 4.20. The figures that are under the same hopping update rate uses the same input sequence to make sure the comparison basis is fair.

In Fig. 4.11 and Fig. 4.12, the equalizer coefficients convergence time and error is similar in original case and the case with ping-pong update scheme. If we divide the hopping update rate to half of data rate, the result starts to have differ-ence. The coefficients convergence time of Fig. 4.13 is shorter than it of Fig. 4.14.

That means reducing the calculation of sign of error really loses some information for coefficients adaptation and extends the convergence duration. The case of 1/4 adaptation frequency as shown in Fig. 4.15 and Fig. 4.15, coefficients convergence time delay phenomenon is more obvious than the two previous cases. Moreover, in the cases of 1/8 and 1/16 hopping update rate, the error is bias when the coefficients do not converge. Following the same principle, we list the Eave and Tcon in Table 4.2.

In fact, we can consider the mechanism as a modification of slowing down the coefficients adaptation frequency. Although the mechanism do not really slow down the coefficients adaptation block operation frequency, the coefficients will be updated based on the value of input data. We can call the mechanism as data dependent coefficients update strategy. In a communication system that guaran-tees the transitions of data sequence, the strategy will be appropriate because the two data paths will process high and low data in nearly equal probability. From the simulation results of subsection 4.4.2, we observe that adaptation system can work properly even if a part of information is lost. The proposed scheme is under such concept to reduce some hardware blocks. For the data sequence that is often model as PRBS, the two paths will have the same probability to calculate the sigh of error for update equalizer coefficients. That means the calculation will not be halt for a long period.

Because the input data sequences are different in the five situations of dif-ferent coefficients adaptation frequency, we show a simulation that adopts the ping-pong coefficients update scheme under three different bits for hopping coef-ficients update scheme, hopping per bit, per 4 bits, and per 16 bits in Fig 4.21 to Fig. 4.23. The three cases are under the same input data sequence. The Eave and Tcon of these three simulations are listed in Table 4.3. Moreover, for the considering of some popular application in serial link, we also run the same simu-lation that uses the 8b/10b encoding data as the input data sequence as shown in Fig 4.24 to Fig. 4.26, and the Eave and Tcon of these three simulations are listed

in Table 4.4. We can find that the value of Eave and Tcon of 8b/10b input data sequency have similar performance with that of PRBS input data sequence. The 8b/10b encoding pattern will guarantee the transition per 5 bits. These transi-tions will increase the probability of error calculation in the ping-pong coefficients update scheme.

For the hopping coefficients update scheme, we can reduce the power con-sumption of coefficients update block. The original update frequency is equal to the data rate fs. Under the hopping coefficients update scheme, the update frequency can be divided by how many bits the coefficients update once. That means the power can be save for the same ratio due the power consumption is proportional to the operation frequency. The ping-pong update scheme can save one comparator that calculates the sign error in each data path. In the case of the architecture in our model, the saving is two comparators due to the half-rate architecture.

(a)

(b)

Figure 4.11: Hopping update scheme under data rate without ping-pong update scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.12: Hopping update scheme under data rate with ping-pong update scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.13: Hopping update scheme under 1/2 data rate without ping-pong update scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.14: Hopping update scheme under 1/2 data rate with ping-pong up-date scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.15: Hopping update scheme under 1/4 data rate without ping-pong update scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.16: Hopping update scheme under 1/4 data rate with ping-pong up-date scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.17: Hopping update scheme under 1/8 data rate without ping-pong update scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.18: Hopping update scheme under 1/8 data rate with ping-pong up-date scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.19: Hopping update scheme under 1/16 data rate without ping-pong update scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.20: Hopping update scheme under 1/16 data rate with ping-pong update scheme. (a) DFE coefficients. (b) error

Table 4.2: Eave and Tcon for hopping update scheme with/without ping-pong update scheme under five different data rate

data rate 1 1/2

ping-pong scheme No Yes No Yes

mean of absolute error value (Eave) 0.2426 0.2427 0.2463 0.2473 Convergence time (bit) 2400 2340 2800 4130

data rate 1/4 1/8

ping-pong scheme No Yes No Yes

mean of absolute error value (Eave) 0.2297 0.2343 0.2394 0.2371 Convergence time (bit) 4400 7700 9000 13200

data rate 1/16 –

ping-pong scheme No Yes –

mean of absolute error value (Eave) 0.2411 0.2457 – –

Convergence time (bit) 17440 24470 – –

(a)

(b)

Figure 4.21: Hopping update scheme under data rate with ping-pong update scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.22: Hopping update scheme under 1/4 data rate with ping-pong up-date scheme. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.23: Hopping update scheme under 1/16 data rate with ping-pong update scheme. (a) DFE coefficients. (b) error

Table 4.3: Eave and Tcon for hopping update scheme under three different data rate with ping-pong update scheme.

update frequency (data-rate) 1 1/4 1/16 mean of absolute error value (Eave) 0.2433 0.2452 0.2431

Convergence time (bit) (Tcon) 2980 5660 24180

(a)

(b)

Figure 4.24: Hopping update scheme under data rate with ping-pong update scheme and 8b/10b input. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.25: Hopping update scheme under 1/4 data rate with ping-pong up-date scheme and 8b/10b input. (a) DFE coefficients. (b) error

(a)

(b)

Figure 4.26: Hopping update scheme under 1/16 data rate with ping-pong update scheme and 8b/10b input data. (a) DFE coefficients. (b) error

Table 4.4: Eave and Tcon for hopping update scheme under three different data rate with ping-pong update scheme and 8b/10b input data.

update frequency (data-rate) 1 1/4 1/16 mean of absolute error value (Eave) 0.2369 0.2375 0.2396

Convergence time (bit) (Tcon) 3010 9100 31880

Chapter 5