BANDWIDTH ADJUSTMENT METHOD AND ASSOCIATED BANDWIDTH ADJUSTMENT CIRCUIT AND PHASE RECOVERY MODULE

Abstract

A bandwidth adjustment method includes obtaining an upper bandwidth limit and a lower bandwidth limit according to an initial upper bandwidth limit and an initial lower bandwidth limit, obtaining an optimum bandwidth according to the upper bandwidth limit and the lower bandwidth limit, and adjusting the initial upper bandwidth limit and the initial lower and width limit according to the optimum bandwidth.

Claims

1. A bandwidth adjustment method, applied to a phase compensation adjustment circuit of a phase recovery module, comprising: obtaining an upper bandwidth limit and a lower bandwidth limit according to an initial upper bandwidth limit and an initial lower bandwidth limit; obtaining an optimum bandwidth according to the upper bandwidth limit and the lower bandwidth limit; adjusting the initial upper bandwidth limit and the initial lower bandwidth limit according to the optimum bandwidth to obtain an adjusted initial upper bandwidth limit and an adjusted initial lower bandwidth limit; and adjusting the optimum bandwidth according to the adjusted initial upper bandwidth limit and the adjusted initial lower bandwidth limit.

2. The bandwidth adjustment method according to claim 1, further comprising: adjusting, according to the upper bandwidth limit and the lower bandwidth limit, a working bandwidth of the phase compensation adjustment circuit to a first bandwidth, wherein the first bandwidth is obtained by performing a first interpolation operation on the upper bandwidth limit and the lower bandwidth limit; measuring, corresponding to the first bandwidth, a plurality of a first phase errors between a compensated input signal and a reference signal, and obtaining a first statistical value of the plurality of first phase errors, wherein the compensated input signal is obtained according to an input signal and a phase compensation signal generated by the phase compensation adjustment circuit; adjusting, according to the upper bandwidth limit and the lower bandwidth limit, the working bandwidth of the phase compensation adjustment circuit to a second bandwidth, wherein the second bandwidth is obtained by performing a second interpolation operation on the upper bandwidth limit and the lower bandwidth limit; measuring, corresponding to the second bandwidth, a plurality of second phase errors between the compensated input signal and the reference clock signal, and obtaining a second statistical value of the plurality of second phase errors; and obtaining the optimum bandwidth according to the first statistical value and the second statistical value.

3. The bandwidth adjustment method according to claim 1, wherein the first bandwidth is greater than the second bandwidth, and the step of adjusting the working bandwidth according to the first statistical value and the second statistical value comprises: when the first statistical value is smaller than the second statistical value, adjusting the lower bandwidth limit to the second bandwidth limit, and obtaining a third bandwidth by performing interpolation the upper bandwidth limit and the adjusted lower bandwidth limit, adjusting the bandwidth of the phase compensation adjusting circuit to the third bandwidth, measuring, corresponding to the third bandwidth, a plurality of third phase errors between the compensated input signal and the reference signal, obtaining a third statistical value of the plurality of third phase errors, and adjusting the working bandwidth according to the first statistical value and the third statistical value; and when the second statistical value is smaller than the first statistical value, adjusting the upper bandwidth to the first bandwidth, obtaining a fourth bandwidth by performing interpolation on the adjusted upper bandwidth limit and the lower bandwidth limit, adjusting the bandwidth of the phase compensation adjustment circuit to the fourth bandwidth, measuring, corresponding to the fourth bandwidth, a plurality of fourth phase errors between the compensated input signal and the reference clock signal, obtaining a fourth statistical value of the plurality of fourth phase errors, and adjusting the working bandwidth according to the second statistical value and the fourth statistical value.

4. The bandwidth adjustment method according to claim 3, wherein the step of obtaining the optimum bandwidth comprises: determining whether a first difference between the adjusted lower bandwidth limit and the adjusted upper bandwidth limit is smaller than a threshold; and when the first difference is smaller than the threshold, obtaining the optimum bandwidth according to one of the adjusted lower bandwidth limit and the adjusted upper bandwidth limit.

5. The bandwidth adjustment method according to claim 1, further comprising: determining whether to adjust the initial upper bandwidth limit and the initial lower bandwidth limit.

6. The bandwidth adjustment method according to claim 5, wherein the step of determining whether to adjust the initial upper bandwidth limit and the initial lower bandwidth limit comprises: at a first time point, measuring, corresponding to the optimum bandwidth, a plurality of fifth phase errors between the compensated input signal and the reference clock signal, and obtaining a fifth statistical value of the plurality of fifth phase errors; at a second time point, measuring, corresponding the optimum bandwidth, measuring a plurality of sixth phase errors between the compensated input signal and the reference clock, and obtaining a sixth statistical value of the plurality of sixth phase errors; determining whether a second difference between the fifth statistical value and the sixth statistical value is greater than a predetermined value; and determining that the initial upper bandwidth limit and the initial lower bandwidth limit are to be adjusted when second difference between the fifth statistical value and the sixth statistical value is greater than the predetermined value.

7. The bandwidth adjustment method according to claim 1, wherein the step of adjusting the initial upper bandwidth limit and the initial lower bandwidth limit according to the optimum bandwidth comprises: calculating the adjusted lower initial bandwidth limit according to the optimum bandwidth; and calculating the adjusted initial upper bandwidth limit according to the optimum bandwidth and the adjusted initial lower bandwidth limit.

8. The bandwidth adjustment method according to claim 7, wherein a first interpolation result obtained by performing the first interpolation operation on the adjusted initial lower bandwidth limit and the adjusted upper bandwidth limit is the optimum bandwidth.

9. The bandwidth adjustment method according to claim 1, wherein the step of adjusting the initial upper bandwidth limit and the initial lower bandwidth limit according to the optimum bandwidth comprises: calculating the adjusted initial upper bandwidth limit according to the optimum bandwidth; and calculating the adjusted initial lower bandwidth limit according to the optimum bandwidth and the adjusted initial upper bandwidth limit.

10. The bandwidth adjustment method according to claim 9, wherein a second interpolation result obtained from performing the second interpolation operation on the adjusted initial lower bandwidth limit and the adjusted initial upper bandwidth limit is the optimum bandwidth.

11. A bandwidth adjustment circuit, for a phase recovery module, comprising: a statistics circuit, recording a plurality of phase errors between an input signal that is compensated by the phase recovery module and a reference signal, and calculating a statistical value of the plurality of phase errors to generate a statistical indication signal; a control circuit, generating a bandwidth indication signal according to the statistical indication signal, wherein the bandwidth indication signal corresponds to an optimum bandwidth; and a conversion circuit, generating at least one filter coefficient of a working bandwidth of a phase compensation adjustment circuit in the phase recovery module according to the bandwidth indication signal.

12. The bandwidth adjustment circuit according to claim 11, wherein the control circuit comprises: a first adder, calculating a difference between an upper bandwidth limit and a lower bandwidth limit, wherein the upper bandwidth limit and the lower bandwidth limit are associated with an initial upper bandwidth limit and an initial lower bandwidth limit; a first multiplier, calculating a product of the difference and a constant; a second adder, calculating a sum of the lower bandwidth limit and the product as a first bandwidth; a third adder, calculating a difference between the upper bandwidth limit and the product as a second bandwidth; a determining unit, adjusting the upper bandwidth limit, the lower bandwidth limit and the bandwidth indication signal according to the statistical indication signal; and an initial bandwidth calculation circuit, adjusting the initial upper bandwidth limit and the initial lower bandwidth limit according to the optimum bandwidth to obtain an adjusted initial upper bandwidth limit and an adjusted initial lower bandwidth limit.

13. The bandwidth adjustment circuit according to claim 12, wherein the initial bandwidth calculation circuit comprises: a second multiplier, multiplying the optimum bandwidth by a first value to generate a first multiplication result; a third multiplier, multiplying the first multiplication result by a second value to generate a second multiplication result; a subtractor, subtracting the second multiplication result from the optimum bandwidth to generate a first subtraction result; and a fourth multiplier, multiplying the first subtraction result by a third value to generate a third multiplication result; wherein, one of the first multiplication result and the third multiplication result is one of the adjusted initial upper bandwidth limit and the adjusted initial lower bandwidth limit.

14. The bandwidth adjustment circuit according to claim 13, wherein the initial bandwidth calculation circuit outputs the adjusted initial lower bandwidth limit as the first multiplication result, and outputs the adjusted initial upper bandwidth limit as the third multiplication result.

15. The bandwidth adjustment circuit according to claim 13, wherein the initial bandwidth calculation circuit outputs the adjusted initial upper bandwidth limit as the first multiplication result, and outputs the adjusted initial lower bandwidth limit as the third multiplication result.

16. A phase recovery module, comprising: a multiplication circuit, multiplying an input signal by a phase compensation signal to generate a compensated input signal; a phase error detection circuit, detecting a phase difference between the compensated input signal and a reference clock signal; a phase compensation adjustment circuit, generating the phase compensation signal according to the phase difference; and a bandwidth adjustment circuit, comprising a statistics circuit, a control circuit and a conversion circuit; wherein, the bandwidth adjustment circuit obtains an upper bandwidth limit and a lower bandwidth limit according to an initial upper bandwidth limit and an initial lower bandwidth limit, obtains an optimum bandwidth according to the upper bandwidth limit and the lower bandwidth limit, adjusts the initial upper bandwidth limit and the initial lower bandwidth limit according to the optimum bandwidth to obtain an adjusted initial upper bandwidth limit and an adjusted lower bandwidth limit, and adjusts the optimum bandwidth according to the adjusted initial upper bandwidth limit and the adjusted initial lower bandwidth limit.

17. The phase recovery module according to claim 16, wherein the control circuit comprises: a first adder, calculating a difference between an upper bandwidth limit and a lower bandwidth limit, wherein the upper bandwidth limit and the lower bandwidth limit are associated with an initial upper bandwidth limit and an initial lower bandwidth limit; a first multiplier, calculating a product of the difference and a constant; a second adder, calculating a sum of the lower bandwidth limit and the product as a first bandwidth; a third adder, calculating a difference between the upper bandwidth limit and the product as a second bandwidth; a determining unit, adjusting the upper bandwidth limit, the lower bandwidth limit and the bandwidth indication signal according to the statistical indication signal; and an initial bandwidth calculation circuit, adjusting the initial upper bandwidth limit and the initial lower bandwidth limit according to the optimum bandwidth to obtain an adjusted initial upper bandwidth limit and an adjusted initial lower bandwidth limit.

18. The phase recovery module according to claim 17, wherein the initial bandwidth calculation circuit comprises: a second multiplier, multiplying the optimum bandwidth by a first value to generate a first multiplication result; a third multiplier, multiplying the first multiplication result by a second value to generate a second multiplication result; a subtractor, subtracting the second multiplication result from the optimum bandwidth to generate a first subtraction result; and a fourth multiplier, multiplying the first subtraction result by a third value to generate a third multiplication result; wherein, one of the first multiplication result and the third multiplication result is one of the adjusted initial upper bandwidth limit and the adjusted initial lower bandwidth limit.

19. The phase recovery module according to claim 18, wherein the initial bandwidth calculation circuit outputs the adjusted initial lower bandwidth limit as the first multiplication result, and outputs the adjusted initial upper bandwidth limit as the third multiplication result.

20. The phase recovery module according to claim 18, wherein the initial bandwidth calculation circuit outputs the adjusted initial upper bandwidth limit as the first multiplication result, and outputs the adjusted initial lower bandwidth limit as the third multiplication result.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 is a block diagram of a phase recovery module according to an embodiment of the present invention;

[0011] FIG. 2 is a relationship diagram of a working bandwidth and a phase error according to an embodiment of the present invention;

[0012] FIG. 3 is a block diagram of the statistics circuit in FIG. 1 according to an embodiment;

[0013] FIG. 4 is a block diagram of the control circuit in FIG. 1 according to an embodiment;

[0014] FIG. 5 is a block diagram of the conversion circuit in FIG. 1 according to an embodiment;

[0015] FIG. 6 is a flowchart of a process according to an embodiment of the present invention; and

[0016] FIG. 7 is a schematic diagram of the initial bandwidth calculation circuit in FIG. 4 according to an embodiment.

DETAILED DESCRIPTION OF THE INVENTION

[0017] FIG. 1 shows a block diagram of a phase recovery module 10 according to an embodiment of the present invention. The phase recovery module 10 is applied to a communication system to compensate a phase error of an input signal IN. Referring to FIG. 1, the phase recovery module 10 includes a multiplication circuit 100, a phase error detection circuit 102, a phase compensation adjustment circuit 104 and a bandwidth adjustment circuit 106. The multiplication circuit 100 multiplies the input signal IN by a phase compensation signal PC to obtain a compensated input signal CIN. The phase error detection circuit 102 obtains a phase error between the compensated input signal CIN and a reference clock signal (not shown in FIG. 1) in the communication system. The phase compensation adjustment circuit 104 includes a filter 108 and an oscillator 110, and adjusts the phase compensation signal PC according to the phase error to minimize the phase error . The bandwidth adjustment circuit 106 calculates a variance of the phase error when the phase compensation adjustment circuit 104 operates in different bandwidths, and accordingly adjusts a working bandwidth BW.sub.F of the phase compensation adjustment circuit 104. The working bandwidth BW.sub.F of the phase compensation adjustment circuit 104 may be adaptively adjusted according to the time varying input signal IN to optimize the performance of the phase recovery module 10.

[0018] It should be noted that, not only the working bandwidth BW.sub.F of the filter 108 affects the phase error , but a corresponding relationship between a phase error variance VAR() and the working bandwidth BW.sub.F also changes with time. FIG. 2 shows a relationship diagram of the working bandwidth BW.sub.F and the phase error variance VAR() according to an embodiment of the present invention. Referring to FIG. 2, the solid line represents a corresponding relationship (represented by a function f.sub.1) of the working bandwidth BW.sub.F and the phase error variance VAR() at a time point t.sub.1, and the dotted line represents a corresponding relationship (represented by a function f.sub.2) of the working bandwidth BW.sub.F and the phase error variance VAR() at a time point t.sub.2. At the time point t.sub.1, the phase error variance VAR() displays a convex function between an initial upper bandwidth limit BW0.sub.U and an initial lower bandwidth limit BW0.sub.L. That is to say, the phase error variance VAR() has a minimum phase error variance VAR().sub.MIN between the initial upper bandwidth limit BW0.sub.U and the initial lower bandwidth limit BW0.sub.L. If the working frequency BW.sub.F of the filter 108 is adjusted to an optimum bandwidth BW.sub.OPT corresponding to the minimum phase error variance VAR().sub.MIN, the phase recovery module 10 can obtain the optimum phase error .

[0019] Thus, in an embodiment of the present invention, the bandwidth adjustment circuit 106 records the phase error variance VAR() of the phase recovery module 10 operating in different working bandwidths BW.sub.F, so as to adjust the working bandwidth BW.sub.F of the filter 108 to the optimum bandwidth BW.sub.OPT corresponding to the minimum phase error variance VAR().sub.MIN. Further, the bandwidth adjustment circuit 106 may use a recursive algorithm to calculate the optimum bandwidth BW.sub.OPT according to the initial upper bandwidth limit BW0.sub.U and the initial lower bandwidth limit BW0.sub.L.

[0020] Further, it should be noted that, the corresponding relationship between the phase error variance VAR() and the working bandwidth BW.sub.F changes with time. In other words, the optimum bandwidth BW.sub.OPT corresponding to the time point t.sub.1 and another optimum bandwidth BW.sub.OPT corresponding to the time point t.sub.2 are different. In this situation, the bandwidth adjustment circuit 106 may again perform the recursive algorithm after a period of time from the time point t.sub.1 (assuming t.sub.2 is after a period of time from t.sub.1) to calculate the optimum bandwidth BW.sub.OPT corresponding to the time point t.sub.2. To ensure that the result of again performing the recursive algorithm at the time t.sub.2 is the optimum bandwidth BW.sub.OPT, the bandwidth adjustment circuit 106 may adjust the initial upper bandwidth limit and the initial lower bandwidth limit (with associated details of the adjustment described shortly) according to the optimum bandwidth BW.sub.OPT obtained at the time point t.sub.1 to obtain an adjusted initial upper bandwidth limit BW0.sub.U and an adjusted initial lower bandwidth limit BW0.sub.L, and again perform the recursive algorithm according to the adjusted initial upper bandwidth limit BW0.sub.U and the adjusted initial lower bandwidth limit BW0.sub.L to calculate the optimum bandwidth BW.sub.OPT corresponding to the time point t.sub.2.

[0021] Operation details of how the bandwidth adjustment circuit 106 adjusts the working bandwidth BW.sub.F of the filter 108 to the optimum bandwidth BW.sub.OPT corresponding to the minimum phase error variance VAR(), and calculates the optimum bandwidth by using the recursive algorithm according to the initial upper bandwidth limit and the initial lower bandwidth limit are given with an example below. When the phase recovery module 10 first starts to operate, a control circuit 114 in the bandwidth adjustment circuit 106 may adjust a bandwidth indication signal BWS according to the initial upper bandwidth limit BW0.sub.U and the initial lower bandwidth limit BW0.sub.L to indicate a bandwidth BM.sub.1, which is between an upper bandwidth limit BW.sub.U and a lower bandwidth limit BW.sub.L and is obtained from interpolating the upper bandwidth limit BW.sub.U and a lower bandwidth limit BW.sub.L. In the first iteration of the recursive algorithm, the upper bandwidth limit BW.sub.U is the initial upper bandwidth limit BU0.sub.U, and the lower bandwidth limit BW.sub.L is the initial lower bandwidth limit BW0.sub.L. In one embodiment, the bandwidth BW.sub.1 may be obtained from performing a first interpolation operation on the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L, and may be represented as:

BW.sub.1=BW.sub.L+C(BW.sub.UBW.sub.L) (1)

[0022] In equation (1), C is a constant between 1 and 0, and may equal to 0.61803. According to the bandwidth indication signal BWS that indicates the bandwidth BW.sub.1, the conversion circuit 116 generates filter parameters K.sub.P and K.sub.I corresponding to the bandwidth BW.sub.1 to the filter 108, so as to adjust the bandwidth of the filter 108 to BW.sub.1. The filter parameters K.sub.P and K.sub.I are directly proportional to the bandwidth BW.sub.1. In a situation where the bandwidth of the filter 108 is the bandwidth BW.sub.1, the communication system starts receiving the input signal IN, and the multiplication circuit 100 adjusts the phase of the input signal IN according to the phase compensation signal PC to generate the compensated input signal CIN. According to the phase error obtained by the phase error detection circuit 102, the filter 108 generates a phase compensation value () to cause the oscillator 110 to adjust the phase compensation signal PC. At this point, the statistics circuit 112 records the phase error as a phase error .sub.1 corresponding to the bandwidth BM.sub.1. The statistics circuit 112 records the corresponding phase error as the phase error .sub.1 each time the communication system samples the input signal IN. After obtaining a predetermined number of phase errors .sub.1, the statistics circuit 112 calculates a variance VAR.sub.1 of the recorded phase error .sub.1, and transmits the variance VAR.sub.1 through the statistical indication signal STA to the control circuit 114.

[0023] The control circuit 114 adjusts the bandwidth indication signal BWS to indicate another bandwidth BW.sub.2, which is also between the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L and is obtained from interpolating the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L. In one embodiment, the bandwidth BW.sub.2 may be interpolated from performing a second interpolation operation on the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L, and may be represented as:

BW.sub.2=BW.sub.UC(BW.sub.UBW.sub.L) (2)

[0024] According to the bandwidth indication signal BWS that indicates the bandwidth BW.sub.2, the conversion circuit 116 generates the filter parameters K.sub.P and K.sub.I corresponding to the bandwidth BW.sub.2 to the filter 108, so as to adjust the bandwidth of the filter 108 to the bandwidth filter BW.sub.2. In a situation where the bandwidth of the filter 108 is changed to the bandwidth BW.sub.2, the communication system continues receiving the input signal IN, and the oscillator 110 continues adjusting the phase compensation signal PC according to the phase compensation value () that the filter 108 generates. At this point, the statistics circuit 112 records the phase error as a phase error .sub.2 corresponding to the bandwidth BW.sub.2 when the bandwidth of the filter 108 is the bandwidth BW.sub.2. After obtaining a predetermined number of phase errors .sub.2, the statistics circuit 112 calculates the variance VAR.sub.2 of the phase errors .sub.2 recorded, and transmits the variance VAR.sub.2 through the statistical indication signal STA to the control circuit 114.

[0025] After obtaining the variances VAR.sub.1 and VAR.sub.2, the control circuit 114 adjusts the bandwidth indication signal BWS according a relationship of the values of the variances VAR.sub.1 and VAR.sub.2, so as to optimize the working bandwidth BW.sub.F of the filter 108.

[0026] In brief, when the variance VAR.sub.1 is smaller than the variance VAR.sub.2, the control circuit 114 may regard the bandwidth BW.sub.2 calculated in the n.sup.th iteration as the lower bandwidth limit BW.sub.L of the (n+1).sup.th iteration; when the variance VAR.sub.2 is smaller than the variance VAR.sub.1, the control circuit 114 may regard the bandwidth BW.sub.1 calculated in the n.sup.th iteration as the upper bandwidth limit BW.sub.U of the (n+1).sup.th iteration.

[0027] In other words, in each iteration, the control circuit 114 reduces the difference between the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L, and the bandwidth adjustment circuit 106 determines that the upper bandwidth limit and the lower bandwidth limit is approximate to the optimum bandwidth BW.sub.OPT when the difference between upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L is smaller than a threshold (i.e., convergence is reached). At this point, according to the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L of the current iteration (when convergence is reached), the bandwidth adjustment circuit 106 obtains the optimum bandwidth BW.sub.OPT as the working bandwidth BW.sub.F of the filter 108. Thus, the working bandwidth BW.sub.F of the filter 108 is optimized, hence enhancing the operation performance of the phase recovery module 10.

[0028] Further, the method by which bandwidth adjustment circuit 106 obtains the optimum bandwidth BW.sub.OPT according to the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L corresponding to the convergence is not limited. For example, the bandwidth adjustment circuit 106 may obtain the lower bandwidth limit BW.sub.L corresponding to the convergence as the optimum bandwidth BW.sub.OPT (BW.sub.OPT=BW.sub.L), obtain the upper bandwidth limit BW.sub.U corresponding to the convergence as the optimum bandwidth BW.sub.OPT (BW.sub.OPT=BW.sub.U), or calculate the optimum bandwidth BW.sub.OPT by performing any interpolation operation on the lower bandwidth limit BW.sub.L and the upper bandwidth limit BW.sub.U as the optimum bandwidth BW.sub.OPT (BW.sub.LBW.sub.OPTBW.sub.U) when convergence is reachedthese examples satisfy the requirements of the present invention and are regarded within the scope of the present invention.

[0029] Other operation details of the phase detection circuit 120, the phase compensation adjustment circuit 104 and the bandwidth adjustment circuit 106 in the phase recovery module 10 of the present invention can be referred from the phase error detection circuit 102, the PLL circuit 104 and the bandwidth adjustment circuit 106 disclosed in the Taiwan Patent No. 1605686 of the Applicant, and shall be omitted herein.

[0030] FIG. 3 shows a block diagram of the statistics circuit 112 in FIG. 1 according to an embodiment. In FIG. 3, the statistics circuit 112 includes an arithmetic circuit 300, an adder 302, a counter 304 and a divider 306. The arithmetic circuit 300 records the phase error , and outputs the square of the phase error (i.e., (.sup.2) to the adder 302. The adder 302 adds .sup.2 with an intermediate sum SUM.sub.M, and outputs the sum to the counter 304. The counter 304 counts the number of times of receiving the sum of .sup.2 and the intermediate sum SUM.sub.M. When the number of times of receiving the sum of the .sup.2 and the intermediate sum SUM.sub.M is smaller than a predetermined number, the counter 304 uses the sum of .sup.2 and the intermediate sum SUM.sub.M as the new intermediate sum SUM.sub.M, and outputs the new intermediate sum SUM.sub.M to the adder 302. When the number of times of receiving the sum of .sup.2 and the intermediate sum SUM.sub.M reaches the predetermined number, the counter uses the sum of .sup.2 and the intermediate sum SUM.sub.M as the sum SUM to be outputted to the divider 306. The divider 306 receives the sum SUM and divides it by the predetermined number.

[0031] FIG. 4 shows a block diagram of the control circuit 114 in FIG. 1 according to an embodiment. As shown in FIG. 4, the control circuit 114 includes adders 400, 404 and 406, a multiplier 402, a determining unit 408 and an initial bandwidth calculation circuit 410. The adder 400 outputs the difference between the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L to the multiplier 402. The multiplier 402 calculates a product of the difference between the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L and a constant C, and sends the product to the adders 404 and 406. The adder 404 adds the lower bandwidth limit BW.sub.L with the output of the multiplier 402 to generate the bandwidth BW.sub.1, and the adder 406 subtracts the upper bandwidth limit BW.sub.U by the output of the multiplier 402 to generate the bandwidth BW.sub.2. According to the statistical indication signal STA, the determining unit 408 adaptive adjusts the upper bandwidth limit BW.sub.U, the lower bandwidth limit BW.sub.L and the bandwidth indication signal BWS. When the difference between the upper bandwidth limit BW.sub.U and the lower bandwidth limit BW.sub.L is smaller than the threshold , the determining unit 408 may adjust the bandwidth indication signal BWS to indicate the optimum bandwidth BW.sub.OPT.

[0032] Further, the time point t.sub.1 corresponds the time at which the time circuit 114 obtains the optimum bandwidth BW.sub.OPT. The initial bandwidth calculation circuit 410 may, after the control circuit 114 obtains the optimum bandwidth BW.sub.OPT for a predetermined period, again calculate the initial upper bandwidth limit and the initial lower bandwidth limit according to the optimum bandwidth BW.sub.OPT, so as to obtain the adjusted initial upper bandwidth limit BW0.sub.U and the adjusted initial lower bandwidth limit BW0.sub.L. Thus, the control circuit 114 may again perform the recursive algorithm according to the adjusted initial upper bandwidth limit BW0.sub.U and the adjusted initial lower bandwidth limit BW0.sub.L to calculate the optimum bandwidth BW.sub.OPT corresponding to the time point t.sub.2 (i.e., the time point after period from the time point t.sub.1).

[0033] Ways for implementing the initial bandwidth calculation circuit 410 are not limited. For example, FIG. 7 shows a schematic diagram of the initial bandwidth calculation circuit in FIG. 4 according to an embodiment. As shown in FIG. 7, the initial bandwidth calculation circuit 410 includes multipliers MUL1, MUL2 and MUL3 and a subtractor SUB. The multiplier MUL1 multiples the optimum bandwidth BW.sub.OPT by a first value CV1 to generate a first multiplication result P1. The multiplier MUL2 multiplies the first multiplication result P1 by a second value CV2 to generate a second multiplication result P2. The subtractor SUB subtracts the second multiplication result P2 from the optimum bandwidth BW.sub.OPT to generate a subtraction result D. The third multiplier MUL3 multiplies the subtraction result D by a third value CV3 to generate a third multiplication result P3.

[0034] Depending on actual conditions, the initial bandwidth calculation circuit 410 may output the first multiplication result P1 or third multiplication result P3 as the adjusted initial upper bandwidth limit BW0.sub.U and the adjusted initial lower bandwidth limit BW0.sub.L For example, when a phase noise is smaller than a predetermined value or the communication system is experiencing an additive white Gaussian noise (AWGN) channel, the initial bandwidth calculation circuit 410 may output the first multiplication result P1 as the adjusted initial lower bandwidth limit BW0.sub.L, and output the third multiplication result P3 as the adjusted initial upper bandwidth limit BW0.sub.U. In other words, the initial bandwidth calculation circuit 410 may calculate the adjusted initial lower bandwidth limit BW0.sub.L according to the optimum bandwidth BW.sub.OPT, and calculate the adjusted initial upper bandwidth limit BW0.sub.U according to the optimum bandwidth BW.sub.OPT and the adjusted initial lower bandwidth limit BW0.sub.L. In one embodiment, the first value CV1 may be 2 raised to the n.sup.th power (n0), the second value CV2 may be 0.61803, and the third value CV3 may be 1/(1CV2) or 2.61801. Thus, if the adjusted initial lower bandwidth BW0.sub.L and the adjusted initial upper bandwidth limit BW0.sub.U is substituted into the first interpolation operation in equation (1), the first interpolation result obtained is the optimum bandwidth BW.sub.OPT. That is, when the control circuit 114 again performs the recursive algorithm, the bandwidth BW.sub.1 may be calculated as the optimum bandwidth BW.sub.OPT (BW.sub.1=BW.sub.OPT), so as to ensure that the control circuit 114 is capable of correctly calculating the optimum bandwidth BW.sub.OPT.

[0035] On the other hand, when the phase noise is greater than a predetermined value, the initial bandwidth calculation circuit 410 may output the third multiplication result P3 as the adjusted initial lower bandwidth limit BW0.sub.L, and output the first multiplication result P1 as the adjusted initial upper bandwidth limit BW0.sub.U. In other words, the initial bandwidth calculation circuit 410 may calculate the adjusted initial upper bandwidth limit BW0.sub.U according to the optimum bandwidth BW.sub.OPT, and calculate the adjusted initial lower bandwidth limit BW0.sub.L according to the optimum bandwidth BW.sub.OPT and the adjusted initial upper bandwidth limit BW0.sub.U. In one embodiment, the first value CV1 may be 2 raised to the n.sup.th power (0n0.69), the second value CV2 may be 0.61803, and the third value CV3 may be 1/(1CV2) or 2.61803. Thus, if the adjusted initial lower bandwidth limit BW0.sub.L and the adjusted initial upper bandwidth BW0.sub.U are substituted into the second interpolation operation in equation (2), the second interpolation result obtained is the optimum bandwidth BW.sub.OPT. That is, when the control circuit 114 again performs the recursive algorithm, the bandwidth BW.sub.2 may be calculated as the optimum bandwidth BW.sub.OPT (BW.sub.2=BW.sub.OPT), so as to ensure that the control circuit 114 is capable of correctly calculating the optimum bandwidth BW.sub.OPT.

[0036] FIG. 5 shows a block diagram of the conversion circuit 116 in FIG. 1. In FIG. 5, the conversion circuit 116 includes an arithmetic circuit 500 and a multiplier 502. The conversion circuit 116 shown in FIG. 5 directly uses the bandwidth indication signal BWS as the filter coefficient K.sub.P (i.e., the filter coefficient K.sub.P is equal to the bandwidth indicated by the bandwidth indication signal BW.sub.S), uses the arithmetic circuit 500 to calculate a square of the bandwidth indicated by the bandwidth indication signal BWS, and then uses the multiplier 502 to calculate a product of the square and a reciprocal of a square of a damping coefficient as the filter coefficient

[0037] Operation details of the bandwidth adjustment circuit 106 may be concluded to a process 60. The process 60 includes following steps.

[0038] In step 600, the process 60 begins.

[0039] In step 601, according to an initial upper bandwidth limit and an initial lower bandwidth limit, an upper bandwidth limit and a lower bandwidth limit are obtained.

[0040] In step 602, according to the upper bandwidth limit and the lower bandwidth limit, an working bandwidth of the phase compensation adjustment circuit is adjusted to a first bandwidth.

[0041] In step 604, corresponding to the first bandwidth, a plurality of phase errors between a compensated input signal and a reference clock signal are measured, and a first statistical value of the first phase errors is obtained.

[0042] In step 606, according to the upper bandwidth limit and the lower bandwidth limit, the working bandwidth of the phase compensation adjustment circuit is adjusted to a second bandwidth.

[0043] In step 608, corresponding to the second bandwidth, a plurality of second phase errors between the compensated input signal and the reference clock signal are measured, and a second statistical value of the second phase errors is obtained.

[0044] In step 610, an optimum bandwidth is obtained according to the first statistical value and the second statistical value.

[0045] In step 603, it is determined whether the initial upper bandwidth limit and the initial lower bandwidth limit are to be adjusted. Step 605 is performed if so, otherwise step 612 is performed if not.

[0046] In step 605, the initial upper bandwidth limit and the initial lower bandwidth limit are adjusted according to the optimum bandwidth.

[0047] In step 612, the process 60 ends.

[0048] While the invention has been described by way of example and in terms of the preferred embodiments, it is to be understood that the invention is not limited thereto. On the contrary, it is intended to cover various modifications and similar arrangements and procedures, and the scope of the appended claims therefore should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements and procedures.