USRE34206E - Method and apparatus for timing recovery - Google Patents
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- USRE34206E USRE34206E US07/666,728 US66672891A USRE34206E US RE34206 E USRE34206 E US RE34206E US 66672891 A US66672891 A US 66672891A US RE34206 E USRE34206 E US RE34206E
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L7/00—Arrangements for synchronising receiver with transmitter
- H04L7/0054—Detection of the synchronisation error by features other than the received signal transition
- H04L7/0062—Detection of the synchronisation error by features other than the received signal transition detection of error based on data decision error, e.g. Mueller type detection
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- This invention relates to digital data transmission systems and is applicable especially to a method and apparatus for timing recovery in subscriber loop interface circuits.
- the digital subscriber loop interface circuit usually will comprise two parts; a transmitter and a receiver.
- the function of the transmitter is to put a series of pulses, usually shaped by some form of filter, on the loop.
- these pulses are likely to be 4-level pulses, particulary encoded as the so-called 2B1Q code (two binary, one quaternary) recommended by the American National Standard Institute (Working Group T1D1 3)
- the function of the receiver is to detect pulses being sent from the far end of the loop, which is difficult because these pulses are distorted.
- One source of distortion is coupling of the transmit pulses, being put onto the loop, directly across the hybrid circuit and into the receiver input as "echoes", which is a common problem when operating on a two-wire system.
- Such transmit pulse echoes are removed by echo-cancellation, typically using a transversal filter to derive a function or model of the transmit signal for subtraction from the received signal.
- the receiver performs a number of functions. As previously mentioned, it takes out the echo and, before the echo is removed, some shaping of the pulses is usually done by means of a receiver filter. Next, the receiver cancels intersymbol interference. This is interference from symbols received before the symbol of interest.
- the final function of the receiver is to decide where in time and at what amplitude to slice or quantize the received signals, to convert them back to pulses, or in some cases, 4-level signals. To do so the receiver must determine the exact timing instant when the pulses arrive and also determine the exact levels.
- the timing instant is determined by a timing recovery circuit.
- Known timing recovery circuits using, for example, threshold crossing detection or time derivatives of the signal at the sampling instant, are generally unsuitable where the signal is digitized at the input to the receiver.
- To implement a traditional analogue approach digitally would result in a complex and expensive system, with an analogue-to-digital conversion rate that could present problems.
- the timing recovery algorithm should preferably operate at the same sampling rate as the echo canceller. Since the echo-canceller requires a large proportion of the receiver complexity it is desirable to minimize the complexity of the receiver by sampling at the minimum possible rate for satisfactory operation. This means sampling at the baud rate.
- a paper entitled "Timing Recovery in Digital Subscriber Loops using Baud-Rate Sampling" by C. P. Jeremy Tzeng, David A. Hodges and David G. Messerschmidt, IEEE Journal on Selected Areas in Communications, Vol. SAC4, No. 8, Nov. 1986 it was proposed to determine the timing instant by detecting the zero crossing, between the precursor undershoot and the main pulse, assuming the peak of the main pulse to be one baud later, and sampling at that position.
- main cursor and “precursor” will be used to refer to the pulse height at sampling instants near the peak of the main pulse and at or near the aforementioned zero crossing, respectively.
- Mueller and Muller disclosed the general procedure for deriving the timing and a specific example directed to two and three level codes, but did not address the problem of recovering timing from a multilevel signal of the 2B1Q kind specified in the .[.T1D1.]. .Iadd.T1E1 .Iaddend.standard.
- a precondition for low variance is to prevent the main cursor (h o ) from appearing in the expression for the variance. This can be guaranteed by a set of nonlinear equations being satisfied, as indicated in the aforementioned paper by Mueller and Muller.
- the solution of these equations is not obvious, however.
- the .Badd.4-level code has two values, +1 and +3; hence two decision levels. Accordingly the timing estimator will encounter +1 and +3 indiscriminately because the data is scrambled. Difficulty arises in achieving consistent timing in the presence of this variation in amplitude as well as the usual time variation.
- the present invention comprises a receiver suitable for a loop interface circuit for a digital data transmission system, said receiver comprising:
- sampling means for sampling a received four-level substantially randomized digital signal
- multilevel decision or slicing means for comparing such received signal selectively with a plurality of thresholds to extract its four symbols
- timing recovery means for determining a sampling instant as a function of a precursor sample and a main pulse sample one baud apart, according to the timing function:
- 1/T is the baud rate
- h(t) and h(t-T) denote the main pulse and precursor, respectively
- r is the ratio between the main pulse sample and the precursor pulse sample
- t is the sampling instant
- said timing recovery means including a timing estimator responsive to baud rate samples (x n and a n ) of the received signal before and after slicing, respectively, by said slicing means for deriving a precursor estimate (z n ) of the difference between the actual sampling instant and a desired sampling instant with reference to the ratio between the main sample pulse and said precursor sample one baud earlier, and means for generating a baud rate clock signal variable in dependence upon said estimate (z n ) the index n denoting the current baud interval;
- sampling means being responsive to said baud rate clock to vary said sampling instant
- timing estimator derives said precursor timing estimate z n in accordance with the expression:
- the timing function, and its estimate, can be thought of as a measure of the phase error due to sampling at time instant t (generally t ⁇ to).
- the timing recovery means determines the sampling instant according to the timing function
- the timing recovery means uses a three-level slicer with two of its decision regions controlling advance and retard, respectively, of the sampling instant, the third region being intermediate the others and serving to inhibit adjustment of the sampling instant until a predetermined phase difference has been reached.
- the timing recovery means has a decision means or slicer which has its thresholds adjustable by a main cursor estimate.
- Such main cursor estimate may be obtained from an adaptive reference control circuit, which derives the estimate in dependence upon loop factors, for example loss.
- FIG. 1 is a block schematic diagram of a transceiver for a U-interface in an ISDN system
- FIG. 2 is a block schematic diagram of a timing recovery circuit of the receiver portion of the transceiver of FIG. 1;
- FIG. 3 is a block schematic diagram of a timing estimator of the timing recovery circuit of FIG. 2;
- FIG. 4 is a block schematic diagram of the remaining parts which, with the timing estimator, form the timing recovery circuit shown in FIG. 2;
- FIG. 5 corresponds to FIG. 4, but shows the parts of a second embodiment of timing recovery circuit
- FIG. 6 shows a typical impulse response for the subscriber loop
- FIG. 7 is a flowchart depicting the operation of the embodiment of FIG. 5 embodied using a digital signal processor with some programmability.
- FIG. 1 which illustrates a U-interface transceiver comprising a transmitter and receiver
- the components encircled by broken lines namely the echo canceller, decision feedback equalizer, adaptive reference circuit (ARC), and timing recovery circuit are embodied in a digital signal processor.
- Digital data for transmission at 160 kb/s is applied to a scrambler 100 which encodes the data into a pseudo-random bit stream which is formatted by framer 102 into frames of 240 bits or 120 bauds, in accordance with specification T1D1.
- the framer 102 also includes a 9-baud signalling word in each frame of data.
- the framed and scrambled signal is applied to 2B1Q encoder 104 where it is converted to a parallel format by a serial-to-parallel converter, which produces dibits in the combinations 00, 01, 10, 11.
- Dibit-to-symbol mapping produces the four corresponding levels -3, -1, +3 and +1.
- Digital-to-analogue converter 106 converts the levels +1, +3, -1, -3 to corresponding voltage levels for application to transmit filter 108.
- the digital-to-analogue converter 106 needs to be at least 3 bits capacity.
- Digital-to-analogue converter 106 converts the binary two's complement representation of the signal on line 148 into a voltage level for application to channel interface 110 for transmission via the hybrid 112 onto the tip and ring of the subscriber loop 114.
- the channel interface 110 comprises a power driver to drive the transmit port of the hybrid 112.
- the transmit filter 108 takes the high frequencies out of the pulses to avoid crosstalk and EMI (electromagnetic interference) effects during transmission.
- the incoming signals from the subscriber loop 114 leave the receive port of the hybrid 112 and are processed by a corresponding 2B1Q receiver employing baud rate sampling and timing recover.
- the receiver comprises a channel interface 116 which includes an anti-aliasing filter to remove high frequencies.
- the filtered signal from the channel interface 116 is applied to a sigma-delta modulator 118 which oversamples the received signal effectively performing analogue-to-digital conversion of the signal.
- the output of the sigma-delta modulator 118 is supplied to a decimator 120 which, with the anti-aliasing filter 116, performs the same functions generally as a low pass filter, sampler, and analogue-to-digital converter.
- the sigma-delta modulator 118 employs an oversampled converter which runs at about 10M hz and hence oversamples the signal by a very large ratio.
- the sampling phase of decimator 120 is adjustable by means of the recovered Baud Rate Clock applied to it on (broken) line 122 from a timing recovery circuit 124. This decimator 120 runs at 10M Hz, so the sampling instant can be moved in 1/10M Hz steps in response to the Recovery Baud Rate Clock, by simply taking a different sample out i.e. by just stepping the clock signal backwards or forwards by one unit of the period of the 10M Hz clock as in a digital phase-locked loop.
- the digitized samples of the received analogue signal, from the output of decimator 120, are filtered by high pass receiver filter 126, which serves as a feed-forward equalizer and enhances high frequencies.
- a typical impulse response at the output of receiver filter 126 is shown in FIG. 6, the main pulse being identified by the reference numeral 600 and the precursor undershoot by the reference numeral 602.
- the steepness of the pulse front, identified as 604 will be increased.
- the amplitude of precursor 602 will be increased and the zero crossing 606 between the precursor and the main pulse will be delayed to occur closer to the peak of the main pulse 600. Consequently, the sampling position, referenced 608, nominally set at one baud after the zero crossing, will also recede closer to the peak of the pulse.
- the "main cursor” is the pulse height at the sampling position 608 and the "precursor” is the first precursor pulse height .Iadd.one baud earlier .Iaddend.at sampling position 610.
- a second precursor would correspond to pulse height .Iadd.one baud earlier still, .Iaddend.at sampling position 612.
- .Iadd.Precursor height 610' represents the position of the first precursor if the sampling instant were retarded to occur after the peak. .Iaddend.
- the precursor is not usually present as the signal leaves the subscriber loop 114 but rather is introduced by the receiver filter 126.
- the precursor 602 is necessary, or at least desirable, to improve the detection of the zero crossing point. When the precursor is absent, the resulting flat portion does not readily facilitate the detection of amplitude variations in the vicinity of the zero crossing.
- correction signals from an echo canceller 128 and a decision feedback equalizer 130 are subtracted from the filtered sample by subtractors 132 and 134, respectively, resulting in an equalized version x n of the far-end signal at the input of adaptive threshold slicer 136.
- the adaptive threshold slicer 136 allocates the individual samples of the received signal to one of the four levels specified for the 2B1Q signal to constitute the recovered far-end symbol a n .
- the thresholds are adapted in response to an adaptive reference signal ARC provided by an ARC (adaptive reference control) circuit 138.
- This circuit estimates the main cursor, i.e. the pulse height at the sampling position and is adapted in the same manner as a decision feedback equalizer tap. It serves basically to provide normalization in various parts of the receiver for loop loss, a function analogous to that of an automatic gain control circuit.
- a multiplier 158 multiplies the recovered far-end signal a n by the adaptive reference signal ARC. The result is subtracted, by means of subtractor 160, from the equalized far-end signal x n to give an adaptation error signal e n which is applied not only to the adaptive reference circuit 138, but also to the echo canceller 128 and the decision feedback equalizer 130.
- the recovered far-end signal a n from the output of adaptive threshold slicer 136 is applied to a 2B1Q decoder 140 which operates in the inverse way to the 2B1Q encoder 104.
- the decoded signal is segregated into its components by a deframer 142 which breaks down the framing. Finally the data is descrambled by descrambler 144.
- Echo canceller 128 generates a replica of the transmitted pulse wave form and subtracts it from the received pulses.
- This echo canceller 128 comprises a shift register 146 which has its input connected to line 148 (the output of encoder 104) and has three outputs, one connected to echo canceller 150, a second connected to an IIR-EC (infinite impulse response) filter 152 and the third connected to a memory echo canceller 154.
- the outputs of the three echo cancellers 150, 152 and 154, respectively, are summed by summing means 156 and subtracted from the filtered sample by subtractor 132.
- Intersymbol interference is corrected by means of the decision feedback equalizer 130 which is supplied by a shift register 158 having an input connected to the output of adaptive threshold slicer 136.
- the output of transversal filter digital feedback equalizer 130 is applied to the negative input of subtractor means 134 for subtraction from the recovered signal.
- timing recovery means 124 which has one input connected to the input of adaptive threshold slicer 136 to receive equalized far-end signal x n , and a second input connected to the output of adaptive threshold slicer 136 to receive recovered far-end signal a n .
- the timing recovery means 124 also receives the adaptation reference signal .[.E n .].
- ARC from the ARC circuit 138 and produces the Baud Rate Clock which, as previously mentioned, is applied to decimator 120 (via the broken line) and controls the sampling instant at which decimator 120 samples the received signal.
- FIG. 2 shows the main stages of the timing recovery circuit 124 in block diagram form.
- the two signals x n and a n are supplied to a timing estimator 202 (to be described in detail later) which generates the timing estimate z n in accordance with the expression:
- the timing estimator 202 generates an estimate every time a new sample is obtained.
- the output of the timing estimator 202, the timing estimate z n is a measure of the sampling phase error--the deviation from the correct sampling phase --and is used initially to acquire correct timing and thereafter to track the changes in the phase and/or frequency of the received signal.
- the output signal z n of the timing estimator 202 is supplied to a loop filter 204 which is controlled by the frame pulse TR.FRM and generates a filtered version Z n of the timing estimate.
- the design of the loop filter 204 can be of varying complexity to meet the desired phase-locked loop (PLL) performance objectives.
- the estimate z n used directly to control the phase once every baud.
- the output z n of the timing estimator 202 would be fed directly to the phase quantizer 206.
- the loop filter will usually be used in ISDN-U applications due to requirements of network terminators with regard to echo degradation caused by phase jump hidden behind the sync word and of line terminators with regard to permanent changes in the echo path requiring the echo canceller to converge again. Generally the loop filter will give lower jitter.
- the loop filter 204 performs averaging (integrate and dump) of the timing estimate z n over a frame of baud rate samples.
- the sampling phase is adjusted once every frame in dependence upon the new value of loop filter output Z n .
- this frame is 120 bauds long and corresponds to the .[.T1D1 .Iadd.T1E1 .Iaddend.frame interval.
- the phase jumps are timed to occur at the start of the frame synchronization word.
- the filtered timing estimate Z n is supplied to a phase quantizer 206.
- the basic function of the phase quantizer 206 is to interpret the output of the loop filter 204 and make a decision as to whether to "advance", "retard", or "hold” the recovered Baud Rate clock.
- the phase quantizer 206 corresponds to a 3-level slicer with decision regions specified by two thresholds which are adaptable in proportion to the output of the adaptive reference circuit 138. For example the threshold may be equal to 2 3 . ARC. The region between the positive threshold and the negative threshold is referred to as the "hold” or "dead zone".
- phase quantizer 206 is followed by a digital-to-analogue converter 208 which generates a corresponding voltage to control an analog voltage controlled oscillator 210.
- the output of the voltage controlled oscillator 210 is the recovered "Baud Rate Clock" signal which is applied to the decimator 124 (FIG. 1).
- the digital-to-analogue converter 208 could be omitted and the analog voltage controlled oscillator replaced by a digital voltage controlled oscillator, for example a programmable counter/frequency divider. Such an arrangement is shown in FIGS. 4 and 5.
- FIG. 3 shows the timing estimator 202 in more detail.
- the signals x n and a n are stored in two memory locations 302 and 304, respectively, which are updated every baud by the baud rate clock signal and used as the "previous" baud values x n-1 and a n-1 in the following baud period.
- the data symbols are repeated as 2-bit values but, to simplify the drawing, only the input s to memory location 304 and multiplier 306 and 308 show them separately--for symbol a n .
- One bit is for sign information (s) and the other bit (m) is for magnitude information, to represent one of the four values -3, -1, +1, or +3.
- the "present" symbol x n and the "previous” symbol x n-1 from the output of memory location 302 are then multiplied by the "previous" and "present” slicer outputs a n-1 and a n , respectively, by means of multipliers 306 and 308, respectively.
- the magnitude bit (m) is multiplied without inversion.
- the sum from adder 312 is applied to a multiplexer 314.
- a .[.one's.]. .Iadd.two's .Iaddend.complement device 316 derives the negatived value of the output of the adder 312 and applies it to a second input of the multiplexer 314.
- Switching of the multiplexer 314 is controlled by the magnitude bit m of the recovered far-end symbol a n from the input to the timing estimator 202.
- the output of the multiplexer .[.312.].
- .Iadd.314 .Iaddend. is a value z n , within a scale factor which can be absorbed by the threshold of the phase quantizer 206 (FIG. 2). It should be noted that the required multiplication is implemented efficiently, needing only an adder, a shifter and a .[.one's.]. .Iadd.two's .Iaddend.complementer, with suitable mapping of the 2-bit values to perform a specific combination of these functions.
- the specific feature of the impulse response that is central to this timing recovery arrangement is the distance between the peak of the main pulse 600 and the zero crossing 606 between the presursor 602 and the main pulse 600. Nominally this is approximatley one baud, as can be seen from FIG. 6. This condition can be expressed more exactly by defining a timing function. If we denote the impulse response, which includes the receive filter, by h(t), and the sampling phase by t, then the timing function f(t) is defined as
- h(t) and h(t-T) denote the main pulse and precursor, respectively, and r is the ratio between the main pulse sample and the precursor pulse sample.
- sampling phase t o is defined such that
- correct timing will be achieved by adjusting the sampling instant until the precursor sample value is zero.
- the timing estimator 202 computes an estimate of the timing function, referred to as the timing estimate z n , according to the following expresion;
- An estimate of h(t) is readily provided by the adaptive reference tap ARC. With the combination of these two estimates (z n and ARC) an estimate y n f(t) can be formed as:
- An alternative implementation would be to simply compute z n at every baud and carry out the averaging over the full frame, and introduce ARC in the final term only at the end of the frame, prior to phase quantization. This can be done by adding a scaled version of ARC, including r in it, adding it to the averaged z n , and feeding the result to the phase quantizer.
- An advantage of embodiments of the invention is that they are relatively easy to implement because manipulation of the symbols 1 and 3 requires merely the shifting and adding of the binary values.
- FIG. 4 shows the remainder of the timing recovery circuit 124, in the loop filter the signal z n , from the timing estimator 202 (FIGS. 2 and 3) is summed with an accumulated value from an accumulator 408 which is periodically reset by the frame signal TR-FRM which is set to one during one baud of the frame and is otherwise equal to zero.
- TR-FRM is generated by a frame search circuit which tries to find the location of the farme synchronization word.
- the output of the summer 402 is applied to the accumulator 408 by way of a saturation device 404 which serves to detect overflow or underflow of the incoming signal and correct for it without wraparound.
- This saturation device 404 could be omitted if the hardware were designed to have a capacity equal to the maximum number of bits anticipated in the signal.
- the output of the saturation device 404 is also applied to a slicer 410.
- ADVANCE and RETARD are applied to a multiplexer 412 which is switched by the transmitter frame signal TR.FRM to select between the "hold" condition and the output of the slicer 410.
- the output of multiplexer 412 is applied to divider 414 which takes a nominal high frequency master clock, f o , for example 10.24M Hz in the case of ISDN-U, and divides it by N, N-1, N+1.
- the ADVANCE and RETARD signals adjust the divider 414 which cause the shift in phase of the recovered Baud Rate Clock, and hence adjusts the sampling instant.
- FIG. 5 shows an alternative and preferred embodiment of the loop filter/phase quantizer part of the circuit
- the output z n of the timing estimator 202 (FIGS. 2 and 3) is applied to a summer 502.
- a saturation device 504 detects overflow/underflow and prevents wrap-around as in the embodiment of FIG. 4.
- the output of the saturation device 504 is applied to an accumulator 506.
- This part of the circuit corresponds generally to the circuit in FIG. 4.
- the CLR input of the accumulator 506 is controlled by an AND gate 508 which has one input controlled by the frame pulse TR-FRM and the other connected to the output of a slicer 510. This slicer 510 differs from the slicer 410 used in FIG.
- the accumulator 506 Only when the transmit frame pulse TR-FRM occurs when the slicer 510 is calling for advancing or a retarding of the sampling phase will the accumulator 506 be reset. In the absence of such a call, the accumulator 506 will continue to average the signal z n and the slicer 510 will be in its dead zone or HOLD condition.
- This dead zone corresponds to a precursor sample in the vicinity of point 606 in FIG. 6 that is approximately zero. As the frequency starts to drift and the estimated precursor value starts to increase, it will remain in the dead zone for a certain period of time. Eventually its amplitude will become great enough to exceed one of the thresholds which will then trigger a call to either advance or retard the phase.
- a benefit of this dead zone is a reduction in jitter of the sampling instant.
- the output of the slicer 510 is applied by way of a multiplexer 512 to a digital voltage controlled oscillator or programmable counter 514 which delivers the baud rate clock as its output.
- Multiplexer 512 and programmable counter 514 correspond to the multiplexer 412 and programmable counter 414 shown in FIG. 4 and are connected and operate in the same way.
- the three-level slicer 510 has a further input for the adaptive reference control signal (ARC) from adaptive reference circuit 138 (FIG. 1).
- the ARC signal is used to determine the threshold levels of the slicer.
- the ARC circuit 138 is designed to accommodate variations in the data signals due to different loop configurations (length, bridge taps, gauge, etc.) and adjust the thresholds to take account of the differences in amplitude i.e., a relatively small signal from a long loop would be the equivalent of a much larger signal from a short loop because of the variations in attenuation.
- the ARC signal is also used to adjust the thresholds in the slicer of the timing recovery circuit 124 (FIG. 1).
- An advantage of using the ARC signal is that it avoids having to put a gain controller before the adaptive threshold slicer 136 (FIG. 1). It has been found during experiments that a gain control in this position may cause instability due to the gain converging to zero and the DFE/slicer combination oscillating in isolation .[...]. .Iadd., at .Iaddend.least with 2B1Q signals.
- the use of the ARC signal to control the slicer thresholds in the timing recovery circuit 124 proved to be a good solution to the problem of stability.
- timing recovery circuit including timing estimator, loop filter and phase quantizer
- firmware specifically a programmable digital signal processor. Operation of such a digital signal processor implementation is illustrated by the flowchart shown in FIG. 7, which relates specifically to the U-interface modified as illustrated in FIG. 5.
- step 702 corresponds to completion of the slicing step and in step 704 the programmable counter 514 (FIG. 5) has its phase adjusted, i.e. is instructed to perform a phase jump.
- the register containing the value JUMP has HOLD written into it, in effect the function of switching the multiplexer 512 to the HOLD position.
- the frequency divider 514 uses this register to obtain the ratio by which the master clock has to be divided.
- step 706 computation of the timing estimate z n takes place. .[.computation.]. .Iadd.Computation .Iaddend.of the timing .[.estimator.]. .Iadd.estimate .Iaddend.z n is performed in the timing estimator 202 and the individual values of z n for each baud are accumulated over a complete frame as indicated by step 708 to give .[.Z(n).]. .Iadd.Z n .Iaddend.,
- decision step 710 determines whether or not the frame pulse TR.FRM is asserted If the frame pulse is not asserted, loop 712 takes the process back to the beginning and another baud is processed. If it is, decision step 714 determines whether or not .[.Z(n).]. .Iadd.Z n .Iaddend.is greater than zero. If .[.Z(n).]. .Iadd.Z n .Iaddend.is greater than zero, path 716 and process step 718 writes ADVANCE into the JUMP register. In the subsequent process step 722, a value W is computed as the magnitude of the function .[.Z(n).].
- step 724 determines whether .[.w.]. .Iadd.W .Iaddend.is less than zero or not, and in so doing effectively compares the magnitude of the timing estimate with the threshold, as adapted by the ARC signal. If W is less than the threshold, i.e. within the dead zone, decision step 724 causes the HOLD signal to be written into the JUMP register, step 728.
- step 726 clears the accumulator for the next frame to be accumulated with zero initial condition (no memory). This is indicated by writing zero into the .[.Z(n).]. .Iadd.Z n .Iaddend.register.
- HOLD refers to the setting for the next baud
- JUMP refers to the setting for the current baud.
- the programmable counter is in fact triggered every baud and will either shift phase or not depending on whether JUMP or HOLD has been programmed.
- steps 718 and 720 determine the direction of any phase shift depending on the value of .[.Z(n).]. .Iadd.Z n .Iaddend.i.e. to advance or retard the programmable counter.
- Step 722 determines whether or not the value Zn is still within the dead zone. If it is, no phase shift will be performed, and decision step 724 will cause the process step 728 to maintain HOLD in the jump register.
Abstract
f(t)=(1/r)h(t)-h(t-T)
z.sub.n =(-1).sup.m.(a.sub.n-1x.sub.n -a.sub.n x.sub.n-1)
Description
f(t)=(1/r)h(t)-h(t-T)
z.sub.n =(-1).sup.m.(a.sub.n-1 x.sub.n -a.sub.n x.sub.n-1)
f(t)=-h(t-T)
z.sub.n =(-.Badd.1).sup.m.(a.sub.n-1 x.sub.n -a.sub.n x.sub.n-1)
f(t)=(1/r)h(t)-h(t-T)
f(t.sub.o)=0
f(t)=-h(t-T)
Z.sub.n =(-1).sup.m (a.sub.n-1 x.sub.n -a.sub.n x.sub.n-1)
.[.y.sub.n =(ARC/r)-Zn).]. .Iadd.y.sub.n =(ARC/r)+z.sub.n .Iaddend.
.[.Z(n)=z(n)+Z(n-1).]. .Iadd.Z.sub.n =z.sub.n +Z.sub.n-1 .Iaddend.
Claims (22)
f(t)=(1/r)h(t)-h(t-T)
z.sub.n =(-1).sup.m.(a.sub.n-1 x.sub.n -a.sub.n x.sub.n-1)
f(t)=(1/r)h(t)-h(t-T)
z.sub.n =(-1).sup.m.(a.sub.n-1 x.sub.n -a.sub.n x.sub.n-1)
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US07/261,134 US4896334A (en) | 1988-10-24 | 1988-10-24 | Method and apparatus for timing recovery |
US07/666,728 USRE34206E (en) | 1988-10-24 | 1991-03-08 | Method and apparatus for timing recovery |
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US5343502A (en) * | 1991-11-29 | 1994-08-30 | Nec Corporation | Symbol timing detecting circuit |
WO1997003507A1 (en) * | 1995-07-13 | 1997-01-30 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and apparatus for timing recovery |
US20010017902A1 (en) * | 2000-01-31 | 2001-08-30 | Taku Yamagata | Timing error detection circuit, demodulation circuit and methods thereof |
US6327666B1 (en) * | 1998-01-27 | 2001-12-04 | Globespan, Inc. | System and method for external timing using a complex rotator |
US6414990B1 (en) * | 1998-09-29 | 2002-07-02 | Conexant Systems, Inc. | Timing recovery for a high speed digital data communication system based on adaptive equalizer impulse response characteristics |
US20030016734A1 (en) * | 2001-04-30 | 2003-01-23 | Blake Roy B. | Jitter control processor and a transceiver employing the same |
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US7068731B1 (en) * | 2000-10-24 | 2006-06-27 | Agere Systems, Inc. | Apparatus and method for multi-channel receiver |
US20030016734A1 (en) * | 2001-04-30 | 2003-01-23 | Blake Roy B. | Jitter control processor and a transceiver employing the same |
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US20060029174A1 (en) * | 2001-04-30 | 2006-02-09 | Agere Systems Incorporated | Transceiver having a jitter control processor with a receiver stage and a method of operation thereof |
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US20080240318A1 (en) * | 2007-03-29 | 2008-10-02 | Ehud Shoor | Recovering precoded data using a Mueller-Muller recovery mechanism |
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