WO1998001961A2 - Frequency domain signal reconstruction in sampled digital communications systems - Google Patents
Frequency domain signal reconstruction in sampled digital communications systems Download PDFInfo
- Publication number
- WO1998001961A2 WO1998001961A2 PCT/SE1997/001248 SE9701248W WO9801961A2 WO 1998001961 A2 WO1998001961 A2 WO 1998001961A2 SE 9701248 W SE9701248 W SE 9701248W WO 9801961 A2 WO9801961 A2 WO 9801961A2
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- signal
- spectral
- echo
- sampling
- filter
- Prior art date
Links
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B3/00—Line transmission systems
- H04B3/02—Details
- H04B3/20—Reducing echo effects or singing; Opening or closing transmitting path; Conditioning for transmission in one direction or the other
- H04B3/23—Reducing echo effects or singing; Opening or closing transmitting path; Conditioning for transmission in one direction or the other using a replica of transmitted signal in the time domain, e.g. echo cancellers
Definitions
- the present invention relates to signal reconstruction in sampled digital communication systems, and in one particular o example application, to a method and apparatus for frequency domain adaptive echo cancellation that compensates in the frequency domain for sampling phase adjustments made in the time domain as a result of frequency drift, phase jitter, and changes in a communications channel.
- digital data to be transmitted by a "near end" transceiver modulates the amplitude of a train of identically shaped pulses.
- the modulated pulses are then transmitted over the communications channel.
- Some portion of the transmitted signal is reflected back on the communications loop and mixes in with the "far end" signal received by that near end transceiver.
- the transceiver uses an echo canceller to remove this reflected signal—commonly referred to as "echo.” Achieving high accuracy echo cancellation is difficult for a number of reasons.
- the echo signal cannot be assumed to be exactly the same as the corresponding originally transmitted signal.
- the communications channel has a transfer function defined by its impulse response which modifies signals (typically pulses) traveling over that communications channel. That transfer function also modifies echos.
- echo cancellers use digital transversal filters, such as finite impulse response (FIR) filters, to model the communications channel transfer function and process the transmitted signal in accordance with that channel model.
- FIR finite impulse response
- Digital filters are generally implemented using a tap delay line where delayed versions of the transmitted signal are "tapped” at each delay, “weighted” or multiplied by corresponding filter coefficients, and summed. These coefficients are the filter model of the communications channel. To accommodate changes in the communications channel model, such digital filters typically use some type of recursive algorithm to adapt the coefficients to those changes.
- One of the more commonly used recursive algorithms is the Widrow-Hoff, gradient-based, least mean squared (LMS) algorithm described, for example, in B. Woodrow & S.D. Stearns, A daptive Signal Processing, Prentice-Hall, Inc., Englewood Cliffs, New Jersey 1985.
- a third complicating factor already mentioned is the extremely low bit error rate required in many communication applications.
- the 10 "7 bit error rate for ISDN interfaces to subscriber loops does not leave much tolerance, especially when the channel and/or a transceiver parameters change. It's one thing to deliver this low BER most of the time; it's a more challenging task to maintain it all the time through such changes and adjustments.
- sampling clock of a receiving transceiver must be continually adjusted to account for a number of factors to ensure accurate, synchronized operation including: (1) setting the instant when received signals are sampled at the optimal or near optimal sampling point, (2) tracking and compensating for frequency drift between the timing oscillators located in both the receiving transceiver and in the transmitting transceiver for a particular communication; and (3) tracking and compensating for changes in the transmission media, i.e., the 5 communications channel.
- a great challenge in this technological arena is that of maintaining this incredibly low level of noise BER when the sampling phase of the receiving transceiver is changed for any of the above reasons.
- a problem the present invention addresses is how to o compensate an echo canceller to ensure that the echo received at the moment of transceiver clock phase adjustment is precisely cancelled to avoid a momentary increase of uncancelled echo and therefore bit error rate. Otherwise, that phase adjustment introduces a significant risk of erroneous symbol detection because of the momentary 5 increase of imperfectly cancelled echo.
- Kanemasa et al. "Compensation for the Residual Echo Increase due 5 to a Timing Clock Phase Jump," Proc. IEEE Globecom '87, pp. 1971-1975; S.A. Cox, "Clock Sensitivity Reduction in Echo Cancellers,” Elect. Lett., vol. 21, no. 14, July 1985, pp. 585-586; O.E. Agazzi et al., “Two-phase Decimation and Jitter Compensation in Full-Duplex Data Transceivers,” Proc. IEEE Int. Symp. Circuit Syst., San Diego, CA, May 10-13, 1992, pp. 1717-1720.
- predicted values of the echo canceller adaptive filter coefficients are calculated just before the phase adjustment occurs.
- the adaptive filter coefficients are set to the predicted values.
- approximations in the time domain are complicated to implement in real life applications.
- approximations are just that - approximations.
- An approximate model of an echo typically does not cancel an actually received echo within the very low BER requirements described above, especially when sampling phase adjustments or other changes occur. The other major drawback with these approaches is that the Nyquist requirement is often not satisfied.
- the typical sampling rate real worked digital communication systems are set at or near the minimum possible rate, i.e., at the symbol transmission rate, since complexity and cost increase with the sampling rate. This means that the received signal often is not sampled fast enough so that it can not be perfectly reconstructed. As a result, higher frequency signal components that exceed half of the sampling rate in the received signal are aliased to low frequency components directly in the baseband frequency of the signal of interest.
- Figs. 1(A) and 1(B) illustrate this aliasing effect which is sometimes referred to as foldover distortion.
- f s is the sampling frequency and BW is the bandwidth of the input signal
- f s is greater than 2B W
- the resulting spectrum of a pulse amplitude modulation (PAM) pulse train can be recovered by simply low pass filtering the separated PAM signal spectrum with an output filter.
- PAM pulse amplitude modulation
- output distortion occurs because the frequency spectrum centered about the sampling frequency overlaps the original spectrum and cannot be separated from the original spectrum by filtering as shown in Fig. 1(A).
- Fig. 1(B) illustrates an aliasing process occurring in speech if a 5.5 kHz signal is sampled at an 8 kHz rate. The sampled values are identical to those obtained from a 2.5 kHz input signal. After the sampled signal passes through a 4 kHz output filter, a 2.5 kHz signal arises that did not come from the source.
- An object of the present invention is to precisely reconstruct a sampled signal rather than approximate it, even in situations where the phase of the sampling signal is adjusted.
- echo cancellation it is an object of the present invention to accurately model in the frequency domain the transfer function of an echo channel impulse response.
- the present invention seeks to overcome the above described limitations and meet these and other objects.
- the present invention compensates in the frequency domain a transfer function of the channel impulse response for a sampling phase adjustment that occurs in time.
- that transfer function is an echo transfer function of the echo channel impulse response.
- the present invention accounts for
- Aliased components present in the echo impulse response which is particularly important for maintaining accurate echo cancellation when sampling phase changes. Aliased components are identified and compensated for in the frequency domain by treating each spectral coefficient of the echo transfer function as the sum of a o baseband component and an aliased component.
- each transceiver samples a signal received over the communication channel in accordance with a sampling signal.
- the present invention may be 5 advantageously employed in an echo canceller in each transceiver and typically is implemented as a digital filter.
- a signal transmitted from the transceiver is input to the digital filter and delayed for a plurality of delay stages to generate a series of input signals. Those input signals are transformed into the frequency domain to create a series 0 of input spectral components.
- Each spectral component is then multiplied by a corresponding spectral filter coefficient to generate a corresponding product.
- the products are then summed to generate a filter output signal that corresponds to the expected echo.
- the filter output signal is subtracted from the received signal to cancel echo 5 leaving some error signal that represents a remaining uncancelled echo in addition to a "far end" signal and noise.
- the spectral filter coefficients recursively are adapted to minimize that error.
- new values of the spectral filter coefficients are predicted in the frequency domain to accurately compensate for the sampling signal adjustment. Those predicted values model the echo transfer function after the 5 phase of the sampling signal is adjusted. More specifically, the spectral filter coefficients are corrected in the frequency domain by an amount corresponding to the amount of time the sampling signal is adjusted.
- Each spectral filter coefficient is analyzed as having at least o two spectral components including a baseband frequency component corresponding to the echo and an aliased frequency component.
- each spectral filter coefficient is predicted using two previously obtained values of the spectral filter coefficients.
- the baseband and aliased spectral 5 components for each spectral filter coefficient are calculated based on the two previously obtained values of the spectral filter coefficient.
- the present invention may be advantageously applied to echo cancellers, the present invention may also be used in any digital communication system where transceivers communicate over a digital communications channel.
- a signal received over the communications channel is sampled in accordance with a timing/sampling signal.
- a 5 transfer function is developed corresponding to the impulse response of the communications channel. That transfer function is then compensated in the frequency domain for a phase adjustment in the sampling signal that occurs in the time domain. If the transfer function is a Fourier transform, the spectral coefficients of the transfer function in the frequency domain are corrected by an amount corresponding to the amount of time the timing signal is adjusted.
- these spectral coefficients of the transfer function are analyzed as each having plural components such as a baseband frequency component and an aliased frequency component.
- a significant advantage of the approach of the present o invention is that in addition to accurately compensating for sampling phase adjustments, traditional sampling constraints are considerably relaxed. In other words, lower sampling frequencies can be used because an adaptive digital filter in accordance with the present invention accounts for aliased frequency components generated as a 5 result of the sampling frequency being less than twice as high as the highest frequency in the sampled signal. Reduced sampling rates translate directly into reduced monetary and signal processing costs. Because the present invention reconstructs a received signal from signal samples taking into account aliased frequency components, the 0 fact that a signal is no longer sampled at greater than twice the highest frequency component of received signal it does not undermine the accuracy of the reconstructed signal.
- FIGS. 1(A) and 1(B) are graphs illustrating principles of the Nyquist sampling theorem and foldover distortion/aliasing resulting from undersampling;
- FIG. 2 is a function block diagram of an example of a digital signal
- FIG. 3 is a function block diagram of a U-type transceiver that may be used in an ISDN communication system
- FIG. 4 is a function block type diagram showing an example application of the present invention in an echo canceller
- FIG. 5 is a graph illustrating increased signal-to-noise ratio coincident with phase adjustment
- FIGS. 6 and 7 are graphs illustrating the variation of the phase and magnitude, respectively, of the echo-path transfer function after a change of sampling instance for the cases of no compensation (solid line), phase compensation according to the frequency shift theorem (dashed line), and phase forcibly set to the correct value (dotted line);
- FIG. 8 is a function block type diagram showing further illustrative details of the phase comparator 37 shown in FIGS. 3 and 4; and FIG. 9 is a graph illustrating compensation of a phase adjustment in accordance with one simulated example implementation of the present invention.
- Fig. 2 shows an overall block diagram of one data communications environment, i.e., the integrated services digital network (ISDN) 10, to which the present invention may be applied.
- a building 12 may, for example, include telephone subscribers (16 and 18) and data subscribers (personal computer 14) linked over a local area network to a U-transceiver 20 (via an S-transceiver not shown).
- the U-transceiver 20 is connected by a 2-wire "subscriber loop" transmission line 22 to another U-transceiver 26 at telephone switching and services network 24 which provides digital switching and other messaging/call processing services.
- One important function of the U-transceivers 20 and 26 is the accurate and stable recovery of timing information from an incoming digital signal sampled at the baud rate so that symbol synchronization is achieved between the two transceivers.
- the present invention is described hereafter in the context of such an ISDN network that uses U-transceivers and 2B1Q line codes.
- the 2-binary, 1-quaternary (2B1Q) line code which employs a four level, pulse amplitude modulation (PAM), non-redundant code.
- PAM pulse amplitude modulation
- Each pair of binary bits of information to be transmitted is converted to a quaternary symbol (-3, -1, +1 and +3). For example, "00” is coded to a -3, "01” is coded to a -1 , "10” is coded to a +3, and "11” is coded to a +1.
- the present invention may be applied to other types of data communication networks and other types of line codes/symbols.
- FIG. 3 illustrates a U-interface transceiver 30 comprising a transmitter and receiver.
- a U-interface transceiver for use in conjunction with an ISDN digital communications network
- the present invention of course could be applied to other high speed data environments such as high bit rate digital subscriber lines (HDSL), etc.
- Binary data for transmission is applied to a scrambler 31 which encodes the data into pseudo-random bit stream formatted by a framer 32 into frames of 240 bits or 120 (2B1Q) symbols in accordance with ISDN specification T1D1.
- the framer inserts a 9-symbol signaling word used for frame synchronization in each frame of data so that 111 symbols are left for the scrambled data.
- the framed and scrambled binary signal is applied to a 2B1Q encoder where it is converted into a parallel format by a serial-to-parallel converter which produces digits in the combinations of 00, 01, 10, and 1 1.
- Digit-to-symbol mapping in the encoder produces the four corresponding symbol levels -1, +1, -3, and +3.
- Digital-to-analog converter (DAC) 38 converts the encoded signal to a voltage level suitable for application to the hybrid 44 which is connected to subscriber loop 45.
- the transmit filter 40 removes high frequencies from the digital pulses output by the digital-to-analog converter 38 to reduce cross-talk and electromagnetic interference that occur during transmission over the subscriber loop 45.
- Incoming signals from the subscriber loop 45 are transformed in hybrid 44 and processed by the receiver which, at a general level, synchronizes its receiver clock with the transmitter clock (not shown) so that the received signal can be sampled at the symbol/baud transmission rate, i.e., the rate at which symbols were transmitted at the far end of the loop.
- the received signal is converted into a digital format using analog-to-digital converter (ADC) 48.
- ADC analog-to-digital converter
- the sampling rate of the analog-to-digital converter 48 which is tied to the receiver clock, is adjusted using a control signal from timing recovery circuit 70.
- A-to-D converter 48 may sample at a sampling rate of 80 kHz even though it has a built-in higher frequency clock permitting phase adjustment in smaller intervals, e.g., a period of 15.36 MHz.
- a phase compensator 96 adjusts the phase of the timing recovery clock to account for frequency drift, phase jitter, and changes in a communications channel by stepping the clock signal forward or backward usually by a fixed time increment ⁇ .
- the digitized samples are filtered by a receive filter 50, the output of which is provided to summing block 52.
- Receive filter 50 increases the signal-to-noise ratio of the received signal by suppressing the "tail" of the received signal.
- the other input to summer 52 is an output from echo canceller 36.
- echo canceller 36 As described above, pulses transmitted onto subscriber loop 45 result in echo on the receiver side of the hybrid 44 due to impedance mismatch. Unfortunately, it is difficult to separate the echoes of these transmitted pulses (using for example a filter) from the pulses being received from subscriber loop 45. Accordingly, echo canceller 36 generates a replica of the transmitted pulse waveform and subtracts it at summer 52 from the received pulses. The echo canceller is adjusted based upon an error signal between the received symbol and the detected symbol output at summer 66.
- Such an adaptive echo canceller is typically realized as a traversal, finite impulse response (FIR) filter whose impulse response is adapted to the impulse response of the echo path.
- FIR finite impulse response
- the error is used to adjust the filter coefficients to "converge" the filter's response to the impulse response model of the communications channel.
- the direction (forward or backward in time) and magnitude ⁇ of that adjustment are provided to the echo canceller 36 so that the impulse response of the echo path modeled by the filter coefficients are accurately adjusted to accommodate that phase change as is described in detail below.
- the echo cancelled signal is processed by adaptive gain controller 54 to adjust the amplitude to levels specified for the symbols in the 2B1Q line code.
- the gain applied to the input signal is adapted by comparison of the input signal to fixed amplitude thresholds and increasing or decreasing the gain as necessary to achieve the amplitudes standardized for symbols -3, -1, 5 +l, and +3.
- the output of the adaptive gain controller is provided to a feedforward filter 56 which in physical terms enhances high frequencies of pulses in the received signal which translates into an increase in the steepness or slope of the rising edge of the digital pulse.
- known digital communications systems o refer to this feedforward filter 56 as a precursor filter because its purpose is to suppress the precursor portion of received pulses.
- the present invention analyzes and processes signals in the 0 frequency domain because it is more accurate and precise.
- the discrete sequence of transmitted data from the transmitter portion of the transceiver is defined as an input signal represented by x-,; the filter output signal is represented by y n ; and the received signal made up of the far end signal, echo, and noise is represented by __,.
- An 5 error ⁇ n is generated from the difference between ⁇ and y n with the difference indicating the degree to which the echo channel model modeled by the filter coincides with the actual channel that carries the echo.
- An adaptive Least Mean Squares (LMS) signal processor processes the error and adapts filter coefficients to minimize the mean square error ⁇ n by adjusting the FIR filter coefficients as specified by a filter coefficients vector C n .
- the error ⁇ n at the time instance t n equals
- C n is a vector of the filter coefficients
- ⁇ is a vector of the input sequence
- N depicts the length of the filter, i.e., the number of taps.
- the filter coefficients vector C n is updated at the sampling rate, and on the i-th iteration is:
- ⁇ is a fixed constant which controls the stability and convergence rate of the filter.
- the transform-domain equivalent of the filter output y n can be obtained by an orthogonal transformation, i.e.
- W is the transformation matrix, i.e., W • W is a unitary NxN matrix
- W • X ⁇ and (W j • C are transformed vectors of the input sequence and the filter coefficients, respectively.
- a Discrete Fourier Transform (DFT) is used, i.e., ⁇ W '1 ) - W*, where ( )* depicts a complex conjugate.
- DFT Discrete Fourier Transform
- the DFT algorithm replaces the N coefficients of the time domain filter with — + 1 complex Fourier coefficients in the frequency domain, the other half of transform being conjugate symmetric.
- each Fourier or "spectral" coefficient is the value of the Fourier transform for a single discrete frequency.
- the spectral coefficients vector A ⁇ converges to the transform domain equivalent of the optimum solution in the time-domain. See for example, "Transform Domain LMS Algorithm,” Narayan et al, IEEE Trans., Acoust. Speech, Signal Processing, Vol. ASSP-31, no. 3, June 1983, pp. 609-615.
- a uniform convergence rate may be obtained if the spectral coefficients a n k are updated independently using an individual step size of ⁇ as follows:
- G n,k a n - ⁇ ,k + 1 ⁇ . ⁇ W' X n _ ⁇ (EQ. 8)
- a transform domain adaptive echo canceller 36 as illustrated in Fig. 4 that may be implemented using discrete hardware components, a DSP, an ASIC chip, a programmed microprocessor, or other equivalent signal processor(s).
- the transmitted signal x_ from a "near end" transceiver is delayed through delay elements 80a, 80b, ... , 80N to generate N+l discrete signal samples transformed in Discrete Fourier Transformer 82.
- a discrete Fourier transform DFT is readily computed in real time, and the frequency domain LMS algorithm such as that described above executed by the adaptive LMS signal processor 90 may be more effectively implemented as a running fast Fourier transform (FFT) or frequency sampling filter.
- FFT running fast Fourier transform
- the echo canceller 36 (implemented as an adaptive digital filter) essentially estimates the echo impulse response of the echo path in the time domain. Like any communications channel, that echo path or channel is a function of many variables some of which change such as the transmission line, transformer, balance, network transmit and receive filters, sigma-delta modulator, etc. in wire line systems, and fading and adjacent channel interference in radio systems.
- the adaptive LMS signal processor 90 converges the adaptive filter coefficients to the overall transfer function F( ⁇ ) of the echo communications channel, i.e., the Fourier transform of the echo impulse response.
- a significant advantage of the present invention operating in the frequency domain is that a phase correction to the sampling clock, i.e., a time shift that in practice usually is only approximated in the "time domain,” may be precisely and readily implemented using the"shift theorem" in the frequency domain as set forth below:
- the shift theorem states that time shifting the impulse response by time ⁇ in the time domain corresponds to shifting the phase of the transfer function of the impulse function in the frequency domain.
- Equation (11) is the formula for linear interpolation the time domain. Truncating the power series expansion to only two of its terms means that all of the information contained in the higher terms is lost. Thus, accuracy is necessarily limited.
- the inventor of the present invention recognized that using the shift theorem, changes in the timing phase influence the spectral coefficients in the DFT model of the echo channel transfer function (i.e., the Fourier transform of the echo channel impulse response). Since the direction of the phase correction and the magnitude of the phase increment are known, e.g., from the timing recovery unit 70 in Fig. 3, the frequency shift corresponding to that phase adjustment direction and magnitude can be accurately reflected in the echo channel model.
- the received signal includes the "far end” transmitted signal, noise, and the echo signal from the "near end” transmitted signal reflected back to the near end receiver.
- the far end transmitted signal, noise, and the echo signal are all affected by the characteristics of the communications channel and by intersymbol interference. Accordingly, the signal received by the echo canceller 36 in an ideal case when no "far end” signal or noise are present is represented by
- Fourier transformer 82 are multiplied by adaptive filter coefficients 84a, 84b, ...84n corresponding to a,, 0 , a n>1 , ... , a-, ⁇ . ⁇ .
- Each of the "weighted" spectral components is then summed in summer 86 to generate the filter output signal y n which is the filter's estimate of the echo.
- a difference is obtained between the received signal d n and the filter output y n in combiner 88 to generate a difference or error signal ⁇ n .
- Adaptive LMS signal processor 90 then updates the filter coefficients a ⁇ k in accordance with equation (8) set forth above.
- the timing recovery and phase adjuster circuit generate switching control and enabling signals (TR) which are provided to switches 92 and 94 as well as to recursive phase shift compensator 96.
- the timing recovery circuit 70 and phase adjuster 37 provide the direction and magnitude of phase shift ⁇ v to recursive phase shift compensator 96.
- the recursive phase shift compensator 96 corrects the updated filter coefficients using the shift theorem of equation (9) so that they accurately model the echo transfer function when the phase change occurs.
- a sampling phase shift ⁇ is effected in each filter coefficient as a spectral phase shift ⁇ f> ⁇ .
- the simulated performance of the echo canceller 36 is illustrated for an example case in Fig. 5.
- the example case simulates line configurations specified by ANSI, "Integrated Services Digital Network (ISDN) - Basic Access Interface for Use on Metallic Loops for Application on the Network Side of NT (layer 1 Specification),” ANSI Tl .601-1988, Jan. 9, 1991, and by ETSI, "Transmission and Multiplexing (TM): Integrated Services an Digital Network (ISDN) basic rate access digital transmission system on metallic local line," ETSI Technical Report, ETR 080, July 1993.
- the noise to received far end signal (i.e., the desired signal) ratio shows an extremely low value after the filter converges, e.g., -50 dB. Stated differently, the echo that actually needs to be cancelled an the near end transceiver is cancelled by echo canceller 36 in the normal mode with a very high degree of precision.
- the spectral coefficients of the adaptive filter 36 are not accurately adjusted, and the signal-to-noise ratio deteriorates causing the noise spikes shown in Fig. 4.
- the magnitude of the Fourier transfer function of the echo path impulse response is not constant. Instead, it varies dramatically when the sampling phase is changed.
- Fig. 6 graphs the phase of the echo transfer function after a change of sampling instance for the following three situations: no compensation (shown as a solid line), compensation according the shift theorem as described above (shown as a dashed line), and the correct values (shown as a dotted line).
- Fig. 7 graphs the magnitude of the echo transfer function after a change of sampling instance for the following three situations: no compensation (shown as a solid line), compensation according the shift theorem as described above (shown as a dashed line), and the correct values (shown as a dotted line).
- each adaptive filter coefficient vector A ⁇ (defined previously in EQS. 7 and 8) should be considered as the vector sum of plural translated transforms.
- the filter coefficients include plural o spectral components as represented mathematically below.
- each filter spectral coefficient a ⁇ k may be regarded as the superposition of two complex spectral components: a baseband component b v k (corresponding to the first term in EQ. 14) and an aliased or folded component b v ⁇ _ k from the band ⁇ 2 ⁇ s (corresponding to the second term in EQ. 14):
- v is a time instant when a sampling phase change is made.
- time instance v i.e., they are constant except for small statistical fluctuations.
- an average of the filter coefficients a v is used instead of the current filter coefficient values. Recognizing that time instance v+1 is the first sampling instance after phase correction, the new predicted filter coefficient values a v + ⁇ ⁇ maintain echo cancellation accuracy despite abrupt changes in sampling phase and despite the presence of aliased frequency components. Equation 16 may be expressed more compactly using matrix notation:
- the filter coefficient a y+l k may be predicted using the value of the coefficient at two earlier sampling instances, i.e., two prior values of ⁇ v k and ⁇ v _ ⁇ k determined in accordance with the following:
- Equation (17) One technique for obtaining the values of spectral components b . and b vj N /_-k. is now described.
- the problem in equation (17) is that of solving for y+] k which is a function of two unknowns b v k and b v N _ k .
- those two equations can be solved to determine the values of the two unknown variables b v k and v,N-k using basic algebraic substitution techniques employed in solving any two equations having only two unknowns.
- the spectral filter coefficients may be predicted in accordance using the following:
- the predicted filter coefficients a ⁇ ⁇ calculated in accordance with equation (19) above can be solved after some elementary mampulation of equation (19) as follows:
- Fig. 8 shows a first filter 98 which consists of a single delay element 100 and summer 102.
- the first filter 98 receives a current phase change value ⁇ v from the timing recovery circuit 70.
- the output of filter 98 is either negative, zero, or positive corresponding to the sign of the phase change. If the two consecutive values of ⁇ are both positive, the output of filter 98 is positive; if their signs are different, the output of the filter is zero; and if their signs are both negative, the output of filter 98 is negative.
- the output of filter 98 provides an input to selector 104 whose function is to address values of the coefficients c ⁇ k and c l k . All three possible values of the coefficients c ⁇ k and c 2 k for various successive phase changes are determined in accordance with EQ. (21) and stored in ROM 106 in look-up table format. Thereafter, the appropriate values of C j k and c 2 k are retrieved from ROM 106 and used to adjust the adaptive filter coefficients a ⁇ j k in accordance with EQ. (20):
- Second filter 108 receives input spectral filter coefficients ⁇ k updated by adaptive LMS signal processor 90 via switch 92 which is then delayed in delay 110 to provide at its output the immediately preceding spectral filter coefficients ⁇ ⁇ . k
- the coefficients c ⁇ k and c 2 k retrieved by selector 104 from ROM 106 in accordance with the sign of the phase change are used to "weight" the two prior sets of filter coefficients a ⁇ , k and a ⁇ j k using multipliers 112 and 1 14, respectively.
- the multiplier products are then summed in summer 1 16 to generate the predicted spectral filter coefficients a ⁇ k compensated for the most recent sampling phase change.
- the magnitude of a sampling phase correction is set to a constant incremental value ⁇ as mentioned above, the phase is either advanced by ⁇ (+ ⁇ ) or retarded by ⁇ (- ⁇ ).
- the sampling instance is first adjusted by - ⁇ and then subsequently by + ⁇ (or first by + ⁇ and then by - ⁇ )
- the net sampling phase change is zero. Accordingly, the same coefficients can be used that were used before the last sampling phase change occurred.
- the spectral filter coefficient a ⁇ k is multiplied in multiplier 112 by coefficient c x k provided by ROM 106.
- Multiplier 1 14 multiplies a ⁇ k by the value of coefficient c 2 from ROM 106.
- a preferred implementation of calculating a ⁇ , +1 is to take advantage of the fact that the only difference between the two sets of coefficients c ⁇ k and c used by compensating the spectral filter coefficients a ⁇ k and a ⁇ . j k for phase adjustments is the sign of its imaginary part as described above.
- Figure 9 shows a typical learning curve during a first abrupt change in the sampling instance. Comparing Fig. 5 with Fig. 9, and assuming that the change of sampling instance is ⁇ T/192, the learning curve exhibits a strong rise after the sampling instance was changed for the first time only. However, during further operation of the echo canceller in accordance with the present invention, in contrast with 5 the results shown in Fig. 5, almost perfect compensation of the sampling instant adjustments at times 2, 2.5, 3, and 3.5 is achieved. In other words, no transients are observed as the filter coefficients are switched to the predicted values. Of course, the first noise spike after the very first phase change at time 1.5 must be expected since the o values of b v k and b v n. may be correctly evaluated only after the echo canceller has converged at two different sampling positions as described above. Thus, the present invention retains very high accuracy during sampling phase adjustments even under severe communication conditions.
- the present invention has been primarily described above in the context of an echo canceller implemented as an adaptive digital filter for purposes of illustration only, those skilled in the art will appreciate that the present invention has wide application in digital communications.
- the present invention can be employed in 0 any environment where a signal received over communications channel is sampled and then reconstructed.
- a transfer function is estimated in the frequency domain corresponding to the impulse response of that communications channel.
- aliased signal content is specifically taken into account in correcting the spectral coefficients of the transfer function.
- the spectral coefficients of the transfer function are analyzed as having at least two spectral components with the first component including baseband frequency components and a second spectral component including aliased frequency components.
- the present invention can be particularly advantageous not only in accurately reconstructing signals when the o Nyquist criteria may not or cannot be satisfied, e.g., when the sampling phase is adjusted, as well as in relaxing sampling rate requirements to something less than the Nyquist rate since aliased components are adequately accounted for to permit accurate reconstruction of the signal.
- Lower sampling rates translate directly 5 into reduced signal processing overhead and economic cost.
Abstract
Description
Claims
Priority Applications (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
EP97933948A EP0908020A2 (en) | 1996-07-09 | 1997-07-08 | Frequency domain signal reconstruction in sampled digital communications systems |
AU37124/97A AU3712497A (en) | 1996-07-09 | 1997-07-08 | Frequency domain signal reconstruction in sampled digital communications systems |
CA002259609A CA2259609A1 (en) | 1996-07-09 | 1997-07-08 | Frequency domain signal reconstruction in sampled digital communications systems |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US08/679,387 | 1996-07-09 | ||
US08/679,387 US5793801A (en) | 1996-07-09 | 1996-07-09 | Frequency domain signal reconstruction compensating for phase adjustments to a sampling signal |
Publications (2)
Publication Number | Publication Date |
---|---|
WO1998001961A2 true WO1998001961A2 (en) | 1998-01-15 |
WO1998001961A3 WO1998001961A3 (en) | 1998-04-23 |
Family
ID=24726719
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/SE1997/001248 WO1998001961A2 (en) | 1996-07-09 | 1997-07-08 | Frequency domain signal reconstruction in sampled digital communications systems |
Country Status (5)
Country | Link |
---|---|
US (1) | US5793801A (en) |
EP (1) | EP0908020A2 (en) |
AU (1) | AU3712497A (en) |
CA (1) | CA2259609A1 (en) |
WO (1) | WO1998001961A2 (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106233638A (en) * | 2014-05-23 | 2016-12-14 | 英特尔公司 | The blind technology selected for the weight sent and receive in structure simultaneously |
Families Citing this family (58)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5758274A (en) * | 1996-03-13 | 1998-05-26 | Symbol Technologies, Inc. | Radio frequency receiver with automatic gain control |
US6141406A (en) * | 1997-03-27 | 2000-10-31 | T-Netix, Inc. | Method and apparatus for detecting a secondary destination of a telephone call based on changes in the telephone signal path |
US6199032B1 (en) * | 1997-07-23 | 2001-03-06 | Edx Engineering, Inc. | Presenting an output signal generated by a receiving device in a simulated communication system |
US6259680B1 (en) * | 1997-10-01 | 2001-07-10 | Adtran, Inc. | Method and apparatus for echo cancellation |
US6577690B1 (en) * | 1998-06-25 | 2003-06-10 | Silicon Automation Systems Limited | Clock recovery in multi-carrier transmission systems |
US6205220B1 (en) * | 1998-06-29 | 2001-03-20 | Texas Instruments Incorporated | Method to mitigate the near-far fext problem |
US7515896B1 (en) | 1998-10-21 | 2009-04-07 | Parkervision, Inc. | Method and system for down-converting an electromagnetic signal, and transforms for same, and aperture relationships |
US6091940A (en) | 1998-10-21 | 2000-07-18 | Parkervision, Inc. | Method and system for frequency up-conversion |
US6694128B1 (en) | 1998-08-18 | 2004-02-17 | Parkervision, Inc. | Frequency synthesizer using universal frequency translation technology |
US6061551A (en) | 1998-10-21 | 2000-05-09 | Parkervision, Inc. | Method and system for down-converting electromagnetic signals |
US6049706A (en) | 1998-10-21 | 2000-04-11 | Parkervision, Inc. | Integrated frequency translation and selectivity |
US7236754B2 (en) | 1999-08-23 | 2007-06-26 | Parkervision, Inc. | Method and system for frequency up-conversion |
US6542722B1 (en) | 1998-10-21 | 2003-04-01 | Parkervision, Inc. | Method and system for frequency up-conversion with variety of transmitter configurations |
US6560301B1 (en) | 1998-10-21 | 2003-05-06 | Parkervision, Inc. | Integrated frequency translation and selectivity with a variety of filter embodiments |
US7039372B1 (en) | 1998-10-21 | 2006-05-02 | Parkervision, Inc. | Method and system for frequency up-conversion with modulation embodiments |
US6813485B2 (en) | 1998-10-21 | 2004-11-02 | Parkervision, Inc. | Method and system for down-converting and up-converting an electromagnetic signal, and transforms for same |
US6370371B1 (en) | 1998-10-21 | 2002-04-09 | Parkervision, Inc. | Applications of universal frequency translation |
US6061555A (en) | 1998-10-21 | 2000-05-09 | Parkervision, Inc. | Method and system for ensuring reception of a communications signal |
US6201831B1 (en) * | 1998-11-13 | 2001-03-13 | Broadcom Corporation | Demodulator for a multi-pair gigabit transceiver |
US6704549B1 (en) | 1999-03-03 | 2004-03-09 | Parkvision, Inc. | Multi-mode, multi-band communication system |
US6704558B1 (en) | 1999-01-22 | 2004-03-09 | Parkervision, Inc. | Image-reject down-converter and embodiments thereof, such as the family radio service |
US6473409B1 (en) * | 1999-02-26 | 2002-10-29 | Microsoft Corp. | Adaptive filtering system and method for adaptively canceling echoes and reducing noise in digital signals |
US6853690B1 (en) | 1999-04-16 | 2005-02-08 | Parkervision, Inc. | Method, system and apparatus for balanced frequency up-conversion of a baseband signal and 4-phase receiver and transceiver embodiments |
US6879817B1 (en) | 1999-04-16 | 2005-04-12 | Parkervision, Inc. | DC offset, re-radiation, and I/Q solutions using universal frequency translation technology |
US7065162B1 (en) | 1999-04-16 | 2006-06-20 | Parkervision, Inc. | Method and system for down-converting an electromagnetic signal, and transforms for same |
US7693230B2 (en) | 1999-04-16 | 2010-04-06 | Parkervision, Inc. | Apparatus and method of differential IQ frequency up-conversion |
US7110444B1 (en) | 1999-08-04 | 2006-09-19 | Parkervision, Inc. | Wireless local area network (WLAN) using universal frequency translation technology including multi-phase embodiments and circuit implementations |
ATE368344T1 (en) * | 1999-04-22 | 2007-08-15 | Broadcom Corp | GIGABIT ETHERNT WITH TIME SHIFT BETWEEN TWISTED CABLE PAIRS |
US6535552B1 (en) * | 1999-05-19 | 2003-03-18 | Motorola, Inc. | Fast training of equalizers in discrete multi-tone (DMT) systems |
US8295406B1 (en) | 1999-08-04 | 2012-10-23 | Parkervision, Inc. | Universal platform module for a plurality of communication protocols |
US6744854B2 (en) * | 1999-12-09 | 2004-06-01 | Harris Corporation | Detection of bridge taps by frequency domain reflectometry-based signal processing with precursor signal conditioning |
US6704349B1 (en) * | 2000-01-18 | 2004-03-09 | Ditrans Corporation | Method and apparatus for canceling a transmit signal spectrum in a receiver bandwidth |
US7010286B2 (en) | 2000-04-14 | 2006-03-07 | Parkervision, Inc. | Apparatus, system, and method for down-converting and up-converting electromagnetic signals |
US7672447B1 (en) * | 2000-06-01 | 2010-03-02 | Telefonaktiebolaget Lm Ericsson (Publ) | Frequency domain echo canceller |
US6870881B1 (en) * | 2000-08-24 | 2005-03-22 | Marvell International Ltd. | Feedforward equalizer for DFE based detector |
US7454453B2 (en) | 2000-11-14 | 2008-11-18 | Parkervision, Inc. | Methods, systems, and computer program products for parallel correlation and applications thereof |
US6804695B1 (en) * | 2000-11-22 | 2004-10-12 | Marvell International Ltd. | Method and apparatus for constraining tap coefficients in an adaptive finite impulse response filter |
US7072427B2 (en) | 2001-11-09 | 2006-07-04 | Parkervision, Inc. | Method and apparatus for reducing DC offsets in a communication system |
US7003027B2 (en) * | 2001-12-10 | 2006-02-21 | Agere Systems Inc. | Efficient PCM modem |
US7379883B2 (en) | 2002-07-18 | 2008-05-27 | Parkervision, Inc. | Networking methods and systems |
US7460584B2 (en) | 2002-07-18 | 2008-12-02 | Parkervision, Inc. | Networking methods and systems |
US20060146925A1 (en) * | 2002-11-12 | 2006-07-06 | Koninklijke Philips Electronics N.V. | Transform-domain sample-by-sample decision feedback equalizer |
US6942660B2 (en) * | 2002-11-19 | 2005-09-13 | Conmed Corporation | Electrosurgical generator and method with multiple semi-autonomously executable functions |
DE60318141T2 (en) * | 2003-01-15 | 2008-12-04 | Verigy (Singapore) Pte. Ltd. | Modeling an electronic device |
US20060193371A1 (en) * | 2003-03-21 | 2006-08-31 | Irena Maravic | Synchronization And Channel Estimation With Sub-Nyquist Sampling In Ultra-Wideband Communication Systems |
US7720015B2 (en) * | 2005-08-17 | 2010-05-18 | Teranetics, Inc. | Receiver ADC clock delay base on echo signals |
US8284870B1 (en) * | 2006-02-07 | 2012-10-09 | Link—A—Media Devices Corporation | Timing loop |
US7917563B1 (en) | 2006-02-07 | 2011-03-29 | Link—A—Media Devices Corporation | Read channel processor |
US7760960B2 (en) * | 2006-09-15 | 2010-07-20 | Freescale Semiconductor, Inc. | Localized content adaptive filter for low power scalable image processing |
DE602006015376D1 (en) * | 2006-12-07 | 2010-08-19 | Akg Acoustics Gmbh | DEVICE FOR HIDING OUT SIGNAL FAILURE FOR A MULTI-CHANNEL ARRANGEMENT |
US8229706B2 (en) * | 2008-06-10 | 2012-07-24 | Advantest Corporation | Sampling apparatus, sampling method and recording medium |
JP2012509614A (en) * | 2008-11-11 | 2012-04-19 | アクシス ネットワーク テクノロジー リミテッド. | Efficient adaptive digital precompensation system for resources |
US8031747B2 (en) | 2009-04-29 | 2011-10-04 | Juniper Networks, Inc. | Apparatus and method of compensating for clock frequency and phase variations by processing packet delay values |
US8891607B2 (en) | 2012-09-06 | 2014-11-18 | Avago Technologies General Ip (Singapore) Pte. Ltd. | Feed forward equalizer tap weight adaptation based on channel estimation |
US8964827B2 (en) | 2013-03-07 | 2015-02-24 | Avago Technologies General Ip (Singapore) Pte. Ltd. | Adaptation of equalizer settings using error signals sampled at several different phases |
MX2020010810A (en) * | 2018-04-20 | 2021-01-08 | Ericsson Telefon Ab L M | Method and apparatus for energy efficient transmission and reception of a signal using aliasing. |
TWI733240B (en) | 2019-11-05 | 2021-07-11 | 瑞昱半導體股份有限公司 | Transceiver and signal processing method applied in transceiver |
CN116136602B (en) * | 2023-04-14 | 2023-06-23 | 福建福大北斗通信科技有限公司 | Device and method for in-band spectrum amplitude and time delay consistency of Beidou anti-interference channel |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP0454242A1 (en) * | 1990-04-27 | 1991-10-30 | Koninklijke Philips Electronics N.V. | Digital echo canceller comprising a double-talk detector |
US5317596A (en) * | 1992-12-01 | 1994-05-31 | The Board Of Trustees Of The Leland Stanford, Junior University | Method and apparatus for echo cancellation with discrete multitone modulation |
US5384806A (en) * | 1991-09-23 | 1995-01-24 | At&T Bell Laboratories | Modem with time-invariant echo path |
Family Cites Families (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US5555285A (en) * | 1995-03-30 | 1996-09-10 | Westell Incorporated | Multi-variate system having an intelligent telecommunications interface with automatic adaptive delay distortion equalization (and related method) |
-
1996
- 1996-07-09 US US08/679,387 patent/US5793801A/en not_active Expired - Lifetime
-
1997
- 1997-07-08 EP EP97933948A patent/EP0908020A2/en not_active Withdrawn
- 1997-07-08 WO PCT/SE1997/001248 patent/WO1998001961A2/en not_active Application Discontinuation
- 1997-07-08 CA CA002259609A patent/CA2259609A1/en not_active Abandoned
- 1997-07-08 AU AU37124/97A patent/AU3712497A/en not_active Abandoned
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP0454242A1 (en) * | 1990-04-27 | 1991-10-30 | Koninklijke Philips Electronics N.V. | Digital echo canceller comprising a double-talk detector |
US5384806A (en) * | 1991-09-23 | 1995-01-24 | At&T Bell Laboratories | Modem with time-invariant echo path |
US5317596A (en) * | 1992-12-01 | 1994-05-31 | The Board Of Trustees Of The Leland Stanford, Junior University | Method and apparatus for echo cancellation with discrete multitone modulation |
Non-Patent Citations (3)
Title |
---|
IEEE TRANSACTIONS ON COMMUNICATIONS, vol. 33, no. 8, August 1985, pages 826-832, XP000615714 FALCONER D D: "TIMING JITTER EFFECTS ON DIGITAL SUBSCRIBER LOOP ECHO CANCELLERS: PART I - ANALYSIS OF THE EFFECT" cited in the application * |
See also references of EP0908020A2 * |
SERVING HUMANITY THROUGH COMMUNICATIONS. SUPERCOMM/ICC, NEW ORLEANS, MAY 1 - 5, 1994, vol. VOL. 1, no. -, 1 May 1994, INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS, pages 307-310, XP000438930 HO M ET AL: "TIMING RECOVERY FOR ECHO-CANCELLED DISCRETE MULTITONE SYSTEMS" * |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106233638A (en) * | 2014-05-23 | 2016-12-14 | 英特尔公司 | The blind technology selected for the weight sent and receive in structure simultaneously |
EP3146646A4 (en) * | 2014-05-23 | 2018-04-25 | Intel Corporation | Blind technique for weight selection in simultaneous transmit and receive structure |
Also Published As
Publication number | Publication date |
---|---|
WO1998001961A3 (en) | 1998-04-23 |
US5793801A (en) | 1998-08-11 |
AU3712497A (en) | 1998-02-02 |
EP0908020A2 (en) | 1999-04-14 |
CA2259609A1 (en) | 1998-01-15 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US5793801A (en) | Frequency domain signal reconstruction compensating for phase adjustments to a sampling signal | |
US6421377B1 (en) | System and method for echo cancellation over asymmetric spectra | |
US5317596A (en) | Method and apparatus for echo cancellation with discrete multitone modulation | |
US6597746B1 (en) | System and method for peak to average power ratio reduction | |
Messerschmitt | Echo cancellation in speech and data transmission | |
US5117418A (en) | Frequency domain adaptive echo canceller for full-duplex data transmission | |
JP4455015B2 (en) | Canceller circuit and control method | |
US4760596A (en) | Adaptive echo cancellation and equalization system signal processor and method therefor | |
US4362909A (en) | Echo canceler with high-pass filter | |
US7826609B1 (en) | Method and apparatus for digital near-end echo/near-end crosstalk cancellation with adaptive correlation | |
US6618480B1 (en) | DAC architecture for analog echo cancellation | |
US6240128B1 (en) | Enhanced echo canceler | |
US6434233B1 (en) | Method and apparatus for canceling periodic interference signals in a digital data communication system | |
GB2219469A (en) | A decision feedback equaliser and a method of operating a decision feedback equaliser | |
JP2001505004A (en) | Method and apparatus for timing recovery | |
JP2001007746A (en) | High-speed training of equalizer in dmt system | |
WO1991002407A1 (en) | Wideband digital equalizers for subscriber loops | |
US7068780B1 (en) | Hybrid echo canceller | |
EP0965206A1 (en) | Signal processing method and apparatus for reducing equalizer error | |
CA2060250A1 (en) | Method and apparatus for echo cancellation of a multicarrier signal | |
US6965578B1 (en) | Echo canceling method and apparatus for digital data communication system | |
KR100502414B1 (en) | Echo canceller of adsl system and method for training thereof | |
GB2075313A (en) | Echo cancellers | |
US4964118A (en) | Apparatus and method for echo cancellation | |
US20030081763A1 (en) | Efficient echo channel, estimation mechanism for an ADSL echo canceller |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
AK | Designated states |
Kind code of ref document: A2 Designated state(s): AL AM AT AU AZ BA BB BG BR BY CA CH CN CU CZ DE DK EE ES FI GB GE GH HU IL IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MD MG MK MN MW MX NO NZ PL PT RO RU SD SE SG SI SK TJ TM TR TT UA UG UZ VN YU AM AZ BY KG KZ MD RU TJ TM |
|
AL | Designated countries for regional patents |
Kind code of ref document: A2 Designated state(s): GH KE LS MW SD SZ UG ZW AT BE CH DE DK ES FI FR GB GR IE IT LU MC NL PT SE BF |
|
DFPE | Request for preliminary examination filed prior to expiration of 19th month from priority date (pct application filed before 20040101) | ||
AK | Designated states |
Kind code of ref document: A3 Designated state(s): AL AM AT AU AZ BA BB BG BR BY CA CH CN CU CZ DE DK EE ES FI GB GE GH HU IL IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MD MG MK MN MW MX NO NZ PL PT RO RU SD SE SG SI SK TJ TM TR TT UA UG UZ VN YU AM AZ BY KG KZ MD RU TJ TM |
|
AL | Designated countries for regional patents |
Kind code of ref document: A3 Designated state(s): GH KE LS MW SD SZ UG ZW AT BE CH DE DK ES FI FR GB GR IE IT LU MC NL PT SE BF |
|
121 | Ep: the epo has been informed by wipo that ep was designated in this application | ||
ENP | Entry into the national phase |
Ref document number: 2259609 Country of ref document: CA Ref country code: CA Ref document number: 2259609 Kind code of ref document: A Format of ref document f/p: F |
|
WWE | Wipo information: entry into national phase |
Ref document number: 1997933948 Country of ref document: EP |
|
WWP | Wipo information: published in national office |
Ref document number: 1997933948 Country of ref document: EP |
|
REG | Reference to national code |
Ref country code: DE Ref legal event code: 8642 |
|
NENP | Non-entry into the national phase |
Ref country code: JP Ref document number: 1998505159 Format of ref document f/p: F |
|
WWW | Wipo information: withdrawn in national office |
Ref document number: 1997933948 Country of ref document: EP |