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    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS, VOL. 54, NO. 9, SEPTEMBER 2007 1891

    Adaptive Noise Cancellation Techniques inSigmaDelta Analog-to-Digital Converters

    Bahar Jalali-Farahani, Member, IEEE, and Mohammed Ismail, Fellow, IEEE

    AbstractAdaptive noise cancellation (ANC) techniques thatextract a desired signal from background noise have manyapplications in different engineering disciplines. In ANC, thecorrupted signal is passed through a filter that tends to sup-press the noise while leaving the original signal unchanged. Thispaper demonstrates that the adaptive noise cancellation tech-nique can be embedded in the digital signal postprocessing of asigmadelta analog-to-digital converter and effectively reducesthe quantization noise as well as the thermal noise at the outputof the converter. The combination of ANC and the noise-shapingtechnique enable high-resolution analog-to-digital conversion inwideband applications where noise shaping alone cannot provideenough suppression of quantization noise due to the low oversam-

    pling ratio.

    Index TermsAdaptive, analog-to-digital converter, noise can-cellation, sigmadelta modulator.

    I. INTRODUCTION

    CONTINUOUS development in broadband wireless sys-

    tems forces analog-to-digital converters to provide more

    resolution in larger signal bandwidths. Although Nyquist rate

    analog-to-digital converters can operate in high speeds, they are

    limited in resolution, and higher speed comes with a significant

    increase in power consumption. Oversampling sigmadelta

    modulators are a better choice for high resolution in low tomedium speeds. For broadband signals, a large oversampling

    ratio cannot be chosen; therefore, sigmadelta converters do not

    gain much benefit from noise shaping. Besides a lower over-

    sampling ratio, they also suffer from analog circuit nonidealities

    which become more prominent in deep submicron technology.

    Different techniques have been proposed to improve the perfor-

    mance of sigmadelta modulators for wideband applications.

    Distributing zeros of the noise-transfer function across the

    signal bandwidth is proposed in [1] to achieve 8-bit resolution

    in the 40-MHz bandwidth. A Chebyshev-based loop filter de-

    sign is used in [2] to provide more effective noise shaping in a

    low oversampling ratio than a conventional modulator. Higherresolution in sigmadelta converters can be achieved by using

    higher order multistage noise shaping (MASH) stages without

    sacrificing stability; however, nonidealities in the analog cir-

    cuits cause the incomplete cancellation of the quantization

    noise at the output of a modulator and degrade its performance.

    Manuscript received October 27, 2005; revised February 5, 2007. This worksupported by the Semiconductor Research Corporation (SRC).

    B. Jalali-Farahani is with the Department of Electrical Engineering, ArizonaState University, Tempe, AZ 85287-1203 USA (e-mail: [email protected]).

    M. Ismail is with the Analog Very Large Scale Integration Lab, Departmentof Electrical and Computer Engineering, The Ohio State University, Columbus,OH 43210 USA (e-mail: [email protected]).

    Digital Object Identifier 10.1109/TCSI.2007.904655

    Fig. 1. Block diagram adaptive noise cancellation (ANC) technique.

    This paper explores a new approach to enhance the signal-to-

    noise ratio of a sigmadelta modulator for broadband applica-

    tions by using an adaptive noise cancellation (ANC) technique.

    An ANC that extracts the desired signal from the corrupted

    noise has found many applications in different engineering dis-

    ciplines, such as the suppression of periodic interference in tele-

    phone lines [3], acoustic noise cancellation [4], adaptive line

    enhancement [5][7], and automatic speech recognition [8] to

    mention a few. The idea is to use an adaptive filter that exploits

    the spectral difference between the desired signal and the noise

    to separate them from each other. In case of sigmadelta ADC,

    we used ANC to extract the narrowband signal from the wide-

    band quantization noise. Since ANC is added to the output of a

    sigmadelta modulator, all of the required signal processing is

    performed in the digital domain and no complexity is added to

    the modulator itself.

    This paper is organized as follows. Section II describes the

    principles of the ANC technique. The application of ANC in

    sigmadelta modulators is proposed in Section III. The transfer

    function of the ANC filter in presence of the high-passed quan-

    tization noise is derived and the amount of improvement in the

    signal-to-noise ratio is formulated. Section IV presents the sim-

    ulation results to apply this technique to different sigmadeltamodulators. Practical considerations regarding the linearity of

    the adaptive filter and the digital complexity associated with the

    ANC block are presented in Section V. This paper concludes in

    Section VI.

    II. PRINCIPLES OF ANC TECHNIQUE

    Fig. 1 shows the block diagram of the ANC system. An input

    to the ANC block is the desired signal corrupted with wideband

    noise, defined as

    (1)

    1549-8328/$25.00 2007 IEEE

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    1892 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS, VOL. 54, NO. 9, SEPTEMBER 2007

    ANC separates the two components of this signal by using an

    adaptive filter. A delayed version of the input signal is passed

    through the adaptive filter to generate the error signal given by

    (2)

    Using (1) and (2), the error signal can be written as

    (3)

    The least mean-squared algorithm (LMS) is used to tune the

    coefficient of adaptive filter so that the error signal in (3) is min-

    imized in the mean-squared sense. The mean-squared value of

    the error is calculated by taking expectation from both sides of

    (3)

    (4)

    If the adaptive filter is implemented by a finite-impulse-re-sponse (FIR) filter of order , the output of the filter can be

    written as

    (5)

    It can be expressed in terms of signal and noise components by

    (6)

    If noise is a wideband random signal and the delay line is

    long enough, different delayed samples of noise are completely

    uncorrelated. Therefore, the current sample of the filter output

    , expressed by (6), is also uncorrelated with the current

    sample of noise signal which makes the third term in (4)

    equal to zero. The second term in (4) is constant and is equal to

    the noise variance . Therefore, minimizing the mean-squared

    error in (4) forces the output sample to be a close estimate

    of the desired signal .

    Therefore, filter output in the ANC system provides the best

    estimate of the desired narrowband signal in the mean-squared

    sense, provided that noise is wideband compared to the signal

    and has uncorrelated samples. In the next section, this problem

    is formulated for the case where is the output of ath-order sigmadelta modulator and is composed of the

    desired signal and the highpass-filtered quantization noise.

    III. APPLICATION OF ANC TO SIGMADELTA ADCS

    The adaptive noise cancellation technique shown in Fig. 1

    can be used to improve the signal-to-noise ratio (SNR) at the

    output of a sigmadelta modulator without any modification to

    the analog circuit [9]. ANC relaxes the requirements on the fol-

    lowing lowpass filter, which usually needs to be implemented

    by a long FIR filter and is based on the application; it may even

    remove the need for such filtering completely. The biggest ad-

    vantage of ANC is its adaptability. Contrary to the fixed coef-ficient lowpass filters, ANC adapts its coefficients based on its

    Fig. 2. Block diagram of a sigmadelta ADC including ANC.

    input signal. Fig. 2 shows how ANC can be a part of digital post-

    processing of a sigmadelta modulator.

    In this section, the transfer function of the system shown in

    Fig. 1 is derived at steady state with the assumption that the

    coefficients of the adaptive filter have been already converged

    to their optimum values given by the Wiener solution. All of

    the signals are as indicated in Fig. 1. Under this assumption,

    the ANC block is a linear discrete-time system with the transfer

    function defined as

    (7)

    where and are the -transforms of the filter output

    and desired signal, respectively. An input to the ANC block is

    composed of a desired sinusoidal signal corrupted by the high-

    pass filter quantization noise

    (8)

    The filter output can be expressed in terms of an input signal

    and filter coefficients as

    (9)

    Since the input to the filter is the delayed version of the

    desired signal, (9) results in

    (10)

    Using (7) and (10), the transfer function of the ANC system is

    given by

    (11)

    where is the th coefficient of the filter and is the delay line

    shown in Fig. 1.

    It is shown in the Appendix that the transfer function in (11)

    can be written in terms of modulator parameters: filter order

    ( ), input signal parameters amplitude ( ), and frequency ( ),

    ANC block delay ( ), and adaptive filter order ( ). Equation

    (A.25) is repeated here

    (12)

    where , , , and are defined in (A.26), (A.27), (A.12),and (A.20), respectively.

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    JALALI-FARAHANI AND ISMAIL: ANC TECHNIQUES IN SIGMADELTA ADCS 1893

    As explained in the Appendix, for large filter orders, ANC

    almost has a unity transfer function for the sinusoidal input

    (13)

    However, wideband noise is attenuated by the factor given by(A.34)

    (14)

    which results in an improvement in SNR given by (A.37)

    (15)

    From (15), it can be seen that SNR improvement caused

    by the ANC block is a function of three design parameters:

    sigmadelta modulator order , signal bandwidth , and

    ANC adaptive filter order . The effects of these parameters on

    SNR are depicted in Fig. 3 and the following observations are

    made.

    SNR improvement depends on the adaptive filter order. In

    fact, (12) suggests that the ANC block is a bandpass filter

    with a center frequency equal to the input frequency .

    The quality factor of this filter is increasedas the filter order

    is increased which results in a better separation of signaland noise and, therefore, more improvement in the SNR.

    SNR improvement obtained by the ANC block is almost

    independent of the order of the sigmadelta modulator.

    The ANC block is more effective when the oversampling

    ratio is low. In this case, there is a significant amount of

    inband quantization noise that can be effectively removed

    by the ANC block.

    IV. SIMULATION RESULTS

    This section provides simulation results to support the con-

    clusions drawn in Section III and the Appendix. It also shows

    different aspects of using an adaptive noise cancellation tech-

    nique. A fourth-order sigmadelta modulator is considered in

    this section which is digitizing GSM as well as WLAN signals

    in a multistandard transceiver. Fig. 4 shows a block diagram of

    the sigmadelta ADC designed for this multistandard receiver.

    All of the blocks are used for the GSM system. In the WLAN

    mode, only the blocks with solid-line borders are used. There-

    fore, the fourth-order modulator with 6-bit quantizer, five stages

    of comb filter, a 10th-order halfband filter, and a 25th-order FIR

    filter are used for GSM mode. Only the first stage of the modu-

    lator, three stages of the comb filter and the 25th-order FIR filter

    are used for the WLAN mode. Specifications for decimation and

    lowpass filters are decided based on the system requirement fora direct homodyne receiver as explained in [10].

    Fig. 3. SNR improvement as predicted by (15). Results are plotted for a full-

    scalesinusoidal input signal, second-order sigmadelta modulator with O S R = 8 and adaptive filter order = 4 0 . The plots show the SNR improvement as afunction of (a) adaptive filter order with constant N and ! , (b) sigmadeltamodulator order with constant L and ! , and (c) oversampling ratio with con-stant N and L .

    Fig. 4. Block diagram of the two-mode sigmadelta ADC used forGSM/WLAN standards.

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    1894 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS, VOL. 54, NO. 9, SEPTEMBER 2007

    Fig. 5. Same as Fig. 4, but with an ANC block instead of a fixed-coefficient

    FIR filter.

    Fig. 6. Output spectrum of the sigmadelta ADC designed for the GSM stan-dard with and without using the ANC block.

    Fig. 4 is modified by using an adaptive filter in an ANC con-

    figuration as shown in Fig. 5. Simulation results provided in this

    section are based on these two block diagrams. The normalizedleast mean square (NLMS) algorithm is used in ANC for up-

    dating the coefficients.

    A. Adaptive FIR Filter for GSM

    The spectrum of an output signal in GSM mode is depicted in

    Fig. 6 for the sigmadelta ADC with a conventional FIR filter

    (i.e., Fig. 4) as well as ANC (i.e., Fig. 5). As seen in this figure,

    ANC provides more attenuation of quantization noise inside the

    signal bandwidth; however, its performance degrades in higher

    frequencies. Overall SNR improvement is around 5 dB as also

    predicted by (15). More significant improvements are achieved

    by ANC when the oversampling ratio is low which is the case forthe WLAN modulator and is considered next. Filter coefficients

    are converged after 10 000 iterations. Fig. 7 illustrates the con-

    vergence of the first six coefficients of the 25th-order FIR filter.

    B. Adaptive FIR Filter for WLAN

    As predicted by (15) and Fig. 3, ANC results in significant

    SNR improvement when the oversampling ratio is low. The

    amount of inband quantization noise is significant for low over-

    sampling ratios and can be effectively reduced by the ANC

    block. Fig. 8 shows the results for the WLAN system where an

    oversampling ratio is only 8. The SNR is improved from 69 dB

    to 78 dB using the ANC block. The amount of SNR improve-ment predicted by (15) for and is 13 dB.

    Fig. 7. Iteration of the adaptive filter coefficients in the ANC block.

    Fig.8. Output spectrum of the sigmadelta ADCdesigned for the WLAN stan-dard with and without using an ANC block.

    C. Reducing Effect of Thermal Noise

    The adaptive noise cancellation technique has been originally

    used to extract a narrowband signal from white random noise

    [5]. This implies a double benefit of using the ANC at the output

    of a sigmadelta modulator: ANC not only attenuates the high-

    pass quantization noise but also removes the white random noisecaused by the thermal noise of analog devices. In a conven-

    tional design of a sigmadelta modulator, the analog circuit is

    designed so that thermal noise of the circuit is less than the

    quantization noise of the converter. This results in large capac-

    itors in switched-capacitor implementation as well as higher

    power consumption and area. The fact that ANC reduces the

    thermal noise can be exploited to relax the requirements on

    analog circuits and to decrease the power consumption. The re-

    duction of thermal noise is shown in Fig. 9 for the modulator de-

    signed for the WLAN system. An input-referred thermal noise

    of nV Hz is chosen. The SNR of the sigmadelta

    modulator becomes 63 dB due to the additional thermal noise.

    A 45th-order adaptive FIR filter is used in the ANC block to ex-tract the signal from the thermal and the quantization noise. A

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    JALALI-FARAHANI AND ISMAIL: ANC TECHNIQUES IN SIGMADELTA ADCS 1895

    Fig. 9. Outputspectrum of the sigmadelta ADC designed for the WLAN stan-dard in the presence of thermal noise with and without using an ANC block.

    comparison of the output spectrum for the ADC, equipped with

    an ANC block and the one without ANC, is shown in Fig. 9 and

    the results show that the SNR improves from 63 to 71.4 dB.

    V. PRACTICAL CONSIDERATIONS

    A. Nonlinearity of the Adaptive Filter

    The derivation of the ANC transfer function presented in

    Section III and in the Appendix was accomplished based on

    the assumption that the adaptive filter coefficients have already

    converged to theiroptimum Wiener solution. Under this assump-

    tion, the ANC block with transfer function (7) is a discrete linearsystem and should not cause any distortion or intermodulation

    product.

    In fact, the LMS filter weights are the sum of the time-in-

    variant Wiener coefficients and a time-varying misadjustment

    component [11]

    (16)

    Therefore, the output filter expression in (9) should be revised

    as

    (17)

    where is the Wiener solution as given in (9) and

    is the misadjustment term. can be reduced by choosing

    a smaller step size for the LMS algorithm that updates the filter

    weights. A smaller step size, however, results in a slower con-

    vergence rate. The effect of the misadjustment term in causing

    nonlinearity is depicted in Fig. 10 which shows the result of

    the two-tone test. As shown in this figure, when data are taken

    before the complete convergence of the filter taps, large spurs

    caused by intermodulation products and harmonic terms are

    seen in the output spectrum. The output spectrum is also plotted

    for the data taken after coefficients convergence,1 where the in-

    termodulation products are not visible anymore.

    1Filter coefficients converge after approximately 10 000 samples as depictedin Fig. 7.

    Fig. 10. Two-tonetest on thesigmadelta ADC withan ANC usedfor the GSMsystem.

    Fig. 11. CSD accumulative multiplication unit [12].

    B. Implementation and Digital Complexity

    The ANC block shown in Fig. 1 involves three major

    calculations.

    1) Calculating filter output

    (18)

    2) Calculating error signal

    (19)

    3) Updating filter coefficients

    (20)

    The three steps need multipliers, adders, and 1

    subtractor. However, the multiplierless implementation is also

    possible [12] and is preferable since it results in lower power

    consumption. In multiplierless implementation, all numbers are

    represented by the canonical signed digit (CSD) representations.

    In CSD, numbers are sums or differences of powers of two

    which enable replacing the multiplier with a shifter and adder.

    Fig. 11 shows a CSD multiplication unit which is composed ofa shifter and an adder. Moreover, step size in (20) is chosen

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    1896 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS, VOL. 54, NO. 9, SEPTEMBER 2007

    Fig. 12. ANC block using the multiplierless implementation of an adaptive FIR filter as proposed in [12].

    as a power of two (i.e., ) to replace the multiplication

    needed in step 3 with a shifter.

    The multiplierless FIR adaptive filter can be implemented as

    depicted in Fig. 12 using adders, 1 subtractor, shifters,

    and CSD multiplier unit.

    VI. CONCLUSION

    In this paper, a simple adaptive noise cancellation tech-

    nique has been presented that can be used to boost the SNR

    of sigmadelta modulators. Mathematical derivation of the

    system shows that ANC uses the statistical difference be-

    tween the signal and noise and the fact that noise samples are

    uncorrelated from each other whereas signal samples have

    a much stronger correlation. Simulation results show that

    ANC can effectively remove the inband as well as remaining

    out-of-band quantization noise and reduces the thermal noise

    of the sigmadelta modulator significantly. The proposed tech-

    nique is all implemented digitally and, hence, does not bring

    any complexity to the analog circuitry. Although this paper hasdemonstrated the application of ANC in a switched-capacitor

    sigmadelta ADC, it is as well applicable to other oversampling

    data converters (e.g., continuous-time sigmadelta modulators).

    APPENDIX

    It was shown in Section III that the ANC block, including

    the adaptive FIR filter, can be approximated with a linear time-

    invariant (LTI) system with a transfer function givenin (11). The

    LTI assumption is true at steady state where the filter coefficients

    have been already converged to their optimum values given by

    the Wiener solution as

    (A.1)

    In this equation, is the auto-correlation matrix of the input

    signal and is the cross-correlation vector between the filter

    input and the desired signal of the filter.

    The following steps show the derivations of these two

    matrices.

    Calculate Autocorrelation Matrix : is input to the

    adaptive filter and is composed of the sinusoidal signal andthe quantization noise shaped by the sigmadelta modulator.

    Since signal and noise are uncorrelated, the autocorrelation of

    the input data would be sum of autocorrelation of the signal and

    autocorrelation of the quantization noise

    (A.2)

    First, we calculate the autocorrelation of the signal. Considering

    a sinusoidal signal

    (A.3)

    is a random phase uniformly distributed on .

    The autocorrelation is calculated as

    (A.4)

    The autocorrelation matrix is a symmetric matrix

    with each component calculated as in (A.4)

    (A.5)

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    JALALI-FARAHANI AND ISMAIL: ANC TECHNIQUES IN SIGMADELTA ADCS 1897

    where is a matrix defined as

    (A.6)

    In order to calculate autocorrelation of noise, it should be noted

    that noise here is the shaped quantization noise. Assuming a

    white uniformly distributed quantization noise, the power spec-

    tral density of the quantization noise is given by

    (A.7)

    After being shaped by the noise transfer function of the

    th-order sigmadelta modulator, the power spectral density

    would be

    (A.8)

    Substituting in (A.7) results in

    (A.9)

    The autocorrelation function and power spectral density of a sta-

    tionary stochastic process form a Fourier transform pair. There-

    fore, knowing the power spectral density of noise, the autocor-

    relation of noise is found as

    (A.10)

    However, different samples of noise are uncorrelated and, there-

    fore, (A.10) is zero for all nonzero values of and the autocor-

    relation matrix of noise will be

    (A.11)

    (A.12)

    Finally, the autocorrelation matrix of filter input data can

    be written using (A.2), (A.5), and (A.11)

    (A.13)

    Calculate Cross-Correlation Vector: The cross-correlation

    vector is calculated as the correlation between the desired signal

    and the input signal, which is the delayed version of the de-

    sired signal by samples. Since noise components are uncor-

    related from each other, only signal components will appear in

    the cross-correlation vector

    (A.14)

    or in matrix form

    (A.15)

    where is defined as in (A.6) and is equal to

    (A.16)

    In order to find the filter coefficients using (A.1), needs

    to be calculated. Using inverse lemma and (A.13), can be

    written as

    (A.17)

    Therefore, filter coefficients are given by

    (A.18)

    where the term in parenthesis is

    (A.19)

    where and are

    (A.20)

    (A.21)

    Finally, the transfer function of the ANC system defined in (11)

    can be written as

    (A.22)

    with

    (A.23)

    Substituting using (A.18)

    (A.24)

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    1898 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS, VOL. 54, NO. 9, SEPTEMBER 2007

    Using (A.6), (A.11), (A.16), and (A.23) to substitute for , ,

    , and , respectively, (A.24) results in

    (A.25)

    where

    (A.26)

    (A.27)

    Calculate SNR Improvement: This section calculates SNR

    improvement caused by the ANC block. Since the desired input

    signal is sinusoidal with amplitude , the input signal power is

    (A.28)

    The signal power at the output of ANC block is given by

    (A.29)

    For large values of , hence

    . The noise component of the input signal is the high-

    pass quantization noise of the sigmadelta modulator with noise

    power given by

    (A.30)

    The total noise power at the output of ANC is equal to

    (A.31)

    which can be also expressed as

    (A.32)

    where

    (A.33)

    Therefore, noise is reduced by a factor of

    (A.34)

    From (A.34), it is seen that SNR improvement depends on

    the value of . This integral has a simple

    closed-form expression for where

    (A.35)

    and

    (A.36)

    which allows the SNR improvement to be equal to

    (A.37)

    ACKNOWLEDGMENT

    The authors would like to thank the reviewers for their valu-

    able comments and suggestions that have been incorporated into

    this paper.

    REFERENCES

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    [2] A. Rusu and H. Tenhunen, A multi-bit sigma delta modulator forwideband applications, in Proc. 9th Int. Conf. Electron. Circuits Syst.,Sep. 2002, vol. 1, pp. 335338.

    [3] G. Keratiotis et al., A novel method for periodic interference suppres-sion on local telephone loops, IEEE Trans. Circuits Syst. I: Fundam.Theory Appl., vol. 47, no. 7, pp. 10961100, Jul. 2000.

    [4] M. M. Sondhi, An adaptive echo canceller, Bell Syst. Tech. J., vol.46, pp. 497511, Mar. 1967.

    [5] J. R. Treicher, The spectral line enhancerThe concept, an imple-mentation, and an application, Ph.D. dissertation, Dept. Elect. Eng.,Stanford Univ., Stanford, CA, 1977.

    [6] P. Handel, Predictive digital filtering of sinusoidal signals, IEEETrans. Signal Process., vol. 46, no. 2, pp. 364 374, Feb. 1998.

    [7] M. Ghogho, M. Ibnkahla, and N. J. Bershad, Analytic behavior of theLMS adaptive line enhancer for sinusoids corrupted by multiplicativeand additive noise, IEEE Trans. Signal Process., vol. 46, no. 9, pp.23862393, Sep. 1998.

    [8] L. J. Griffiths, An adaptive noise canceling procedure for multidimen-sional systems, presented at the IEEE Circuits Syst. Conf., Asilomer,CA, Nov. 1976.

    [9] B. J. Farahani, Adaptive digital calibration techniques for high speedhigh resolution sigma delta ADCs for broadband wireless applica-tions, Ph.D. dissertation, Dept. Elect. Comp. Eng., The Ohio StateUniv., Columbus, OH, 2005.

    [10] A. Ghazel, L. Naviner, and K. Grati, On design and implementationof a decimation filter for multistandard wireless transceivers, IEEETrans. Wireless Commun., vol. 1, no. 4, pp. 558562, Oct. 2002.

    [11] M. Reuter and J. R. Zeidler, Nonlinear effects in LMS adaptive equal-izers,IEEE Trans. Signal Process., vol. 47, no. 6, pp. 15701579, Jun.1999.

    [12] L. S. DeBrunner, Y. Wang, V. DeBrunner, and M. Tull, Multiplierlessimplementation of adaptive FIR filters, in Proc. 37th Asilomar Conf.Signals, Syst. Comput., Nov. 2003, vol. 2, pp. 22322236.

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    JALALI-FARAHANI AND ISMAIL: ANC TECHNIQUES IN SIGMADELTA ADCS 1899

    Bahar Jalali-Farahani (M02)receivedthe B.S. andM.S. degrees in electrical engineering from Univer-sity of Tehran, Tehran, Iran, in 1996 and 1999, re-spectively, and the Ph.D. degree in electrical engi-neering from The Ohio State University, Columbus,in 2005.

    She was with the Advanced Technology, DataConverter Research Group, Freescale, Tempe, AZ,

    in 2005, where she was working on the calibrationtechniques for high-performance analog-to-digitalconverters. She became an Assistant Professor with

    Arizona State University, Tempe, in 2006. Her research interests are in signal-processing techniques for high-performance analog circuits, low-power low-

    voltage analog design, and analog-to-digital and digital-to-analog converters.

    Mohammed Ismail (F97) received the B.S. andM.S. degrees in electronics and communicationsfrom Cairo University, Giza, Egypt, and the Ph.D.degree in electrical engineering from the Universityof Manitoba, Winnipeg, MB, Canada.

    Hehasmorethan25 years ofexperiencein R&Dinthe fields of analog, RF, and mixed-signal integratedcircuits (ICs). He has held several positions in both

    industry and academia and has served as a corporateconsultant to nearly 30 companies in the U.S., Eu-rope, and the Far East. He is Professor of Electrical

    and Computer Engineering and theFounding Director of the Analog Very LargeScaleIntegration Lab, The Ohio StateUniversity, Columbus. His currentinterestlies in research involving digitally programmable/configurable fully integratedradios with a focus on low-voltage/low-power firstpass solutions for third-gen-eration (3G) and fourth-generation (4G) wireless handhelds. He publishes in-tensively in this area and has been awarded 11 patents. He has coedited andcoauthored several books including a text on Analog VLSI Signal and Informa-tion Processing (McGraw-Hill, 1994). He authored Radio Design in NanometerTechnologies (Springer, 2007). He advised the thesis work of 43 Ph.D. studentsand of more than 85 M.Sc. students. He cofounded ANACAD-Egypt (now partof Mentor Graphics Inc.) and Firstpass Technologies Inc., a developer of CMOSradio and mixed-signal Internet protocols for handheld wireless applications. Heis the Founder of the International Journal of Analog Integrated Circuits andSignal Processing (Springer) and serves as the Editor-In-Chief.

    Dr.Ismail hasbeen therecipient of several awardsincluding theU.S. NationalScience Foundation Presidential Young Investigator Award, the U.S. Semicon-ductor Research Corp Inventor Recognition Awards in 1992 and 1993, The Col-lege of Engineering Lumley Research Award in 1992, 1997, 2002, and 2007anda Fulbright/Nokia fellowship Award in 1995.He has served as Associate Editorfor many IEEE TRANSACTIONS, is on the International Advisory Boards of sev-eral journals, and was on the Board of Governors of the IEEE Circuits and Sys-tems Society.