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1 This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore. Title An adaptive filtering algorithm for direct conversion receivers : architecture performance analysis Author(s) Citation Zheng, Yuanjin; Cao, Mingzheng; Teo, Edmund K. H.; Garg, Hari K. Zheng, Y., Cao, M., Teo, K. H., & Garg, H. K. (2008). An Adaptive Filtering Algorithm for Direct-Conversion Receivers: Architecture Performance Analysis. IEEE Transactions on Circuits Systems I. 55(4), Date 2008 URL Rights 2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly technical work. Copyright all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. This material is presented to ensure timely dissemination of scholarly technical work. Copyright all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

2 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 55, NO. 4, MAY An Adaptive Filtering Algorithm for Direct-Conversion Receivers: Architecture Performance Analysis Yuanjin Zheng, Member, IEEE, Mingzheng Cao, Student Member, IEEE, Edmund K. H. Teo, Hari K. Garg, Senior Member, IEEE Abstract An adaptive filtering algorithm is proposed in this paper to remove mismatch, dc offsets, flicker noise, intersymbol interference (ISI) simultaneously in a direct-conversion receiver. mismatch is cancelled by a real valued adaptive mismatch canceller, dc offsets are removed with one complex tap. In addition, flicker noise is modeled as a complex autoregressive (AR) rom process so the system to be identified transforms to an ARX model. After estimating the coefficients in the model during the training period, the desired signal can be estimated using the decision feedback method. To accelerate the convergence of the algorithm to reduce the estimation variance, an internal iterative algorithm is introduced. The convergence analysis of the proposed algorithm is also given, the closed form of the minimum mean square error of the proposed algorithm is derived. Simulation results are provided to verify the superior performance of the proposed algorithm. Index Terms ARX model, convergence, dc offsets, direct-conversion receivers, flicker noise, mismatch, minimum meansquare error (MMSE). I. INTRODUCTION IN THE PAST, direct-conversion receivers (DCRs), illustrated in Fig. 1, are rarely used due to issues such as mismatch, dc offsets, even-order distortion, flicker noise [1] [4]. Among these issues, dc offsets flicker noise are more serious challenging [2], [5]. Several methods have been proposed to solve mismatch, dc offsets, flicker noise [2] [4], [7]. In [2], the dc offset is removed by employing an ac coupling which may corrupt the signal s dc components due to its high corner frequency [1], [7]; in addition, the flicker noise is regarded as equivalent in its effect on intersymbol interference (ISI) is mitigated only by employing a finite-impulse response (FIR) minimum mean-square-error linear equalizer (MMSE-LE); it is also difficult to design a suitable ac coupling because the exact roll-off frequency is unknown in practice. In this paper, a novel adaptive method to estimate the transmitted signal corrupted by ISI, mismatch, dc offsets, Manuscript received January 12, 2006; revised December 30, This paper was recommended by Associate Editor P. Regalia. Y. Zheng is with the ICS Laboratory, Institute of Microelectronics, Singapore ( yuanjin@ime.a-star.edu.sg). M. Cao, E. K. H. Teo, H. K. Garg are with the Department of Electrical Computer Engineering, Faculty of Engineering, National University of Singapore, Singapore ( eleghk@nus.edu.sg). Digital Object Identifier /TCSI Fig. 1. Physical model of a DCR with a system block diagram of our baseb filter. flicker noise is proposed. A real valued adaptive mismatch canceller is employed to cancel mismatch, the varying dc offsets are removed by one complex tap [3], [8]. In addition, the flicker noise is modeled as a complex AR rom process (Fig. 2), so the system transforms to an ARX model [9], [10]. By estimating the coefficients in the model during the training period, the desired signal can then be estimated by the decision feedback method. To accelerate the convergence of the algorithm to reduce the estimation variance, an internal iterative algorithm is introduced [8]. On top of that, the convergence analysis of the proposed algorithm is given, the closed form of the MMSE of the algorithm is derived as the lower bound of its performance. The received signal model, architecture of the proposed adaptive filters, detailed algorithm, convergence analysis, simulation results are illustrated explained in Sections II VI, respectively. Finally, the conclusions are drawn in Section VII. II. SIGNAL MODEL Let denote the transmitted signal, constant dc offset, varying dc offset, flicker noise, respectively. In this paper, the bold lower case letters represent complex variables, the upper case letters represent vectors, bold /$ IEEE

3 1142 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 55, NO. 4, MAY 2008 imaginary parts, respectively. Then, can be modeled by using a matrix notation according to [4] as (5) Fig. 2. PSD of flicker noise. upper case letters represent matrices. Here, denotes the discrete time index. Then, the received signal corrupted by ISI, dc offsets, flicker noise can be written as Here, are the coefficients of the channel discrete-time impulse response (assuming minimum phase channel in this paper) is the order of channel response. Since is a highly colored noise, it can be modeled as an AR rom process as [9], [11] Here, is the order, are the coefficients, is the innovation. is chosen to make the power spectral density (PSD) of the generated close to the PSD of the flicker noise. as Then, the -transform of can be represented as where is the -transform of in (2). Next, we take the transceiver mismatch into consideration. Assume that denote the amplitude gains of the channels, respectively; denotes the phase splitter mismatch is split equally between the channels for symmetry; denotes the equivalent transceiver mismatch induced signal, where are its real (1) (2) (3) (4) Here, represents the mismatch matrix. The mismatch model in (5) is applied to an AR model in (1) through signal. Since all of the delay effect due to the channel is modeled in (1), the mismatch delay (if any) is also modeled in (5). When, (5) becomes, there is no mismatch. When, amplitude mismatch occurs. When, phase mismatch occurs. If mismatch exists, it can be mitigated by inverse modeling (e.g., refer to [11, Sec ]). Considering that there are four elements in the matrix, a four-real-tap equalizer is employed to model the inverse of it. According to the model in (5), a four-real-tap equalizer can remove both the amplitude mismatch the phase mismatch simultaneously. Furthermore, considering the effect of additive white Gaussian noise (AWGN), the digitalized baseb signal after the ADC can be represented as Note that this paper deals with the baseb equivalent model. It can be verified that the noise generated in the RF front-end can be modeled equivalently in (6), which is a digital baseb equivalent model [13]. III. ARCHITECTURE OF THE ADAPTIVE FILTER Based on the system model in Section II, an integrated adaptive filter equalizer is proposed in Fig. 3. It is composed of, in sequence, a mismatch canceller, a dc offsets canceller, a complex feed-forward equalizer (CFFE), a complex decision-feedback equalizer (CDFE). In this sequence, the mismatch matrix will also be applied to the dc offset flicker noise. However, the model is still valid, as typically the dc offset is generated due to the self-mixing of the mixer transistor mismatch in either mixer in the or channel [1]. Thus, the equivalent dc offset in the channels can be different, this can be modeled by the mismatch model. Similarly, flicker noise is mainly generated due to the usage of CMOS transistors in building the RF front-end (LNA mixer). Since the transistors built into the channel have some mismatch with those in the channel during fabrication, the equivalent total flicker noise generated in the channel is different from that in the channel, thus the mismatch model is also applied to flicker noise to account for this effect. In the mismatch canceller, which is a four-real-tap equalizer, the taps are used to cancel the amplitude imbalance while the taps are used to cancel the component of in the component of in, respectively. The output of the mismatch canceller is treated as a complex valued signal with the signal in the channel as its real part the signal in the channel as its imaginary part. At (6)

4 ZHENG et al.: ADAPTIVE FILTERING ALGORITHM FOR DCRS: ARCHITECTURE AND PERFORMANCE ANALYSIS 1143 Drop replace in (1) with. Take the transform, according to (2) (4), we obtain (11) Here,. are the -transforms of, respectively. can also be represented as (12) In this paper, we assume that the channel is minimum phase. Since (11) is an ARX model, given, the coefficients of can be estimated as, respectively, during training period. Then, the desired signal can be estimated during decision period by [8], [10] (13) Fig. 3. Signal flow the proposed adaptive filter. Here, denotes the estimated transmitted sequence. The output the filtering error signal during training period are, a complex valued tap cancels off the dc offsets [3]. After which, CFFE mitigates ISI followed by CDFE, which mitigates flicker noise provides data estimation. IV. ALGORITHM Using the model in Section II, the output of the mismatch canceller, as in Fig. 3, is denotes the taps of the mismatch can- denotes the tap of the dc offsets canceller, then can be represented as Here, celler, the output (7) (8) (9) (10) The superscript * denotes complex conjugation, all of the taps of the filters are given in their complex conjugation forms in Fig. 3. During the derivation of the algorithm, AWGN is dropped. Despite this, simulated results (with AWGN) using the derived algorithm are still very good. In addition, in practical situations, the input SNR for receiver is normally high (around 20 db), so neglecting AWGN here is reasonable. Referring to Fig. 3, is with mismatch dc offsets cancelled. (14) (15) where denote the orders of the CFFE CDFE taps, respectively. denote the CFFE tap values, CDFE tap values, the training signal, respectively. The coefficients of in (11) are estimated by the taps in (14), respectively, by using the least-mean-square (LMS) algorithm [11], [12]. Without loss of generality, assume. In this case, the estimated coefficients will be obtained by the adaptations of, respectively. as the step sizes for adjusting, respectively. According to the LMS algorithm, the closed forms of the taps adaptations are given as (16) (17) (18) (19)

5 1144 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 55, NO. 4, MAY 2008 where in (16) can be derived by taking partial derivatives of with respect to. It is obvious that the adaptations of influence mutually. Hence, we propose an internal iterative algorithm below to accelerate the convergence of the algorithm to reduce the estimation variance [8]. Let denote the total number of internal iterations. denote the updated values of, respectively, after internal iterations at time. To reduce the complexity of the algorithm, are only updated do not take part in the internal iterations at time. Simulation results show that whether or not take part in the internal iterations makes little difference to the performance. Hence, the internal iterations for are as follows: (20) (21) It is obvious that the algorithm will converge only when the taps of all of the equalizers converge the convergence of CFFE CDFE plays a dominant role. as the maximum eigenvalues of, respectively. When are kept fixed, can be regarded as a channel response of input 1. Therefore, when only considering CFFE CDFE, they will converge when meet the following requirements (see [11, Sec. 6.2]): (30) (31) Equations (30) (31) only guarantee the convergence of CFFE CDFE. When are adapted to two sets of values, e.g., (not necessarily the optimum convergence values), the algorithm will converge when converge as well. In the following convergence analysis of are regarded as constant values. (32) (33) (22) (23) (34) (35) (24) as the mean square error. Then where above are general symbolic functions. At time, the initial tap values are the latest updated tap values at time. The next internal iteration goes so forth. After all of the taps converged to their optimum values, the training sequence is replaced by the estimated sequence. (36) A. Convergence Analysis V. PERFORMANCE ANALYSIS (25) (26) According to the LMS algorithm (37) (27) (38) During training period, according to (14), as (28) can be written (29), where the subscript represents the optimum value. By taking the expectation of (38) setting to zero, it can be obtained that (39)

6 ZHENG et al.: ADAPTIVE FILTERING ALGORITHM FOR DCRS: ARCHITECTURE AND PERFORMANCE ANALYSIS 1145 Therefore, the convergence condition for is (40) mismatch canceller, dc canceller, CFFE, CDFE are close to their optimum, according to (14), the output can be represented as By similar derivations, it can be obtained that (40) is also the convergence condition for. The convergence condition for is (41) Combining (40) (41), the will converge when mismatch canceller (48) From (15), (46), (48), it can be obtained that (42) It can be obtained that (43) (44) (49) Recall that. Assume that is white, zero mean with covariance ; are mutually independent; are zero mean; are independent of, respectively. Then (45) (50) Here, is obtained by setting to zero. Then, the convergence condition of the dc offset canceller is (51) (46) Because we can always find to satisfy (30), (31), (42), (46) simultaneously, the mean convergence of the algorithm is guaranteed. B. MMSE Analysis According to (11), in time domain can be written as (47) Here, represents the received signal vector with mismatch dc offsets fully cancelled, i.e., are at their optimum values, respectively. Let denote the estimated vectors of, respectively, represent the weight-error vectors, represents the error vector caused by the estimation error of. Then, after all of the taps of the (52) as the error caused by the weight-error vectors as the errors caused by the, respectively. Then, according to the derivations in [11, Sec ], we have (53) (54) (55) (56)

7 1146 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 55, NO. 4, MAY 2008 According to the misadjustment analysis of the LMS algorithm in [11, Sec ], it can be approximated that (57) (58) where is a constant that is determined by the optimum values of. Similarly, it can be obtained that (59) Here, denotes the minimum element of in (25). The weight-error vector is much smaller than the true vector when the taps are near convergence. Assuming that the value of is 10% that of, then is only 1% of. Therefore, can be ignored in (56). Thus, when, (56) can be written as Fig. 4. BER performance of the mismatch canceller. (60) When there is no mismatch canceller, dc offsets canceller, CDFE,, then (60) becomes (61) If there is no mismatch, dc offsets, or flicker noise, then. The received signal to be processed by the adaptive filter becomes the transmitted signal that is only corrupted by ISI a white noise with variance of. The autocorrelation matrix of the transmitted signal corrupted by ISI in this case becomes. Then, (61) becomes the MMSE of a stard LMS algorithm. VI. SIMULATION RESULTS In Fig. 4, five curves are illustrated to show the efficiency of the mismatch canceller when the dc offset canceller is absent. In the simulations, 16 quaternary amplitude modulation (QAM) signals are passed through a given channel then corrupted by mismatch AWGN. In condition 1,,, in condition 2,. Without the mismatch canceller, the bit error rates (BERs) of the two curves are around, but with the canceller they decreased dramatically. The method to cancel dc offsets by one tap is discussed in many papers [3], [8]. Fig. 5 is obtained when quaternary phaseshift keying (QPSK) signals are passed through a given channel. When only flicker noise ISI exist, only CFFE is employed, the BER is around. However, after employing the CDFE, the BER reaches at db. When ISI, flicker noise, mismatch, varying dc offsets with the similar energy of the transmitted Fig. 5. BER performance of the proposed algorithm. signal exist simultaneously, the BER reaches at SNR 25 db. Fig. 6 is obtained when the QPSK signal is passed through a given channel corrupted by mismatch, dc offsets, flicker noise, AWGN as modeled in Section II. In the simulations, the internal iterative number. The learning curve of the algorithm is obtained by an ensemble average of the sequence over 100 independent runs. As shown in Fig. 6, the learning curve with internal iterations converges within 1000 iterations, which is much faster than that without internal iterations. The MSE of the algorithm with internal iterations is also smaller than that of the algorithm without internal iterations. Generally, the proposed algorithm is applied to a slow fading channel. For a fast fading channel, the proposed algorithm should improve convergence speed by incorporating some dedicated speeding algorithm. To verify the proposed algorithm, comprehensive simulation results are given when binary phase-shift keying (BPSK), QPSK, 16-QAM signals are passed through a given

8 ZHENG et al.: ADAPTIVE FILTERING ALGORITHM FOR DCRS: ARCHITECTURE AND PERFORMANCE ANALYSIS 1147 Fig. 6. Learning curve of the proposed algorithm without with internal iterations. Fig. 8. Comprehensive BER performance of QPSK. Fig. 7. Comprehensive BER performance of BPSK. Fig. 9. Comprehensive BER performance of 16 QAM. channel are corrupted by all of the distortions such as mismatch, dc offsets, flicker noise, AWGN, respectively. As shown in Figs. 7 9, the lower bound is obtained when the transmitted signal is only corrupted by ISI AWGN. In the simulations, SDR 10 db where SDR represents the power ratio of the desired signal to the dc offset. The flicker noise is generated as modeled in Section II, but its power is changed accordingly. In condition 1, SFR db. Here, SFR represents the power ratio of the desired signal to the flicker noise. In condition 2, SFR db. In condition 3, SFR db. As shown in Figs. 7 9, the BER curves of the three conditions are close to one another are robust to mismatch flicker noise. Fig. 10 shows the learning curve of MSE the derived MMSE. It is obtained when a QPSK signal is passed through a given channel corrupted by mismatch, dc offsets, flicker noise. The learning curve of the algorithm is obtained by an ensemble average of the sequence over 100 indepen- Fig. 10. Learning curve of MSE the derived MMSE. dent runs. As shown in Fig. 10, the derived MMSE provides a close lower bound for the steady-state MSE.

9 1148 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 55, NO. 4, MAY 2008 VII. CONCLUSION In this paper, an adaptive algorithm has been proposed to cancel mismatch, dc offsets, flicker noise, ISI simultaneously in both the channels in DCRs by using adaptive filters. To accelerate the convergence of the algorithm to reduce the estimation variance, an internal iterative algorithm is proposed. In addition, the convergence analysis of the proposed algorithm is given, the closed form of the MMSE of the proposed algorithm is derived. Simulation results are provided to verify the superior performance of the proposed algorithm. REFERENCES [1] B. Razavi, Design considerations for direct-conversion receivers, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 44, no. 6, pp , Jun [2] W. Namgoong T. H. Meng, Direct-conversion RF receiver design, IEEE Trans. Commun., vol. 49, no. 3, pp , Mar [3] M. Faulkner, DC offset IM2 removal in direct conversion receivers, IEE Proc. Commun., vol. 149, no. 3, pp , [4] J. K. Cavers M. W. Liao, Adaptive compensation for imbalance offset losses in direct conversion transceivers, IEEE Trans. Veh. Technol., vol. 42, no. 4, pp , Oct [5] B. Razavi, RF IC design challenges, in Proc. Design Automation Conf., San Francisco, CA, 1998, pp [6] A. A. Abidi, Direct-conversion radio transceivers for digital communications, IEEE J. Solid-State Circuits, vol. 30, pp , [7] H. Yoshida, H. Tsurumi, Y. Suzuki, DC offset canceller in a direct conversion receiver for QPSK signal reception, in Proc. 9th IEEE Int. Symp. Pers., Indoor Mobile Radio Commun., 1998, vol. 3, pp [8] C. Mingzheng, Z. Yuanjin, H. K. Garg, A novel adaptive equalizer compensator for direct conversion receivers, in Proc. 9th IEEE Singapore Int. Conf. Commun. Syst., 2004, pp [9] C. Mingzheng, Z. Yuanjin, H. K. Garg, A novel algorithm for DC offsets flicker noise cancellation in direct conversion receivers, in Proc. 9th IEEE Singapore Int. Conf. Commun. Syst., 2004, pp [10] L. Ljung, System Identification: Theory for the User, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, [11] B. F. Boroujeny, Adaptive Filters: Theory Applications. New York: Wiley, [12] S. Haykin, Adaptive Filter Theory, 4th ed. Upper Saddle River, NJ: Prentice-Hall, [13] J. G. Proakis, Digital Communicationis, 4th ed. New York: McGraw- Hill, Mingzheng Cao (S 07) received the B.Sc. degree in electrical engineering automation from Tianjin University, Tianjin, China, in 1996, the M.Sc. degree in electrical engineering from the National University of Singapore (NUS), Singapore, in He is currently working toward the Ph.D. degree in electrical engineering at the New Jersey Institute of Technology (NJIT), Newark. From 1996 to 2001, he was with the China Petroleum Chemical Corporation (Sinopec), from 2001 to 2003, he was with Automation Drive Group, Siemens Ltd., China. During his graduate studies at NUS, he was with the Institute of Microelectronics (IME) of Singapore, where he was involved with the distortion mitigation for direct-conversion receiver design. His research focuses on signal processing for wireless communications. E. K. H. Teo received the B.Eng. (Hons.) degree in electrical engineering from the National University of Singapore (NUS), Singapore, in He is now with the Defence Science Organisation (DSO) National Laboratories, Singapore. His research interests are digital signal processing system implementations on FPGAs. Hari K. Garg (SM 07) received the B.Tech. degree in electrical engineering from the Indian Institute of Technology, Delhi, in 1981, the M.Eng. Ph.D. degrees from Concordia University, Montreal, QC, Canada, in , respectively, the M.B.A. degree from Syracuse University, Syracuse, NY, in He was a faculty member with Syracuse University from 1985 until He has been with the National University of Singapore since 1995, with the exception of , when he was with Philips. His research interests are in the areas of digital signal/image processing, wireless communications, coding theory, digital watermarking. He has published extensively on these related topics. He is also the founder of several companies in the space of mobile telephony. Yuanjin Zheng (M 03) received the B.S. M.Eng. degrees from Xi an Jiaotong University, China, in , respectively, the Ph.D. degree from Nanyang Technological University, Singapore, in From July 1996 to April 1998, he was with the National Key Lab of Optical Communication Technology, University of Electronic Science Technology of China, as a Research Scientist. In March 2001, he joined the Institute of Microelectronics, A*STAR, Singapore, where he has helped to develop various wireless such as WLAN, WCDMA, UWB radio transceiver ICs. His research interests are RF transceiver communication systems, analog digital ICs, DSP algorithm design implementations. He has published over 60 international journal conference papers one book chapter has four U.S. patents granted two U.S. patents pending.