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Signal Reconstruction Algorithms for Time-Interleaved ADCs
Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

An analog-to-digital converter (ADC) is a key component in many electronic systems. It is used to convert analog signals to the equivalent digital form. The conversion involves sampling which is the process of converting a continuous-time signal to a sequence of discrete-time samples, and quantization in which each sampled value is represented using a finite number of bits. The sampling rate and the effective resolution (number of bits) are two key ADC performance metrics. Today, ADCs form a major bottleneck in many applications like communication systems since it is difficult to simultaneously achieve high sampling rate and high resolution. Among the various ADC architectures, the time-interleaved analog-to-digital converter (TI-ADC) has emerged as a popular choice for achieving very high sampling rates and resolutions. At the principle level, by interleaving the outputs of M identical channel ADCs, a TI-ADC could achieve the same resolution as that of a channel ADC but with M times higher bandwidth. However, in practice, mismatches between the channel ADCs result in a nonuniformly sampled signal at the output of a TI-ADC which reduces the achievable resolution. Often, in TIADC implementations, digital reconstructors are used to recover the uniform-grid samples from the nonuniformly sampled signal at the output of the TI-ADC. Since such reconstructors operate at the TI-ADC output rate, reducing the number of computations required per corrected output sample helps to reduce the power consumed by the TI-ADC. Also, as the mismatch parameters change occasionally, the reconstructor should support online reconfiguration with minimal or no redesign. Further, it is advantageous to have reconstruction schemes that require fewer coefficient updates during reconfiguration. In this thesis, we focus on reducing the design and implementation complexities of nonrecursive finite-length impulse response (FIR) reconstructors. We propose efficient reconstruction schemes for three classes of nonuniformly sampled signals that can occur at the output of TI-ADCs.

Firstly, we consider a class of nonuniformly sampled signals that occur as a result of static timing mismatch errors or due to channel mismatches in TI-ADCs. For this type of nonuniformly sampled signals, we propose three reconstructors which utilize a two-rate approach to derive the corresponding single-rate structure. The two-rate based reconstructors move part of the complexity to a symmetric filter and also simplifies the reconstruction problem. The complexity reduction stems from the fact that half of the impulse response coefficients of the symmetric filter are equal to zero and that, compared to the original reconstruction problem, the simplified problem requires only a simpler reconstructor.

Next, we consider the class of nonuniformly sampled signals that occur when a TI-ADC is used for sub-Nyquist cyclic nonuniform sampling (CNUS) of sparse multi-band signals. Sub-Nyquist sampling utilizes the sparsities in the analog signal to sample the signal at a lower rate. However, the reduced sampling rate comes at the cost of additional digital signal processing that is needed to reconstruct the uniform-grid sequence from the sub-Nyquist sampled sequence obtained via CNUS. The existing reconstruction scheme is computationally intensive and time consuming and offsets the gains obtained from the reduced sampling rate. Also, in applications where the band locations of the sparse multi-band signal can change from time to time, the reconstructor should support online reconfigurability. Here, we propose a reconstruction scheme that reduces the computational complexity of the reconstructor and at the same time, simplifies the online reconfigurability of the reconstructor.

Finally, we consider a class of nonuniformly sampled signals which occur at the output of TI-ADCs that use some of the input sampling instants for sampling a known calibration signal. The samples corresponding to the calibration signal are used for estimating the channel mismatch parameters. In such TI-ADCs, nonuniform sampling is due to the mismatches between the channel ADCs and due to the missing input samples corresponding to the sampling instants reserved for the calibration signal. We propose three reconstruction schemes for such nonuniformly sampled signals and show using design examples that, compared to a previous solution, the proposed schemes require substantially lower computational complexity.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. , 80 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1672
National Category
Communication Systems
Identifiers
URN: urn:nbn:se:liu:diva-117826DOI: 10.3384/diss.diva.117826ISBN: 978-91-7519-062-4 (print)OAI: oai:DiVA.org:liu-117826DiVA: diva2:810966
Public defence
2015-06-12, NOBEL BL32, B-huset, Campus Valla, Linköping, 17:15 (English)
Opponent
Supervisors
Available from: 2015-05-22 Created: 2015-05-08 Last updated: 2015-05-25Bibliographically approved
List of papers
1. Two-rate based low-complexity time-varying discrete-time FIR reconstructors for two-periodic nonuniformly sampled signals
Open this publication in new window or tab >>Two-rate based low-complexity time-varying discrete-time FIR reconstructors for two-periodic nonuniformly sampled signals
2012 (English)In: Sampling Theory in Signal and Image Processing, ISSN 1530-6429, Vol. 11, no 2-3, 195-220 p.Article in journal (Refereed) Published
Abstract [en]

This paper deals with time-varying finite-length impulse response (FIR) filters used for reconstruction of two-periodic nonuniformly sampled signals. The complexity of such reconstructorsincreases as their bandwidth approaches the whole Nyquist band. Reconstructor design that yields minimum reconstructor order requires expensive online redesign while those methods that simplify online redesign result in higher reconstructor complexity. This paper utilizes a two-rate approach to derive a single-rate structure where part of the complexity of the reconstructor is moved to a symmetric filter so as to reduce the number of multipliers. The symmetric filter is designed such that it can be used for all time-skew errors within a certain range, thereby reducing the number of coefficients that need online redesign. The basic two-rate based reconstructor is further extended to completely remove the need for online redesign at the cost of a slight increase in the total number of multipliers.

Place, publisher, year, edition, pages
Sampling Publishing, 2012
Keyword
Finite-length impulse response (FIR) filters, least-squares design, two-rate approach, periodic nonuniform sampling, time-interleaved analog-to-digital converters (TI-ADCs), reconstruction filters
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-105470 (URN)2-s2.0-84896442526 (Scopus ID)
Funder
Swedish Research Council
Available from: 2014-03-25 Created: 2014-03-25 Last updated: 2017-12-05
2. Efficient signal reconstruction scheme for M-channel time-interleaved ADCs
Open this publication in new window or tab >>Efficient signal reconstruction scheme for M-channel time-interleaved ADCs
2013 (English)In: Analog Integrated Circuits and Signal Processing, ISSN 0925-1030, E-ISSN 1573-1979, Vol. 77, no 2, 113-122 p.Article in journal (Refereed) Published
Abstract [en]

In time-interleaved analog-to-digital converters (TI-ADCs), the timing mismatches between the channels result in a periodically nonuniformly sampled sequence at the output. Such nonuniformly sampled output limits the achievable resolution of the TI-ADC. In order to correct the errors due to timing mismatches, the output of the TI-ADC is passed through a digital time-varying finite-length impulse response reconstructor. Such reconstructors convert the nonuniformly sampled output sequence to a uniformly spaced output. Since the reconstructor runs at the output rate of the TI-ADC, it is beneficial to reduce the number of coefficient multipliers in the reconstructor. Also, it is advantageous to have as few coefficient updates as possible when the timing errors change. Reconstructors that reduce the number of multipliers to be updated online do so at a cost of increased number of multiplications per corrected output sample. This paper proposes a technique which can be used to reduce the number of reconstructor coefficients that need to be updated online without increasing the number of multiplications per corrected output sample.

Place, publisher, year, edition, pages
Springer, 2013
Keyword
Finite-length impulse response (FIR) filters, Least-squares design, Two-rate approach, Periodically nonuniform sampling, Time-interleaved analog-to-digital converters (TI-ADCs), Reconstruction filters
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-100965 (URN)10.1007/s10470-013-0115-x (DOI)000326453400004 ()
Funder
Swedish Research Council
Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2017-12-06Bibliographically approved
3. Low-complexity two-rate based multivariate impulse response reconstructor for time-skew error correction in m-channel time-interleaved ADCs
Open this publication in new window or tab >>Low-complexity two-rate based multivariate impulse response reconstructor for time-skew error correction in m-channel time-interleaved ADCs
2013 (English)In: IEEE International Symposium on Circuits and Systems (ISCAS), 2013, IEEE , 2013, 2936-2939 p.Conference paper, Published paper (Refereed)
Abstract [en]

Nonuniform sampling occurs in time-interleaved analog-to-digital converters (TI-ADC) due to timing mismatches between the individual channel analog-to-digital converters (ADCs). Such nonuniformly sampled output will degrade the achievable resolution in a TI-ADC. To restore the degraded performance, digital time-varying reconstructors can be used at the output of the TI-ADC, which in principle, converts the nonuniformly sampled output sequence to a uniformly sampled output. As the bandwidth of these reconstructors increases, their complexity also increases rapidly. Also, since the timing errors change occasionally, it is important to have a reconstructor architecture that requires fewer coefficient updates when the value of the timing error changes. Multivariate polynomial impulse response reconstructor is an attractive option for an M-channel reconstructor. If the channel timing error varies within a certain limit, these reconstructors do not need any online redesign of their impulse response coefficients. This paper proposes a technique that can be applied to multivariate polynomial impulse response reconstructors in order to further reduce the number of fixed-coefficient multipliers, and thereby reduce the implementation complexity.

Place, publisher, year, edition, pages
IEEE, 2013
Series
IEEE International Symposium on Circuits and Systems, ISSN 0271-4310
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-106537 (URN)10.1109/ISCAS.2013.6572494 (DOI)000332006803036 ()978-1-4673-5760-9 (ISBN)
Conference
IEEE International Symposium on Circuits and Systems (ISCAS), 19-23 May 2013, Beijing, China
Available from: 2014-05-12 Created: 2014-05-09 Last updated: 2015-05-22Bibliographically approved
4. Efficient Recovery of Sub-Nyquist Sampled Sparse Multi-Band Signals Using Reconfigurable Multi-Channel Analysis and Modulated Synthesis Filter Banks
Open this publication in new window or tab >>Efficient Recovery of Sub-Nyquist Sampled Sparse Multi-Band Signals Using Reconfigurable Multi-Channel Analysis and Modulated Synthesis Filter Banks
2015 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 19, 5238-5249 p.Article in journal (Refereed) Published
Abstract [en]

Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal. Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid samples. In order to recover the missing uniform-grid samples, the sequence obtained via CNUS is passed through a reconstructor. At present, these reconstructors have very high design and implementation complexity that offsets the gains obtained due to sub-Nyquist sampling. In this paper, we propose a scheme that reduces the design and implementation complexity of the  reconstructor. In contrast to the existing reconstructors which use only a multi-channel synthesis filter bank (FB), the proposed reconstructor utilizes both analysis and synthesis FBs which makes it feasible to achieve an order-of-magnitude reduction of the complexity. The analysis filters are implemented using polyphase networks whose branches are allpass filters with distinct fractional delays and phase shifts. In order to reduce both the design and the implementation complexity of the  synthesis FB, the synthesis filters are implemented using a cosine-modulated FB. In addition to the reduced complexity of the reconstructor, the proposed multi-channel recovery scheme also supports online reconfigurability which is required in flexible (multi-mode) systems where the user subband locations vary with time.

Place, publisher, year, edition, pages
IEEE, 2015
Keyword
Sub-Nyquist sampling, sparse multi-band signals, reconstruction, nonuniform sampling, time-interleaved analog-to-digital converters, filter banks
National Category
Communication Systems
Identifiers
urn:nbn:se:liu:diva-117824 (URN)10.1109/TSP.2015.2451104 (DOI)000360852200017 ()
Available from: 2015-05-08 Created: 2015-05-08 Last updated: 2017-12-04Bibliographically approved
5. A sub-band based reconstructor for M-channel time-interleaved ADCs with missing samples
Open this publication in new window or tab >>A sub-band based reconstructor for M-channel time-interleaved ADCs with missing samples
2014 (English)In: 2014 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE conference proceedings, 2014Conference paper, Published paper (Refereed)
Abstract [en]

This paper proposes a scheme for the recovery of a uniformly sampled sequence from the output of a time-interleaved analog-to-digital converter (TI-ADC) with static time-skew errors and missing samples. Nonuniform sampling occurs due to timing mismatches between the individual channel ADCs and also due to missing input samples as some of the sampling instants are reserved for estimating the mismatches in the TI-ADC. In addition to using a non-recursive structure, the proposed reconstruction scheme supports online reconfigurability and reduces the computational complexity of the reconstructor as compared to a previous solution.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2014
Series
International Conference on Acoustics Speech and Signal Processing ICASSP, ISSN 1520-6149
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-103931 (URN)10.1109/ICASSP.2014.6854378 (DOI)000343655304030 ()978-1-4799-2893-4 (ISBN)
Conference
IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014), Florence, Italy, May 4-9, 2014
Available from: 2014-02-03 Created: 2014-02-03 Last updated: 2015-05-22Bibliographically approved
6. Two reconstructors for M-channel time-interleaved ADCs with missing samples
Open this publication in new window or tab >>Two reconstructors for M-channel time-interleaved ADCs with missing samples
2014 (English)In: IEEE 12th International New Circuits and Systems Conference (NEWCAS), 2014, IEEE conference proceedings, 2014, 41-44 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we explore two nonrecursive reconstructors which recover the uniform-grid samples from the output of a time-interleaved analog-to-digital converter (TI-ADC) that uses some of the sampling instants for estimating the mismatches in the TI-ADC. Nonuniform sampling occurs due to timing mismatches between the individual channel ADCs and also due to missing input samples. Compared to a previous solution, the reconstructors presented here offer substantially lower computational complexity.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2014
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-106048 (URN)10.1109/NEWCAS.2014.6933980 (DOI)000363906700011 ()
Conference
12th IEEE International New Circuits and Systems Conference (NEWCAS), Trois-Rivières, Canada, June 22-25, 2014.
Available from: 2014-04-19 Created: 2014-04-19 Last updated: 2015-12-03Bibliographically approved
7. Prefilter-Based Reconfigurable Reconstructor for Time-Interleaved ADCs With Missing Samples
Open this publication in new window or tab >>Prefilter-Based Reconfigurable Reconstructor for Time-Interleaved ADCs With Missing Samples
2015 (English)In: IEEE Transactions on Circuits and Systems - II - Express Briefs, ISSN 1549-7747, E-ISSN 1558-3791, Vol. 62, no 4, 392-396 p.Article in journal (Refereed) Published
Abstract [en]

This brief proposes a reconstruction scheme for the compensation of frequency-response mismatch errors at the output of a time-interleaved analog-to-digital converter (TI-ADC) with missing samples. The missing samples are due to sampling instants reserved for estimating the channel mismatch errors in the TI-ADC. Compared with previous solutions, the proposed scheme offers substantially lower computational complexity.

Place, publisher, year, edition, pages
IEEE Press, 2015
Keyword
Reconstruction, frequency-response mismatch errors, time-interleaved analog-to-digital converters, reconfigurable reconstructors
National Category
Communication Systems
Identifiers
urn:nbn:se:liu:diva-117769 (URN)10.1109/TCSII.2014.2387651 (DOI)000352306200016 ()
Available from: 2015-05-08 Created: 2015-05-08 Last updated: 2017-12-04Bibliographically approved

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