Adaptive Filtering & Synchronization

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Raised Cosine

Equations for the Raised Cosine and Square-Root Raised Cosine Shapes [https://engineering.purdue.edu/~ee538/SquareRootRaisedCosine.pdf]

Pulse Shaping Filter [https://wirelesspi.com/pulse-shaping-filter/]

TODO 📅

Bandpass Modulation

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Pulse Amplitude Modulation (PAM)

David A. Johns, ECE1392H - Integrated Circuits for Digital Communications - Fall 2001 [System Overview]

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\(S_m\) Google AI mode [https://share.google/aimode/BzYr2logpVTVs83LQ]

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snr_mpam = @(m,simga) 10*log10((4^m-1)/simga^2/3);

sigma = 0.1547;

SNR_m2 = snr_mpam(2, sigma);  % 23.1999
SNR_m3 = snr_mpam(3, sigma);  % 29.4324

Lecture 3, Tuesday January 13th 2026 - Modulation Types (PAM/QAM) [https://cioffi-group.stanford.edu/ee379a/Lectures/L3.pdf]

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Carrier & Symbol Synchronization

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\(\Delta\tau \lt \pm \frac{1}{100} T\) don't ensure \(\Delta \phi \ll 2\pi\) due to \(T \gg \frac{1}{f_c}\)

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Carrier Synchronization

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[https://ndl.ethernet.edu.et/bitstream/123456789/87843/14/LECT_13%2614.Synchronization.pdf]

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Symbol Synchronization

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[https://www.ieee802.org/3/dm/public/1125/cordaro_3dm_01_1125.pdf]

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Mathuranathan, Symbol Timing Recovery for QPSK (digital modulations) [https://www.gaussianwaves.com/2013/11/symbol-timing-recovery-for-qpsk-digital-modulations/]

Qasim Chaudhari. Early-Late Bit Synchronizer in Digital Communication [https://wirelesspi.com/early-late-bit-synchronizer-in-digital-communication/]

Igor Freire. Symbol Timing Synchronization: A Tutorial [blog, code]

BPSK synchronization Matlab

But the problem here is: "How does the receiver know the ideal sampling instants?". The solution is "someone has to supply those ideal sampling instants". A symbol time recovery circuit is used for this purpose.

Synchronization in receiver with timing recovery, matched filter for QPSK

Early/Late Symbol Recovery algorithm

  • non-decision-directed timing estimator exploits the symmetry properties of the signal

Early late synchronization

  1. If the Early Sample = Late Sample : The peak occurs at the on-time sampling instant \(T\). No adjustment in the timing is needed.
  2. If |Early Sample| > |Late Sample| : Late timing, the sampling time is offset so that the next symbol is sampled \(T-\delta/2\) seconds after the current sampling time.
  3. If |Early Sample| < |Late Sample| : Early timing, the sampling time is offset so that the next symbol is sampled \(T+\delta/2\) seconds after the current sampling time.

David Johns. ECE1392H - Integrated Circuits for Digital Communications - Fall 2001: [Timing Recovery]

Dither in Quantized Zero Crossing Detection (QZCD) (so-called 'Bang Bang' Phase Detector)

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Mueller and Muller Timing Synchronization

K. Mueller and M. Muller, "Timing Recovery in Digital Synchronous Data Receivers," in IEEE Transactions on Communications, vol. 24, no. 5, pp. 516-531, May 1976 [pdf]

Qasim Chaudhari. Mueller and Muller Timing Synchronization Algorithm [https://wirelesspi.com/mueller-and-muller-timing-synchronization-algorithm/]

Eduardo Fuentetaja. "Analysis of the M&M Clock Recovery Algorithm" [https://edfuentetaja.github.io/sdr/m_m_analysis/]

C.-P. Tzeng, D. Hodges and D. Messerschmitt, "Timing Recovery in Digital Subscriber Loops Using Baud-Rate Sampling," in IEEE Journal on Selected Areas in Communications, vol. 4, no. 8, pp. 1302-1311, November 1986 [pdf]

Google AI Mode [https://share.google/aimode/QVyCXCCXO1URdDnKD]

H. Meyr, M. Moeneclaey, and S. A. Fechtel. "Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing." Wiley [pdf]

T. Musah and A. Namachivayam, "Robust Timing Error Detection for Multilevel Baud-Rate CDR," in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 69, no. 10, pp. 3927-3939, Oct. 2022 [https://sci-hub.jp/10.1109/TCSI.2022.3191740]

Fulvio Spagna, CICC2018 Clock and Data Recovery Systems [pdf]

TODO 📅

Intersymbol Interference (ISI)

L.W. Couch, Digital and Analog Communication Systems, 8th Edition, Pearson, 2013. [pdf]

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Nyquist discovered three different methods for pulse shaping that could be used to eliminate ISI

  • Nyquist's First Method (Zero ISI): physically unrealizable (i.e., the impulse response would be noncausal and of infinite duration), inaccurate sync will cause ISI

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  • Nyquist's second method: allows some ISI to be introduced in a controlled way

  • Nyquist's third method: area under the \(h_e(t)\) pulse within the desired symbol interval, \(T_s\), is not zero, but the areas under \(h_e(t)\) in adjacent symbol intervals are zero

Nyquist Criterion & Pulses

David A. Johns, ECE1392H - Integrated Circuits for Digital Communications - Fall 2001 [System Overview]

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Matched-Filter (MF)

David A. Johns, ECE1392H - Integrated Circuits for Digital Communications - Fall 2001 [System Overview]

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Noise Enhancement in Linear Equalizers

John M. Cioffi, Lecture 13, Thursday February 19th 2026 - Intersymbol Interference, MMSE, and SNR [https://cioffi-group.stanford.edu/ee379a/Lectures/L13.pdf]

—, Lecture 14, Tuesday February 24th 2026 - Linear Equalizers [https://cioffi-group.stanford.edu/ee379a/Lectures/L14.pdf]

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Shannon–Hartley theorem

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David A. Johns, ECE1392H - Integrated Circuits for Digital Communications - Fall 2001 [Introduction]

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reference

Proakis, John G., and Masoud Salehi. Digital Communications. 5th ed. McGraw-Hill, 2008. [pdf]

Sklar, Bernard. Digital communications: fundamentals and applications. Pearson, 2021.

Ling, F. (2017). Synchronization in Digital Communication Systems. Cambridge: Cambridge University Press.

Barry, John R., Edward A. Lee, and David G. Messerschmitt. Digital communication. Springer, 2003.

Qasim Chaudhari, Wireless Communications From the Ground Up – An SDR Perspective

John M. Cioffi, [Chapter 3 - Equalization], [Chapter 6 - Fundamentals of Synchronization]

Sen M. Kuo. Real-Time Digital Signal Processing: Fundamentals, Implementations and Applications, 3rd Edition. John Wiley & Sons 2013

Stankovic, Ljubisa. (2015). Digital Signal Processing with Selected Topics.

Paulo S. R. Diniz, Adaptive Filtering: Algorithms and Practical Implementation, 5th edition [pdf], [matlab], [python]

B. Farhang-Boroujeny (2013), Adaptive Filters: Theory and Applications (2nd ed.). John Wiley & Sons, Inc.

Simon O. Haykin (2014), "Adaptive Filter Theory" Prentice-Hall, Inc. 5rd edition

A. Chan Carusone and D. A. Johns, "Analog Filter Adaptation Using a Dithered Linear Search Algorithm," IEEE Int. Symp. Circuits and Syst., May 2002. [PDF], [Slides]

—, Ph. D. Thesis, "Digital Algorithms for Analog Adaptive Filters", Feb. 2002. [http://www.eecg.utoronto.ca/~tcc/thesis.pdf]

—, "Analog Adaptive Filters," tutorial at the IEEE Int. Symp. Circuits and Syst., Bangkok, Thailand, May 2003. [http://www.eecg.utoronto.ca/~tcc/iscas03_tutorial.pdf]

—, 2022 Optimization Tools for Future Wireline Transceivers [https://www.ieeetoronto.ca/wp-content/uploads/2022/12/UofT-Future-of-Wireline-Workshop-2022.pdf]

David Johns, "Integrated Circuits for Digital Communications" [https://www.eecg.toronto.edu/~johns/nobots/courses/ece1392/slides.pdf]

Chris Li, mmse_dfe [https://github.com/ChrisZonghaoLi/mmse_dfe]

ScottXjw, equalizer-code-FFE-DFE-VolterraFFEandDFE [https://github.com/ScottXjw/equalizer-code-FFE-DFE-VolterraFFEandDFE]

Qasim Chaudhari. Maximum Likelihood Estimation of Clock Offset [https://wirelesspi.com/maximum-likelihood-estimation-of-clock-offset/]

—. Channel Estimation in Wireless Communication. [https://wirelesspi.com/channel-estimation-in-wireless-communication/]

—. Phase Locked Loop (PLL) in a Software Defined Radio (SDR) [https://wirelesspi.com/phase-locked-loop-pll-in-a-software-defined-radio-sdr/]

—. Phase Locked Loop (PLL) for Symbol Timing Recovery [https://wirelesspi.com/phase-locked-loop-pll-for-symbol-timing-recovery/]

—. How Decision Feedback Equalizers (DFE) Work [https://wirelesspi.com/how-decision-feedback-equalizers-dfe-work/]

—. Maximum Likelihood Sequence Estimation (MLSE Equalizer) [https://wirelesspi.com/maximum-likelihood-sequence-estimation-mlse-equalizer/]

—. Gardner Timing Error Detector: A Non-Data-Aided Version of Zero-Crossing Timing Error Detectors [https://wirelesspi.com/gardner-timing-error-detector-a-non-data-aided-version-of-zero-crossing-timing-error-detectors/]

—. Digital Filter and Square Timing Recovery [https://wirelesspi.com/digital-filter-and-square-timing-recovery/]

—. What is a Symbol Timing Offset and How It Distorts the Rx Signal [https://wirelesspi.com/what-is-a-symbol-timing-offset-and-how-it-distorts-the-rx-signal/]

—. How Excess Bandwidth Governs Timing Recovery in Digital Communication Systems [https://wirelesspi.com/how-excess-bandwidth-governs-timing-recovery-in-digital-communication-systems/]

—. How Automatic Gain Control (AGC) Works [https://wirelesspi.com/how-automatic-gain-control-agc-works/]