This graduate course is to provide students with the capability of identifying spectrally correlated random processes and properly processing them by exploiting the spectral correlation.
The applications are mainly to signal processing, digital communications, and sensing.

EECE574 Probability and Random Processes

3 midterms and final exam
homeworks and project

No textbook
Papers published by CISL on the topic of spectrally correlated random processes will be studied thoroughly through this course.

* [J6] J. H. Cho, ``Joint transmitter and receiver optimization in additive cyclostationary noise,'' IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3396--3405, Dec. 2004.
* [J10] J. H. Cho and W. Gao, ``Continuous-time equivalents of Welch bound equality sequences,'' IEEE Trans. Inf. Theory, vol. 51, no. 9, pp. 3176--3185, Sep. 2005.
* [DJ1] Y. H. Yun and J. H. Cho, ``Joint Tx-Rx optimization in additive cyclostationary noise with zero forcing criterion,'' The Journal of KICS (Korea Information and Communication Society), vol. 32, no. 7, pp. 724--729, Jul. 2007.
* [J13] J. H. Cho, Q. Zhang, and L. Gao, ``A comparison of frequency-division systems to code-division systems in overloaded channels," IEEE Trans. Commun., vol. 56, no. 2, pp. 289--298, Feb. 2008.
* [J14] J. H. Cho, ``Multi-user constrained water-pouring for continuous-time overloaded Gaussian multiple-access channels,'' IEEE Trans. Inf. Theory, vol. 54, no. 4, pp. 1437--1459, Apr. 2008.
* [J15] Y. H. Yun and J. H. Cho, ``An optimal orthogonal overlay for a cyclostationary legacy signal, '' IEEE Trans. Commun., vol. 58, no. 5, pp. 1557-1567, May 2010.
* [J16] Y. G. Yoo and J. H. Cho, ``Asymptotically optimal low-complexity SC-FDE in data-like co-channel interference,'' IEEE Trans. Commun., vol. 58, no. 6, pp. 1718-1728, June, 2010.
* [J17] Y. G. Yoo and J. H. Cho, ``Asymptotic optimality of binary faster-than-Nyquist signaling,'' IEEE Commun. Letters, vol. 14, no. 9, pp. 788-790, Sept. 2010.
* [J18] B. W. Han and J. H. Cho, ``Capacity of Second-Order cyclostationary Gaussian noise channels,'' IEEE Trans. Commun., vol. 60, no. 1, pp. 89--100, Jan., 2012.
* [J19] Y. H. Yun and J. H. Cho, ``Sum-rate optimal multi-code CDMA systems: An equivalence result,'' IEEE Trans. Inf. Theory ,vol. 59, no. 12, pp. 8295--8317, Dec. 2013.
* [J20] J. Yeo and J. H. Cho, ``Asymptotic frequency-shift properizer for block processing of improper-complex DT SOCS random processes,'' IEEE Trans. Inf. Theory, vol. 60, no. 7, pp. 4083-4100, July 2014.
* [J22] J. Yeo, J. H. Cho, and J. S. Lehnert, ``Joint transmitter and receiver optimization for improper-complex second-order stationary data sequence,'' Journal of Communications and Networks, vol. 17, no.1, pp.1--11, Feb. 2015.
* [J23] J. Yeo, B. W. Han, J. H. Cho, and J. S. Lehnert, ``Capacity of an orthogonal overlay channel,'' IEEE Trans. Wireless Commun., vol. 14, no. 11, pp. 6111--6124, Nov. 2015.
* [J24] M. Kim, J. H. Cho, and J. S. Lehnert, ``Asymptotically optimal low-complexity SC-FDE with noise prediction in data-like improper-complex interference,'' IEEE Transactions on Wireless Commun., vol. 15, no. 3, pp. 2090--2103, Mar. 2016.
* [J28] J. Choi, J. Kim, J. H. Cho, and J. S. Lehnert,``Widely-linear Nyquist criteria for DFT-spread OFDM of constellation-rotated PAM symbols,'' IEEE Trans. Commun., vol. 69, no. 5, pp2909--2922, May 2021.
* [J29] J. Choi, J. H. Cho, and J. S. Lehnert, ``Continuous-phase modulation for DFT-spread localized OFDM,'' IEEE Open Journal of Communications Society, vol. 2, pp. 1405--1418, June 2021.
* [J31] J. Chae, J. Choi, J. Kim, and J. H. Cho, ``A low-complexity widely-linear MMSE equalizer for DFT-spread OFDM with frequency-domain spectrum shaping," IEEE Trans. Wireless Commun., vol. 23, no. 4, pp. 3465--3479, Apr. 2024.
* [J32] J. Chae and J. H. Cho, ``An ADC-aware receiver design for multi-user MIMO underlay system with strong cyclostationary legacy signal,'' IEEE Access, vol. 11, pp. 119788--119801, 2023.

References
[1] Papoulis, Probability, Random Variables and Stochastic Processes
[2] Peebles, Probability, Random Variables, and Random Signal Principles
[3] Schreier and Scharf, Statistical Signal Processing of Complex-Valued Data
[4] Gardner, Cyclostationarity in communications and signal processing
[5] Napolitano, Cyclostationary Processes and Time Series
[6] Napolitano, Generalizations of Cyclostationary Signal Processing

1 Random Process
2 Real-Valued Process and Spectral Correlation
3 Real-Valued Wide-Sense Stationary Random Process and Spectral Correlation
4 Real-Valued Wide-Sense Cyclostationary Random Process and Spectral Correlation
5 Complex-Valued Process and Spectral Correlation
6 Proper-Complex Random Process and Spectral Correlation
7 Proper-Complex Wide-Sense Stataionary Random Process and Spectral Correlation
8 Proper-Complex Wide-Sense Cyclostataionary Random Process and Spectral Correlation
9 Improper-Complex Random Process and Spectral Correlation
10 Improper-Complex Wide-Sense Stataionary Random Process and Spectral Correlation
11 Improper-Complex Wide-Sense Cyclostataionary Random Process and Spectral Correlation
12 Digitally-Modulated Signal as a Cyclostationary Random Process
13 Digitally-Modulated Signal and Spectral Correlation
14 Digitally-Modulated Signal and Linear Estimation
15 Digitally-Modulated Signal and Widelay-Linear Estimation

Classroom meetings