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Machine Learning for RAN: Delusion or Salvation? Slawomir Stanczak

Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

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Page 1: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Machine Learning for RAN: Delusion or Salvation?

Slawomir Stanczak

Page 2: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Why ML for Communications (=MLC)?

• Entry points for ML-based improvements

1. high complexity (bad models)

2. inefficient computation (limited resources)

3. slow convergence (low latency applications)

• Potential benefits

1. enable to cope with increased complexity

2. enhance efficiency

3. facilitate cognitive network management

4. provide robust predictions

Page 3: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Load Learning

Serving link from

cell 1

Interference from

cell 2

Test point 1 Test point 2

Test point 3

Cell 2 Cell 1

General case: M cells, N test points

Reliable rate-load mapping

estimates/predictions are

key to reliable QoS predictions

e.g. coverage holes or strong inter-cell

interference need to be predicted

Problem

What are users’ rates as a function

of the load at each base station?

• R. L. G. Cavalcante, Y. Shen, S. Stańczak, "Elementary Properties of Positive Concave Mappings with Applications to Network Planning and Optimization," IEEE Trans. Signal Processing, vol. 64, no. 7, pp. 1774-1783, April 2016

Page 4: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Performance Improvement due to Predicitons

• D. Külzer, S. Stańczak, M. Botsov, ”Novel QoS Control Framework for Automotive Safety-Related and Infotainment Servcies," submitted, Nov. 2019

Page 5: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Classic vs. ML Approach (inspired by David Wipf)

➔ ML is much more than neural networks!

ML approach (data-driven)Classic approach (model-driven)

Problem

Page 6: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

6

[Andrew Ng] Key issues:

• Energy efficiency neglected

• Domain knowledge ignored

➔ Function properties not preserved

• Choice of performance metrics

• Amount of training data

Which Tools for MLC?

Collection of training data is limited

• Fast time-varying channels and interference

• Short stationarity interval (V2X: 10-40ms)

• Distributed data

• Limitations on computational power/energy

Huge datasets are available but

• Incomplete data (missing measurements for long periods)

• Erroneous data (e.g. software bugs)

• Misaligned data (different times)

• Time series (i.i.d. unrealistic)

Lower layers (PHY/MAC) Higher layers

According to Andrew Ng

Page 7: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Load Learning (cont.)

Challenge: The rate-load mapping (RLM) is highly dynamic and

nonlinear owing to interference

➔ training must be short

➔ important properties must be preserved

• Model-based approaches require too much a priori information

But we should not ignore models

• The RLM has a rich structure (e.g., monotonicity and Lipschitz)

They are hard to exploit in typical machine learning tools

Page 8: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Hybrid-driven robust methods under uncertainty (e.g., few training samples)

Robust Online Load Learning

• D. A. Awan, R. L. G. Cavalcante, and S. Stańczak, "A robust machine learning method for cell-load approximation in wireless networks," in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2018

0 50 100 150 200

Sample Size (K)

10-1

100

Err

or

Lev

el

99.99% Error Quantile

Robust Learning

2-Nearest Neighbor

GPR- Linear

GPR- Gaussian

0 50 100 150 200

Sample Size (K)

0.2

0.4

0.6

0.8

1

Pea

rso

n's

Co

rr. C

oef

f.

Sample Correlation

Robust Learning

GPR - Gaussian

2-Nearest Neighbor

GPR - Linear

Page 9: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Demands on MLC

• Robust online ML with good tracking capabilities

➔ ML with small (uncertain) data sets

• Exploit domain knowledge (e.g. models, correlations, AoA)

➔ Hybrid-driven ML approaches (e.g. use production data)

➔ Learn features that change slowly over frequency, time...

➔ Preserve important function properties

• Distributed learning under communication constraints

➔ New functional architectures for Big Data analytics

• Low-complexity, low-latency implementation

➔ New algorithms, massive parallelization

Page 10: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

• I. Yamada and N. Ogura, “Adaptive projected subgradient method for asymptotic minimization of sequence of nonnegative convex functions,” Numerical Functional Analysis and Optimization, vol. 25, no. 7/8, pp. 593–617, 2004.

Learning in (Reproducing Kernel) Hilbert Spaces

Use projection methods in RKHS:

➔ Easy to exploit side information

➔ Initial fast speed

➔ Low complexity

➔ Convergence guarantees

➔ Massive parallelization via

APSM for fast learning on GPUs

Page 11: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

1. Generate and send TX signal

2. Transmission

4. Post processing and display

3. Recept ion

Learning-based Reception for 5G NOMA

• D. A. Awan, R. L. G. Cavalcante, M. Yukawa, and S. Stańczak, "Detection for 5G-NOMA: An Online Adaptive Machine Learning Approach," in Proc. IEEE International Conference on Communications (ICC), May 2018

• D. A. Awan, R.L.G. Cavalcante, M. Yukawa, and S. Stanczak. Adaptive Learning for Symbol Detection: A Reproducing Kernel Hilbert Space Approach. Wiley, 2019. to appear.

• M. Mehlhose et.al., “Machine Learning-Based Adaptive Receive Filtering: Proof-of-Concept on an SDR Platform” submitted Oct. 2019

20 40 60 80 100 120 140 160 180 200

measurement time index

0

500

1000

1500

2000

det

ecti

on

del

ay [µ

s]

Detailed Processing Time

machine learning algorithm

MMSE

MMSE SIC

Fig. 6: User 5: ωL = 0.6 and ωG = 0.4 with T length = 685

20 40 60 80 100 120 140 160 180 200

measurement time index

0

500

1000

1500

2000

2500d

ete

cti

on

del

ay [µ

s]

Detailed Processing Time

machine learning algorithm

MMSE

MMSE SIC

Fig. 7: User 6: ωL = 0.6 and ωG = 0.4 with T length = 685

20 40 60 80 100 120 140 160 180 200

measurement time index

10-4

10-2

100

SE

R

Symbol Error Rate

machine learning algorithm

MMSE

MMSE SIC

Fig. 8: Mean over all users: ωL = 0.6 and ωG = 0.4

20 40 60 80 100 120 140 160 180 200

measurement time index

0

200

400

600

800

1000

1200

dete

ctio

n d

elay [µ

s]

Detailed Processing Time

machine learning algorithm

MMSE

MMSE SIC

Fig. 9: Mean over all users: ωL = 0.6 and ωG = 0.4

the nonlinearMMSE-SIC in a hardware-in-the-loop system.

The results show that the proposed ML based multiuser is

simpler yet powerful alternative to conventional nonlinear

receivers.

ACKNOWLEDGMENTS

The work is supported by the European commission and

5G Infrastructure Public Private Partnership (5G-PPP) and re-

ceived funding from the EC H2020/5G-PPP program ONE5G

(ICT-760809) project [19].

The authors would like to thank for the contribution of their

colleagues in the project and Andreas Forck, Holger Gäbler

as well as Kirsten Krüger for the ongoing expansion of the

NAMC-SDR firmware with new key features and updates.

REFERENCES

[1] “Study on Non-Orthogonal Multiple Access (NOMA) for NR,” 3rdGeneration Partnership Project, Tech. Rep. 38.812, Dec. 2018.

[2] K. Slavakis, S. Theodoridis, and I. Yamada, “Adaptive constrainedlearning in reproducing kernel hilbert spaces: The robust beamformingcase,” IEEE Transactions on Signal Processing, vol. 57, no. 12, pp.4744–4764, Dec 2009.

[3] M. Yukawa, “Adaptive learning in cartesian product of reproducingkernel hilbert spaces,” IEEE Transactions on Signal Processing, vol. 63,no. 22, pp. 6037–6048, Nov 2015.

[4] A. Benjebbour and Y. Kishiyama, “Combination of noma and mimo:Concept and experimental trials,” in 2018 25th International Conferenceon Telecommunications (ICT), June 2018, pp. 433–438.

[5] U. S. S. S. Arachchillage, D. N. K. Jayakody, S. K. Biswash, andR. Dinis, “Recent advances and future research challenges in non-orthogonal multiple access for 5g networks,” in 2018 IEEE 87th Ve-hicular Technology Conference (VTC Spring), June 2018, pp. 1–6.

[6] Z. Ding, X. Lei, G. K. Karagiannidis, R. Schober, J. Yuan, and V. K.Bhargava, “A survey on non-orthogonal multiple access for 5g networks:Research challenges and future trends,” IEEE Journal on Selected Areasin Communications, vol. 35, no. 10, pp. 2181–2195, Oct 2017.

[7] W. Cai, C. Chen, L. Bai, Y. Jin, and J. Choi, “Subcarrier and powerallocation scheme for downlink ofdm-noma systems,” IET Signal Pro-cessing, vol. 11, no. 1, pp. 51–58, 2017.

[8] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, andK. Higuchi, “Non-orthogonal multiple access (noma) for cellular futureradio access,” in 2013 IEEE 77th Vehicular Technology Conference(VTCSpring), June 2013, pp. 1–5.

[9] S. Abeywickrama, L. Liu, Y. Chi, and C. Yuen, “Over-the-airimplementation of uplink NOMA,” CoRR, vol. abs/1801.05541, 2018.[Online]. Available: http://arxiv.org/abs/1801.05541

[10] S. Verdu, Multiuser Detection, 1st ed. New York, NY, USA: CambridgeUniversity Press, 1998.

[11] O. Elijah, C. Y. Leow, T. A. Rahman, S. Nunoo, and S. Z. Iliya,“A comprehensive survey of pilot contamination in massive mimo—5gsystem,” IEEE Communications Surveys Tutorials, vol. 18, no. 2, pp.905–923, Secondquarter 2016.

[12] D. A. Awan, R. L. G. Cavalcante, M. Yukawa, and S. Stanczak,“Detection for 5g-noma: An onlineadaptivemachine learning approach,”in 2018 IEEE International Conference on Communications (ICC), May2018, pp. 1–6.

[13] U. Mitra and H. V. Poor, “Neural network techniques for adaptivemultiuser demodulation,” IEEE Journal on Selected Areas in Commu-nications, vol. 12, no. 9, pp. 1460–1470, Dec 1994.

[14] Y. Isik and T. Necmi, “Multiuser detection with neural network and picin cdma systems for awgn and rayleigh fading asynchronous channels,”Wireless Personal Communications, vol. 43, no. 4, pp. 1185–1194, Dec2007. [Online]. Available: https://doi.org/10.1007/s11277-007-9293-0

[15] B. Aazhang, B. . Paris, and G. C. Orsak, “Neural networks for mul-tiuser detection in code-division multiple-access communications,” IEEETransactions on Communications, vol. 40, no. 7, pp. 1212–1222, July1992.

20 40 60 80 100 120 140 160 180 200

measurement time index

0

500

1000

1500

2000

det

ecti

on

dela

y [µ

s]

Detailed Processing Time

machine learning algorithm

MMSE

MMSE SIC

Fig. 6: User 5: ωL = 0.6 and ωG = 0.4 with T length = 685

20 40 60 80 100 120 140 160 180 200

measurement time index

0

500

1000

1500

2000

2500

det

ecti

on

dela

y [µ

s]

Detailed Processing Time

machine learning algorithm

MMSE

MMSE SIC

Fig. 7: User 6: ωL = 0.6 and ωG = 0.4 with T length = 685

20 40 60 80 100 120 140 160 180 200

measurement time index

10-4

10-2

100

SE

R

Symbol Error Rate

machine learning algorithm

MMSE

MMSE SIC

Fig. 8: Mean over all users: ωL = 0.6 and ωG = 0.4

20 40 60 80 100 120 140 160 180 200

measurement time index

0

200

400

600

800

1000

1200

det

ecti

on

del

ay [µ

s]

Detailed Processing Time

machine learning algorithm

MMSE

MMSE SIC

Fig. 9: Mean over all users: ωL = 0.6 and ωG = 0.4

the nonlinearMMSE-SIC in a hardware-in-the-loop system.

The results show that the proposed ML based multiuser is

simpler yet powerful alternative to conventional nonlinear

receivers.

ACKNOWLEDGMENTS

The work is supported by the European commission and

5G Infrastructure Public Private Partnership (5G-PPP) and re-

ceived funding from the EC H2020/5G-PPP program ONE5G

(ICT-760809) project [19].

The authors would like to thank for the contribution of their

colleagues in the project and Andreas Forck, Holger Gäbler

as well as Kirsten Krüger for the ongoing expansion of the

NAMC-SDR firmware with new key features and updates.

REFERENCES

[1] “Study on Non-Orthogonal Multiple Access (NOMA) for NR,” 3rdGeneration Partnership Project, Tech. Rep. 38.812, Dec. 2018.

[2] K. Slavakis, S. Theodoridis, and I. Yamada, “Adaptive constrainedlearning in reproducing kernel hilbert spaces: The robust beamformingcase,” IEEE Transactions on Signal Processing, vol. 57, no. 12, pp.4744–4764, Dec 2009.

[3] M. Yukawa, “Adaptive learning in cartesian product of reproducingkernel hilbert spaces,” IEEE Transactions on Signal Processing, vol. 63,no. 22, pp. 6037–6048, Nov 2015.

[4] A. Benjebbour and Y. Kishiyama, “Combination of noma and mimo:Concept and experimental trials,” in 2018 25th International Conferenceon Telecommunications (ICT), June 2018, pp. 433–438.

[5] U. S. S. S. Arachchillage, D. N. K. Jayakody, S. K. Biswash, andR. Dinis, “Recent advances and future research challenges in non-orthogonal multiple access for 5g networks,” in 2018 IEEE 87th Ve-hicular Technology Conference (VTC Spring), June 2018, pp. 1–6.

[6] Z. Ding, X. Lei, G. K. Karagiannidis, R. Schober, J. Yuan, and V. K.Bhargava, “A survey on non-orthogonal multiple access for 5g networks:Research challenges and future trends,” IEEE Journal on Selected Areasin Communications, vol. 35, no. 10, pp. 2181–2195, Oct 2017.

[7] W. Cai, C. Chen, L. Bai, Y. Jin, and J. Choi, “Subcarrier and powerallocation scheme for downlink ofdm-noma systems,” IET Signal Pro-cessing, vol. 11, no. 1, pp. 51–58, 2017.

[8] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, andK. Higuchi, “Non-orthogonal multiple access (noma) for cellular futureradio access,” in 2013 IEEE 77th Vehicular Technology Conference(VTCSpring), June 2013, pp. 1–5.

[9] S. Abeywickrama, L. Liu, Y. Chi, and C. Yuen, “Over-the-airimplementation of uplink NOMA,” CoRR, vol. abs/1801.05541, 2018.[Online]. Available: http://arxiv.org/abs/1801.05541

[10] S. Verdu, Multiuser Detection, 1st ed. New York, NY, USA: CambridgeUniversity Press, 1998.

[11] O. Elijah, C. Y. Leow, T. A. Rahman, S. Nunoo, and S. Z. Iliya,“A comprehensive survey of pilot contamination in massive mimo—5gsystem,” IEEE Communications Surveys Tutorials, vol. 18, no. 2, pp.905–923, Secondquarter 2016.

[12] D. A. Awan, R. L. G. Cavalcante, M. Yukawa, and S. Stanczak,“Detection for 5g-noma: An onlineadaptivemachine learning approach,”in 2018 IEEE International Conference on Communications (ICC), May2018, pp. 1–6.

[13] U. Mitra and H. V. Poor, “Neural network techniques for adaptivemultiuser demodulation,” IEEE Journal on Selected Areas in Commu-nications, vol. 12, no. 9, pp. 1460–1470, Dec 1994.

[14] Y. Isik and T. Necmi, “Multiuser detection with neural network and picin cdma systems for awgn and rayleigh fading asynchronous channels,”Wireless Personal Communications, vol. 43, no. 4, pp. 1185–1194, Dec2007. [Online]. Available: https://doi.org/10.1007/s11277-007-9293-0

[15] B. Aazhang, B. . Paris, and G. C. Orsak, “Neural networks for mul-tiuser detection in code-division multiple-access communications,” IEEETransactions on Communications, vol. 40, no. 7, pp. 1212–1222, July1992.

Page 12: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Can we design better neural networks?

Page 13: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Sparsity in Communication Systems

• Sparsity in the data (soft sparsity)

• Sparsity in the channel (soft sparsity)

• Sparsity in the user activity (hard sparsity)

• Sparsity in the network flow (hard sparsity)

Page 14: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Sparsity in Communication Systems

• We can use -balls to model sparse signals

• S. Limmer and S. Stanczak, "Towards optimal nonlinearities for sparse recovery using higher-order statistics," 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP), Vietri sul Mare, 2016, pp. 1-6.

Page 15: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Sparse Recovery via a Deep Neural Network

• CS methods are not suitable for low-latency applications

• Training must be short➔Design a good DNN for sparse recovery

Page 16: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

{slawomir.stanczak,renato.cavalcante}@hhi.fraunhofer.de August 27, 2019 146

Optimizing Nonlinear Activation FunctionsNumerical simulations for Approximate MMSE network

optimal activation σ for ETF A

Interesting shape of result ing polynomial activations

September 21, 2018 19/ 29

• S. Limmer and S. Stanczak, "Towards optimal nonlinearities for sparse recovery using higher-order statistics," 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP), Vietri sul Mare, 2016, pp. 1-6.

Optimization for MMSE Recovery

• S. Limmer and S. Stanczak, "Towards optimal nonlinearities for sparse recovery using higher-order statistics," 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP), Vietri sul Mare, 2016, pp. 1-6.

Page 17: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

• Input uniformly distributed on

• The conditional MMSE estimator is a

polytope centroid under certain conditions.

➔ Volume and moment computation

• Implementable using the DL architecture

Designing DNNs via Laplace Techniques

Page 18: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Numerical Experiments with Training

• S. Limmer and S. Stanczak, “A neural architecture for Bayesian compressive sensing via Laplace techniques“, IEEE Trans. On Signal Processing, Nov. 2018

Real data

Page 19: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Take-away Message

• ML/AI might be a “salvation” for industrial communication

• But there is a strong need for robust online ML methods

➔ Exploit domain knowledge: Hybrid-driven distributed ML

➔ Learn feature insensitive to frequency bands, phases …

• No time and data for extensive training of DNN

➔ Design good NN architectures for a given task

Page 20: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

Exploiting „Interference“ for Learning

Sensor data and wireless nodes

Fusion node

Harness interference for

computing SVM classifier

• K. Ralinovski, M. Goldenbaum and S. Stanczak, Energy-efficient Classification for Anomaly Deteciton: The Wireless Channel as a Helper, IEEE ICC, 2016

• S. Limmer, J. Mohammadi, S. Stanczak, “A Simple Algorithm for Approximation by Nomographic Functions”, 53rd Annual Allerton Conference on Communication, Control, and Computing, 2015

• M. Raceala-Motoc and S. Limmer and I. Bjelakovic and S. Stanczak (2018). Distributed Machine Learning in the Context of Function Computationover Wireless Networks. 52nd Asilomar Conference on Signals, Systems and Computers 2018,

• Bjelakovic, M. Frey and S. Stanczak (2019). Distributed Approximation of Functions over Fast Fading Channels with Applications to Distributed Learning and the Max-Consensus Problem. 57th Annual Allerton Conference on Communication, Control, and Computing, 24-27 Sept. 2019 in Urbana, IL, USA

Page 21: Machine Learning for RAN: Delusion or Salvation? · Hybrid-driven robust methods under uncertainty (e.g., few training samples) Robust Online Load Learning • D. A. Awan, R. L. G

References• M. Kasparick, R. L. G. Cavalcante, S. Valentin, S. Stańczak, and M. Yukawa, "Kernel-Based Adaptive Online Reconstruction of Coverage Maps with

Side Information," IEEE Transactions on Vehicular Technology, vol. 65, no. 7, pp. 5461-5473, July 2016

• Z.Utkovski, P. Agostini, M.Frey, I.Bjelakovic, and S. Stanczak. Learning radio maps for physical-layer security in the radio access. In IEEE International Workshop on Signal Pro- cessing Advances in Wireless Communications (SPAWC), Cannes, France, July 2-5 2019. (invited).

• M.A. Gutierrez-Estevez, R.L.G. Cavalcante, and S. Stanczak. Nonparametric radio maps reconstruction via elastic net regularization with multi-kernels. In IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2018.

• R. L. G. Cavalcante, M. Kasparick, and S. Stańczak, "Max-min utility optimization in load coupled interference networks," IEEE Trans. Wireless Comm., vol. 16, no. 2, pp. 705-716, Feb. 2017

• D. Schäufele, et.al. “Tensor Completion for Radio Map Reconstruction using Low Rank and Smoothness“, SPAWC, June 2019

• R. L. G. Cavalcante, Y. Shen, S. Stańczak, "Elementary Properties of Positive Concave Mappings with Applications to Network Planning and Optimization," IEEE Trans. Signal Processing, vol. 64, no. 7, pp. 1774-1783, April 2016

• R.L.G. Cavalcante, Q. Liao, and S. Stanczak. Connections between spectral properties of asymptotic mappings and solutions to wireless network problems. IEEE Trans. on Signal Processing, 2019. (accepted)

• D. A. Awan, R. L. G. Cavalcante, and S. Stańczak, "A robust machine learning method for cell-load approximation in wireless networks," IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2018

• D. A. Awan, R.L.G. Cavalcante, M. Yukawa, and S. Stanczak. Adaptive Learning for Symbol Detection: A Reproducing Kernel Hilbert Space Approach. Wiley, 2019. to appear.

• D. A. Awan, R. L. G. Cavalcante, M. Yukawa, and S. Stańczak, "Detection for 5G-NOMA: An Online Adaptive Machine Learning Approach," in Proc. IEEE International Conference on Communications (ICC), May 2018

• L. Miretti, R. L. G. Cavalcante, and S. Stańczak, "Downlink channel spatial covariance estimation in realistic FDD massive MIMO systems," in Proc. IEEE GlobalSIP 2018 (https://arxiv.org/abs/1804.04892)

• R. L. G. Cavalcante, L. Miretti, and S. Stańczak, "Error bounds for FDD massive MIMO channel covariance conversion with set-theoretic methods," in Proc. IEEE Global Telecommunications Conference (GLOBECOM), Dec. 2018 (https://arxiv.org/abs/1804.08461)

• J. Fink, D. Schaeufele, M. Kasparick, R. L.G. Cavalcante, and S. Stanczak. Cooperative localization by set-theoretic estimation. In Workshop on Smart Antennas (WSA), Vienna, Austria, April 24-26 2019.

• R. Ismayilov et.al. “Power and Beam Optimization for Uplink Millimeter-Wave Hotspot Communication Systems,”IEEE WCNC April 2019.

• R.L.G. Cavalcante, S. Stanczak, J. Zhang, and H. Zhuang. Low complexity iterative algorithms for power estimation in ultra-dense load coupled networks. IEEE Trans. on Signal Processing, 64(22):6058–6070, May 2016.

• S. Limmer and S. Stanczak, "Towards optimal nonlinearities for sparse recovery using higher-order statistics," 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP), Vietri sul Mare, 2016, pp. 1-6.

• S. Limmer and S. Stanczak, “A neural architecture for Bayesian compressive sensing via Laplace techniques“, IEEE Trans. On Signal Processing, Nov. 2018