Use of Hidden Markov Model Technique to Characterize and Classify the Wideband Mobile Radio Channel in Different Environments

Azevedo, Rafael S.; Cataldo, Edson; Matos, Leni J.

doi:10.1590/2179-10742024v23i1276299

Rafael S. Azevedo

Telecommunications Engineering Department, Fluminense Federal University, Niterói, Rio de Janeiro, Brazil.

http://orcid.org/0000-0002-3025-5392

Edson Cataldo

Telecommunications Engineering Department, Fluminense Federal University, Niterói, Rio de Janeiro, Brazil.

http://orcid.org/0000-0003-4515-2473

Leni J. Matos

Telecommunications Engineering Department, Fluminense Federal University, Niterói, Rio de Janeiro, Brazil.

http://orcid.org/0000-0002-8035-2916

rafaelazevedo@id.uff.br

ecataldo@id.uff.br

lenijm@id.uff.br

Figures (14)
Tables (8)

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Fig. 1
Hidden states and observable states from HMM technique.

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Fig. 2
Plant layout of the measurement campaign environments [²⁵[25] C. F. Souza, “Análise da dispersão temporal de canais de banda ultralarga (UWB) através de medidas realizadas em ambientes internos e externos”, M.S. thesis, College of Eng., Fluminense Federal Univ., Niterói, 2006. https://www.ppgeet.uff.br/site/wp-content/uploads/2021/01/Christiano_Freitas_De_Souza.pdf.
https://www.ppgeet.uff.br/site/wp-conten... ].

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Fig. 3
Map of 6-by-6 quadrangular grid creating 36 reception dots equally spaced by 15 cm at each location RX [¹⁶[16] L. G. Ribeiro, L. J. Matos, and E. Cataldo, “Aplicação de modelos ocultos de Markov na modelagem do canal rádio móvel”, 2020 MOMAG, 19th Brazilian Symposium of Microwave and Optoelectronics (SBMO) and 14th Brazilian Congress of Electromagnetism (CBMAG), Niterói, Brazil, vol. 1, pp. 296-300, 2021.].

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Fig. 4
The adoption of the HMM technique and Bakis topology to characterize the MRC.

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Fig. 5
Bakis topology and the pre-defined state transitions for simulation 1 and simulation 2.

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Fig. 6
Results of transitions between hidden states, from RX1 to RX2 (1-2).

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Fig. 7
Results of transitions between hidden states, from RX2 to RX3 (2-3).

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Fig. 8
Results of transitions between hidden states, from RX3 to RX4 (3-4).

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Fig. 9
Results of 3 transitions between 4 hidden states from site 2.

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Fig. 10
Bakis topology and the pre-defined states transitions for simulation 3 and simulation 4.

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Fig. 11
Results of 8 transitions between 6 hidden states from site 2.

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Fig. 12
Results of 8 transitions between 6 hidden states from site 3.

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Fig. 13
Bakis topology and the pre-defined states transitions for simulation 5.

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Fig. 14
Results of 9 transitions between 7 hidden states from site 4.

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TABLE I
CHANNEL SOUNDING PARAMETERS [²⁵[25] C. F. Souza, “Análise da dispersão temporal de canais de banda ultralarga (UWB) através de medidas realizadas em ambientes internos e externos”, M.S. thesis, College of Eng., Fluminense Federal Univ., Niterói, 2006. https://www.ppgeet.uff.br/site/wp-content/uploads/2021/01/Christiano_Freitas_De_Souza.pdf.
https://www.ppgeet.uff.br/site/wp-conten... ]

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TABLE II
DETAILS OF THE CHOSEN THRESHOLD VALUES [¹⁶[16] L. G. Ribeiro, L. J. Matos, and E. Cataldo, “Aplicação de modelos ocultos de Markov na modelagem do canal rádio móvel”, 2020 MOMAG, 19th Brazilian Symposium of Microwave and Optoelectronics (SBMO) and 14th Brazilian Congress of Electromagnetism (CBMAG), Niterói, Brazil, vol. 1, pp. 296-300, 2021.]

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TABLE III
PSEUDOCODE THAT FITS THE HMM TO DATA

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TABLE IV
CONFUSION MATRIX FOR TRANSITIONS SET OF SITE 1

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TABLE V
CONFUSION MATRIX FOR ALL TRANSITIONS SET OF SITE 1

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TABLE VI
CONFUSION MATRIX FOR ALL TRANSITIONS SET OF SITE 2

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TABLE VII
CONFUSION MATRIX FOR ALL TRANSITIONS SET OF SITE 3

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TABLE VIII
CONFUSION MATRIX FOR ALL TRANSITIONS SET OF SITE 4

Parameters	Value	Unit
Frequency band	960 to 1,710	MHz
Bandwidth	750	MHz
Transmitted power level	+10	dBm
Low Noise Amplifier (LNA) gain	25	dB
Antennas gain	2.14	dBi
Frequency resolution - ∆f	0.46875	MHz
Sweep-measuring samples	1,601	-
Sweep-measuring time	696	ms
Delay resolution - ∆τ	1.333	ns
Maximum delay - τ_MAX	2,133	ns

Threshold values	Description
1. Mean of log-likelihoods	Simple arithmetic mean between the average of the log-likelihoods of the location under analysis and other locations.
2. Cross-mean of values	The average of the log-likelihoods of the location under analysis is multiplied by the standard deviation of the log-likelihoods of the other locations. The average of the log-likelihoods of the other locations is multiplied by the standard deviation of the log-likelihoods of the location under analysis. The simple arithmetic mean of the two values obtained is calculated.
3. Percentile P20 of log-likelihoods	It is the boundary that represents the upper value from the 20th percentile of the log-likelihood data presented.
4. Percentile P20 of p.d.f.	It is the boundary that represents the upper value from the 20th percentile of the probability density functions (p.d.f.)

Pseudocode	Pseudocode output
1. Calculate τ_m and σ_T for each dot at the 6-by-6 quadrangular grid.	Parameters τ_m and σ_T for each dot at the 6-by-6 quadrangular grid.
2. Create 36 (6-by-6) x 2 (τ_m and σ_T) two-dimensional matrix.	Matrix of local characteristics (hidden state).
3. Define the transition between hidden states.	Transition follows the Bakis topology.
4. For each transition between two hidden states: - Group 2-by-2 randomly the 36 parameters τ_m and σ_T. - Create 2 x 2 x 36 three-dimensional matrix.	Matrix of transition characteristics (observable state).
5. Group all matrices of transition characteristics.	Feature base matrix (four-dimensional)
6. For feature base matrix: - Create the matrix of training base. - Create the matrix of test base.	Matrix of training base (half of feature base matrix). Matrix of test base (half of feature base matrix).
7. For matrix of training base: - Run HMM initialization and training.	Trained HMM.
8. For matrix of test base: - Calculate log-likelihood values. - Remove the outliers. - For remaining log-likelihood values: - Create the matrix of reference group. - Create the matrix of test group.	Matrix of reference group (half of remaining log-likelihood values). Matrix of test group (half of remaining log-likelihood values).
9. For matrix of reference group: Calculate four different threshold values.	Four different threshold values.
10. For matrix of test group: Calculate the probability density function.	Probability density function (p.d.f.).
11. Calculate the p.d.f. versus threshold values.	Probability density graph.
12. Check which threshold value is the best fit in the identification of valid log-likelihoods.	Best threshold value selected.
13. Calculate the confusion matrix using the best threshold value.	Confusion matrix.

Hidden state transition under analysis	True positive	False negative	True negative	False positive
1-2	87.5% (7/8)	12.5% (1/8)	100.0% (16/16)	0% (0/16)
2-3	100.0% (8/8)	0% (0/8)	100.0% (16/16)	0% (0/16)
3-4	87.5% (7/8)	12.5% (1/8)	100.0% (16/16)	0% (0/16)

Hidden state transition	True positive	False negative	True negative	False positive
1-2 / 2-3 / 3-4	84.6% (22/26)	15.4% (4/26)	0% (0/0)	0% (0/0)

Hidden state transition	True positive	False negative	True negative	False positive
1-2 / 2-2 / 2-3 / 3-4 / 4-4 / 4-5 / 5-6 / 6-6	91.4% (64/70)	8.6% (6/70)	0% (0/0)	0% (0/0)

Hidden state transition	True positive	False negative	True negative	False positive
1-2 / 2-2 / 2-3 / 3-4 / 4-4 / 4-5 / 5-6 / 6-6	90.0% (63/70)	10.0% (7/70)	0% (0/0)	0% (0/0)

Hidden state transition	True positive	False negative	True negative	False positive
1-2 / 2-2 / 2-3 3-4 / 4-4 / 4-5 5-6 / 6-6 / 6-7	92.4% (73/79)	7.6% (6/79)	0% (0/0)	0% (0/0)

[1] rafaelazevedo@id.uff.br

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Use of Hidden Markov Model Technique to Characterize and Classify the Wideband Mobile Radio Channel in Different Environments

Abstract