# Characterization of Slow and Fast Fading in Off-Body Communication at 2.45 GHz with Space Diversity Scheme in an Indoor Environment

Authors: Szymon Wiszniewski; Slawomir J. Ambroziak
Journal: International Journal of Antennas and Propagation
 (2019)

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## Abstract

The characterization of slow and fast fading in wireless body area networks with space diversity scheme has been presented. The analysis, based on the measurements at 2.45 GHz in an indoor environment, has shown that for all investigated configurations of receiving wearable antennas, the correlation coefficient values of the received signals’ parameters are below the assumed value of 0.5, being close to zero for the vast majority of cases. It has been shown that the slow fading component may be modelled by a lognormal distribution with zero average and the standard deviation from the range of [1.43, 1.98] dB. The fast fading component is the best modelled by a Rice distribution with the noncentrality parameter and the scale parameter being in the range [0.8125, 0.9624] and [0.5269, 0.6954], respectively.


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## Body

## 1. Introduction

Nowadays, when the wireless body area networks (WBANs) become more and more popular, and the amount of the wearable sensors used by people are increasing, there is a need to model the radio channel around the human body with higher accuracy. The human body itself and its motion should be considered as significant elements that influence the total system loss in WBANs [1]. Since there are applications of such networks (e.g., the healthcare [2] or military), in which the proper radio coverage and the errorless communication are of the high importance, the accurate modeling of radio channel becomes crucial.The various diversity schemes, that can be used in off-body communications in WBANs, can significantly increase the quality of the received signals. This technique allows receiving uncorrelated replicas of the same radio signal and, in addition to one of the possible combining methods, can significantly increase the signal-to-noise ratio. It is very useful especially when the multipath propagation occurs. Depending on the signal decorrelation method, one can distinguish polarization diversity or space diversity. In this article, the concept of the space diversity scheme in WBANs has been presented. Additionally, the characterization of the slow and fast fading for different placements of the received antennas has been performed.There are some research work on the space diversity concept, but they are focused on in-body to on-body [3] or on-body communication [4, 5]. The off-body communication is taken into account in [6]; however, there is a limited number of considered receiving antennas’ positions, i.e., two receiving antennas have been placed on the chest. Moreover, the current standard for WBANs, [7] does not raise the issue of channel models with diversity schemes. The novelty of the article is the investigation of the influence of different mutual positions of the receiving antennas on the correlation of slow and fast fading of received signal.The rest of the article is structured as follows. In the next section, the measurement stand, scenarios, and investigated environment have been briefly described. The third section consists the description of the measurement data processing. The analysis of the correlation coefficient between the received signal parameters obtained by different antennas is presented in the following section. The last part of the paper consists of the summary and concluding remarks.


## 2. Description of the Measurements

The measurement stand used for the space diversity investigations has been presented in Figure1. The detailed description of the equipment may be found in [8]. In the article, only the most important parameters have been presented.Figure 1
Measurement stand for space diversity investigations.The transmitting (TX) section consists of the vector signal generator (Rohde & Schwartz SMU200A) and the omnidirectional, linear polarized antenna (Cobham OA2-0.3-10.0V/1505), with a 2 dBi gain and half-power beam width of 360° and 65° in the H- and E-planes, respectively. It has been designed for operation in the frequency range of 0.3-10.0 GHz. The generator provides the RF signal with BPSK modulation at 2.45 GHz frequency, modulated by the pseudorandom sequence with the 23 bit of length and 3 kbit/s rate.The receiving (RX) section consists of two wideband receivers (Rohde & Schwartz EM550), connected to the wearable patch antennas, operating at 2.45 GHz frequency. These antennas have linear polarization, 3 dBi gain, and half-power beam width of 115° and 40° in the H- and E-planes, respectively.All RF connections have been realized by the 10 m long high-frequency cable SUCOFLEX 126E with the attenuation of 4 dB at the investigated frequency. Obviously, this value has been taken into account during the calibration process.The measurements were performed in a typical indoor office environment, with the following dimensions:7×5×3m3. Two receiving antennas were placed on one user, with a height of 1.65 m and a weight of 64 kg. In Figure 2, the layout of the investigated indoor environment has been presented.Figure 2
Layout of the investigated indoor environment (dimensions are in meters).During measurements, the dynamic scenario has been investigated—the user was walking ten times along the axis of the room in the direction indicated in Figure2. The TX antenna was mounted in the middle of the room, at 2.6 m close to the wall. The six most popular RX antenna placements have been considered: torso front (TOF), torso back (TOB), bottom part of the left arm (ABL), bottom part of the right arm (ABR), left side of the head (HEL), and right side of the head (HER). Based on the above antenna locations, nine space diversity configurations (C1–C9) have been defined in Table 1.Table 1
Positions of RX antennas for different space diversity configurations.
Configuration
Position of RX antenna no. 1
Position of RX antenna no. 2
C1
TOF
TOB
C2
TOF
ABL
C3
TOF
ABR
C4
TOF
HEL
C5
TOF
HER
C6
TOB
ABL
C7
TOB
ABR
C8
TOB
HEL
C9
TOB
HERIn Figure3, one can see the RX antennas mounted on the user body for configurations C2 and C4.Figure 3
Exemplary placements of receiving antennas for configurations C2 (a) and C4 (b).
(a)
(b)


## 3. Measurement Data Processing

This section describes how the slow and fast fading components have been extracted from the instantaneous system loss values,LSL. Firstly, the mean system loss, LSLd¯, has been obtained by fitting a logarithmic function of distance to the composite component, LCSL¯, which is a space-averaged values of total system loss, where the averaging window width is taken as a 5-wavelength interval. It should be noted that this fitting has been performed separately for the cases of user approaching to and departing from the transmitting antenna, when the distance was increasing and decreasing, respectively. Next, the slow fading component, Lsf, has been extracted by subtracting the mean system loss from the composite component, what may be expressed as follows:
(1)LsfdB=LSLddB¯−LCSLdB¯.Finally, the fast fading component, also known as a multipath fading component,Lff, has been obtained by subtracting the composite component from the instantaneous values of the measured system loss, i.e.,
(2)LffdB=LSLdB−LCSLdB¯.For statistical analysis of the slow and fast fading, the most commonly used probability distribution functions (PDFs) were taken into consideration [9–13]. Table 2 presents the selected PDFs and their parameters [14].Table 2
Probability distributions functions selected forLsf and Lff analysis.
Name of PDF
PDF parameters
Rice
Noncentrality parameter:sRice
Scale parameter:σRice
Nakagami-m
Shape parameter:m
Scale parameter:Ω
Weibull
Shape parameter:b
Scale parameter:a
Rayleigh
Scale parameter:σRay
—
Lognormal
Mean [dB]:μL
Standard deviation [dB]:σLThe Rice, Nakagami-m, Weibull, and Rayleigh distributions have been used to characterize the multipath fading, while the lognormal distribution has been used with respect to the slow fading. The fitting of the empirical distributions of slow and fast fading has been evaluated by the use of the χ2 and correlation tests. Additionally, the Akaike Information Criterion (AIC) has been used in order to select the best-fitted distribution among those that have passed the abovementioned tests.


## 4. Results Analysis

### 4.1. Fast Fading Characteristics

The results of PDFs fitting for the fast fading component are presented in Table3(a) (for configurations C1–C4) and Table 3(b) (for configurations C5–C9). Both tables include the distribution parameters and the results of evaluation tests. The χ2, χ2crit, and AIC stand for the χ2 test statistics, the critical value of this statistics for the significance level of 5%, and the AIC statistic, respectively. It should be reminded that the χ2 test is passed when the value of χ2 statistics is below the critical value, and the lowest AIC value indicates the best-fitted PDF [15]. The name of the distributions with the best-fitting results for each configuration has been bolded in the Table 3.Table 3
(a)
Results of the fast fading distribution fitting for configurations C1–C4
Configuration
RX ant.
Distribution
Parameters
χ2
χ2crit
AIC
Correlation
C1
TOF
Rice
sRice
0.9602
σRice
0.5269
21.19
27.59
19389
0.98
Nakagami
m
1.1750
Ω
1.4772
15.81
27.59
20474
0.90
Weibull
a
1.2479
b
2.4021
18.39
27.59
20056
0.95
Rayleigh
σRay
0.8594
—
—
13.35
28.87
20689
0.83
TOB
Rice
sRice
0.8943
σRice
0.6212
27.69
27.59
22092
0.98
Nakagami
m
1.0356
Ω
1.5714
22.17
27.59
22551
0.93
Weibull
a
1.2704
b
2.1638
24.73
27.59
22438
0.96
Rayleigh
σRay
0.8864
—
—
21.26
28.87
22560
0.92
C2
TOF
Rice
sRice
0.9129
σRice
0.5661
19.12
27.59
20517
0.98
Nakagami
m
1.1325
Ω
1.4743
15.25
27.59
21207
0.90
Weibull
a
1.2415
b
2.3043
17.36
27.59
20945
0.94
Rayleigh
σRay
0.8586
—
—
13.12
28.87
21339
0.86
ABL
Rice
sRice
0.8918
σRice
0.6090
25.74
27.59
21938
0.99
Nakagami
m
1.0614
Ω
1.5371
20.98
27.59
22432
0.93
Weibull
a
1.2593
b
2.1956
23.32
27.59
22287
0.96
Rayleigh
σRay
0.8767
—
—
19.61
28.87
22462
0.91
C3
TOF
Rice
sRice
0.9475
σRice
0.5493
22.04
27.59
22173
0.97
Nakagami
m
1.1249
Ω
1.5012
16.53
27.59
23224
0.87
Weibull
a
1.2537
b
2.3339
19.20
27.59
22856
0.93
Rayleigh
σRay
0.8664
—
—
14.54
28.87
23351
0.81
ABR
Rice
sRice
0.8651
σRice
0.6488
27.45
27.59
24718
0.98
Nakagami
m
1.0225
Ω
1.5903
22.44
27.59
25098
0.94
Weibull
a
1.2752
b
2.1318
25.14
27.59
25013
0.96
Rayleigh
σRay
0.8917
—
—
21.71
28.87
25101
0.94
C4
TOF
Rice
sRice
0.9624
σRice
0.5346
20.00
27.59
21404
0.95
Nakagami
m
1.1202
Ω
1.4977
14.39
27.59
22688
0.81
Weibull
a
1.2530
b
2.3608
17.00
27.59
22257
0.89
Rayleigh
σRay
0.8654
—
—
12.80
28.87
22804
0.76
HEL
Rice
sRice
0.8319
σRice
0.6909
27.00
27.59
25501
0.98
Nakagami
m
0.9525
Ω
1.6467
21.39
27.59
25705
0.94
Weibull
a
1.2872
b
2.0339
23.73
27.59
25722
0.96
Rayleigh
σRay
0.9074
—
—
22.88
28.87
25726
0.95
(b)
Results of the fast fading distribution fitting for configurations C5–C9
Configuration
RX ant.
Distribution
Parameters
χ2
χ2crit
AIC
Correlation
C5
TOF
Rice
sRice
0.9203
σRice
0.5614
22.99
27.59
21081
0.96
Nakagami
m
1.1532
Ω
1.4772
18.61
27.59
21843
0.88
Weibull
a
1.2451
b
2.3400
21.23
27.59
21529
0.92
Rayleigh
σRay
0.8594
—
—
15.84
28.87
22022
0.82
HER
Rice
sRice
0.9106
σRice
0.5737
24.84
27.59
21534
0.97
Nakagami
m
1.1224
Ω
1.4874
20.08
27.59
22225
0.90
Weibull
a
1.2461
b
2.2924
22.80
27.59
21966
0.94
Rayleigh
σRay
0.8624
—
—
17.50
28.87
22344
0.85
C6
TOB
Rice
sRice
0.9200
σRice
0.5503
19.75
27.59
21571
0.97
Nakagami
m
1.1620
Ω
1.4521
15.84
27.59
22399
0.89
Weibull
a
1.2351
b
2.3490
17.97
27.59
22062
0.94
Rayleigh
σRay
0.8521
—
—
13.51
28.87
22606
0.83
ABL
Rice
sRice
0.8445
σRice
0.6828
24.46
27.59
26078
0.98
Nakagami
m
0.9567
Ω
1.6456
19.31
27.59
26314
0.94
Weibull
a
1.2878
b
2.0434
21.40
27.59
26324
0.96
Rayleigh
σRay
0.9071
—
—
20.46
28.87
26332
0.95
C7
TOB
Rice
sRice
0.9240
σRice
0.5803
25.60
27.59
22718
0.98
Nakagami
m
1.0866
Ω
1.5272
19.82
27.59
23490
0.90
Weibull
a
1.2598
b
2.2595
22.76
27.59
23243
0.94
Rayleigh
σRay
0.8739
—
—
17.92
28.87
23552
0.86
ABR
Rice
sRice
0.8772
σRice
0.6334
29.30
27.59
23859
0.99
Nakagami
m
1.0495
Ω
1.5719
24.49
27.59
24278
0.94
Weibull
a
1.2712
b
2.1669
27.04
27.59
24161
0.97
Rayleigh
σRay
0.8865
—
—
23.06
28.87
24298
0.93
C8
TOB
Rice
sRice
0.9285
σRice
0.5585
22.17
27.59
21709
0.98
Nakagami
m
1.1337
Ω
1.4860
17.37
27.59
22553
0.89
Weibull
a
1.2471
b
2.3203
19.86
27.59
22240
0.94
Rayleigh
σRay
0.8620
—
—
15.10
28.87
22695
0.84
HEL
Rice
sRice
0.8125
σRice
0.6954
29.38
27.59
25188
0.99
Nakagami
m
0.9802
Ω
1.6274
24.55
27.59
25382
0.97
Weibull
a
1.2821
b
2.0552
26.84
27.59
25370
0.98
Rayleigh
σRay
0.9020
—
—
25.26
28.87
25384
0.97
C9
TOB
Rice
sRice
0.9221
σRice
0.5469
22.68
27.59
20419
0.98
Nakagami
m
1.1964
Ω
1.4485
18.64
27.59
21173
0.91
Weibull
a
1.2362
b
2.3858
21.15
27.59
20828
0.95
Rayleigh
σRay
0.8510
—
—
15.25
28.87
21453
0.84
HER
Rice
sRice
0.9027
σRice
0.5988
27.07
27.59
22514
0.97
Nakagami
m
1.0737
Ω
1.5320
21.66
27.59
23121
0.89
Weibull
a
1.2595
b
2.2254
24.58
27.59
22932
0.93
Rayleigh
σRay
0.8752
—
—
19.80
28.87
23165
0.86For all analyzed cases, theχ2 test has been passed, except for TOB in C1 configuration, where the statistics value is comparable with the critical one, but slightly higher. Considering the AIC values, as well as the correlation test for all configurations and RX antennas’ positions, the best-fitted distribution for fast fading component is Rice. It was expected since for the analyzed scenarios and environment there is a high probability of the existence of strong dominant component in the received signal. The noncentrality parameter, sRice, whose squared value corresponds to the power of dominant component of received signal, is in the range from 0.8125 (for C8-HEL) up to 0.9624 (for C4-TOF configuration). On the other hand, the scale parameter, σRice, whose doubled-squared value corresponds to the power of scattered components, is between 0.5269 (for C1-TOF) and 0.6954 (for C8-HEL configuration). The abovementioned values show that, for each case, the power of dominant component is higher than the power of the scattered ones.Figure4 shows the exemplary graph of the selected PDFs (Rice, Nakagami, Weibull, and Rayleigh) fitted to the empirical distribution of the fast fading magnitude in linear scale, α. As one can see, the shape of the Rice distribution is the closest to the empirical one, what is expected after consideration of the numerical data from Tables 3(a) and 3(b).Figure 4
Exemplary fast fading distributions for C1 configuration and RX antenna placed on TOF.


### 4.2. Slow Fading Characteristics

Analogous results of the lognormal distribution fitting for the slow fading component have been gathered in Table4. For all cases, the χ2crit value is the same and equals 27.59 for a significance level of 5%.Table 4
Results of the lognormal distribution fitting for the slow fading component and for all configurations.
Configuration
RX ant.
Parameters
χ2
Correlation
C1
TOF
μL [dB]
-0.20
σL [dB]
1.54
2.67
0.97
TOB
μL [dB]
-0.19
σL [dB]
1.76
5.25
0.97
C2
TOF
μL [dB]
-0.12
σL [dB]
1.56
4.92
0.98
ABL
μL [dB]
-0.16
σL [dB]
1.46
1.59
0.98
C3
TOF
μL [dB]
-0.16
σL [dB]
1.68
3.88
0.96
ABR
μL [dB]
-0.21
σL [dB]
1.34
1.17
0.98
C4
TOF
μL [dB]
-0.16
σL [dB]
1.71
3.78
0.98
HEL
μL [dB]
-0.23
σL [dB]
1.91
4.68
0.95
C5
TOF
μL [dB]
-0.17
σL [dB]
1.67
4.02
0.94
HER
μL [dB]
-0.11
σL [dB]
1.87
11.49
0.70
C6
TOB
μL [dB]
-0.18
σL [dB]
1.98
6.78
0.97
ABL
μL [dB]
-0.17
σL [dB]
1.42
2.91
0.95
C7
TOB
μL [dB]
-0.20
σL [dB]
1.90
4.09
0.97
ABR
μL [dB]
-0.22
σL [dB]
1.58
3.75
0.98
C8
TOB
μL [dB]
-0.17
σL [dB]
1.84
4.91
0.97
HEL
μL [dB]
-0.20
σL [dB]
1.81
4.82
0.96
C9
TOB
μL [dB]
-0.20
σL [dB]
1.79
4.10
0.98
HER
μL [dB]
-0.13
σL [dB]
1.56
4.16
0.97Since the values ofχ2 statistics are below the critical value for all the cases, and the correlation is over 95% for the vast majority of them, one can say that the lognormal distribution fits well to the empirical one. Moreover, the average of the slow fading component (μL) is close to zero in the log domain for all configurations. It confirms that the slow fading component have been obtained properly in the data processing phase. On the other hand, the standard deviation of the slow fading component (σL) is below 2 dB, being in the range of [1.43, 1.98] dB, which is a relatively low value.In Figure5, the exemplary graph of the lognormal PDF fitting to the empirical distribution of the slow fading magnitude (α), obtained from the measurements for the antenna placed on the torso in C1 configuration, has been presented. One can observe the good fitting of both distributions.Figure 5
Exemplary slow fading distribution for C9 configuration and antenna placed on TOB.


### 4.3. Spatial Decorrelation of Received Signal

In order to realize any of the diversity schemes (spatial, polarization, etc.), one has to ensure the proper decorrelation level of two or more received replicas of radio signal and use one of the well-known diversity combining techniques (e.g., maximal-ratio combining or equal-gain combining). Focusing on the decorrelation issue, it may be assumed that it is sufficient to have the correlation coefficient lower than 0.5, in order to obtain a satisfactory value of the diversity gain. One of the commonly used methods for decorrelation of the received signal’s replicas, propagating through different radio paths, is the spatial separation of two (or more) receiving antennas, as it has been done in the presented research.Table5 summarizes the correlation coefficient between system loss values (ρl), slow fading component (ρsf), and fast fading component (ρff), calculated based on the signals received by two wearable antennas. One can see that for almost all analyzed cases the correlation coefficient values are close to zero, which means that the signals received by two antennas are practically uncorrelated. The outstanding values have been obtained for C1 (ρsf=0.33), C9 (ρl=−0.11, ρsf=0.29, and ρff=−0.14), and C7 (ρl=−0.15 and ρsf=−0.18), but even these values are below the assumed threshold of 0.5. Presented results justify the need for the spatial diversity scheme application in WBANs.Table 5
Correlation coefficient between system loss values (ρl), slow fading component (ρsf), and fast fading component (ρff), calculated based on the signals received by two wearable antennas.
Configuration
RX ant.
ρl
ρsf
ρff
C1
TOF-TOB
-0.07
0.33
-0.01
C2
TOF-ABL
0.02
0.03
-0.04
C3
TOF-ABR
0.02
0.04
0.00
C4
TOF-HEL
0.01
0.06
-0.02
C5
TOF-HER
-0.08
0.08
-0.06
C6
TOB-ABL
-0.07
0.03
-0.01
C7
TOB-ABR
-0.15
-0.18
-0.04
C8
TOB-HEL
-0.10
-0.08
-0.04
C9
TOB-HER
-0.11
0.29
-0.14The exemplary graphs of the slow and fast fading components in a single scenario realization have been presented in Figures6 and 7, respectively. It may be noticed that in both cases, the magnitudes of fading at the same time are different for particular RX antennas. It confirms graphically the results presented in Table 5.Figure 6
Exemplary graph of the slow fading component in a single realization of scenario for C7.Figure 7
Exemplary graph of the fast fading component in a single realization of scenario for C4.


## 4.1. Fast Fading Characteristics

The results of PDFs fitting for the fast fading component are presented in Table3(a) (for configurations C1–C4) and Table 3(b) (for configurations C5–C9). Both tables include the distribution parameters and the results of evaluation tests. The χ2, χ2crit, and AIC stand for the χ2 test statistics, the critical value of this statistics for the significance level of 5%, and the AIC statistic, respectively. It should be reminded that the χ2 test is passed when the value of χ2 statistics is below the critical value, and the lowest AIC value indicates the best-fitted PDF [15]. The name of the distributions with the best-fitting results for each configuration has been bolded in the Table 3.Table 3
(a)
Results of the fast fading distribution fitting for configurations C1–C4
Configuration
RX ant.
Distribution
Parameters
χ2
χ2crit
AIC
Correlation
C1
TOF
Rice
sRice
0.9602
σRice
0.5269
21.19
27.59
19389
0.98
Nakagami
m
1.1750
Ω
1.4772
15.81
27.59
20474
0.90
Weibull
a
1.2479
b
2.4021
18.39
27.59
20056
0.95
Rayleigh
σRay
0.8594
—
—
13.35
28.87
20689
0.83
TOB
Rice
sRice
0.8943
σRice
0.6212
27.69
27.59
22092
0.98
Nakagami
m
1.0356
Ω
1.5714
22.17
27.59
22551
0.93
Weibull
a
1.2704
b
2.1638
24.73
27.59
22438
0.96
Rayleigh
σRay
0.8864
—
—
21.26
28.87
22560
0.92
C2
TOF
Rice
sRice
0.9129
σRice
0.5661
19.12
27.59
20517
0.98
Nakagami
m
1.1325
Ω
1.4743
15.25
27.59
21207
0.90
Weibull
a
1.2415
b
2.3043
17.36
27.59
20945
0.94
Rayleigh
σRay
0.8586
—
—
13.12
28.87
21339
0.86
ABL
Rice
sRice
0.8918
σRice
0.6090
25.74
27.59
21938
0.99
Nakagami
m
1.0614
Ω
1.5371
20.98
27.59
22432
0.93
Weibull
a
1.2593
b
2.1956
23.32
27.59
22287
0.96
Rayleigh
σRay
0.8767
—
—
19.61
28.87
22462
0.91
C3
TOF
Rice
sRice
0.9475
σRice
0.5493
22.04
27.59
22173
0.97
Nakagami
m
1.1249
Ω
1.5012
16.53
27.59
23224
0.87
Weibull
a
1.2537
b
2.3339
19.20
27.59
22856
0.93
Rayleigh
σRay
0.8664
—
—
14.54
28.87
23351
0.81
ABR
Rice
sRice
0.8651
σRice
0.6488
27.45
27.59
24718
0.98
Nakagami
m
1.0225
Ω
1.5903
22.44
27.59
25098
0.94
Weibull
a
1.2752
b
2.1318
25.14
27.59
25013
0.96
Rayleigh
σRay
0.8917
—
—
21.71
28.87
25101
0.94
C4
TOF
Rice
sRice
0.9624
σRice
0.5346
20.00
27.59
21404
0.95
Nakagami
m
1.1202
Ω
1.4977
14.39
27.59
22688
0.81
Weibull
a
1.2530
b
2.3608
17.00
27.59
22257
0.89
Rayleigh
σRay
0.8654
—
—
12.80
28.87
22804
0.76
HEL
Rice
sRice
0.8319
σRice
0.6909
27.00
27.59
25501
0.98
Nakagami
m
0.9525
Ω
1.6467
21.39
27.59
25705
0.94
Weibull
a
1.2872
b
2.0339
23.73
27.59
25722
0.96
Rayleigh
σRay
0.9074
—
—
22.88
28.87
25726
0.95
(b)
Results of the fast fading distribution fitting for configurations C5–C9
Configuration
RX ant.
Distribution
Parameters
χ2
χ2crit
AIC
Correlation
C5
TOF
Rice
sRice
0.9203
σRice
0.5614
22.99
27.59
21081
0.96
Nakagami
m
1.1532
Ω
1.4772
18.61
27.59
21843
0.88
Weibull
a
1.2451
b
2.3400
21.23
27.59
21529
0.92
Rayleigh
σRay
0.8594
—
—
15.84
28.87
22022
0.82
HER
Rice
sRice
0.9106
σRice
0.5737
24.84
27.59
21534
0.97
Nakagami
m
1.1224
Ω
1.4874
20.08
27.59
22225
0.90
Weibull
a
1.2461
b
2.2924
22.80
27.59
21966
0.94
Rayleigh
σRay
0.8624
—
—
17.50
28.87
22344
0.85
C6
TOB
Rice
sRice
0.9200
σRice
0.5503
19.75
27.59
21571
0.97
Nakagami
m
1.1620
Ω
1.4521
15.84
27.59
22399
0.89
Weibull
a
1.2351
b
2.3490
17.97
27.59
22062
0.94
Rayleigh
σRay
0.8521
—
—
13.51
28.87
22606
0.83
ABL
Rice
sRice
0.8445
σRice
0.6828
24.46
27.59
26078
0.98
Nakagami
m
0.9567
Ω
1.6456
19.31
27.59
26314
0.94
Weibull
a
1.2878
b
2.0434
21.40
27.59
26324
0.96
Rayleigh
σRay
0.9071
—
—
20.46
28.87
26332
0.95
C7
TOB
Rice
sRice
0.9240
σRice
0.5803
25.60
27.59
22718
0.98
Nakagami
m
1.0866
Ω
1.5272
19.82
27.59
23490
0.90
Weibull
a
1.2598
b
2.2595
22.76
27.59
23243
0.94
Rayleigh
σRay
0.8739
—
—
17.92
28.87
23552
0.86
ABR
Rice
sRice
0.8772
σRice
0.6334
29.30
27.59
23859
0.99
Nakagami
m
1.0495
Ω
1.5719
24.49
27.59
24278
0.94
Weibull
a
1.2712
b
2.1669
27.04
27.59
24161
0.97
Rayleigh
σRay
0.8865
—
—
23.06
28.87
24298
0.93
C8
TOB
Rice
sRice
0.9285
σRice
0.5585
22.17
27.59
21709
0.98
Nakagami
m
1.1337
Ω
1.4860
17.37
27.59
22553
0.89
Weibull
a
1.2471
b
2.3203
19.86
27.59
22240
0.94
Rayleigh
σRay
0.8620
—
—
15.10
28.87
22695
0.84
HEL
Rice
sRice
0.8125
σRice
0.6954
29.38
27.59
25188
0.99
Nakagami
m
0.9802
Ω
1.6274
24.55
27.59
25382
0.97
Weibull
a
1.2821
b
2.0552
26.84
27.59
25370
0.98
Rayleigh
σRay
0.9020
—
—
25.26
28.87
25384
0.97
C9
TOB
Rice
sRice
0.9221
σRice
0.5469
22.68
27.59
20419
0.98
Nakagami
m
1.1964
Ω
1.4485
18.64
27.59
21173
0.91
Weibull
a
1.2362
b
2.3858
21.15
27.59
20828
0.95
Rayleigh
σRay
0.8510
—
—
15.25
28.87
21453
0.84
HER
Rice
sRice
0.9027
σRice
0.5988
27.07
27.59
22514
0.97
Nakagami
m
1.0737
Ω
1.5320
21.66
27.59
23121
0.89
Weibull
a
1.2595
b
2.2254
24.58
27.59
22932
0.93
Rayleigh
σRay
0.8752
—
—
19.80
28.87
23165
0.86For all analyzed cases, theχ2 test has been passed, except for TOB in C1 configuration, where the statistics value is comparable with the critical one, but slightly higher. Considering the AIC values, as well as the correlation test for all configurations and RX antennas’ positions, the best-fitted distribution for fast fading component is Rice. It was expected since for the analyzed scenarios and environment there is a high probability of the existence of strong dominant component in the received signal. The noncentrality parameter, sRice, whose squared value corresponds to the power of dominant component of received signal, is in the range from 0.8125 (for C8-HEL) up to 0.9624 (for C4-TOF configuration). On the other hand, the scale parameter, σRice, whose doubled-squared value corresponds to the power of scattered components, is between 0.5269 (for C1-TOF) and 0.6954 (for C8-HEL configuration). The abovementioned values show that, for each case, the power of dominant component is higher than the power of the scattered ones.Figure4 shows the exemplary graph of the selected PDFs (Rice, Nakagami, Weibull, and Rayleigh) fitted to the empirical distribution of the fast fading magnitude in linear scale, α. As one can see, the shape of the Rice distribution is the closest to the empirical one, what is expected after consideration of the numerical data from Tables 3(a) and 3(b).Figure 4
Exemplary fast fading distributions for C1 configuration and RX antenna placed on TOF.


## 4.2. Slow Fading Characteristics

Analogous results of the lognormal distribution fitting for the slow fading component have been gathered in Table4. For all cases, the χ2crit value is the same and equals 27.59 for a significance level of 5%.Table 4
Results of the lognormal distribution fitting for the slow fading component and for all configurations.
Configuration
RX ant.
Parameters
χ2
Correlation
C1
TOF
μL [dB]
-0.20
σL [dB]
1.54
2.67
0.97
TOB
μL [dB]
-0.19
σL [dB]
1.76
5.25
0.97
C2
TOF
μL [dB]
-0.12
σL [dB]
1.56
4.92
0.98
ABL
μL [dB]
-0.16
σL [dB]
1.46
1.59
0.98
C3
TOF
μL [dB]
-0.16
σL [dB]
1.68
3.88
0.96
ABR
μL [dB]
-0.21
σL [dB]
1.34
1.17
0.98
C4
TOF
μL [dB]
-0.16
σL [dB]
1.71
3.78
0.98
HEL
μL [dB]
-0.23
σL [dB]
1.91
4.68
0.95
C5
TOF
μL [dB]
-0.17
σL [dB]
1.67
4.02
0.94
HER
μL [dB]
-0.11
σL [dB]
1.87
11.49
0.70
C6
TOB
μL [dB]
-0.18
σL [dB]
1.98
6.78
0.97
ABL
μL [dB]
-0.17
σL [dB]
1.42
2.91
0.95
C7
TOB
μL [dB]
-0.20
σL [dB]
1.90
4.09
0.97
ABR
μL [dB]
-0.22
σL [dB]
1.58
3.75
0.98
C8
TOB
μL [dB]
-0.17
σL [dB]
1.84
4.91
0.97
HEL
μL [dB]
-0.20
σL [dB]
1.81
4.82
0.96
C9
TOB
μL [dB]
-0.20
σL [dB]
1.79
4.10
0.98
HER
μL [dB]
-0.13
σL [dB]
1.56
4.16
0.97Since the values ofχ2 statistics are below the critical value for all the cases, and the correlation is over 95% for the vast majority of them, one can say that the lognormal distribution fits well to the empirical one. Moreover, the average of the slow fading component (μL) is close to zero in the log domain for all configurations. It confirms that the slow fading component have been obtained properly in the data processing phase. On the other hand, the standard deviation of the slow fading component (σL) is below 2 dB, being in the range of [1.43, 1.98] dB, which is a relatively low value.In Figure5, the exemplary graph of the lognormal PDF fitting to the empirical distribution of the slow fading magnitude (α), obtained from the measurements for the antenna placed on the torso in C1 configuration, has been presented. One can observe the good fitting of both distributions.Figure 5
Exemplary slow fading distribution for C9 configuration and antenna placed on TOB.


## 4.3. Spatial Decorrelation of Received Signal

In order to realize any of the diversity schemes (spatial, polarization, etc.), one has to ensure the proper decorrelation level of two or more received replicas of radio signal and use one of the well-known diversity combining techniques (e.g., maximal-ratio combining or equal-gain combining). Focusing on the decorrelation issue, it may be assumed that it is sufficient to have the correlation coefficient lower than 0.5, in order to obtain a satisfactory value of the diversity gain. One of the commonly used methods for decorrelation of the received signal’s replicas, propagating through different radio paths, is the spatial separation of two (or more) receiving antennas, as it has been done in the presented research.Table5 summarizes the correlation coefficient between system loss values (ρl), slow fading component (ρsf), and fast fading component (ρff), calculated based on the signals received by two wearable antennas. One can see that for almost all analyzed cases the correlation coefficient values are close to zero, which means that the signals received by two antennas are practically uncorrelated. The outstanding values have been obtained for C1 (ρsf=0.33), C9 (ρl=−0.11, ρsf=0.29, and ρff=−0.14), and C7 (ρl=−0.15 and ρsf=−0.18), but even these values are below the assumed threshold of 0.5. Presented results justify the need for the spatial diversity scheme application in WBANs.Table 5
Correlation coefficient between system loss values (ρl), slow fading component (ρsf), and fast fading component (ρff), calculated based on the signals received by two wearable antennas.
Configuration
RX ant.
ρl
ρsf
ρff
C1
TOF-TOB
-0.07
0.33
-0.01
C2
TOF-ABL
0.02
0.03
-0.04
C3
TOF-ABR
0.02
0.04
0.00
C4
TOF-HEL
0.01
0.06
-0.02
C5
TOF-HER
-0.08
0.08
-0.06
C6
TOB-ABL
-0.07
0.03
-0.01
C7
TOB-ABR
-0.15
-0.18
-0.04
C8
TOB-HEL
-0.10
-0.08
-0.04
C9
TOB-HER
-0.11
0.29
-0.14The exemplary graphs of the slow and fast fading components in a single scenario realization have been presented in Figures6 and 7, respectively. It may be noticed that in both cases, the magnitudes of fading at the same time are different for particular RX antennas. It confirms graphically the results presented in Table 5.Figure 6
Exemplary graph of the slow fading component in a single realization of scenario for C7.Figure 7
Exemplary graph of the fast fading component in a single realization of scenario for C4.


## 5. Conclusions

Even though the wireless body area networks are gaining popularity, there are still not many investigations about the space diversity scheme. In situations when the number of wearable devices is getting higher, it is reasonable to consider the use of such a technique to achieve better quality of received signal.In the article, the characterization of slow and fast fading in WBAN networks with space diversity scheme has been presented. The analysis, based on the measurements at 2.45 GHz in an indoor environment, has also shown that for all investigated configurations, the correlation coefficient values of the received signals’ parameters are below the assumed value of 0.5, being close to zero for the vast majority of cases.It has been shown that the slow fading component may be modelled by a lognormal distribution with zero average and the standard deviation from the range of [1.43, 1.98] dB. The fast fading component is best modelled by a Rice distribution with the noncentrality parameter and the scale parameter being in the range [0.8125, 0.9624] and [0.5269, 0.6954], respectively.Presented results justify the need for further research in the field of channel modelling in the space diversity scheme and its application in WBANs.



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*Source: 6181435-2019-02-21.xml*