Performance analysis of multiplexing and error control scheme for body area networks
 Kento Takabayashi^{1}Email author,
 Hirokazu Tanaka^{2},
 Chika Sugimoto^{1} and
 Ryuji Kohno^{1}
https://doi.org/10.1186/s1363801605610
© Takabayashi et al. 2016
Received: 6 September 2015
Accepted: 18 February 2016
Published: 1 March 2016
Abstract
In this paper, we theoretically analyze the performance of a multiplexing and error control scheme for body area networks. In our previous work, we proposed a quality of service (QoS) control optimization method that achieves optimal QoS control by introducing a multiplexing scheme over the media access control (MAC) layer. This multiplexing scheme combines Weldonbased hybrid automatic repeat request (ARQ) with a decomposable errorcorrecting code. In this paper, we present a theoretical analysis of our proposed scheme as an extension of our previous work. In this proposed system, the decomposable code which has simpler structure is utilized. We then show that our proposed multiplexing layer can achieve optimal performance at E _{s}/N _{0} = 3, 5, and 6 dB in the additive white Gaussian noise (AWGN) channel and at E _{s}/N _{0} = 8, 11, and 14 dB in the Rayleigh fading channel by arbitrarily selecting parameters for the errorcorrecting code and hybrid ARQ. Then, we show that the proposed system obtains over 1.2 dB gain in the AWGN channel and over 4.2 dB gain in the Rayleigh fading channel than IEEE802.15.6 in the optional pattern.
Keywords
1 Introduction

Ultralow power consumption
Although this has been considered in the above standards, substantially lower powerconsuming media access control (MAC) and physical layer (PHY) technologies are required.

Coexistence with other networks
The 2.4GHz industrial, scientific, and medical (ISM) band is globally assigned for common use in local area network (LAN) and personal area network (PAN) devices. This frequency band is potentially a good candidate for BANs; however, when using this band, interference from other systems must be taken into consideration.

Optimal quality of service (QoS) control
A wearable vital sensor can connect various types of sensors, with the data rate of such sensors varying widely. Further, their respective allowable delay times depend on their application. Therefore, optimal QoS control for input data is an important factor in transmitting sensor data.
From the above requirements, we have proposed an optimal QoS control scheme that employs a multiplexing layer and a decomposable error control coding scheme [20–22]. In [20], we proposed a QoS control scheme using Weldonbased hybrid automatic repeat request (ARQ) [23] with ReedMuller codes. However, the errorcorrecting capability could not be increased effectively because of characteristics of ReedMuller codes which we selected in [20]. So, we conducted simulations to evaluate the performance of the proposed system utilizing Weldon’s ARQ with decomposable codes based on punctured convolutional codes in the additive white Gaussian noise (AWGN) channel [21] and a wearable BAN channel model [22] by comparing it with IEEE 802.15.6. Assuming that the wearable sensor device has multiple sensors, each sensor’s input data are transmitted through a common MAC and PHY layer [21, 22].
Because we evaluated the effectiveness of our proposed scheme only via simulation in our previous work, in this paper, we present a theoretical analysis of our proposed scheme in [21] and [22] under the AWGN channel and the Rayleigh fading channel as an extension of our previous work. We have not evaluated and analyzed the case of the Rayleigh fading channel in our previous work. Then, in this proposed system, the structure of our decomposable code is modified to be much simpler than that in our previous work [21, 22] in order to analyze it more easily. In general, an evaluation of ARQ requires a large number of simulation trials to fully evaluate the given system; however, we can specifically evaluate the throughput in a stable state by sound theoretical analysis. More specifically, we can easily obtain detailed characteristics of our proposed scheme by this formulization. We derived a lower bound on throughput performance and an upper bound on residual bit error rate in the AWGN channel and the Rayleigh fading channel. In addition, we investigated QoS parameters to further optimize our system. For example, we identified the optimum parameters according to various policies, as shown in Tables 3 and 4. Figure 8 shows the results of our throughput optimization by using the parameters of Table 4.
The remainder of this paper is organized as follows. In Section 2, we briefly review the system model of our proposed scheme. Section 3 explains the theoretical analysis of our proposed scheme under the AWGN channel and the Rayleigh fading channel. Performance evaluations by theoretical analysis and simulations are presented in Section 4. Finally, we conclude our paper and provide directions for future work in Section 5.
2 System model
2.1 System concept
In the MAC module, the error control process is performed according to the instructions from the multiplexing module. In the PHY module, this multiplexed data is modulated. In this paper, coherent phase shift keying (PSK) is used for basic analysis. Then, direct sequence spread spectrum (DSSS) is applied to increase robustness against multipath fading and multiuser interference. At the receiver, the transmission operation is processed in the reverse order. Finally, after the process at the demultiplexing module is complete, error detection is performed on the data.
2.2 Decomposable code
In our proposed scheme, Weldon’s ARQ [23] is employed rather than selective repeat ARQ, and decomposable code is employed as errorcorrection code for hybrid ARQ. The proposed scheme can provide an error control method that satisfies various QoS requirements by coordinating the number of data copies and changing how the decomposable code is combined.
As an example of decomposable code, a punctured convolutional code with constraint length K set to 3 and coding rates 8/9, 4/5, 2/3, and 1/2 is used. In [21] and [22], we selected coding rates 7/8, 5/6, 3/4, and 1/2. However, those punctured matrices in [21] and [22] are very complicated, and then it is very difficult to analyze its performance in theory. On the other hand, punctured matrices which we select in this paper are quite simple and can be analyzed more easily.
The errorcorrection capability increases as the coding rate decreases in the order 8/9, 4/5, 2/3, and 1/2.
2.3 Procedure of the proposed scheme
3 Theoretical analysis
Here, P _{ i } is the packet error rate (PER), m _{ i } is the number of transmitted bits, and n _{ i } is the number of copy blocks of Weldon’s ARQ at the ith transmission. Then, P _{ i } changes in stages because the received data is decoded by decomposable codes with coding rates varying in order of Eq. 1. Note that throughput T is described as the above approximate equation due to the maximum retransmission limit.
Here, d _{ free } is the free distance of the code, and a _{ d } is the number of incorrect paths or adversaries of the Hamming weight d, d ≤ d _{ free }. In addition, c _{ d } is the total number of information bit errors produced by the incorrect paths of the Hamming weight.
Here, r _{ B,q } is P _{ B } in the case of a code with rate R _{ q }.
The transfer function T(D,N) changes according to the punctured matrices. Further details of the transfer function T(D,N) are provided in the Appendix.
4 Performance evaluation
4.1 Simulation condition
In this subsection, we evaluate our proposed scheme by theoretical analysis and simulations.
Number of copies n _{ i } for each pattern under the AWGN channel
i  0  1  2  3  4  q = 5 

Pattern 1, n _{ i }  1  1  1  1  2  4 
Pattern 2, n _{ i }  1  2  2  4  4  6 
R _{ i }  8/9  4/5  2/3  1/2  1/2  1/2 
Number of copies n _{ i } for each pattern under the Rayleigh fading channel
i  0  1  2  3  4  q = 5 

Pattern 1, n _{ i }  1  1  1  1  1  3 
Pattern 2, n _{ i }  1  3  4  4  5  5 
R _{ i }  8/9  4/5  2/3  1/2  1/2  1/2 
Simulation parameters
Parameter  Detail 

Channel model  AWGN 
Rayleigh fading  
IEEE802.15.6 CM3  
Modulation  BPSK 
FEC  R = 8/9, 4/5, 2/3 and 1/2 
K = 3 convolutional codes  
Decoding  Soft decision 
Viterbi decoding  
ARQ protocol  Weldon’s ARQ 
L _{info}  504 bits 
Data rate  487 kbps 
Roundtrip time  9.84 ms 
4.2 Numerical results
Relative to the simulation, the performance of the modified punctured convolutional codes is the same as that of the ideal punctured matrices, unlike results of the upper bound. This occurs because the number of trials in the simulation is not large enough. Further, the difference between the errorcorrecting capacity of the ideal matrix and that of the modified one is very small in the simulation. Hence, the difference does not clearly emerge in the graph without the huge number of trials. The difference between the upper bound and the simulation becomes greater as E _{ s }/N _{0} decreases.
Optimal number of copies n _{ i } for minimum latency while satisfying PER ≤ 10^{− 5}. Channel model is the AWGN channel
E _{s}/N _{0}  n _{0}  n _{1}  n _{2}  n _{3} 

3 dB  1  1  10 i = q  – 
5 dB  1  7 i = q  –  – 
6 dB  1  4 i = q  –  – 
R _{ i }  8/9  4/5  2/3  1/2 
Optimal number of copies n _{ i } for maximum throughput while satisfying PER ≤ 10^{− 5}. Channel model is the AWGN channel
E _{s}/N _{0}  n _{0}  n _{1}  n _{2}  n _{3} 

3 dB  1  1  1  3 i = q 
5 dB  1  1  2 i = q  – 
6 dB  1  1  1 i = q  – 
R _{ i }  8/9  4/5  2/3  1/2 
Optimal number of copies n _{ i } for minimum latency while satisfying PER ≤ 10^{− 5}. Channel model is the Rayleigh fading channel
E _{s}/N _{0}  n _{0}  n _{1}  n _{2}  n _{3}  n _{4}  n _{5} 

8 dB  1  1  1 i = q  3  –  – 
11 dB  1  1 i = q  4  –  –  – 
14 dB  1  7 i = q  –  –  –  – 
R _{ i }  8/9  4/5  2/3  1/2  1/2  1/2 
Optimal number of copies n _{ i } for maximum throughput while satisfying PER ≤ 10^{− 5}. Channel model is the Rayleigh fading channel
E _{s}/N _{0}  n _{0}  n _{1}  n _{2}  n _{3}  n _{4}  n _{5} 

8 dB  1  1  1  1  1  1 i = q 
11 dB  1  1  1  1  1 i = q  – 
14 dB  1  1  1  1 i = q  –  – 
R _{ i }  8/9  4/5  2/3  1/2  1/2  1/2 
5 Conclusions
In this paper, we presented a theoretical analysis of our proposed scheme to evaluate it under the AWGN channel and the Rayleigh fading channel as an extension of our previous work. We investigated QoS parameters to further optimize our system, showing that our proposed system can achieve optimal performance by arbitrarily selecting parameters of the errorcorrecting code and Hybrid ARQ. Performance evaluations by theoretical analysis and simulations showed that our proposed scheme has greater flexibility for optimizing QoS parameters according to the required QoS for each input data. Moreover, our evaluations showed that the performance of our proposed scheme is better than that of the conventional scheme.
In the future, we will consider a dynamic channel model and situation such as a multiple WBAN environment that can be theoretically analyzed. Then, optimal parameters for that case should also be investigated.
Declarations
Acknowledgements
The first author would like to thank members of Kohno laboratory, Yokohama National University, Japan for their great inspiration and kindness.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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