The theoretical calculation result and simulation result of BER are compared to verify the validity of close-form of BER. Furthermore, the Bose - Chaudhuri - Hocquenghem code and the convolutional code are applied to multiple-hop MIMO relay systems and the BER of both channel codes is compared to find out the suitable channel code for medical application.
Research INVESTIGATION OF CHANNEL CODE FOR MULTIPLE-HOP MIMO RELAY SYSTEMS Vu Van Son* Abstract: In order to improve performance of wireless systems, a multiple-hop relay system was proposed in several papers, however the bit error rate (BER) was not taken into consideration Consequently, we have proposed the BER calculation method for the multiple-hop system in the recent work, and in this work several channel codes is applied into multiple-hop systems and the BER of whole system is calculated and discussed The theoretical calculation result and simulation result of BER are compared to verify the validity of close-form of BER Furthermore, the Bose - Chaudhuri - Hocquenghem code and the convolutional code are applied to multiple-hop MIMO relay systems and the BER of both channel codes is compared to find out the suitable channel code for medical application Keywords: Multiple-hop MIMO relay system, Bit error rate calculation method, BCH code, Convolutional code. INTRODUCTION In recent years, multiple-input multi-output (MIMO) technology using multiple antennas at both the access point (base station) and user terminal sides has become a popular research field of next generation mobile communication systems. The increase of the system channel capacity under finite frequency bandwidth has made the MIMO system unique and efficient in data transmission. In terms of the scientific underpinnings, MIMO research can be divided into three following areas, namely, 1) array antennas and adaptive signal processing for the implementation of antenna configurations and control methods, 2) information theory and coding schemes (space-time coding) for the implementation of an efficient data transmission, and 3) radio wave propagation for the modeling of MIMO channel [1]-[6]. The MIMO channel capacity can be decreased when the distance between a base station and an user terminal is much larger than the base station and user terminal scatter radius, this leads to a wave-guiding structure with a small rank of the MIMO matrix, even though the signals between antenna elements are uncorrelated. This effect has been termed “keyhole” or “pinhole” (hereafter, we call it keyhole). In the keyhole environment, the multi-stream transmission becomes impossible, and high-speed, high-reliability transmission cannot be expected [7]-[9]. In the future, it is believed that more MIMO service area will be established. Thus, an expansion of an service area to an isolated area is anticipated. Based on this idea, the authors have proposed a general idea of a MIMO relay system that can maintain the ability of high-speed and/or high-reliability data transmission [10]. A MIMO relay system can relay radio signals from a MIMO service area to an isolated area. In general, when a MIMO relay systems has only one relay, the whole channel in the MIMO relay systems is equivalent to a MIMO multi-keyhole environment. In a multi-keyhole environment, the probability density functions (PDFs) of singular values of channel response matrix or eigenvalues of correlation Journal of Military Science and Technology, Special Issue, No 51A, 11 - 2017 17 Electronics & Automation matrix are important from a viewpoint of system designing such as transmission characteristic meaning channel capacity and bit error rate analysis. Furthermore, these papers showed that the performance of system becomes better when the number of relays increases, however the BER was not taken into consideration. In multiple-hop system, the error bit of previous link affects the channel quality of the following links. Therefore, we proposed BER calculation method for multiple-hop MIMO relay systems and then investigate the number of relays for the best performance [11]. However, the validity of close-form BER calculation method was not verified, furthermore the investigation of channel code in multiplehop relay system was not taken into consideration. Therefore, in this work, we compare the theoretical calculation method and the simulation method to verify the close-form of BER and analyze the BER of multiple-hop system in different channel codes. The rest of paper is as follows. Section 2 explains the system model, and then the BER calculation method is proposed and the close-form is verified in Section 3. The calculation result of BER for different channel code is presented in Section 4. Section 5 concludes the paper. SYSTEM MODEL Figure The concept of multiple-hop MIMO relay systems. The detail of system model is described in [11], however in order to help readers easily follow the work, it is breafly represnted once again. Fig shows m relays intervened multi-hop MIMO relay system. Here, Ki (i = 0 ·· · m+1) denotes the number of the antenna elements at the Tx, the Rx and each relay node. di (i = 0, ·· ·, m) represents the distance between each transceivers. The distance between the Tx and the Rx is fixed as d. The signal is transmitted from the Tx to the RS1. At the RS1, the signal is decoded, encoded and transmitted to the RS2. Similarly, the signal is transmitted over and over until the signal reaches to the final receiver. We assume the transmit power of each relay is 18 Vu Van Son, “Investigation of channel code MIMO relay systems.” Research equally divided into each antenna element. In other site, as described in Section I, if the number of antenna elements at one relay is smaller than the other, this relay will be the bottleneck of system and the channel capacity of the system will be restricted by this relay. Since in this paper we consider the distance and transmit power, the number of antenna elements at each relay is assumed to be the same as that of the Tx and the Rx and be denoted by M. Let Hii+1 denotes a Ki+1 x Ki channel matrix between the RSi and the RSi+1 Since the path loss is taken into consideration, Hii+1 is the composite matrix. We model Hii+1 as: H ii 1 lii 1 H wii 1 , i 0,···, m (1) where Hwii+1 is a matrix with independent and identically distributed (i.i.d.), zero mean, unit variance, circularly symmetric complex Gaussian entries, and lii+1 represents the path loss between the RSi and the RSi+1. The path loss is described in detail in the following section. On the other hand, we assume the time division multiple access (TDMA) algorithm is applied to control the transmission of each relay node. The allocation m time for each relay in unit time is denoted by ti, i 0 ti Moreover, in order to explain controlling of distance and transmit power clearly, the treating of allocation time is left to the future work, in this paper allocation time of each relay node is assumed to be the same, ti m 1 BER OF MULTIPLE-HOP MIMO RELAY SYSTEMS 3.1 BER of every hop The BER after modulation is as follows [12]: pi = α.erfc( SNRi ) i = 0, …, m (2) M Where erfc is the complementary error function, α and β are the factors based on the modulation scheme and summarized in Table 1, SNRi is the signal to noise ratio at relay i. Table Factor α and β of several modulation schemes Modulation scheme α β index BPSK 1/2 1 1 QPSK 1/2 2 2 8PSK 1/3 1/ sin2(π/8) 3 Journal of Military Science and Technology, Special Issue, No 51A, 11 - 2017 19 Electronics & Automation 16QAM 3/8 10 4 64QAM 7/24 42 6 256QAM 15/64 170 8 In order to improve the quality of service (QoS) of system, the channel code is applied. In this work, we investigate the effect of BER at every hop on QoS of whole system whether the QoS of every hop. Therefore, any channel code can be used as an example to analyze of performance and the well-known (63, 57) Bose - Chaudhuri - Hocquenghem (BCH) is applied. The other parameter of BCH code as shown in Table 2 can be used instead of (63,57), the result (is discussed in the following section. Due to application of the BCH code, the BER after decoding at the RSi is described as follows [13]: m m BERi = ( j ) pij (1-pi)m-j, (3) j t 1 where m and t denote the block length and the error correction capability of BCH code, respectively. Here k denotes the number of information bits in every block code. Thus, the code rate, r, becomes r = k/m. 3.2 BER of multiple-hop system Figure State transition diagram of an information bit b. As explained in the previous section, the bit can be error at every hop and the state transition diagram of an information bit b which is transmitted from the TX to the RX is described in Fig 2. At a hop the information bit b can be in error and become the error bit, -b, however the error bit -b can be in error again and turn back to the correct information bit, b. Consequently, at the destination, the information bit b is correctly transmitted if it has no error or the number of errors is even, whereas the information bit b is uncorrectly transmitted and it becomes the error bit, -b, if the number of error is odd in whole transmission process. Thus, the BER of whole system is represented as follows. m m i 0 j 0 m m BERi= ( BERi (1 BERi )) + ( BER BER BER (1 BER )) (4) i i j k j k l l i , j ,k 20 Vu Van Son, “Investigation of channel code MIMO relay systems.” Research However, the BER of any link is much smaller than 1, therefore we can ignore three (3) or over power to BER and the BER of whole system is rewritten by: m m BER = BERi 2 BERi BE R j (5) i 0 i j 3.3 Comparison of theoretical and simulation result Fig 3 shows the BER of whole system while the number of hops and Eb/No are changing. The theoretical result and the simulation result also are compared in Fig 3. The BER of whole system deteriorates when the number of hops increase, this is appropriate to the equation of BER (5). The result of theoretical method and simulation is perfect match, therefore we can say that the derived close-form of BER is propriety and can be used instead of simulation method to calculate the BER of multiple-hop systems. Figure 3. Comparison of theoretical and simulation results. COMPARISON OF BCH AND CONVOLUTIONAL CODE 4.1 Channel codes There are two type of channel codes, one is block code and the other one is convolutional codes. In IEEE 802.15.6, the BCH code is specified, therefore in this work we use BCH code as the representation of block code. In order to keep fairness for both BCH code and convolutional codes, the code rate of both channel codes is set to ½. The detail of each one is represented as follows. The BCH codes are a generalization of Hamming codes which allow multiple error correction. BCH code is the one of the very powerful cyclic codes that broadens options such as block length, code rate, bit size, error correction capability and so on [13]. If the block length is a remarkably long as hundreds of bits, this code characteristic is good than other codes which have same block Journal of Military Science and Technology, Special Issue, No 51A, 11 - 2017 21 Electronics & Automation lengths and code rate. Moreover, the most widely used BCH code uses code word block length as m = 2n – 1 (n = 3,4, ). BCH code is the most easily defined in terms of the roots of the generator polynomial. The soft-decision decoding of block code is complex, thus the hard-decision is applied in this work. Convolutional code is that perform coding bit sequence or symbol sequence with any lengths sequentially. This code word has any number of lengths. As decoding method, Viterbi algorithm is commonly used. Convolutinal code encodes with the previous any bits, response between information data and coding data is sequentially. Code rate r = k/m, where, k is information bits, m is coding bits. The detail of both codes is described in Table 2, the code rate of both them is ½. Table BCH code and convolutional code for comparison Constraint Code (m,k) Code rate length (7,4), (15,7), (31,16), k/m BCH code (63,30), (63,36), ( = ½) (127,64) Convolutional 3,5,7,9 1/2 code 4.2 Calculation result We evaluate BCH and convolutional codes in Fig 4. The calculation result shows that bit error rate characteristic of (31,16) BCH code is the same as convolutional codes of code rate ½ and constraint length 7 or more. Furthermore, BCH code is less computation than convolutional codes in comparison of amount of calculation for decoding if using the same code rate. if the amount of calculation is low, it leads to reduce complexity and delay transmission time. Furthermore, the BER is low meaning the system is reliable. Consequently, in situation of medical application, BCH code is more suitable than convolutional codes. Figure Comparison of BCH and convolutional codes. 22 Vu Van Son, “Investigation of channel code MIMO relay systems.” Research CONCLUSIONS In this paper, the close-form of calculation method of BER for multiple-hop MIMO relay system was verified by BCH code, and as the result it is said that this close-form is suitable and can be used instead of simulation method. Moreover, the representation of block code, BCH code, was compared to convolutional codes with the constant of code rate ½. The BCH code has lower amount of computation and better BER, it is suitable for medical application than the convolutional codes. However, in this paper, BCH code and convolutional code are compared, another code will be compared in the future work, and the combination of channel code with control scheme on MAC layer will be taken into consideration. REFERENCES [1]. K. Miyashita, T. Nishimura, T. Ohgane, Y. Ogawa, Y. Takatori, and K. 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TÓM TẮT NGHIÊN CỨU MÃ KÊNH CHO HỆ THỐNG CHUYỂN TIẾP ĐA CHẶNG MIMO Để cải thiện hiệu cho mạng vô tuyến, cấu hình đa chặng chuyển tiếp đề xuất số cơng trình, nhiên tỉ lệ lỗi bít (BER) khơng khảo sát, đánh giá cách cụ thể Vì thế, chúng tơi đề xuất phương pháp tính BER cho hệ thống đa chặng chuyển tiếp nghiên cứu gần đây, nghiên cứu số mã kênh áp dụng cho hệ thống đa chặng BER khảo tính tốn, khảo sát Kết tính tốn BER theo phương pháp lý luận toán học so sánh với phương pháp mơ để xác minh thích hợp cơng thức gần tính BER theo phương pháp tốn học Ngồi ra, mã kênh BCH mã chập áp dụng vào hệ thống đa chặng chuyển tiếp MIMO, BER hai mã so sánh để tìm mã kênh thích hợp cho ứng dụng y tế Từ khố: Hệ thống đa chặng chuyển tiếp MIMO, Tỉ lệ lỗi bít, Phương pháp tính tỉ lệ lỗi bít, Mã kênh BCH, Mã chập Received date, 26th Sep., 2017 Revised manuscript, 17th Oct., 2017 Published, 01st Nov., 2017 Author affiliations: Military Technical Academy; * Corresponding author: sonthuy0912@gmail.com 24 Vu Van Son, “Investigation of channel code MIMO relay systems.” ... following links. Therefore, we proposed BER calculation method for multiple- hop MIMO relay systems and then investigate the number of relays for the best performance [11]. However, ... BER is low meaning the system is reliable. Consequently, in situation of medical application, BCH code is more suitable than convolutional codes. Figure Comparison of BCH and convolutional codes. 22 Vu Van Son, Investigation of channel code MIMO relay. .. Son, Investigation of channel code MIMO relay systems. ” Research However, the BER of any link is much smaller than 1, therefore we can ignore three (3) or over power to BER and the BER of whole system is rewritten by: