论文研究-The performance analysis of LDPC in MIMO Two-Way Relay Network under Nakagami-m Fading.pdf

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Nakagami-m衰落下MIMO双向中继网络中LDPC的性能分析,刘元玮,李绍胜,本文基于MIMO双向中继的背景下,与模拟网络编码想结合,提出了两种LDPC解码算法。本文的中继结构为多根天线基于一根中继天线进行放�
山国科技论文在线 http:/www.paper.edu.cn it. ifh =-1 it means that all this standard matrix is all-zero matrix: ifh ,=0. it means that this standard matrix is the base matrix. If hi, is other number, it means that it will rotate right hi, times to get the new standard matrix. For the reason that we want to apply this kind of ldPc coding and decoding method into hardwarc implementation in our unmanned helicopter relay projcct in the future, a largc input and output will be needed. In this project, we define the H matrix is 768 rows and 1536 columns. That is m , =24 andn,=12.Z=64 90 2.2 LLR BP algorism First wc should introducc somc dcfinitionS: H is the vary check matrix of thc LDPC codc Hi,j is the element in the position (i]), N(m)=n: Hm, n-1 is the set that n variable nodes which is connected with m parity check nodes. M(n)=m: Hm, n=1 is the set that m parity check nodes which is connected with n variable nodes. N(m)n is the N(m) set that except the nth variable node 95 itself, M(n)m is m(n)set that except the nth check node itself. The LLR BP algorism need through initialization, iterative decoding and judgment these threc progresses Initialization: The input sequence is the information LLRn of n variable nodes. For each (m, n) belongs to (ijHi, j=1, calculate 1+e-1 +1LLR≥0 100 Zm= sign(LLR, )log which sign(LLR,) e lLR <0 Iterative decode 1). For check node for each (m, n) E((i)Hi,j=1) 1+ og ∏sign(Zm),ii 105 2). For variable nodes: for each(m, n) belongs ILLR sign(llrm n)log LLR in it, Llr=LLR+∑L ∈M(n)m For cach n, updated LLRn information is LLR =LLR +L ∈M(n) 110 Judgment a) Make hard judgment to LLRI/, LLR2/,.....LLRn/, if LLRn/>0, then x-0, otherwise, x=1 b) If Hx=0, then the decoding progress is end, otherwise it will continue iteration until the max number of the set iteration 115 2.3 Modified UMP bP Based algorism UMP BP Based algorism can make some simplification to the LLR BP algorism; the key is to simplify the calculation. First we should make a definition amn as the result of hard judgment according 山国武技论文在线 http:/www.paper.edu.cn ● Initializatie LLRn o Iterative decoding: for each cycle it will run the three progress below: 1). Check nodes For every m,n 0.Z<0 125 For every m ∑ 62 For every m n k*(-1)9 r∈N(m)M∈ k-0.8 is the modified factor which can let the approximation more accurate) 130 2). Variable nodes For every m, n mm. n n+∑ m n m∈eM(n)m For every n Zn=y+∑ 1∈ M(n) 135● Judgment: a)If Zn>0, then Cn-1: Otherwise, Cn-0 b)If H*c=0, then the decoding is end, otherwise it will continue iteration until the max number of the set iteration 2.4 Comparison of the two algorisms 140 Now BP algorism is the common algorism, based BP algorism, there are some developed algorisms Hcrc wc comparc LLR BP and UMP BP bascd algorisms. The main diffcrencc bctwccn them is that the process of check node updates was simplified, that is: in the check node update process, for the relevant data it only solves the minimum value addition to its own outside, and then it uses the value ofthe combination of the sign bit as the feedback information This UMP BP 145 based algorithm reduces the index, logarithmic computation to a large extends and it is a very practical dccoding algorithm. Bccausc the UMP BP bascd algorithm is cqual to gct thc approximation of LLR BP, so the Modified UMP BP based algorism is using a modified factor to fix the error to let this result more accurate Thus, a series based on LLR-BP algorithm is coming. In many simplified algorithm, when the 150 check node degree is small, the Modified UMP-BP algorism seek the balance between the performance and the decoding complexity and for this reason, it is widely used. 4 山国科技论文在线 http:/www.paper.edu.cn 3 NUMERICAL results In this section, numerical results to examine the impacts of antenna configuration and transmit power on the Sum Symbol Error Rate(SSer)are presented. All our results are based on 155 BPSK, and the Fading channel is Nakagami-m Fading channel. Thc simulation mcthod is Montc Carlo simulation When m=l. the Nakagami Fading is reduced to Rayleigh Fading, this case will not be introduced here because it is normal case and comparatively easy First we comparc the Sser of un-coded and coded information for N4=NB The SSER of Nakagami distribution Uncoded ○LRDP -+JMP BP SNR Fig 2 SSER of MIMO under Nakagami-m Fading when m=2, N,=Nr=2 The SSER of Nakagami distribution Uncoded -UMP BP -LLR BP 1 810121416182 SMR l65 Fig 3 SSER of MIMO under Nakagami-m Fading when m-3, N=NR=2 国科技论文在线 http:/www.paper.edu.cn The SseR of Nakagami distributi -e-LLR BP Fig 4. SSER of MIMO under Nakagami-m Fading when m=3, N=NR=3 170 From Fig.2 to Fig 4, it could be seen that when N,=NR, as m and N increased, the SSer of the information is progressively reduced Then we compare the Sser of un-coded and coded information for N he Sser of Nak cami distribution UMP. EP ig. 5 SSER of MIMO under Nakagami-m lading when m=2, N,=2,Nr=1 175 The SSER of Nakagami dis 10 SNR Fig 6 SSER of MIMO under Nakagami-m Fading when m=3, NA=3, NR=1 Compared Fig. 5 with Fig. 6, it could be seen that when N,>M B, as m and N increased, 国科技论文在线 http:/www.paper.edu.cn 180 the Sser of the information is progressively reduced Compared Fig. 2 with Fig. 5, and Fig 3 with Fig. 6, it could be seen that as N increased, the SSeR of the information is progressively reduced. And the performance of N=NR is better than the performance of N>NB From Fig. 2 to Fig. 6, it could be clearly seen that no matter the Modified UMP BP Based 185 LDPC dccoding algorism or the llr BP Bascd LDPC dccoding algorism, the performancc of the transmission in this model has improved to a large extent. To be more precise, the sser under Nakagami-m fading improve over 20 dB performance when the Sser is 10y However, compared Modified UMP bP based algorism with LLR BP Based algorism, there 190 S only a little difference: LLR BP Based is a little better than Modified UMP BP Based within 190 less than l dB in this model case. Based on this, when do the implementation in the future, the less complex algorism Modified UMP BP Based algorism will be the first choice in this kind of model 4 Conclusion In this paper, the ldPc coding and decoding method is applied into the mimo two-way aF relaying in which thc communication bctwccn two nodcs, with Na and NB antennas, is aided by 195 a single antenna relay under Nakagami-m Fading LLR BP Based algorism and Modified UMP BP Based algorism are compared in detail and the following points are clarified: 1)As m and N increased, the Sser of the information is progressively reduced. 2 )Compared with the un-coded mcthod, the SSEr undcr Nakagami-m fading of the coded information improvc ovcr 20 dB performance when the SseR is 10. 3)LLR BP Based is only a little better than Modified UMP 200 BP Based within less than 1 dB References [1] B. Rankov, A. Wittneben. Spectral efficient protocols for halfduplex fading relay channels[ J]. IEEE J. Sel Areas Commun, Feb. 2007, vol. 25, no 2, pp, 379-389 205 [2]S. Katti, S. Gollakota, D Katabi. Embracing wireless interference: analog network coding[J]. in Proc. ACM SIGCOMM 2007, Aug 2007, Kyoto, Japan, pp. 397-408 []T Q Duong, L.-N. Hoang. V N.Q. Bao. On the performance of two-way amplify-and-forward relay[]. EICE Trans. Commun., Dec. 2009, vol. E92-B no. 12, pp. 3957-3959 210 [4]R. H. Y. Louie, Y. Li, B. Vucetic. Practical physical layer network, coding for two-way relay channels performance analysis and comparison]. EEE Trans. Wireless Commun., Feb. 2010, vol 9, no. 2, pp. 764-777 [5]. Yang, P Fan, T. Q. Duong, X Lei. Exact performance of two-way, AF relaying in Nakagami-m fading environment[J]. IEEE Trans. Wireless Commun., Mar 2011, vol 10, no. 3, pp. 980-987 [6 N,Yang, Phcc Lcp Ycoh. Two-Way Relaying With Multi-Antcnna Sources: Bcamforming and Antenna Selection [J].IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, NOVEMBER 2012, VOL 61, NO. 9, 215p.3996-4006 [7]D J C. Mackay. Near Shannon Limit Performance of Low Density Parity Check Codes[J]. Electronics Letters In Electronics Letters, (1997), Vol 33, No 6. pp. 457-458 [8 Chen Y, Hocevar D. A FPGA and ASIC implementation of rate 1/2, 8088-bit irregular low density parity check decoder[J]. IEEE GLOBECOM03, Dec 2003, VoL 1, pp. 113-11 220 [9]Zhang T, Parhi K.K. Joint (3, k)-Rcgular LDPC Codc and Decoder/Encoder Design [], IEEE Transactions on Signal Processing, April. 2004, pp. 1065-1079 10] Fossorier M, Mihaljevic M. Reduced complexity iterative decoding of low-density parity check codes based on belief propagation[J]. IEEE Transactions On Communications, 1999, pp. 673-680 225 7 国科技论文在线 http:/www.paper.edu.cn Nakagami-m衰落下MIMO双向中继网络中LDPC 的性能分析 230 刘元玮,李绍肥 (北京邮电大学信息与通信工程学院,北京100876) 摘要:本文基于MMO双向中继的背景下,与模拟网络编码想结合,提出了两种LDPC解 码算法。本文的中继结构为多裉天线基于一根中继天线进行放大转发。具体来说,本文通过 仿真比较分析了未编码和编码的信息在基于 Nakagami衰落下的双向中继的性能,并分析了 235各种MIMO情况下的SSER。本文得出了一个关键性的结论,基于这个模型,随着衰落系数 m和天线数N的增加,信息的SSER是逐渐减小的, LLR BP算法比修正后的 UMP BP算 法的性能好ldB 关键词:双向中继网络;MMO;LDPC: LLR BP; Modified ump bp; Nakagami-m衰落 中图分类号:TN9295 240 8

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