迭代接收机性能建模方法研究进展

doi:10.3969/j.issn.1000-436x.2014.09.017

Abstract

Abstract:

Aiming at the performance modeling for Turbo receivers,the research results are summarized,in the mean-while,the characteristics and future trends are concluded in terms of equivalent model,transitive parameter,performance abstraction and transitive relation.The Gaussian distribution of equivalent model for log-likelihood ratiois the founda-tionof performance modeling research.Representative methods for application scenarios such as performance analysis,performance optimization and joint design with link are to derive the transfer chart with mutual information as transitive parameter,to derive semi-analytical transitive relation with bit error rate or fidelity as transitive parameterand to derive semi-analytical transitive relation with mutual information as transitive parameter,respectively.These methods represent the development direction of performance modeling for turbo receivers.

Key words: Turbo receivers, distribution of log-likelihood ratio, transitive parameter, performance abstraction, transitive relation

Yun XUE,Bin JIANG,Xi-qi GAO. Advance of performance modeling for Turbo receivers[J]. Journal on Communications, 2014, 35(9): 164-174.

Figures/Tables 10

SISO单元	软信息分布或符号转移概率	等效模型
均衡器	$f (\hat{s} \| s) = {ϕ^{'}}_{μ, σ_{v}^{2}}$	$\hat{s} = μ s + n_{v}$
检测器	$f_{A, D E T} (l \| \tilde{x}) = ϕ_{μ_{A, D E T}, σ_{A, D E T}^{2}}$	$L_{A, D E T} (x) = μ_{A, D E T} \tilde{x} + n_{A, D E T}$
检测器	$f_{E, D E T} (l \| \tilde{x}) = ϕ_{μ_{E, D E T}, σ_{E, D E T}^{2}}$	$L_{E, D E T} (x) = μ_{E, D E T} \tilde{x} + n_{E, D E T}$
解调器	$f (z \| s) = {ϕ^{'}}_{0, 1 / γ}$	z=s+?
解调器	$f (c_{q} {\| \tilde{x}}_{q}) = ϕ_{0, 1 / γ}$	$c_{q} = {\tilde{x}}_{q} + n_{0}, q \in {1, 2, \dots, Q}$
	$f (c \| \tilde{x}) = ϕ_{0, w}$	$c = \tilde{x} + n_{w}$
译码器	$f_{A, D E C} (l \| \tilde{x}) = ϕ_{μ_{A, D E C}, σ_{A, D E C}^{2}}$	$L_{A, D E C} (x) = μ_{A, D E C} \tilde{x} + n_{A, D E C}$
	$f_{E, D E C} (l \| \tilde{x}) = ϕ_{μ_{E, D E C}, σ_{E, D E C}^{2}}$	$L_{E, D E C} (x) = μ_{E, D E C} \tilde{x} + n_{E, D E C}$

传递参数	传递参数的定义	传递参数的近似表达式
均值	$μ = \sum_{\tilde{x} \in \tilde{B}} P (\tilde{x}) \int_{- \infty}^{\infty} \tilde{x} l f (l \| \tilde{x}) d l$	$μ \approx \frac{1}{N} \sum_{n = 1}^{N} {\tilde{x}}_{n} L (x_{n})$
方差	$σ^{2} = \frac{1}{2} \sum_{\tilde{x} \in \tilde{B}} \int_{- \infty}^{\infty} \tilde{x} (l^{2} - μ^{2}) f (l \| \tilde{x}) d l$	$σ^{2} \approx \frac{1}{N} \sum_{n = 1}^{N} L {(x_{n})}^{2} - μ^{2}$
误比特率	$P_{b} = \frac{1}{2} \sum_{\tilde{x} \in \tilde{B}} \int_{- \infty}^{0} \tilde{x} f (l \| \tilde{x}) d l$	$P_{b} \approx \frac{1}{N} \sum_{n = 1}^{N} \frac{1}{2} (1 - {\tilde{x}}_{n} s i g n (L (x_{n})))$
保真度	$M = 1 - \int_{- \infty}^{\infty} \frac{2}{1 + \exp (l)} f (l \| \tilde{x} = + 1) d l$	$M \approx \frac{1}{N} \sum_{n = 1}^{N} \tanh (L (x_{n}) / 2)$
互信息	$I = \frac{1}{2} \sum_{\tilde{x} \in \tilde{B}} \int_{- \infty}^{+ \infty} f (l \| \tilde{x}) 1 b (\frac{2 f (l \| \tilde{x})}{f (l \| + 1) + f (l \| - 1)}) d l$	—

传递参数	检测器传递关系	译码器传递关系
均值	μ_E,DET=T_DET(μ_A,DET)	μ_E,DEC=T_DEC(μ_A,DEC)
方差	$σ_{E, D E T}^{2} = T_{D E T} (σ_{A, D E T}^{2})$	$σ_{E, D E C}^{2} = T_{D E C} (σ_{A, D E C}^{2})$
误比特率	P_b,E,DET=T_DET(P_b,A,DET)	P_b,E,DEC=T_DEC(P_b,A,DEC)
保真度	M_E,DET=T_DET(M_A,DET)	M_E,DEC=T_DEC(M_A,DEC)
互信息	I_E,DET=T_DET(I_A,DET)	I_E,DEC=T_DEC(I_A,DEC)

建模单元	半公式化传递关系
均衡器	$γ_{k}^{(i)} = T_{E Q} (H, σ^{2}, v_{s}^{(i - 1)})$
解调器	$I_{E, D E M}^{(i)} = T_{D E M} (γ_{k}^{(i)}, I_{A, D E M}^{(i)})$
译码器调制器联合	$({\bar{I}}_{E, D E C}^{(i)}, v_{s}^{(i)}) = T_{J D M} ({\bar{I}}_{A, D E C}^{(i)})$

建模单元	半公式化传递关系
均衡器	$γ_{k}^{(i)} = T_{E Q} (H, σ^{2}, v_{s}^{(i - 1)})$
解调器、译码器及调制器联合	$({\bar{I}}_{E, J D D}^{(i)}, v_{s}^{(i)}) = T_{J D D} ({\bar{I}}_{A, D E M}^{(i)})$

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符号	说明
(·)^H	矩阵或向量的共轭转置
(·)^T	矩阵或向量的共轭转置
a_m	向量a的第m个元素
A]_m,n	矩阵A的第(m,n)个元素
I_N	N×N 单位矩阵
e_k	第k个元素为1，其他元素为0的列向量
E{·}	随机变量的期望
Var{·}	随机变量的方差

Advance of performance modeling for Turbo receivers

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