Joint Symbol Detection Algorithm for Multi-antenna Signals over Flat-fading Channels Based on Variational Bayes
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摘要: 该文针对平坦衰落信道下存在信道参数差异的多天线接收信号联合参数估计和符号检测问题，提出一种基于变分贝叶斯的联合处理算法。算法直接利用多个接收数据流进行信息符号的估计，抑制传统信号合成与解调解耦处理带来的性能损失。将问题建模为已知多组观测数据条件下发送符号、信道传输时延、信道增益和噪声功率的联合最大后验估计问题。基于变分贝叶斯理论对该最大后验进行近似求解，在相对熵最小化的准则下，推导得到了各个待估参数解析形式的近似后验分布——变分分布。所提算法无需计算各参数精确的点估计值，而是采用信道参数和信息符号变分分布迭代处理的方式进行联合求解。仿真结果表明，所提算法通过多信号、多参数的联合处理能够获得优于经典解耦处理和部分联合处理技术的系统误码率性能，且在接收天线数目较多和观测数据长度较短时性能优势体现更加明显。Abstract: For the issue of joint parameter estimation and symbol detection for multi-antenna signals with channel parameters difference over flat-fading channels, a new joint processing scheme is proposed based on the Variational Bayes (VB) method. The proposed scheme uses directly multiple received signals for the estimation of information symbols, restraining the information loss in conventional decoupled scheme of signals combination and demodulation. The problem is modeled as the joint Maximum A Posteriori (MAP) estimation of information symbols, time-delays, complex channel gains, and noise powers, given multiple observations, and approximately solved by means of VB approach. Based on the criterion of minimum relative entropy, analytical-form of the approximate distributions, i.e., variational distributions, for all unknown parameters are derived. There is no need to determine accurate point estimates of the parameters. Instead, the proposed scheme proceeds iteratively by alternating between the variational distributions of channel parameters and the information symbols. Simulation results show that the proposed joint processing scheme has significant performance improvements in comparison with conventional decoupled or partly joint processing schemes especially with large array sizes and short signal lengths.
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Key words:
- Multi-antenna arraying /
- Flat-fading /
- Joint processing /
- Variational Bayes
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表 1 算法流程
步骤1 初始化相关参数
令 $i = 0$, ${\bar s_n} = s_n^0$, $\left\langle {{{\left| {{s_n}} \right|}^2}} \right\rangle = {\left| {s_n^0} \right|^2}$, ${\beta _p} = 1$, $w_p^m = {1 / M}$,
${\alpha _p} = {1 / P}$, ${\rho _p} = {\delta _p} = {a_p} = {c_p} = {10^{ - 10}}$；步骤2 计算各路信道复增益的变分后验均值 ${\mu _p}$和方差 ${\lambda _p}$； 步骤3 更新时延加权因子 $w_p^m$； 步骤4 计算 ${\beta _p}$的后验均值 ${\bar \beta _p}$； 步骤5 计算 ${\alpha _p}$的后验均值 ${\bar \alpha _p}$； 步骤6 计算符号序列的后验概率 $q({s_n} = s)$，并进一步计算发送
符号的1阶/2阶统计量 ${\bar s_n}$和 $\left\langle {{{\left| {{s_n}} \right|}^2}} \right\rangle $；步骤7 令 $i = i + 1$； 步骤8 若前后两次关于 ${\bar{ {s}}}$的估计值误差小于 ${10^{ - 6}}$或 $i$大于 $20$，则
结束循环，否则重新从步骤2开始；步骤9 利用收敛后得到的信道估计结果进行符号判决。 
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表 2 本文算法与合成算法、现有联合处理算法运算量对比
算法 操作说明 乘法运算次数 SC EM&ImM2M4 信号合成 $\cal{O}(PN{I_{{\rm{sump}}}})$ 同步运算 $\cal{O}[PN(2M + {N_{\operatorname{intp} }}/2)]$ 权值估计 $\cal{O}(PN)$ BC EM&SS 波形校准及信号合并 $\cal{O}[PMN(M + {N_{{\rm{intp}}}}/2){I_{{\rm{sump}}}}]$ 同步运算 $\cal{O}[N(2M + {N_{{\rm{intp}}}}/2)]$ 权值估计 $\cal{O}(P{N^3})$ Shen&ImM2M4 多路联合校准 $\cal{O}(PMN{I_{{\rm{em}}}})$ 权值估计 $\cal{O}(PN{I_{{\rm{em}}}})$ 本文算法 信道参数估计 $\cal{O}(PMN{I_{{\rm{vb}}}})$ 符号估计 $\cal{O}(PMN\left| \cal{S} \right|{I_{{\rm{vb}}}})$
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