Time-Offset Generalized Frequency Division Multiplexing Communication in Doubly-selective Channels
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摘要: 当信道存在时间-频率双选择性时，严重的子载波间干扰和子符号间干扰将导致广义频分复用(GFDM)系统性能显著下降。为此，该文提出一种时间偏移GFDM系统(TO-GFDM)，通过对传统GFDM系统的原型滤波器进行时间偏移，来提高双选择信道下GFDM系统的性能。该文推导了GFDM信号在双选择信道中的平均信干比公式，并提出基于离散导频的联合迭代信道估计与符号检测算法，该算法利用信道估计器与串行干扰消除符号检测器之间的信息交换，逐步减小干扰信号，提高信道估计与符号检测的精度。理论分析与仿真实验结果表明，在双选择信道条件下，时间偏移GFDM比传统的GFDM具有更高的平均信干比和误码率性能；并且，联合迭代信道估计与符号检测算法能有效降低系统误码率。Abstract: The performance of Generalized Frequency Division Multiplexing (GFDM) systems significantly degrades over time-frequency doubly selective channels due to the severe inter-carrier interference and inter-subsymbol interference. To this end, a Time-Offset GFDM (TO-GFDM) is proposed, which can improve the performance of GFDM systems under doubly selective channel environment by introducing a time-offset to the prototype filter of conventional GFDM systems. The average signal-to-interference ratio of GFDM systems in doubly selective channels is analytically derived, and a pilot-aided joint iterative channel estimation and symbol detection algorithm is proposed. The proposed algorithm can progressively decrease the interference signal and improve the performance of channel estimation and symbol detection with the information exchanging between the channel estimation unit and the successive interference cancellation based symbol detection unit. The results of theoretical analysis and simulation demonstrate that in doubly selective channels, the time-offset GFDM outperforms the conventional GFDM in terms of average signal-to-interference ratio and bit error rate, and the joint iterative channel estimation and symbol detection algorithm can reduce the bit error rate effectively.
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表 1 迭代联合信道估计与符号检测算法
(1) 令迭代次数指示变量$i = 0$； (2) 通过式(20)计算得到符号判决统计量${{{r}}^{(i)}}$； (3) 利用式(23)估计导频符号的广义信道矢量${\tilde{ h}}_{\rm{P}}^{{\rm{LS}}(i)}$； (4) 基于${\tilde{ h}}_{\rm{P}}^{{\rm{LS}}(i)}$，利用式(25)估计广义信道矩阵${{\tilde {\mathbb {H}}}^{(i)}}$； (5) $i = i + 1$； (6) 利用式(36)消除导频符号对数据符号的干扰，即${{{r}}^{(i)}} = {{{r}}^{(0)}} - {{\tilde {\mathbb {H}}}^{(i - 1)}}{{{d}}_{\rm{p}}}$； (7) 利用式(37)确定最佳检测符号的索引值$({k^ * },{m^ * })$，并基于${{{{({r_{{k^ * },{m^ * }}})}^{(i)}}}/{{{(\tilde H_{{k^ * },{m^ * }}^{0,0})}^{(i - 1)}}}}$的值进行硬判决，得到估计值${({\tilde d_{{k^ * },{m^ * }}})^{(i)}}$； (8) 对符号判决统计量${{{r}}^{(i)}}$进行更新，${ {{r} }^{(i)} } = { {{r} }^{(i)} } - {[{\tilde {{H} }^{(i - 1)} }]_{ {k^ * } + {m^ * }K} }{({\tilde d_{ {k^ * },{m^ * } } })^{(i)} }$； (9) 返回第(7)步，对剩余未处理的数据符号依次完成硬判决； (10) 更新判决统计量，${{{r}}^{(i)}} = {{{r}}^{(0)}} - {{\tilde {\mathbb {H'}}}^{(i - 1)}}({\tilde{ d}}_{\rm{d}}^{(i)} + {{{d}}_{\rm{p}}})$； (11) 返回第(3)步，直至到达设定的迭代次数或者收敛。 
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表 2 系统仿真参数设定
参数 参数值 子载波数目 32 原型滤波器 升余弦函数 滚降因子$\alpha $ 0.4 采样频率 4.8 MHz 调制方式 QPSK 信道功率延迟分布 [0, –1, –9, –10, –15, –20] dB 时变信道模型 Jakes $\sigma _{\rm{p}}^2/\sigma _{\rm{d}}^2$ 2
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