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首页> 外文会议>IEEE Global Communications Conference >Closed-form Cramér-Rao lower bounds for CFO and phase estimation from turbo-coded square-QAM-modulated signals
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Closed-form Cramér-Rao lower bounds for CFO and phase estimation from turbo-coded square-QAM-modulated signals

机译：CFO和从Turbo编码的方形QAM调制信号进行相位估计的封闭式Cramér-Rao下限

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摘要

We consider the problem of joint phase and carrier frequency offset (CFO) estimation from turbo-coded square-QAM modulated signals. We derive for the first time the closed-form expressions for the exact Cramér-Rao lower bounds (CRLBs) of this estimation problem. In particular, we introduce a new recursive process that enables the construction of arbitrary Gray-coded square-QAM constellations. Some hidden properties of such constellations will be revealed and carefully handled in order to decompose the likelihood function (LF) into the sum of two analogous terms. This decomposition makes it possible to carry out analytically all the statistical expectations involved in the Fisher information matrix (FIM). The new analytical CRLB expressions corroborate the previous attempts to evaluate the underlying perfromance bounds empirically. In the low-to-medium signal-to-noise ratio (SNR) region, the CRLB for code-aided (CA) estimation lies between the bounds for completely blind [non-data-aided (NDA)] and completely data-aided (DA) estimation schemes, thereby highlighting the coding gain potential in CFO and phase estimation. Most interestingly, in contrast to the NDA case, the CA CRLBs start to decay rapidly and reach the DA bounds at relatively small SNR thresholds. The derived bounds are also valid for LDPC-coded systems and they can be evaluated in the same way when the latter are decoded using the turbo principal.
机译：我们考虑了从涡轮编码的方形QAM调制信号进行联合相位和载波频率偏移（CFO）估计的问题。我们首次导出了此估计问题的确切Cramér-Rao下界（CRLB）的闭式表达式。特别是，我们引入了一种新的递归过程，该过程使得能够构造任意格雷编码的方形QAM星座图。为了将似然函数（LF）分解为两个相似项的和，将揭示并仔细处理此类星座的某些隐藏属性。这种分解使得可以进行费舍尔信息矩阵（FIM）中涉及的所有统计期望的分析。新的分析CRLB表达式证实了先前尝试根据经验评估基本性能边界的尝试。在中低信噪比（SNR）区域中，用于代码辅助（CA）估计的CRLB位于完全盲[非数据辅助（NDA）]和完全数据辅助的边界之间（DA）估计方案，从而突显了CFO和相位估计中的编码增益潜力。最有趣的是，与NDA情况相反，CA CRLB开始迅速衰减并以相对较小的SNR阈值达到DA范围。导出的边界对于LDPC编码的系统也有效，并且使用turbo原理对后者进行解码时，可以用相同的方式对其进行评估。

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