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首页> 外文期刊>IEEE Transactions on Communications >The Cramer-Rao Bound for Training Sequence Design for Burst-Mode CPM
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The Cramer-Rao Bound for Training Sequence Design for Burst-Mode CPM

机译：用于突发模式CPM的训练序列设计的Cramer-Rao界

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摘要

In this paper, we study the Cramer-Rao bound (CRB) for continuous phase modulation (CPM) signals where frequency offset, carrier phase, and symbol timing are jointly estimated when transmitted over an additive white Gaussian noise (AWGN) channel. We consider a data-aided (DA) estimation scenario in which the estimator takes advantage of a known training sequence at the start of each burst. Thus, we first derive the joint CRBs as functions of a known training sequence and CPM parameters. By analyzing the CRB expressions, we propose the optimum training sequence for which the CRB is minimized. We show that the same training sequence is optimum for all three estimation parameters. Additionally, we compare the performance of the optimum training sequence with a random one by providing a closed-form expression for the unconditional CRB (UCRB) for symbol timing estimation of CPM signals. Comparing the UCRB and the CRB for the optimum training sequence reveals that a DA estimator with the optimum training sequence leads to significant gains in terms of the mean-square error of the estimation parameter when the underlying CPM scheme is non-binary and/or partial response.
机译：在本文中，我们研究了用于连续相位调制（CPM）信号的Cramer-Rao界线（CRB），其中在加性高斯白噪声（AWGN）信道上传输时，联合估计了频率偏移，载波相位和符号定时。我们考虑一种数据辅助（DA）估计方案，其中，估计器在每个脉冲串开始时利用已知的训练序列。因此，我们首先根据已知训练序列和CPM参数得出联合CRB。通过分析CRB表达式，我们提出了将CRB最小化的最佳训练序列。我们表明，对于所有三个估计参数，相同的训练序列是最佳的。此外，我们通过为CPM信号的符号时序估算提供无条件CRB（UCRB）的闭式表达式，将最佳训练序列的性能与随机序列进行比较。比较最佳训练序列的UCRB和CRB表明，当基础CPM方案为非二进制和/或部分CPM方案时，具有最佳训练序列的DA估计器会导致估计参数的均方误差显着增加响应。

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