High Accuracy Carrier Frequency Estimation of Multi-band Communication Signals Based on Undersampling
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摘要: 为根本解决当前主流的基于调制宽带转化器(MWC )的欠采样频率估计方法存在的3个问题，即采样通道数目多、载频估计精度低、信源频带分布稀疏度条件高，该文提出基于互素谱相位差校正的通信信号载频估计方法。通过将两路互素欠采样取代多路调制宽带转化器欠采样，克服了其耗费欠采样通道数目多的缺陷；基于此，既推导出全景谱谱峰位置与两路互素输出IDFT支路序号对的映射关系，又推导出相邻快拍下该序号对的IDFT相位差与载频值的解析关系，从而克服了主流方法的载频估计精度低的缺陷；通过将最小尺寸全相位滤波器对半分解方法融入原型滤波器设计，构造出两路并行互素谱分析器，还彻底克服了对信源频带分布稀疏度条件高的依赖。仿真表明，相比于主流方法，该文方法仅需耗费不足其1/2的样本数量，载频估计的相对误差降至其1/20以下。Abstract: To essentially overcome the 3 deficiencies of the mainstream Modulation Wideband Converter (MWC )-based undersampling frequency estimator (i.e., over-consumption of undersampling channels, low accuracy of carrier frequency estimation, high sparsity of the source distribution), this paper proposes the phase-difference corrector based on coprime spectral analysis for the carrier frequency estimation of multi-band communication signals. Specifically, by substituting the multi-path MWC undersampling with the 2-path coprime undersampling, the consumption of undersampling channels is greatly reduced; Further, by developing the mapping relationship between the panoramic spectrum peak indices and the IDFT index pairs of coprime analyzers, the phase difference of the adjacent snapshots’ IDFT outputs corresponding to these index pairs can be analytically extracted, thus achieving much higher estimation accuracy compared to the mainstream MWC method. Meanwhile, by means of incorporating the minimum-sized half-decomposition based all-phase filter design into the prototype filter design, a two-path paralleled coprime spectral analyzer can be constructed, which thoroughly gets rid of the dependency of the high sparsity of the source distribution. Numerical results show that, compared to the mainstream MWC method, the proposed spectral corrector’s estimation error is no more than 1/20 of the former, while only consuming less than half of the sample amount.
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1 多频带通信信号载频估计流程
初始化 给定谱分析检测上限$ {F_N} $，设定互素整数对$ M,\;N $，依据式(17)设计两路并行互素谱分析器的原型滤波器；确定欠采样速率$ {F_{{{\mathrm{S}}}1}} = {{{F_{N}}} \mathord{\left/ {\vphantom {{{F_{N}}} N}} \right. } N} $, $ {F_{\rm{S}2}} = {{{F_{N}}} \mathord{\left/ {\vphantom {{{F_{N}}} M}} \right. } M} $，给定持续L+1个快拍时段的互素欠采样样本$ {x_1}(n) = x(Nn) $, $ {x_2}(n) = x(Mn) $； 步骤1 将$ {x_1}(n) $, $ {x_2}(n) $馈入两路并行互素谱分析器，获得全景谱，扫描其$[0,{F_{N}}/2)$范围内的所有谱峰； 步骤2 对于每个谱峰，依据式(18)的频点集合$ {\varGamma _1} $和$ {\varGamma _2} $，确定其所隶属的互素谱分析器以及所对应的谱序号i，将i代入式可得余数对k, l； 步骤3 在该互素谱分析器内，依据式(22)–式(24)分别计算上、下通道中第k路、第l路IDFT输出的L个相邻快拍相位差$ {\widehat{\delta }}_{v,k},{\widehat{\delta }}_{v,l}，v=1,2,\cdots,L $，将其代入式(25)算出高精度的频偏估计值$ \hat \delta $； 步骤4 将谱序号i, $ \hat \delta $代入式可得该谱峰的估计值$ {\hat f_i} $； 步骤5 重复步骤 2～4，直至全景谱$[0,{F_{N}}/2)$范围内的全部谱峰估计完毕。 
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