A Signal Acquisition Method Based on Multi-Sample Serial Fast Fourier Transform in High Dynamic and Low SNR Environment
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摘要: 高超音速技术是未来空间飞行器的发展趋势，同时对通信平台在超高动态、低信噪比环境下的快速捕获能力也提出了新的挑战。针对经典捕获算法受频偏影响的局限性，该文提出一种基于信号多样本点串行快速傅里叶变换的信号捕获算法(MS-FFT)，所提算法通过串行执行多个样本点的FFT，采用非相干合并后的峰值搜索得到捕获结果，在不增加复杂度的条件下，避免了频偏对捕获性能的影响。通过对峰值信噪比(PSNR)理论公式的推导，证明了MS-FFT的频偏适应范围取决于采样率，随着数模转换器件采样能力的不断提升，具有比经典算法更大的频偏适应范围。最后，通过仿真验证了上述理论推导的正确性，证明了所提算法更加适合超高动态环境的应用场景。Abstract: Hypersonic technology is the development trend of space vehicles in the future. It also poses new challenges for the fast acquire capability of communication platforms in ultra-high dynamic and low signal-to-noise ratio environments. To overcome the limitation of the classic acquisition algorithm affected by frequency offset, a signal acquisition algorithm based on Multi-sample Serial Fast Fourier Transform (MS-FFT) is proposed. The proposed algorithm serially executes the FFT of multiple samples and runs the peak searching after non-coherent combining to obtain the acquire result. Without increasing the complexity, the influence of frequency offset on the acquisition performance is avoided. By deriving the theoretical formula of the Peak Signal-to-Noise Ratio (PSNR), it is proved that the frequency offset adaptation range of MS-FFT depends on the sampling rate and can be larger than the classical algorithm with the continuous improvement of the sampling capability of digital-analog conversion devices. Finally, the correctness of the above theoretical derivation is verified by simulation, and it is proved that the proposed algorithm is more suitable for the application scenarios of ultra-high dynamic environment.
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表 1 MS-FFT算法流程表
输入：接收信号$y[n]$，本地参考序列$c$，同步头长度$N$，下采样率$d$，门限$T$，常数${\rm{C}}$ 输出：同步位置${n_s}$，频偏估计${f_{{\rm{est}}}}$ (1) (初始化设置)：接收序列序号$n = - 1$，${P_n} = 0,y[n] = 0(n \le 0)$，设置${n_{\rm{A}}},{n_{\rm{B}}},{n_{\rm{C}}},{n_{\rm{S}}} = 0,{f_{{\rm{est}}}} = 0$; While ${n_{\rm{B}}} = = 0$ (2) 更新序号$n = n + 1$; (3) (更新接收序列)：根据式(5)和式(6)得到并更新当前时刻$n$下的矩阵${{p}}$; (4) (FFT)：计算矩阵${{p}}$最后一列的FFT，结果记为${{{P}}_n} = \{ {P_{j,{N_C} - 1}}\} _{j = 0}^{d - 1}$; (5) (非相干叠加)：${z_n}(j) = \displaystyle\sum\nolimits_{i = n - d + 1}^n { { {\left| { {P_{ji} } } \right|}^2}\;,\;j = 0,1,···,N/d - 1}$; (6) (取最大值及下标)：${\hat z_n} = \mathop {\max }\limits_{j = 0,1,···,N/d - 1} {z_n}(j)$，$k' = \mathop {\arg \max }\limits_{j = 0,1,···,N/d - 1} {z_n}(j)$; (7) (信号检测)：若连续${{C} }$次检测$\{ {\hat { {z} }_n} > {\rm{T} }\& \& {\hat {{z} }_{n - { {C} } } } \le {T_{ {\rm{lb} } } }\}$为真，记${n_{\rm{A}}} = n$; 若$\{ {n_{\rm{A} } } \ne 0\& \& {\hat {\rm{z} }_n} \le T\}$为真，记${n_{\rm{B}}} = n$; end While
(8) (同步位置确定)：${n_{\rm{C} } } = \mathop {\arg \max }\limits_{n = {n_{\rm{A} } } - {{C} } + 1,{n_{\rm{A} } } - {\rm{C} }, ··· ,{n_{\rm{B} } } } {\hat z_n}$, ${n_{\rm{S} } } = {n_{\rm{A} } } + {n_{\rm{C} } } - {{C} } + 1$;(9) (频偏估计)：${{{{\overset{\frown}{{P}}} }}_{k'}} = {[{P_{{n_s} - d + 1,k'}},{P_{{n_s} - d + 2,k'}},···,{P_{{n_s},k'}}]^{\rm{T}}}$; ${ {{D} }_{k'} } = {\rm{diag} }(1,{{\rm{e}}^{ {\rm{j} }2\pi k'/N} },{{\rm{e}}^{ {\rm{j} }2\pi k' \cdot 2/N} }, ··· ,{{\rm{e}}^{j2\pi k' \cdot (d - 1)/N} })$; ${{P}}_{k'}^{(f)} = {\rm{FFT}}\{ {{{D}}_{k'}}{{{{\overset{\frown}{{P}}} }}_{k'}}\} = \{ {{P}}_{k'i}^{(f)}\} _{i = 0}^{d - 1}$;
$L = \mathop {\arg \max }\limits_{i = 0,1, ··· ,d - 1} {{P}}_{k'i}^{(f)}$;${f_{ {\rm{est} } } } = {f_{\rm{s}}}(k' + {N_{ {\rm{NC} } } }L)/N$。 
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