Abstract

The phase multifrequency methods of radar range measurements from the viewpoint of solving the problem of digital spectral analysis are proposed in this study. At present, the OFDM type orthogonal signals have gained widespread use for solving the range finding problems. However, the measurement methods based on using these signals lead to errors in range finding in the presence of Doppler frequency shift. In addition, such methods feature limited spectral efficiency and noise immunity. All this in full measure can be referred to the well-known methods of superresolution. The fundamental distinction of the approach proposed in this paper is the use of multifrequency nonorthogonal signals (N-OFDM) in which the location of frequencies of harmonic components is not tied to maximums of the amplitude frequency characteristics (AFC) of filters synthesized by using the fast Fourier transform (FFT). The nonorthogonal signal based methods considered in this paper could be viewed as a more general case with respect to OFDM. An advantage of the proposed method is the possibility of arbitrary variations of multifrequency signal parameters, including frequencies of harmonic components (subcarriers) and the length of sample observed. It allows us to take into account the Doppler shift of subcarriers, provide for the control of range resolution magnitude and the attainable signal-to-noise ratio. Such approach makes it possible to implement an adaptive offset from frequency concentrated interference by the selection of values of subcarrier frequencies that are least susceptible to negative impact, to reduce the peak factor of multifrequency signal mixture, and improve the electromagnetic compatibility of radar equipment at the expense of signal frequency bandwidth narrowing. In addition, the nonorthogonal frequency plan prevents the communications surveillance means to determine the distance to radar using the same phase difference of subcarriers that is possible, in principle, while using the fixed frequency grid in the case of OFDM signals. Based on the theory of multichannel analysis, the paper presents a system of equations derived that ensures the system solution in the case of several targets. The range estimation method proposed in this paper and based on the maximum likelihood can potentially guarantee the attainment of the lower Cramer-Rao bound for dispersions of unbiased estimates of signal parameters. In this case, all the other methods of superresolution with respect to the maximum likelihood method are known to be quasioptimal.

中文翻译：

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基于N-OFDM信号数字频谱分析的相位范围寻找

摘要

本研究从解决数字频谱分析问题的角度提出了雷达测距的相位多频方法。目前，OFDM 型正交信号已广泛用于解决测距问题。然而，基于使用这些信号的测量方法在存在多普勒频移的情况下导致测距误差。此外，此类方法具有有限的频谱效率和抗噪性。所有这些都可以参考众所周知的超分辨率方法。本文提出的方法的根本区别是使用多频非正交信号 (N-OFDM)，其中谐波分量的频率位置与通过使用合成的滤波器的幅频特性 (AFC) 的最大值无关。快速傅里叶变换 (FFT)。本文中考虑的基于非正交信号的方法可以看作是 OFDM 的更一般情况。所提出的方法的一个优点是多频信号参数的任意变化的可能性，包括谐波分量（副载波）的频率和观察到的样本长度。它允许我们考虑副载波的多普勒频移，提供对距离分辨率幅度和可达到的信噪比的控制。这种方法可以通过选择最不容易受到负面影响的副载波频率值来实现对频率集中干扰的自适应偏移，以降低多频信号混合的峰值因子，并提高雷达设备的电磁兼容性信号频率带宽变窄的代价。此外，非正交频率规划阻止通信监视装置使用相同的子载波相位差来确定到雷达的距离，这在原则上是可能的，而在 OFDM 信号的情况下使用固定频率网格。基于多通道分析的理论，本文提出了一个方程组，以确保在多个目标情况下的系统解。本文提出的基于最大似然的范围估计方法可以潜在地保证达到信号参数无偏估计的离散度的 Cramer-Rao 下界。在这种情况下，已知所有其他超分辨率方法相对于最大似然方法都是拟最优的。