例如,我们将在第六章看到,在复高斯噪声环境下以0.9的检测概率、10-8的虚警概率对幅度恒定的目标进行检测,单个采样的信噪比需要14.2dB(线性比例约为26.3)。

For example, in Chap. 6 it will be seenthat detection of a constant-amplitude target signal in complex Gaussian noisewith a probability of detection of 0.9 and a probability of false alarm of 10-8requires a single-sample SNR of 14.2 dB (about 26.3 on a linear scale).

通过将每个具有仅5.8dB(线性比例约为3.8)信噪比的10个样本的幅度进行积累,也可以获得相同的概率。

The same probabilities can be obtained byintegrating the magnitude of 10 samples each having an individual SNR of only5.8 dB (3.8 on a linear scale).

当10个样本进行非相干积累时,所需单样本的信噪比降低8.4dB(26.3/3.8 = 6.9)就是隐含的非相干积累增益。

The reduction of 8.4 dB (a factor of26.3/3.8 = 6.9) in the required single-sample SNR when 10 samples arenoncoherently integrated is the implied noncoherent integration gain.

非相干积累比相干积累更难于分析,通常需要推导噪声和信号加噪声情况下的概率密度函数,以确定对检测和参数估计的影响。

Noncoherent integration is much moredifficult to analyze than coherent integration, typically requiring derivationof the probability density functions of the noise-only and signal-plus-noisecases in order to determine the effect on detection and parameter estimation.

因此,非相干积累不如相干积累有效。

Thus, noncoherent integration is lessefficient than coherent integration.

这并不奇怪,因为在非相干积累中,并非所有信号的信息都被使用。

This should not be surprising, since notall of the signal information is used.

1.4.4带宽扩展

1.4.4 Bandwidth Expansion

傅里叶变换的尺度特性表明,如果x(t)的傅里叶变换为X(Ω) =F{x(t)},那么

The scaling property of Fourier transformsstates that if x(t) has Fourier transform X(Ω) = F{x(t)}, then

式(1.34)表明,如果信号x在时域以α > 1压缩,那么其傅立叶变换将以相同的比例因子在频域拉伸展开(Papoulis,1987)。

Equation (1.34) states that if the signal xis compressed in the time domain by the factor α > 1, its Fourier transformis stretched (and scaled) in the frequency domain by the same factor (Papoulis,1987).

当α < 1,式(1.34)表明时域拉伸将导致频域压缩。

When α < 1, Eq. (1.34) shows thatstretching in the time domain results in compression in the frequency domain.

图1.17给出了这种时频域表现相反的描述。

This reciprocal spreading behavior isillustrated in Fig. 1.17.

Figure 1.17. 傅立叶变换时频域特性表现相反的描述。(a)正弦波脉冲及其傅立叶变换的主要频域部分。(b)时域窄脉冲具有更宽的频谱特性。Illustration of reciprocal spreading property of Fourier transforms.(a) A sinusoidal pulse and the main portion of its Fourier transform. (b) Anarrower pulse has a wider transform. See text for details.

图(a)为脉宽1 μs、频率10MHz的正弦脉冲及其傅立叶变换,频域特性表现为中心频率位于10MHz、主瓣瑞利宽度为1MHz(脉宽1 μs的倒数!!!)的sinc函数。

Part (a) shows a sinusoidal pulse with afrequency of 10 MHz and a duration of 1 μs and its Fourier transform, which isa sinc function centered on 10 MHz and with a Rayleigh mainlobe width of 1 MHz,the reciprocal of the 1 μs pulse duration.

图(b)中的脉冲频率也是10MHz,但脉冲宽度只有图(a)的四分之一。

In part (b) the pulse has the samefrequency but only one-quarter the duration.

它的频谱仍然是以10MHz为中心的正弦波,但是瑞利宽度为4MHz,是图(a)的四倍。

Its spectrum is still a sinc centered at 10MHz, but the Rayleigh width is now four times larger at 4 MHz.

频谱振幅也减小了四倍。

The spectrum amplitude is also reduced by afactor of four.

——本文译自Mark A. Richards所著的《Fundamentals of Radar Signal Processing(Second edition)》