英语翻译To appreciate the significance of the proposed spatial C

英语翻译
To appreciate the significance of the proposed spatial CSbased
method in the array signal processing framework,it
can be compared to the conventional methods of the field
directionality estimation.According to the conventional methods,
the beamforming was typically utilized for the noise
filed directionality estimation,and 2-D azimuth sector was
scanned via generation of consecutive directional beams.As
a result,the azimuth resolution was a strong function of the
beamwidth and the array length.According to the proposed
CS-based method,outputs of each array element (rows in
the sensing matrix Φ) provide measurements for the spatially
compressive sensing reconstruction process.Therefore,the
number of available measurements is proportional to the array
length M.According to the compressive sensing theory,the
number of measurements that is required to reconstruct the
J-compressible signal is
M ≈ c2J/(logN)4 ,(15)
where N is the maximal number of distinguishable in the
bearing space signals.The expression in (15) means that for
the given array length M and the field directionality sparsity
J,the maximal number of the array responses to distinct
plane waves is N,which determines the angular resolution
of the estimated field directionality.The exponential relation
in (15) provided the potential for significant improvement in
the angular resolution.
V.SIMULATION RESULTS
The performance of the proposed spatial CS-based field
directionality estimation approach is evaluated in this section.
Consider a ULA with M = 30 elements,and inter-element
spacing d = λ/2.In the first considered scenario,five strong
far-field point sources received at the following bearing angles:
θ = [33o,60o,76o,90o,120o] with signal-to-noise ratios
(SNR):[20,10,15,20,15] dB,were simulated.In [12],the
WS was proposed and it was shown that this method outperforms
other field estimation methods.In this scenario,field
directionality estimation performance of the CS-based method
was compared to the WS.For the WS,a field directionality
was obtained from four array orientations 70o,80o,90o,100o.
Fig.1 shows an estimated field directionality for the CS and
the WS-based methods.This figure shows that the CS-based
estimator outperforms the WS estimator.

为领会提出的基于空间CS的方法在阵列信号处理框架内的意义,可将其与常规的场方向性估计方法进行比较.根据常规方法,波束形成典型来说被应用于噪声场的方向性估计,而2维方位矢量则通过发生连续的定向波束来扫描.因此,方位分辨率是波束宽度和阵列长度的强函数.根据提出的基于CS的方法,每个阵列元件（传感矩阵Φ中的行）的输出都提供用于空间压缩传感重构过程的测量值.因此,可获得的测量值的数目与阵列长度M成正比.根据压缩传感理论,为重构J-可压缩信号所需的测量值的数目为
式中N为象限空间信号中可分辩的最大数目.式（15）的表达式意味着,对于给定的阵列长度M和场方向性稀疏度J,对不同平面波的阵列响应的最大数目是N,这决定了被估计场方向性的角度分辨率.式（15）中的指数关系为角度分辨率的明显改善提供了可能.
5 仿真结果
所提出的基于空间CS的场方向性估计方法的性能在本小节做了评价.考虑一个带有M＝30个元件的,元件间间隔d＝λ/2的ULA.在第一个考虑的情况中,仿真了在以下象限角：θ＝[33°、60°、76°、90°、120°],以以下信噪比：[20、10、15、20、15]dB接收的5个强远场点源.在文献[12]中,WS被提出,并已证明,此方法胜过其他场估计方法.在本情况下,基于CS的场方向性估计方法与WS法做了比较.对于WS法来说,场的方向性由4个阵列取向70°、80°、90°、100°获得.图1示出了基于CS的方法和基于MS的方法所估计的场方向性.此图证明了基于CS的估计量要由于WS的估计量.