通信方面的英文文献翻译,用翻译软件的请勿回答!

通信方面的英文文献翻译,用翻译软件的请勿回答!
IV. SPATIAL COMPRESSIVE SENSING BASED APPROACH
In this work, the spatial CS based approach that is motivated by the following two observations, is proposed. First, discretiz- ing the bearing space into N >> J distinct bearing angles, the field directionality is modeled as a superposition of N far-field point sources at the N distinct bearing angles. Considering that there are only J strong far-field sources, the remaining N − J far-field sources are of the low power that equals to the power of the isotropic noise. Modeling the signals at the sensor array that are induced by the far-field point source as a plane waves, the field directionality can be modeled as a superposition of N planewaves from the N distinct bearing angles, where only J of them are of the high power. This model suggests that the field directionality is J-compressible signal in the bearing space.
Next, note that in the space-time domain, the plane wave, induced by the narrow-band far-field point source can be expressed in the following form:
e(x, t )= eiω0t −k0 x , (10)
and the same wave in the wavenumber-frequency space (re- lated via the Fourier transform) is:
E (k, ω)= δ(ω − ω0 )δ(k − k0 ) . (11) These observations suggest that the field directionality is
J-compressible in the wavenumber-frequency space. In the sparsity basis that spans the wavenumber-frequency space, the field directionality can be represented as follows:
s(k, x)= Ψd + ξ , (12)
where the vector of the sparse coefficients d of size N has J
nonzero entries that corresponds to the strong far-field sources,and ξ contains low-power nonsparse component of the field directionality that is induced by the isotropic noise.
The proposed sparse model for the field directionality
motivates the application of the CS theory to the addressed problem. Moreover, it proposes the efficient structure for the sensing matrix Φ of size M × N, with the columns that contain array response vectors:Φ = [a(θ1 ) ... a(θN )] .(13)
Note that this sensing matrix consists of the complex sinusoids, and therefore, according to the CS theory such a pair of the sparsity and the sensing basses is the most incoherent and requires the least number of measurements.
From (1) and (2), the measurement vector of size M × 1 is
y = ΦΨd + Φξ + w , (14)
and the vector of sparsity coefficients d can be found via solving the minimization problem in (4) with the reconstruc- tion performance bounded in (5). Since the sensing matrix is normalized, it does not change the power of the nonsparse part of the signal ξ.

4 基于空间压缩传感的方法
在本研究中,提出了受到以下两个观察结果激励的基于空间CS的方法.第一是使象限空间分离成N＞＞J的不同的象限角,场方向性被建模为处于N个不同象限角的N个远场点源的叠加.考虑只存在J强远场源,则其余的N－J个远场源就具有等于各向同性的噪声功率的低功率.将传感器阵列处的,由远场点源感生的信号作为平面波建模,则场方向性就可建模为来自N个不同象限角的N个平面波的叠加,其中,它们中只有J具有高功率.这一模型告诉我们场方向性在象限空间是J-可压缩的信号.
其次是注意到,在空间－时间域,由窄带远场点源感生的平面波可以用以下形式表达：
而在波数－频率空间（通过傅立叶变换相关）的相同波为：
这些观察结果告诉我们,场方向性在波数－频率空间是可压缩的.在跨波数－频率空间的稀疏性基础上,场方向性可表达如下：
式中尺度N的稀疏系数d的矢量具有与强远场源对应的J非零入口,而ξ包含由各向同性噪声感生的场方向性的低功率非稀疏分量.
所提出的用于场方向性的稀疏模型激励我们将CS理论应用于着重解决的问题.而且,该模型还为尺度为M×N的传感矩阵Φ提出了高效的结构,其列包含阵列响应矢量：
请注意,这一传感矩阵由复杂正弦波组成,因此根据CS理论,这样一对稀疏度和传感低沉音是最不相干的,并且要求最小数量的测量值.
从式（1）和（2）,尺度为M×1的测量值矢量为：
而稀疏度系数d的矢量可以通过解式（4）中的最小化问题,以式（5）约束的重构性能而得到.由于传感矩阵是归一化的,所以它不改变信号ξ非稀疏部分的功率.