???wv???2jeH?m?1M?j?1m??2m2j?m???2m??1m?j?mMsin???e???2je?2??m?1?M?1???1??2??????2??2???M?1???2??1??sin??m?????22???????K?1??2???k(?2??1)???4sinsink?????, M?2K?1为奇数时?????22?k?1?????? ??K???2??1????1???1???4sin??sin??k?????1??, M?2K为偶数时?k??2????2222?????????k?1??
2sin?1?sin?2???2而在arcsin处，即差波束零点的电相位为两个基本波束电相位的平均值??1。此
22外和差波束的输出值均为实数，即它们或者同相位或者反相位。这一点可由上面直接比幅的分析结果直观得出，和差波束的输出可以直接取两个基本波束输出的矢量和差：
???y2?y1
???y2?y1式中y2, y1分别为指向?2, ?1的基本波束的输出，它们都为正实数
sin?1?sin?2设目标方位?与两基本波束等信号线方位arcsin之差为偏离角?，则
2??0时y2?y1且??, ??同相 ??y1y2??
??0时y2?y1且??, ??反相
由上两式可见，两个基本波束(指向分为?1, ?2)所形成的差波束零点并不在其平均值
?1??2处，
????y2y1??由上图说明：
a. ??, ??理论上应该同相或反相，即其相位差?只可能取0或?。
b. ??0时??0，??0时???，即?的取值取决于目标的偏离方向即偏角?的符号。
c. 当y2?y1时???0，当y2?y1时???0。??的大小可近似认为是比例于目标偏角?的大小。
以前采用模拟器件实现单脉冲和差比幅测角方案为：将差信道的中频接收信号、和信道的中频接收信号分别作为相位检波器的两输入信号，其输出的视频信号幅度为：
E?E??E??E??E??cos? 式中E?, E?表示中频和信号与中频差信号，??0或?表示二者的相位差
为消除目标反射信号强度变化的影响，在和差比幅单脉冲系统中通常以和信号作为差信道的自动增益控制信号，这相当于进行归一化运算，所得结果为：
E?E?EE??2??cos?
EE??上式运算结果通常称为单脉冲比，测角正是利用此值据理想单脉冲曲线插值获得目标的偏角，从而得到目标方位的估值。现在数字技术的发展使得模拟相位检波器被直接中频采样、数字相干检
波方案所替代，即可直接获得视频和差波束值。尽管前面理论分析表明??, ??理论上应该为实数，
?, ???，其相位差??在?0, ??间取值。即同相或反相，相位差??0或?，但实际系统给出的都是复数??一般当目标不在等信号轴上时，相位误差?通常较小。为减小非理想因素引起的相位误差对测角精度的影响，实际单脉冲比仍采用点乘进行，即
????????MPR??2??cos??
??????????作为单脉冲比获得的测角精度高： 下面我们将分三种情况分析上述计算方法较直接用???a. ??0时y2?y1且???0，理想单脉冲比应为0。由于存在相位误差使得实际????0，从而??引入测角误差，但若采用点乘计算单脉冲比，因????2得MPR?0，这与理想情形完全一致，不
6
存在测角误差。
b. ??0时y2?y1且??, ??同相，??0，理想单脉冲比?????0。由于存在相位误差?使得实际
?, ???并不同相，相位差??为锐角。由三角形两边之和大于第三边、两边之差小于第和差波束取值??????、??????，则三边的关系有：?????????0，显然取差和波束模值获得的单脉冲比偏大。?????若采用点乘计算由于乘上cos??因子可使单脉冲比更接近理想值，测角误差减小。
c. ??0时y2?y1且??, ??反相，???，理想单脉冲比?????0。由于存在相位误差?使得实际?, ???并不反相，和差波束取值??，相位差??为钝角。同理可得
???????0，即取差和波束模值获?????得的单脉冲比偏大。若采用点乘计算由于乘上cos??因子可使单脉冲比更接近理想值，测角误差减小。 ?????y1?y2a. ??0????y1?????y1?y2???b. ??0?y1?????y1?y2c. ??0?y1???采用点乘计算单脉冲比，当目标处于两基本波束等信号轴线上时，差波束信号主要由噪声决定，从而引起目标角度左右跳变，此时可考虑采用直接比幅加以辅助确认。
3．超分辨方法
波束扫描法的输出功率为：
P(?)?Y(?)?wRxxw?2Hi?ki,k?1?rMi,kexp[j(i?k)2?dcos??]
可见P(?)为各阵元输出信号空间相关函数的傅里叶变换，即空间谱。波束扫描法就是依此作空间搜索，在P(?)达到极大值时的各方位?即为空间各信号源的方向。这种测向方法实际是一种与谱估计的直接方法相当的空间谱估计方法，因而也具有直接法谱估计的缺点如分辨力不高等。为了获得高分辨力的空间谱估计方法，可以把已知的各种高分辨力的谱估计方法移植过来，从而空域超分辨。基于不同的物理模型，现已发展了许多超分辨方法以突破瑞利准则的限制，如最大熵法(Maximum Entropy Method)、Capon法、投影类算法、最大似然法等。
文[]利用实测的海杂波背景及仿真目标分析了最大熵法在HFSWR中的应用。下面利用岸基HFSWR的实测数据，分别讨论最小无畸变响应波束形成器MVDR(Minimum Variance Distortionless Response)、多信号分类MUSIC(Multiple Signal Classification)及预白化MUSIC的实际应用及处理结果。
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