Multi-Channel Switching Array DOA Estimation Algorithm Based on FRIDA
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摘要: 针对波达方向(Direction Of Arrival, DOA)估计在实际测向系统中系统复杂度受接收通道数目影响的问题，该文提出了一种基于FRIDA(Finite Rate of Innovation Direction-of-Arrival)的多通道切换阵列DOA估计算法。该算法首先利用开关将特定子阵接收的数据传输至通道从而减少测向系统中使用的通道数目，然后通过切换不同的子阵接入通道并采样得到多个少通道接收数据协方差矩阵，利用这些协方差矩阵重构出全通道接收数据向量，以此来构建基于有限新息率(Finite Rate of Innovation, FRI)的DOA估计模型，最后通过近端梯度下降算法获得信号入射方向的估计结果。仿真实验与对实测数据的实验验证了该算法优于同等条件下的其它算法。Abstract:
Objective With the increasing complexity of the electromagnetic environment, the requirements for estimation accuracy in practical direction finding systems are rising. Increasing the size of the antenna array is an effective means of improving the estimation accuracy of the actual direction finding system, but increasing the size of the antenna significantly increases the complexity of the actual direction finding system. This paper aims to reduce the number of channels used while maintaining the performance of DOA estimation for full-channel data. By combining the advantages of the channel compression algorithm in reducing the number of channels used with the structure of time-modulated arrays that incorporate switches in the RF front-end, This paper proposes a Multi-Channel Switching Array DOA Estimation Algorithm Based on FRIDA. Methods The algorithm first introduces a selection matrix consisting of switches between the antenna array and the channel, which is responsible for passing the signal data received by the particular antenna selected into the channel, i.e., a particular subarray is selected to receive the data through the selection matrix. Switching different subarrays to collect different less channel received data covariance matrix, by stipulating the common array elements in each subarray to ensure the phase consistency in the covariance matrix, these covariance matrices recover the dimensionality of the covariance matrix after the weighted summation to obtain the total covariance matrix. The total covariance matrix is weighted and summed to obtain the full-channel received data vector after weighting and summing the elements of the total covariance matrix that correspond to the same spacing of the array elements. The FRI reconstruction model is then constructed using the full-channel received data vector, and finally the estimated incident angle is obtained by using the proximal gradient descent algorithm together with the parameter recovery algorithm. Results and Discussions Simulation results of DOA estimation for SA-FRI at multiple source incidence show that: the full-channel received data vectors constructed using multiple covariance matrices of the less-channeled received data are able to discriminate multi-source incident signals, and their performance in this aspect is approximately the same as that of the full-channeled received data( Fig 2 ). Simulation results of the estimation accuracy with the number of snapshots and SNR under different channel numbers show that the estimation accuracy of the algorithm proposed in this paper with different channel numbers increases with the number of snapshots and SNR, and the more channels are used, the higher the DOA estimation accuracy is under the same SNR and the number of snapshots (Fig 3 ,Fig 4 ). Simulation results of DOA estimation accuracy of four different algorithms under different SNR and number of snapshots show that the DOA estimation accuracy of the four algorithms increases with the increase of SNR and number of snapshots, and the algorithms proposed in this paper outperform the other algorithms under the same conditions(Fig 5 ,Fig 6 ). Meanwhile, the same results were obtained by verifying the actual measured data(Fig 9 ), which further proved the effectiveness of the algorithm proposed in this paper.Conclusions Aiming at the problem of how to reduce the number of channels used in the actual DOA estimation system, this paper proposes an array switching DOA estimation based on proximal gradient descent. The algorithm firstly reduces the number of channels using the switching matrix, and then obtains multiple covariance matrices by switching different subarray access channels for multiple acquisitions, uses these covariance matrices to recover and complete the covariance matrix of the full-channel received data, and uses the matrix, and finally obtains the estimation of the DOA parameter of the incident signal by using the proximal gradient descent algorithm. At the same time, the simulation verifies that the proposed algorithm can reduce the use of channels under the premise of guaranteeing certain estimation accuracy. In addition, the effectiveness of the algorithm is further verified by the DOA estimation of the measured data collected through the actual DOA estimation system, which obtains results similar to those of the simulation. -
1 基于FRIDA的多通道切换阵列DOA估计算法流程
输入： 接收数据$ {Y_1},{Y_2}, \cdots ,{Y_Z} $。 输出： 入射信号的DOA估计结果${\widehat \theta _k}$，$k = 1,2,\cdots,K$。 初始化：Toeplitz算子维度参数$P$，正则化参数$\tau > 0$，参数$n \in {\mathbb{Z}_{ + + }}$，迭代停止阈值$\varepsilon \geqslant 0$， 一类Bessel函数最大阶数参数$Q$，线性映射矩阵$G$，迭代次数$k = 0$，以及初始化向量${b^{\left( 0 \right)}} \in {\mathbb{C}^{2Q + 1}}$； 步骤1：根据${R_{{Y_z}}} = \displaystyle\sum\nolimits_{u = 1}^u {y(u)y{{(u)}^{\rm H}}/U} $计算各接受数据协方差矩阵${R_{{Y_1}}},{R_{{Y_2}}}, \cdots ,{R_{{Y_Z}}}$； 步骤2：根据公式(5)将计算出的$M \times M$维矩阵${R_{{Y_1}}},{R_{{Y_2}}}, \cdots ,{R_{{Y_Z}}}$转化为$L \times L$维矩阵${R_1},{R_2}, \cdots ,{R_Z}$， 根据公式(6)(7)计算出二值选择矩阵$C$； 步骤3：根据公式(8)将矩阵${R_1},{R_2}, \cdots ,{R_Z}$加权求和为$ R $，根据公式(9)(10)(11)计算全通道接收数据向量$r$； 步骤4：根据公式(20)计算$ {b^{\left( {k + 1} \right)}} = pro{x_{\tau H}}\left( {{b^{\left( k \right)}} - 2\tau {G^{\rm H}}\left( {G{b^{\left( k \right)}} - r} \right)} \right) $； 步骤5：判断$\left\| {{b^{\left( {k + 1} \right)}} - {b^{\left( k \right)}}} \right\|_2^2$与$\varepsilon $的大小关系，若$\left\| {{b^{\left( {k + 1} \right)}} - {b^{\left( k \right)}}} \right\|_2^2 \le \varepsilon $，停止迭代，进入步骤6，否则$k = k + 1$，返回步骤4； 步骤6：对得到的${b^{\left( {k + 1} \right)}}$计算$ {T_P}\left( {{b^{(k + 1)}}} \right) $并计算其SVD分解结果$ {T_P}\left( {{b^{(k + 1)}}} \right) = {U_b}{S_b}V_b^{\rm H} $； 步骤7：以矩阵$V$的最后一列为系数，构造多项式$ F $，并计算其零点，记为${\lambda _k}$； 步骤8：计算信号的DOA参数$ {\theta _k} = - angle\left( {{\lambda _k}} \right) $，其中$angle\left( \cdot \right)$表示复数的幅角。 
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表 1 各算法计算复杂度比较
算法 复杂度 SA-FRI $o\left( {n{T_{SA - FRI}}{{(2Q + 1 - P)}^2}P} \right)$ MUSIC $o\left( {{L^3} + {L^2}U + {N_{grid}}{L^2}} \right)$ ${\ell _1}$-svd $o\left( {{L^3}N_{grid}^3} \right)$ ESPRIT $o\left( {{L^3} + {L^2}U} \right)$ ANM $o\left( {{L^3}\log \left( {{1 \mathord{\left/ {\vphantom {1 \varepsilon }} \right. } \varepsilon }} \right)} \right)$ CoFIT $o\left( {{T_{SBL}}\left( {{N_{grid}}{L^2} + {L^3}} \right) + {T_{iter}}{L^3}} \right)$
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表 2 各算法运行时间比较
算法 SA-FRI MUSIC ${\ell _1}$-svd ESPRIT ANM CoFIT 运行时间(秒) 52.79 2.62 140.81 0.13 169.77 179.37
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