基于分布式壓縮感知的寬帶欠定信號(hào)DOA估計(jì)

蔣瑩; 王冰切; 韓俊; 何翼

doi:10.11999/JEIT180723

基于分布式壓縮感知的寬帶欠定信號(hào)DOA估計(jì)

doi: 10.11999/JEIT180723

蔣瑩¹,
王冰切¹,
韓俊¹,
何翼^2, ,

1.
空軍預(yù)警學(xué)院 ??武漢 ??430000
2.
海軍研究院 ??北京 ??100161

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61771484)，湖北省自然科學(xué)基金(2016CFB288)

詳細(xì)信息

作者簡(jiǎn)介:
蔣瑩：女，1991年生，博士生，研究方向?yàn)殡娮訉?duì)抗信息處理

王冰切：男，1972年生，副教授，碩士生導(dǎo)師，研究方向?yàn)槔走_(dá)系統(tǒng)與雷達(dá)對(duì)抗

韓俊：男，1983年生，講師，研究方向?yàn)槔走_(dá)對(duì)抗

何翼：男，1989年生，助理研究員，研究方向?yàn)橐曨l圖像處理及模式識(shí)別與人工智能

通訊作者:
何翼　jty614@163.com

中圖分類號(hào): TN971
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出版歷程
- 收稿日期: 2018-07-18
- 修回日期: 2019-01-11
- 網(wǎng)絡(luò)出版日期: 2019-01-22
- 刊出日期: 2019-07-01

Underdetermined Wideband DOA Estimation Based on Distributed Compressive Sensing

Ying JIANG¹,
Bingqie WANG¹,
Jun HAN¹,
Yi HE^{2
, ,}

1.
Air Force Early Warning Academy, Wuhan 430000, China
2.
Naval Research Academy, Beijing 100161, China

Funds: The National Natural Science Foundation of China(61771484), The Natural Science Foundation of Hubei Province (2016CFB288)

摘要

摘要: 為解決基于稀疏陣列的寬帶欠定信號(hào)到達(dá)角(DOA)估計(jì)問題，該文提出基于分布式壓縮感知(DCS)的寬帶DOA估計(jì)算法。首先，對(duì)稀疏陣列寬帶信號(hào)處理模型進(jìn)行理論推導(dǎo)與分析，將寬帶信號(hào)DOA估計(jì)建模成DCS問題；其次，利用經(jīng)典DCS算法實(shí)現(xiàn)稀疏陣列上的寬帶欠定信號(hào)DOA估計(jì)；最后，引入網(wǎng)格失配誤差，建立包含網(wǎng)格失配參數(shù)的DCS模型，并進(jìn)行迭代求解，實(shí)現(xiàn)對(duì)DOA和網(wǎng)格失配參數(shù)的聯(lián)合估計(jì)。仿真結(jié)果表明，該算法能夠?qū)崿F(xiàn)寬帶欠定信號(hào)DOA估計(jì)，較現(xiàn)有成果而言，在保證測(cè)向精度的同時(shí)，具備分辨率高、運(yùn)算速度快的優(yōu)點(diǎn)。
- 到達(dá)角估計(jì) /
- 分布式壓縮感知 /
- 稀疏陣列 /
- 聯(lián)合稀疏 /
- 網(wǎng)格失配
Abstract: In order to realize underdetermined wideband Direction Of Arrival(DOA) estimation based on sparse array, an algorithm on account of Distributed Compressive Sensing(DCS) is proposed. Firstly, wideband signal processing model based on sparse array is deduced and the underdetermined wideband DOA estimation is formulated as a DCS problem. Then, the DCS-Simultaneous Orthogonal Matching Pursuit(DCS-SOMP) algorithm is utilized to solve this problem. Finally, the off-grid problem is considered and a joint DCS model containing off-grid parameters is established. Estimations of DOAs and off-grid parameters are achieved through iterative solution. Simulation results show that the proposed algorithm is effective and have advantages in resolution and computational complexity.
- Direction Of Arrival(DOA) estimation /
- Distributed Compressive Sensing(DCS) /
- Sparse array /
- Joint sparsity /
- Off-grid problem

HTML全文

圖 1 CACIS型互質(zhì)陣列結(jié)構(gòu)

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圖 2 SS-MUSIC, DCS-SOMP和DCS-JSOMP算法的空間譜

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圖 3 信噪比變化對(duì)測(cè)向精度的影響

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圖 4 頻域快拍次數(shù)變化對(duì)測(cè)向精度的影響

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圖 5 到達(dá)角臨近信號(hào)估計(jì)能力

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表 1 DCS-SOMP算法

輸入：虛擬陣列接收數(shù)據(jù)${{\text{z}}_h}$，過完備字典集${\text{Φ}_h}\left( \psi \right)$，信號(hào)個(gè)數(shù)$K$。
輸出：重構(gòu)信號(hào)${{\text{s}}_h}$，支撐基列標(biāo)集合$\varOmega$。
初始化：迭代計(jì)數(shù)$i = 1,{\varOmega_0}=\varnothing ,{\hat {\text{s}}_h} = {\text{0}}$，殘差初值${{\text{r}}_{h, 0}} = {{\text{z}}_h}$。
步驟 1 ?支撐基選擇： $ {g_i} = \mathop {\arg \max }\limits_{g \in \left\{ {1, 2, \cdots , G} \right\}} \sum\limits_{h = 1}^H {\frac{{\left\| {\left\langle {{{\text{r}}_{h, i - 1}}, {{\text{φ}} _{h, g}}} \right\rangle } \right\|}}{{{{\left\\| {{{\text{φ}} _{h, g}}} \right\\|}_2}}}} ,{\varOmega_i}={\varOmega_{i - 1}} \cup \left\{ {{g_i}} \right\}$；
步驟 2 ?殘差更新：${\hat{\text{ s}}_h}={{\text{Φ}} _{{\varOmega_i}}}^\dagger {{\text{z}}_h},{{\text{r}}_{h, i}} = {{\text{z}}_h} - {{\text{Φ}} _{{\varOmega_i}}}{\hat {\text{s}}_h}$；
步驟 3 ?條件判斷：若$i < K$，則$i = i + 1$跳至步驟1，否則跳至步驟4；
步驟 4 ?結(jié)果結(jié)算：$\varOmega={\varOmega_i},{{\text{s}}_h}={{\text{Φ}} _\varOmega}^\dagger {{\text{z}}_h}$。

下載: 導(dǎo)出CSV

表 2 DCS-JSOMP算法

　輸入：虛擬陣列接收數(shù)據(jù)${{\text{z}}_h}$，過完備字典集${\text{Φ}_h}\left( \text{Ψ} \right)$，網(wǎng)格失配字典${\text{Γ}_h}\left( \text{Ψ} \right)$，信號(hào)個(gè)數(shù)$K$。

　輸出：重構(gòu)信號(hào)${{\text{s}}_h}$，支撐基列標(biāo)集合$\varOmega$，網(wǎng)格失配誤差${\text{Δ}} $。

　初始化：迭代計(jì)數(shù)$i = 1,{\varOmega_0}=\varnothing,{\hat{\text{ s}}_h} = {\text{0}},\hat{\text{β}}_h={\text{0}}$，殘差${{\text{r}}_{h, 0}} = {{\text{z}}_h}$。
　步驟 1 ?支撐基選擇：${c_g} = \sum\limits_{h = 1}^H {\frac{{\left| {\left\langle {{{\text{r}}_{h, i - 1}}, {{\text{φ }}_{h, g}}} \right\rangle } \right|}}{{{{\left\| {{{\text{φ}} _{h, g}}} \right\|}_2}}}} ,{d_g} = \sum\limits_{h = 1}^H {\frac{{\left| {\left\langle {{{\text{r}}_{h, i - 1}}, {\text{γ}_{h, g}}} \right\rangle } \right|}}{{{{\left\| {{\text{γ}_{h, g}}} \right\|}_2}}}} ,{g_i} = \mathop {\arg \max }\limits_{g \in \left\{ {1, 2, \cdots , G} \right\}} \sqrt {{c_g}^2 + {d_g}^2} ,{\varOmega_i}={\varOmega_{i - 1}} \cup \left\{ {{g_i}} \right\}$；

　步驟 2 ?殘差更新：${\hat{\text{ s}}_h} = {{\text{Φ}} _{{\varOmega_i}}}^\dagger \left( {{{\text{z}}_h} - {{\text{Γ}} _{{\varOmega_i}}}{\hat{\text{β}}_h}} \right),{\hat{\text{β}}_h} = {{\text{Γ}} _{{\varOmega_i}}}^\dagger \left( {{{\text{z}}_h} - {{\text{Φ}} _{{\varOmega_i}}}{{\hat {\text{s}}}_h}} \right),{{\text{r}}_{h, i}} = {{\text{z}}_h} - {{\text{Φ}} _{{\varOmega_i}}}{\hat{\text{ s}}_h} - {{\text{Γ}} _{{\varOmega_i}}}{\hat{\text{β}}_h}$；

　步驟 3 ?條件判斷：若$i < K$，則$i = i + 1$跳至步驟1，否則跳至步驟4；
　步驟 4 ?結(jié)果結(jié)算：$\varOmega={\varOmega_i},{{\text{s}}_h} = {{\text{Φ}} _\varOmega}^\dagger \left( {{{\text{z}}_h} - {{\text{Γ}} _\varOmega}{\hat{\text{β}}_h}} \right),{\text{β}_h} = {{\text{Γ}} _\varOmega}^\dagger \left( {{{\text{z}}_h} - {{\text{Φ}} _\varOmega}{{\text{s}}_h}} \right),{\text{Δ}} =\frac{1}{H}\sum\limits_{h = 1}^H {\frac{{{{\text{β}} _h}}}{{{{\text{s}}_h}}}} $。

下載: 導(dǎo)出CSV

表 3 5種算法單次蒙特卡洛實(shí)驗(yàn)用時(shí)(s)

算法	信噪比變化	頻域快拍次數(shù)變化
DCS-SOMP	0.1747	0.1943
DCS-JSOMP	0.3439	0.3784
SS-MUSIC	0.5021	0.5207
WNNSBL	3.3751	3.0231
OGSLIM	0.6068	0.6678

下載: 導(dǎo)出CSV

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