相位響應(yīng)固定幅度響應(yīng)約束的穩(wěn)健波束形成方法
doi: 10.11999/JEIT141513
基金項(xiàng)目:
國(guó)家自然科學(xué)基金(61271293)資助課題
Robust Beamforming with Phase Response Fixed and Magnitude Response Constraint
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摘要: 傳統(tǒng)的幅度約束波束形成器是一個(gè)非凸問(wèn)題，需將原始模型化為線性規(guī)劃進(jìn)行間接求解。該文針對(duì)均勻線陣提出一種相位響應(yīng)固定幅度響應(yīng)約束(PFMC)的穩(wěn)健波束形成方法。利用權(quán)矢量逆序列對(duì)應(yīng)的傳遞函數(shù)與陣列響應(yīng)函數(shù)只差一個(gè)相位因子這一性質(zhì)，將陣列響應(yīng)的相位設(shè)置為固定的線性相位，僅對(duì)陣列響應(yīng)的實(shí)數(shù)幅度進(jìn)行約束，從而得到一個(gè)凸的代價(jià)函數(shù)，最優(yōu)權(quán)矢量可以利用內(nèi)點(diǎn)法求出。同時(shí)考慮到協(xié)方差矩陣誤差，利用最壞(WC)情況性能最優(yōu)原理提出PFMC-WC算法改善PFMC的性能。與傳統(tǒng)幅度約束波束形成器相比，減少了約束個(gè)數(shù)并省掉了恢復(fù)權(quán)矢量過(guò)程，從而降低了計(jì)算量。此外，由于相位響應(yīng)得到保證，該文算法相對(duì)于傳統(tǒng)算法具有更好的性能。仿真實(shí)驗(yàn)驗(yàn)證了該文算法的有效性。
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關(guān)鍵詞:
- 陣列信號(hào)處理 /
- 穩(wěn)健波束形成 /
- 相位響應(yīng)固定幅度響應(yīng)約束 /
- 最壞情況性能最優(yōu)
Abstract: The conventional magnitude constraints beamformer is a non-convex issue which is reformulated as a linear programming issue. A robust beamformer with Phase response Fixed and Magnitude response Constraint (PFMC) is proposed for Uniform Linear Array (ULA). Making use of the property that there is only a phase factor difference between the transfer function of the inverse sequence of the weight vector and the array response function, the phase response is set to be linear and the real magnitude response is constrained. Thus, a convex optimization cost function is established whose optimal solution can be found out by highly efficient interior point method. The PFMC-WC method against covariance matrix error is proposed based on Worst Case (WC) performance optimization to improve the performance of PFMC. Compared with the conventional magnitude response constraint beamformer, the proposed method reduces the number of constraints and leaves out the processing of recovering the weight vector, therefore, the calculation cost is reduced. In addition, due to the guarantee of the phase response, the proposed beamformer has better performance than the traditional magnitude constraint beamformer. Simulation results demonstrate the effectiveness of the proposed beamformer. -
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