采用核密度估计方法，对存在本振误差时的分布式发射波束形成(DTBF)性能进行统计分析.考虑存在载波初始相位偏移、载波频率偏移、相位噪声等3个偏差项，推导了对应的任意阵平均波束图和互补累积分布函数的理论表达式，并选用衰减因子和波束图特征参数分析本振误差对远场波束性能影响.理论分析和模拟结果显示，本振误差会导致DTBF性能出现衰减，并使合成波束图的平均主瓣水平下降，主瓣变宽，旁瓣区域扩展，波束图出现高旁瓣.随着时间的增长，本振误差累积增大，所致性能衰减增大，聚集到目标方位的能量减少.
Using the kernel density estimation method, a stochastic analysis of the performance of distributed transmit beamforming (DTBF) in the presence of node oscillator error is conducted. Considering carrier initial phase offset, carrier frequency offset and phase noise, the corresponding average beampattern and complementary cumulative distribution function are derived. Then the degradation factor and beampattern characteristic parameters are adopted to analyze the influence of local oscillator errors on far-field beam performance. Theoretical analysis and simulation results show that local oscillator error can result in the degradation of DTBF performance, the decrease of average main lobe level, the widening of main lobe, the expansion of sidelobe region, and the emergence of high beampattern sidelobe. Over time, the local oscillator error accumulates gradually, which makes the degradation become bigger and the energy focused on the target location become less.
［1］JAYAPRAKASAM S, RAHIM S K A, LEOW C Y. Distributed and collaborative beamforming in wireless sensor networks: Classifications, trends, and research directions［J］. IEEE Communications Surveys & Tutorials, 2017, 19(4): 2092-2116.
［2］FELICI-CASTELL S, NAVARRO E A, PREZ-SOLANO J J, et al. Practical considerations in the implementation of collaborative beamforming on wireless sensor networks［J］. Sensors, 2017, 17(2): 237-255.
［3］QUITIN F, RAHMAN M M U, MUDUMBAI R, et al. A scalable architecture for distributed transmit beamforming with commodity radios: Design and proof of concept［J］. IEEE Transactions on Wireless Communications, 2013, 12(3): 1418-1428.
［4］SONG S, THOMPSON J S, CHUNG P J, et al. BER analysis for distributed beamforming with phase errors［J］. IEEE Transactions on Vehicular Technology, 2010, 59(8): 4169-4174.
［5］SHI S, ZHU S D, GU X M, et al. Extendable carrier synchronization for distributed beamforming in wireless sensor networks［C］//2016 International Wireless Communications and Mobile Computing Conference (IWCMC). Paphos, Cyprus: IEEE, 2016: 298-303.
［6］HHNE T, RANKI V. Phase noise in beamforming［J］. IEEE Transactions on Wireless Communications, 2010, 9(12): 3682-3689.
［7］OCHIAI H, MITRAN P, POOR H V, et al. Collaborative beamforming for distributed wireless ad hoc sensor networks［J］. IEEE Transactions on Signal Processing, 2005, 53(11): 4110-4124.
［8］SHEN X, HUANG J, LIU P, et al. Analysis of collaborative beamforming for wireless sensor networks with phase offset［J］. Radioengineering, 2014, 23(1): 421-429.
［9］KHANZADI M R, KUYLENSTIERNA D, PANAHI A, et al. Calculation of the performance of communication systems from measured oscillator phase noise［J］. IEEE Transactions on Circuits and Systems I: Regular Papers, 2014, 61(5): 1553-1565.
［10］KHANZADI M R, PANAHI A, KUYLENSTIERNA D, et al. A model-based analysis of phase jitter in RF oscillators［C］//2012 IEEE International Frequency Control Symposium Proceedings. Baltimore, USA: IEEE, 2012: 508-511.
［11］HUANG J Y, WANG P, WAN Q. Collaborative beamforming for wireless sensor networks with arbitrary distributed sensors［J］. IEEE Communications Letters, 2012, 16(7): 1118-1120.
［12］BLETSAS A, LIPPMAN A, SAHALOS J N. Simple, zero-feedback, collaborative beamforming for emergency radio［C］//6th International Symposium on Wireless Communication Systems. Siena, Italy: IEEE, 2009: 657-661.
［13］周玉冰, 屈晨阳. 本振相位噪声及其对GMSK解调性能的影响［J］. 测控技术, 2015, 34(2): 62-65.
ZHOU Yubing, QU Chenyang. Analysis of local oscillator phase noise and its effect on the demodulation performance of GMSK［J］. Measurement & Control Technology, 2015, 34(2): 62-65.
