DBF阵列幅相误差校准及其稳健性算法.docx

DBF阵列幅相误差校准及其稳健性算法
Abstract：
PhasedifferenceerrorreferstothephasedifferenceerrorcausedbythedifferenceintheimpedanceandlengthofthecablebetweentheantennasoftheDBFarray,whichaffectstheaccuracyofthearraysteeringandbeamforming.ThispaperproposesacalibrationalgorithmforphasedifferenceerrorofDBFarraybasedontheleastsquaresmethod,andverifiestheeffectivenessandrobustnessofthealgorithmthroughsimulationexperiments.
Introduction：
ThephasedifferenceerrorofDBFarrayiscausedbythedifferenceintheimpedanceandlengthofthecablebetweentheantennasofthearray,whichwillleadtoerrorsinthearraysteeringandbeamforming,andaffecttheperformanceofthearray.Therefore,itisnecessarytocalibratethephasedifferenceerrorofDBFarraytoimprovetheaccuracyofarraysteeringandbeamforming.
Atpresent,themostcommonmethodtocalibratethephasedifferenceerrorofDBFarrayisthroughhardwareadjustment,suchasadjustingtheimpedanceandlengthofthecablebetweentheantennas.However,thismethodistime-consumingandlaborious,anditisdifficulttoachieveahigh-precisioncalibration.Therefore,itisnecessarytodevelopamoreefficientandaccuratecalibrationalgorithm.
Theory：
ThephasedifferenceerrorofDBFarraycanbeexpressedasfollows:
φ=ωτ+ϕ
Whereφisthephasedifferenceerrorbetweentheantennas,ωistheangularfrequency,τisthedelaybetweentheantennas,andϕisthephaseoffsetbetweentheantennas.
Assumingthatthephasedifferenceerrorbetweenanytwoantennasisknown,andthatthesignalreceivedbyeachantennaiscomplex,thenthereceivedsignalofthearraycanbeexpressedasfollows:
S=r1e^(j(ωt+φ1))+r2e^(j(ωt+φ2))+...+rn*e^(j(ωt+φn))
Wherer1,r2,…,rncorrespondtotheamplitudesofthesignalsreceivedbyeachantenna,andφ1,φ2,…,φncorrespondtothephasedifferenceerrorsbetweeneachpairofantennas.
TocalibratethephasedifferenceerrorofDBFarray,theleastsquaresmethodcanbeusedtosolvethedelayandphaseoffsetbetweeneachpairofantennas.
Thebasicideaoftheleastsquaresmethodistominimizethesumofthesquaresofthedifferencesbetweentheobservedvaluesandthepredictedvalues.Inthiscase,theobservedvaluesarethereceivedsignalsofthearray,andthepre