\relax \citation{506612} \citation{774866} \citation{Stoica199845} \citation{5129272} \citation{4776568} \citation{1011219} \citation{Jakobsson2006710} \citation{Cantoni1976275} \citation{4101656} \@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{1}} \@writefile{toc}{\contentsline {section}{\numberline {II}Background}{1}} \newlabel{sec:background}{{II}{1}} \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {II-A}}Signal Model and MVDR Beamforming}{1}} \newlabel{eq:def_Q}{{4}{1}} \newlabel{eq:uniform_das}{{6}{1}} \newlabel{eq:def_MVDR}{{7}{1}} \citation{506612} \citation{1011219} \citation{Jakobsson2006710} \citation{Stoica199845} \citation{506612} \citation{1011219} \citation{Cantoni1976275} \citation{4101656} \citation{Jansson1999235} \citation{506612} \citation{774866} \citation{Jakobsson2006710} \citation{700967} \@writefile{toc}{\contentsline {subsection}{\numberline {\unhbox \voidb@x \hbox {II-B}}APES Beamformer}{2}} \newlabel{eq:Q_apes}{{9}{2}} \newlabel{eq:def_mAPES}{{10}{2}} \newlabel{eq:def_scm}{{11}{2}} \newlabel{eq:def_R_fb}{{18}{2}} \newlabel{eq:fbnoisecovmat}{{19}{2}} \@writefile{toc}{\contentsline {section}{\numberline {III}Improved Forward-Backward Averaging for S-APES}{2}} \newlabel{sec:contribution}{{III}{2}} \newlabel{eq:def_Qffb}{{20}{2}} \newlabel{eq:Q_ffb_rank}{{22}{3}} \newlabel{eq:prop2_e1}{{25}{3}} \newlabel{eq:prop2_e2}{{26}{3}} \newlabel{eq:N_fb}{{28}{3}} \newlabel{eq:fnorm_fb}{{29}{3}} \newlabel{eq:N_ffb}{{31}{3}} \newlabel{eq:prop2proof_1}{{32}{3}} \newlabel{eq:prop2proof_2}{{33}{3}} \bibstyle{IEEEtran} \bibdata{ForwardBackwardAPES_R1} \bibcite{506612}{1} \bibcite{774866}{2} \bibcite{Stoica199845}{3} \bibcite{5129272}{4} \bibcite{4776568}{5} \bibcite{1011219}{6} \bibcite{Jakobsson2006710}{7} \bibcite{Cantoni1976275}{8} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Low-SNR response for true MVDR (uniform weighting), APES with forward-backward averaging, and APES with full forward-backward averaging.}}{4}} \newlabel{fig:APES_lowSNR}{{1}{4}} \@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusions}{4}} \newlabel{sec:conclusions}{{IV}{4}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Effect of different forward-backward averaging schemes on S-APES RMSE. Signal of interest arriving from $0^{\circ }$ with $A_{s}=1$. Interfering signal arriving from various angles with identical amplitude. M=10, N=10, SNR=0dB. {\bf a)} RMSE vs. interference direction of arrival. {\bf b)} RMSE vs. number of subarrays for interference from $45^{\circ }$.}}{4}} \newlabel{fig:RMSE_M10_L9_N10_SNR30}{{2}{4}} \@writefile{toc}{\contentsline {section}{References}{4}} \bibcite{4101656}{9} \bibcite{Jansson1999235}{10} \bibcite{700967}{11}